Electric Refractory Materials

Electric Refractory Materials edited by

Yukinobu Kumashiro Yokohama National University Hodogaya-ku, Yokohama, Japan

Marcel Dekker, Inc.

New York • Basel

TM

Copyright © 2000 by Marcel Dekker, Inc. All Rights Reserved.

ISBN: 0-8247-0049-X This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896 World Wide Web http:/ /www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright  2000 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA

Preface

This book provides a state-of-the-art overview of electric refractory materials as exotic materials (i.e., metallic and semiconducting refractory materials) from fundamental properties to application in a wide variety of electronics. The metallic ceramics or metalloids are the transition metal carbides, nitrides, and diborides of groups IV and V. The refractory semiconductors are silicon carbide, diamond, boron-based semiconductors, wide gap nitrides, and related mixed crystals. The high melting points and high brittleness of refractory materials make it difficult to prepare single crystals so use of these materials has been limited by hard coating and cutting tools, regardless of their electric uses. After the crystal growth techniques—including thin film growths—were established, such fundamental studies as electronic structures, bonding characters, and various physical properties were clarified with the development of new electric refractory materials. Recently ‘‘hard electronics’’ was used in Japan (International Workshop on Hard Electronics Abstract, 1997) and promised to bring new electronics needed in severe circumstances by utilizing hard materials (adamantine) that were essentially hard themselves and very hard to handle. The final goal of hard electronics involves not only high-temperature electronics, but also various types of electronics that can operate under harsh conditions. Then ‘‘electric refractory materials’’ would replace ‘‘hard electronic materials.’’ Consistency descriptions from preparation, characterization, properties, and electronic applications are shown on the cover, illustrating how electric refractory materials form a bridge of knowledge from the basic sciences to electronic applications. This book emphasizes the importance of refractory metalloids and semiconductors as electric materials from the standpoint of high-temperature technology by reviewing newly developed fundamental research such as chemical bonding, electrical, optical, and thermal properties. This book describes in detail for the first time the most important work done in the field of refractory metalloids and semiconductors. Chapter 1 emphasizes the importance of refractory metalloids and semiconductors as electronic materials by reviewing characterization and properties of materials, and by summarizing a wide variety of synthesis, evaluation, and measurement methods. The transition metal carbides, nitrides, and diborides have aroused theoretical and practical interest in such unique properties as extremely high melting point, extreme hardness, metallic properties, and superconductivity. These unique common properties are closely connected with electronic structures and the band structures resemble each other among the materials with the same crystal structure. The refractory metalloids, described in Chapter 2, have become highly clarified materials. This chapter is an introduction to Chapters 3–14. On the other hand, the communication fields are constantly demanding higher frequencies and power levels. Applications ranging from automobile engines to space telescopes require device operation in harsh environments. Such issues have given rise to a new class of materials known as wide-gap refractory semiconductors because of their potential applications in the devices used for high-power, high-temperature, radiation influence; ultraviolet light influence; and iii

iv

Preface

high-frequency/high power. The major emphasis has been placed on diamond and silicon carbides. Silicon carbide is in a much more advanced stage of development. However, recent development of blue light-emitting devices using GaN-based nitrides in Japan has stimulated the study of nitride semiconductors for blue light-emitted laser, high-temperature, and highfrequency devices. Due to their unique mechanical, thermal, optical, chemical, and electrical properties, the other refractory semiconductors are anticipated to find applications in thermoelectric, electrooptic, piezoelectric, and acousto-optic devices as well as protective coating, hard coatings, and heat sinks. The refractory semiconductors described in Chapters 15–27 are progressing year by year and differ from material to material. These chapters cover the issues related to crystal growth; microstructure; defects; doping; electric, thermal, and optical properties; and device applications, while identifying common themes in heteroepitaxy and the role of defects in doping, compensation, and phase stability of unique classes of materials. The book covers most aspects of electric refractory materials and can serve as a general reference to this new and developing area. I wish to thank all the authors for their contributions. A number of figures and tables have been taken from the literature. I would like to thank the authors and publishers of these materials for permission to reproduce them here. I am also grateful to R. Dekker, M. Ludzki, B. Wrage, E. Stannard, and K. Baldonado, of Marcel Dekker, Inc., for their useful comments, constant encouragement, and invaluable support throughout this project. Finally, I am indebted to Mr. S. Chiba for his assistance in preparing the book’s index and cover art. Yukinobu Kumashiro

Contents

Preface Contributors 1.

Importance and Research Program of Electric Refractory Materials Yukinobu Kumashiro

2.

Survey of Refractory Metalloids: Transition Metal Carbides, Nitrides, and Diborides Yukinobu Kumashiro

iii vii 1

7

3.

Bulk Crystal Growth Yukinobu Kumashiro

19

4.

Thin-Film Preparation Konosuke Inagawa

55

5.

Electronic Structure Adolf Neckel

81

6.

Lattice Vibrations, Heat Capacity, and Related Properties Go¨ran Grimvall

7.

Electrical and Thermal Conductivity and Related Transport Properties at Low Temperatures Go¨ran Grimvall

153

173

8.

High-Temperature Characteristics Yukinobu Kumashiro

191

9.

Surface Electronic Structures and Surface Reactivities Kazuyuki Edamoto

223

10.

Irradiation Properties of Electric Refractory Materials Naoto Kobayashi

245

11.

Transition Metal Carbide Field Emitters Yoshio Ishizawa

269 v

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Contents

12.

NbN Superconducting Devices Masahiro Aoyagi

289

13.

Solar Absorbers—Selective Surfaces Robert Blickensderfer

307

14.

Metalloids for Plasma-Facing Materials Tatsuhiko Tanabe and Masakazu Fujitsuka

321

15.

Synthesis of Diamond from the Gas Phase Andrzej Badzian

347

16.

The Electrical and Optical Properties of Diamond Alan T. Collins

369

17.

Semiconducting Diamond and Diamond Devices Shinichi Shikata and Naoji Fujimori

385

18.

SiC Boule Growth Yuri M. Tairov

409

19.

Epitaxial Growth, Characterization, and Properties of SiC Sadafumi Yoshida

437

20.

Silicon Carbide Power Electronic Devices B. Jayant Baliga

477

21.

Science and Technology of Boron Nitride Osamu Mishima and Koh Era

495

22.

Boron Phosphide Yukinobu Kumashiro

557

23.

Boron and Boron-Rich Compounds Helmut Werheit

589

24.

Boron Films Katsumitsu Nakamura

655

25.

Single Crystal of AlN Takeshi Meguro and Katsutoshi Komeya

675

26.

AlN Sintered Polycrystal Fumio Ueno

691

27.

GaN-AlN-InN Blue Light–Emitting Devices Shuji Nakamura

715

Index

747

Contributors

Masahiro Aoyagi, Ph.D. Electron Devices Division, Electrotechnical Laboratory, Tsukuba, Ibaraki, Japan Andrzej Badzian, Ph.D., Dr.Sc. Materials Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania B. Jayant Baliga, Ph.D. Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina Robert Blickensderfer, Ph.D. Research Metallurgist, Consultant, Albany, Oregon Alan T. Collins, Ph.D., D.Sc. Department of Physics, King’s College London, London, England Kazuyuki Edamoto, D.Sc. Department of Chemistry and Materials Science, Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan Koh Era, Ph.D. Helios Optical Science Laboratory, Inc., Tsukuba, Ibaraki, Japan Naoji Fujimori, Dr.Eng. Itami, Hyogo, Japan

Itami Research Laboratories, Sumitomo Electric Industries, Ltd.,

Masakazu Fujitsuka Department of Mechanical Properties, National Research Institute for Metals, Tsukuba-shi, Ibaraki, Japan Go¨ran Grimvall, Ph.D. Department of Physics, Royal Institute of Technology, Stockholm, Sweden Konosuke Inagawa, Ph.D. Chiba Institute for Super Materials, ULVAC Japan, Ltd., Tsukuba, Ibaraki, Japan Yoshio Ishizawa, Ph.D. Department of Materials Science, Iwaki Meisei University, Iwaki, Fukushima, Japan Naoto Kobayashi, Ph.D. Quantum Radiation Division, Electrotechnical Laboratory, Tsukuba, Ibaraki, Japan vii

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Contributors

Katsutoshi Komeya, Dr.Eng. Department of Engineering, Yokohama National University, Hodogaya-ku, Yokohama, Japan Yukinobu Kumashiro, Ph.D. Department of Engineering, Yokohama National University, Hodogaya-ku, Yokohama, Japan Takeshi Meguro, Ph.D. Department of Materials Chemistry, Yokohama National University, Hodogaya-ku, Yokohama, Japan Osamu Mishima National Institute for Research in Inorganic Materials, Tsukuba, Ibaraki, Japan Katsumitsu Nakamura, Dr.Eng. Department of Chemistry, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo, Japan Shuji Nakamura, Ph.D. Materials Department, University of California, Santa Barbara, California Adolf Neckel, Ph.D. Institute for Physical Chemistry, University of Vienna, Vienna, Austria Shinichi Shikata, M.D. Itami Research Laboratories, Sumitomo Electric Industries, Ltd., Itami, Hyogo, Japan Yuri M. Tairov, Ph.D. Department of Microelectronics, St. Petersburg Electrotechnical University, St. Petersburg, Russia Tatsuhiko Tanabe, Dr.Eng. Department of Mechanical Properties, National Research Institute for Metals, Tsukuba-shi, Ibaraki, Japan Fumio Ueno, Ph.D. Corporate Research and Development Center, Toshiba Corporation, Kawasaki, Japan Helmut Werheit, Prof.Dr.rer.nat. Solid State Physics Laboratory, Gerhard Mercator University, Duisburg, Germany Sadafumi Yoshida, Ph.D. Department of Electrical and Electronic Systems, Saitama University, Urawa, Saitama, Japan

1 Importance and Research Program of Electric Refractory Materials Yukinobu Kumashiro Yokohama National University, Hodogaya-ku, Yokohama, Japan

The extreme technologies involving ultrahigh temperature, ultrahigh pressure, ultralow temperature, and ultravacuum are part of advanced science and technology and important research subjects. Their development and utilization reveal new materials and improve the characteristics of conventional materials, resulting in new phenomena and developments in material science technology. New materials with peculiar characteristics including stability under extreme conditions, such as ultrahigh temperatures ⭌ 2300 K, ultralow temperatures ⬉ 4 K, ultrahigh pressures ⭌ 10 9 Pa, and low vacuum ⬉ 10 ⫺9 Pa, often form exotic materials. The following types of exotic materials would be expected: 1. High-purity materials: Electronic and optical materials and atomic nuclear materials. 2. Perfect crystals: Bulk single crystals with few defects, ultrathin films, whiskers, and ultrafine powders. 3. New material phases: New stoichiometry, quasi-stable amorphous phases, intermetallic compounds, and superlattices. 4. Composites: New cermets, fiber-reinforced materials (FRMs), and functional gradient materials (FGMs). Among these, refractory materials are related to the development of materials with high stability, a long lifetime, and high reliability at high temperatures, promising electronic devices with high capacity and high power density for uses in harsh environments. They would also result in increased conversion efficiency at high temperatures, simplified control systems for apparatus, and improved new systems. Industries such as the aerospace, automotive, and petroleum industries have continuously provided the impetus for the development of fringe technologies that are tolerant of increasingly high temperatures and hostile environments (1). The refractory materials in the present case are nonoxides with high melting points, strong atomic bonding, high hardness, and high thermal shock resistance. The various functions of refractory materials are summarized in Table 1. These functions are closely related to each other as reflected in Fig. 1. The functions are generally influenced by such imperfect characteristics as crystal structure, impurity, atomic vacancy, lattice defect, dislocation, crystal grain boundary, and aggregation texture. Characterization is fundamental to the development of material science and provides indexes for databases in material design. In general, characterization describes those features of the composition and structure in1

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Table 1 Functions and Applications of Refractory Materials Function Electronic function Insulation Conduction

Superconduction Piezoelectricity

Semiconduction

Electron emission

Optical function Fluorescence Light absorption

Light reflection Photosensitivity Mechanical function High strength Hardness Abrasivity and cutting Lubrication Thermal function Refractory Conduction

Device Integrated circuit substrate Passivation film Electrode Resistor Interconnection Superconducting magnet Josephson device Surface acoustic wave device Piezoelectric filter Light guide Acoustic emission (AE) sensor Thermistor Thermoelectric device Diode Transistor Emitter Thermionic generator device Electrode for magnetohydrodynamic generator

Materials AlN, SiC, diamond Si3N4, BN, AlN Transition metal carbides and nitrides TaN, ZrN TiN NbN, NbN-NbC

AlN

B, SiC, BP SiC, BP, B, B4 C SiC, BP, diamond SiC, BP TiC, TaC, TiB2, TiN TiC, TaC, TaB2 Transition metal diborides

Light-emitting diode Solar selective and absorption films Protective film for reflection Solar thermal concentrator Photoelectrochemical cell

BP TiC, TiN BP

Turbine blade, engine Speaker film Abrasive polishing, whetstone cutting tool Solid lubricant

Si3N4, SiC B Diamond, carbides BN, nitrides BN

Refractory structural materials Insulating substrate Heak sink Atomic power and nuclear fusion functions Resistive for radiated ray Nuclear fuel coating materials Control rod Plasma resistance First wall of tokamak Radioactivity detection α-ray detector Neutron detector Chemical function Corrosion resistance Oxidation-resistant materials Acid resistance Catalysis Control of chemical reactions

GaN, SiC, c⋅BN ZrC, HfC

SiC, ZrB2 Diamond, SiC, AlN Diamond, SiC, AlN, BP C, SiC B4C SiC, TiC, TiB2, B4C, B Diamond, SiC BP, B Diborides, SiC Carbides and diborides, BP Transition metal carbides and nitrides

Importance and Research Program

3

Figure 1 The relationship between various functions in refractory materials.

cluding defects of materials that are significant for a particular preparation and study of properties or uses and suffice for the reproduction of the material (2). The assessment of the physical and chemical perfection of crystals has come to be called characterization by crystal growers (2). Many crystals have been characterized to the point where relationships between their properties and the concentration of their constituent atoms have been found. Most important for crystal growers is to relate the growth process to control of the perfection of crystals in desired ways (2). The characterization does not merely examine macro- and microscopic features of materials but clarifies the chemical composition and structure texture as factors reflecting material properties and functions in relation to the history of materials, i.e., raw material → material handling → production. The concept of characterization is illustrated in Fig. 2. The characteristics change dynamically in the functional state, which corresponds to ‘‘status analysis’’ instead of analysis in Fig. 2. Table 2 summarizes the synthesis, evaluation, and measurement technologies for refractory materials. The development of new preparative processes such as plasma, laser, particle, and high-speed ion-ray processes would lead to new exotic materials. In cases in which the preparation of single crystals of refractory materials is very difficult, some film growth techniques are powerful tools for clarifying the intrinsic properties of bulk crystals. Physical vapor deposition (PVD) is supercooling process used to realize a quasi-equilibrium state that could

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Kumashiro

Figure 2 Concept of characterization. The shaded part of the figure represents the status of characterization.

not be attained in the bulk process. Also, status analysis of thin films including surfaces and interfaces is very important for characterization. The evaluation technologies are divided into three categories: microscopic, spectrographic, and diffraction methods. Developments of microscopic evaluation technologies down to the atomic level, such as scanning tunneling microscopy, are due to progress in techniques using secondary electrons and iron, scattered X-rays, together with ultravacuum technology. We could not always discriminate clearly between evaluation and measurement technologies. The Hall effect and lifetime measurements in semiconductors are frequently part of evaluation technology. The measurement technologies require various sophisticated extreme technologies including pulse technology to clarify extreme characteristics. Such inconsistent requirements as simultaneous measurements of static and dynamic properties are one of the problems to be solved. The refractory materials are hard and brittle with superior chemical stability, so that the establishment of such material handling processes as cutting and abrasion, including microprocesses for etching and patterning, is indispensable to the development of electronic device applications of these materials. The electric refractory materials in this book are classified into metallic ceramics (i.e., transition metal carbides, nitrides, and diboride) and wide-gap semiconductors (i.e., diamond, SiC, GaN, BP, AlN, BN, and high-boron base semiconductors.

Table 2 Synthesis, Evaluation, and Measurement Technologies for Refractory Materials Crystal growth technology High-temperature technology Radio-frequency induction heating, infrared heating, arc plasma heating, electron beam heating, CO 2 laser, self-propagating high-temperature synthesis (SHS) High-pressure technology Gas pressure, hydrostatic pressing, hot pressing, isostatic pressing, shock wave synthesis Ultra-vacuum technology Evaporation-condensation, evaporation (reactive evaporation, molecular beam deposition, sputtering), ion beam [ionized cluster beam (ICB), ion plating, electron cyclotron resonance (ECR)]

Importance and Research Program

5

Table 2 Continued Chemical vapor deposition (CVD) Hydrogen reduction, chemical transport, hydrogen decomposition, metal organic CVD, plasma CVD Liquid growth Liquid-phase epitaxy (LPE), flux growth Solid growth Recrystallization, solid-phase epitaxy (SPE) Beam process Radial beam, cluster beam, excimer laser Evaluation technology Crystal structure X-ray diffraction, electron diffraction, neutron diffraction, field ion microscope (FIM) Composition analysis X-ray fluorescence spectroscopy (XRF), X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), Auger electron spectroscopy (AES), electron probe microanalysis (EPMA), particle-induced X-ray emission (PIXE), Rutherford backscattering spectroscopy (RBS) Impurity analysis Secondary ion mass spectroscopy (SIMS), induced coupled plasma mass spectroscopy (ICP-MS) Crystal quality Optical microscope, light scattering method, X-ray and electron diffractions, X-ray topograph bond method, channeling, infrared (IR) spectroscopy, Raman spectroscopy Defect and impurity analysis Deep level transient spectroscopy (DLTS), photoacoustic spectroscopy (PAS), photoluminescence (PL), cathodoluminescence (CL), electron spin resonance (ESR), nuclear magnetic resonance (NMR), transmission electron microscopy (TEM), high-resolution electron microscopy (HREM) Surface structure Low-energy electron diffraction (LEED), reflection high-energy electron diffraction (RHEED), ion scattering spectroscopy (ISS), impact-collision ion scattering spectroscopy (ICISS), electron energy loss spectroscopy (EELS), scanning tunneling microscopy (STM), atomic force microscopy (AFM), X-ray absorption near edge structure (XANES), extended X-ray absorption fine structure (EXAFS), XPS, UPS Measurement technology Electronic properties Conductivity, work function, superconducting transition temperature (Tc), superconducting critical field (H c2), thermoelectric power, Hall effect, photoconductivity, drift mobility, lifetime, piezoelectric constant, breakdown voltage, dielectric loss, dielectric constant Mechanical properties Elastic coefficient (Young’s modulus, shear modulus, Poission ratio, microhardness) Strength (compressive, tensile, impact, fracture, fatigue) Stress (bending, tensile, compressive) Fracture toughness Coefficient of friction, coefficient of abrasion Thermal properties Thermal expansion coefficient, heat capacity, thermal diffusivity, thermal conductivity, vapor pressure Optical properties Emissivity, reflection absorption and absorption edge, refraction index, photomission, brightfringe Chemical properties Diffusion coefficient, oxidation rate, etching rate

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The refractory metallic ceramics are promising candidate materials for the following areas: 1. Very large scale integration (VLSI) technology and electronic devices: Carbides and diborides as field and thermal emitters, TiN as a diffusion barrier in metallization to Si semiconductors, resistive thermoconductive humidity sensors with TaN film, and Josephson tunnel junctions with NbN film. 2. Energy-related materials: Solar-selective surfaces with ZrC thin films, emitters for thermoionic generators, ZrB 2 and HfB 2 electrodes for MHD generators, and first wall coating with TiC or TiB 2 film for tokamaks. Refractory semiconductors are under intense study because of their potential applications in electronic devices for high temperature, high frequency, and high power and blue light– emitting devices (3). Electronics based on the existing semiconductor device technologies with Si and GaAs cannot tolerate greatly elevated temperatures or chemically hostile environments due to the uncontrolled generation of intrinsic carriers and their low resistance to caustic chemicals. The wide-band-gap semiconductors SiC and GaN, and perhaps sometime in the future diamond, with their excellent thermal conductivities, large breakdown fields, and resistance to chemical attack, will be materials of choice for these applications (4). Other refractory semiconductors will continue to be developed and compete for niches. A suitable high-temperature semiconductor technology could allow bulky aircraft hydraulics and mechanical control systems to be replaced with heat-tolerant in situ control electronics. Onsite electronics, actuators, and sensors would reduce complexity and increase reliability. Hydraulic system, a fire hazard in aircraft, and heat radiators in satellites could then be greatly reduced in size and number, yielding a considerable weight reduction (4). In addition, many wide-gap semiconductors are anticipated to find applications in thermoelectric, electro-optic, piezoelectric, and acousto-optic devices and heat sinks.

REFERENCES 1. JJ Gangler. NASA research on refractory compounds. High Temp High Press 3:487, 1971. 2. RA Laudise. In: R Ueda, JB Mullin, eds. Crystal Growth and Characterization. Amsterdam: NorthHolland, 1975, p 255. 3. H Morkoc, S Strite, GB Gao, ME Lim, B Sverdlov, M Burns. Large-band-gap SiC, III–V nitride, and II–VI ZnSe-based semiconductor device technologies. J Appl Phys 76:1363, 1994. 4. Y Kumashiro. Recent developments of refractory semiconductor materials. JRCM News 20:2, 1993.

2 Survey of Refractory Metalloids: Transition Metal Carbides, Nitrides, and Diborides Yukinobu Kumashiro Yokohama National University, Hodogaya-ku, Yokohama, Japan

The transition metal carbides, nitrides, and diborides of groups IV and V of the periodic table are electronically conductive but are also very hard and have high melting points (1). These compounds are characterized by their unique chemical bonding; metal and nonmetal bonds are related to lattice formation, and the metallic, covalent, and ionic (about 15%) bonds contribute simultaneously to the cohesive energy (2). The carbides and nitrides have a B1(NaCl) structure (space group O 5h Fm3m) with wide homogeneity. They are called interstitial compounds, i.e., with a face-centered cubic (fcc) structure at the centers of octahedral interstitial sites or trigonal prismatic voids of the metallic lattice. Physical properties of these compounds are similar and depend on the composition. The cohesive energy relations for carbides and nitrides with rocksalt structures are explained in terms of melting point and bond length (3). Cohesion is due to electron transfer, but the values deviate from a simple exchange relation associated with limited sd band participation in bonding. The carbides of group IV deviate largely from the stoichiometric composition MC 1.00 , and the homogeneity regions for group V carbides are less extended than for the carbides of group IV (4). The VC phase in equilibrium with carbon terminates near VC0.9 rather than the perfect lattice composition. Group V carbides form disordered lower carbides with the hexagonal closepacked (hcp) structure of W2C (L′3) (4). Vanadium carbide exhibits an order-disorder transition in the range of stoichiometry, that is, VC0.83 ⫽ V6C 5 (hexagonal) and VC 0.875 ⫽ V8C 7 (cubic). The chemistry of the material does not change: with no change in the number of particles, the vacancy in the disordered, nonstoichiometric compound becomes ordered, resulting in a different crystal structure (5). Long-range order in these vanadium carbides was detected using nuclear magnetic resonance (NMR) (6) and electron diffraction (ED) (7). Neutron diffraction patterns of annealed NbC x (0.81 ⬉ x ⬉ 0.88) (4,8) and TaC x (0.79 ⬉ x ⬉ 0.90) specimens display weak superstructure peaks along with intense structural lines, suggesting an incommensurate ordered phase with a composition close to M 6C 5 (4). The parameter of the fcc sublattice of metals for the ordered phase is larger than that for the disordered carbides, indicating that the volume of the crystal varies discontinuously during ordering (4). The transition metal nitrides are close to carbides in structure and properties. They are often isostructural and usually form solid solutions with each other. The electrical and thermal conductivities; of hot-pressed stoichiometric carbonitrides appear to behave very similarly (9); i.e., the electronic and thermal conductivities tend to increase with increasing nitrogen content 7

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Kumashiro

Figure 1 Reflectance of stoichiometric titanium carbonitrides Ti(Cx N1⫺x)1.00 and Ti(CxN1⫺x ) 0.82 as a function of [C]/([C] ⫹ [N]) ratio. (From Ref. 9.)

in a similar fashion. The reflectance curves for the carbonitrides are shown in Fig. 1 (9). For the nitrides, a distinct minimum in the reflectance curves in the blue region could be observed, indicative of a yellow appearance of the nitrides. Upon the introduction of carbon, this minimum shifts toward higher wavelengths and becomes weaker. The wavelength shift corresponds to a conversion of the color toward violet. This color change from yellow through violet to gray is shifted toward higher carbon contents, the higher the atomic number of the transition metal. The substoichiometric carbonitrides show almost linear reflectance curves without a pronounced minimum in any spectral region, which is the reason for their gray appearance. The nitrides of group IV have a B1 (NaCl) structure. Those of group V form δ-phases— mononitrides—with an fcc metallic sublattice, as well as ⑀-phases—stoichiometric MN1.00 nitride—with an hcp structure and lower M 2N nitrides with an hcp structure (10). The nitride systems are pressure dependent, and in carbide systems the influence of pressure can be neglected. Many binary nitride phase diagrams are still inexactly known and there exists a great deal of controversy about proposed diagrams (10). One particular problem confounding phase diagram studies of nitrides is the sensitivity of phase stabilities to the method of preparation. The tendency to deviate from stoichiometry causes difficulties in defining the melting points. Loss of nitrogen at high temperatures makes the nitrides nonstoichiometric, resulting in a decrease of the melting temperature so that the melting points of the nitrides cannot be defined unambiguously without defining the nitrogen pressure. The melting point of δ-TaN is expected to take place at about 2800–3000°C and at nitrogen equilibrium a pressure of about 1000–3000 bar (10). The transition metal hexagonal AlB 2-type structure (space group D′6h-P6/mmn) consists of hexagonal closed-packed metal layers (A) and ‘‘graphite’’-like boron layers (H) stacked in the simple sequence AHAHAH ⋅ ⋅ ⋅ (11). The hexagonal unit cell contains metal atoms at (0, 0, 0) and boron atoms at (1/3, 2/3, 1/2) and (2/3, 1/3, 1/2). The bonding within the basal plane is determined by the strong BB bonds within the boron layer, whereas the cohesive force in the c direction is determined mainly by MB bonds (M denotes metal). Furthermore, the microhardness of the VB 2 single crystal in the ⬍1000⬎ direction shows slightly higher values than in the other directions, which would indicate strong BB bonds in the diboride structure (12). The transition metal diborides have melting points ranging from 2000 to 3000°C and relatively low volatility in comparison with the carbides and nitrides. All the diborides with the exception of the niobium and tantalum diborides have a small homogeneity range (13). The boron-rich compositions contain interstitial boron atoms at (0, 0, 1/2) rather than vacancies at the metal position. The simultaneous occurrence of metal vacancies and interstitial boron atoms accommo-

Survey of Refractory Metalloids

9

Figure 2 Microhardness of TaB2 and NbB2 within the homogeneity ranges. (From Ref. 15.)

dated in the larger holes at (1/3, 2/3, 0) and (2/3, 1/3, 0) results in wide homogeneity ranges in NbB2 and TaB2 (14). Microhardness values for two diborides are plotted against boron contents in Fig. 2 (15). The microhardness increases with increasing boron content, consistent with the increase in bond strength for boron-rich NbB2 and TaB2 compositions although an abrupt increase in the hardness of the metal-rich composition of NbB2 can be seen. Transport properties of these compounds are reviewed. The resistivity of MCx single crystals except for VCx at room temperature increases with decreasing x but begins to saturate (1). The contribution of phonon scattering for TiC was found to be 30, 20, and 10% at a composition (C/Ti) of 0.95. 0.9, and ⬍0.8, respectively (16). Also the inverse mobility for nonstoichiometric carbides is proportional to the vacancy concentration, showing evidence that carbon vacancies act as scattering centers for electrons (17). This relationship can be revised to obtain the pointdefect concentration and the chemical composition of a carbide from its resistivity (18). Nearly the entire composition range corresponds to one or the other of the ordered phases in the vanadium-carbon system (5). Only a small region of disorder exists between the regions of order. A single-crystal sample of V8C 7 had the lowest residual resistivity (3.17 µΩ cm) ever measured in a nonsuperconducting group IV or V transition metal carbide. The heat capacity of both ordered and disordered niobium carbide, NbC x, also decreases with decreasing carbon content. An ordered niobium carbide has a higher heat capacity than a disordered carbide of the same composition (19). The maximum value of the difference of the heat capacities of an ordered and a disordered specimen is observed for NbC 0.83 , corresponding to the stoichiometric, composition of an ordered Nb 6 C5 phase. Then the thermal conductivities of the ordered phases V6C 5 and Nb 6C 5 at room temperature are attributable to a decrease in electron vacancy and phonon vacancy scattering. As electrons suffer less scattering in the partially ordered compounds by the Wiedemann-Franz law, K e ⫽ L 0 σT, the resulting electrical conductivity also increases the contribution to the thermal conductivity by electrons, Ke (20). Some transition metal carbides and nitrides show superconductivity above liquid nitrogen temperature. Those having a Tc of 17 K or higher are NbN and compounds represented by the general formula NbC xN 1⫺x , and most of the others have a Tc of 14 K or lower. The factors

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determining Tc are the state density of electrons at the Fermi level N(E F ), the electron-phonon interaction parameter Vph , and the Debye temperature θ D (21). The Fermi level of group IV carbides involves a minimum point of state density, so these materials are not superconducting. In contrast, the group V carbides and group IV and V nitrides become superconducting because of an increase in N(E F ) (21), corresponding to the increase in valence electron number. However, TaN has lower than expected Tc values, which may result from the presence of vacant lattices, since they largely comprise antibonding orbitals and are not reactive. Furthermore, VN has relatively low Tc values for its high N(E F ) values, conceivably resulting from spin fluctuations (21). The high Tc values are due mainly to abnormalities of lattice vibrations (21). Phonon abnormalities are observed with such compounds as NbC, TaC, TiN, ZrN, HfN, and NbN, which have high Tc values, but not with carbides of group IV elements. This is explained directly by comparing the acoustic phonon energy dispersion curves and phonon state densities of NbC and ZrC (Fig. 3). NbC has three depressed parts at (0, 0, 0.7), (0.55, 0.55, 0), and (0.5, 0.5, 0.5) on the dispersion curve. These are referred to as phonon abnormalities, the phenomenon stemming from the negative force constant at a point corresponding to the reciprocal lattice vector of the depressed parts. Also, NbC has a phonon state density whose centroid greatly deviates from that of ZrC to the low-energy side. NbN has a still larger depressed part at point X on the dispersion curve, and its phonon state density is moved farther toward the low-energy side. Thus, the order of magnitude of ⬍ω 2⬎, which determines the electronic phonon coupling constant λ, is ZrC ⬎ NbC ⬎ NbN, and this order is reversed with respect to λ. NbN, with a large λ, has a high Tc . Next we would like to mention the mechanical properties of these compounds. The microhardness anisotropy of a single crystal induces a slip system because the hardness maxima and minima correspond to the effective resolved shear stress minima and maxima, respectively (22). The periodicity of the hardness curve of the carbides in (100) planes and theoretical curves given by Hannink et al. (23) and Kohlstedt (24) indicate that the primary slip system of TaC (25–27) is {111}⬍110⬎, whereas in TiC (28), ZrC (26), and HfC (27) the {110}⬍110⬎ system is found. In the case of VC and NbC with double maxima, the slip systems are coexistent with {111}⬍110⬎ and {110}⬍110⬎ (29,30). But the use of the Burgers vector and transmission electron microscopy for NbC (29) single crystals identifies a slip system of {111}⬍110⬎. Microplasticity has been found in localized regions around hardness indentations revealed

Figure 3 Acoustic phonon dispersion curves and phonon density of states of NbC and ZrC (21). Depressed parts, as indicated by arrows, are formed on the dispersion curve of NbC, which moves the state density of the compound to the low-energy side.

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by slip lines, i.e., the formation of cracks and dislocation motion along the slip systems {110}⬍110⬎ and {100}⬍110⬎. The degree of plastic deformation and the importance of the slip system {111}⬍110⬎ increase as the C-to-Ti ratio decreases from 0.99 to 0.64 (31–33). A new deformation mode induced during high-speed abrasive preparation of TiC single crystals, which involves a stress-induced martensitic transformation from cubic TiC to rhombohedral and hexagonal structures, has been reported (34). The new phase is designated 8H, to reflect the height of the unit cell (eight TiC atom planes) and the hexagonal symmetry (H). The observed martensitic transformation appears to be peculiar to dynamic deformation at high loading rates. The transformed structure would be governed by the Ti sublattice and carbon atoms remaining in octahedral coordination. Under certain types of loading, it might be possible to produce similar transformations in the vicinity of crack tips or other stress concentrations. The slip for TiN and ZrC single crystals from the slip traces produced by microhardness indentations indicates that {111}⬍110⬎ slip is operative (35). The main slip system contributing to the hardness anisotropy of titanium diboride single crystals is found to be (0001) ⬍1120⬎, that of zicronium diboride is {1010} ⬍1210⬎, and that of hafnium diboride single crystals involves both slip systems (36). NbB 2 crystals have an axial ratio (c/a ⫽ 1.06) near unity, so NbB 2 single crystals may have another prismatic slip system {1010} [0001], as well as the two (0001) ⬍1120⬎ and {1010} ⬍1121⬎ types (37). However, Vahldiek and Mersol (35) confirmed slip systems of {1010} [0001] and {1010} [1120] in as-grown diboride single crystals by observing slip patterns on the (0001) and {1010} planes. Considering the shortest Burgers vector of the ⬍1120⬎ directions and the closeness of lattice parameters a and c in the diborides, ⬍1120⬎ would be the primary slip direction and [0001] is also an effective slip direction (35). Figure 4 shows hardness and composition for transition metal nitrides. The hardness decreases with increasing nitrogen content for the group V nitrides (38,39), which would be due to electronically induced lattice softening as a result of the generation of antibonding states. Antibonding states are successively occupied in fcc transition metal compounds with more than eight valence electrons. An increasing valence electron concentration due to increasing nitrogen

Figure 4 Microhardness of δ-TiN and group V nitrides as a function of stoichiometry. (From Ref. 38, 39.)

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content would lead to a decrease in hardness when the number of valence electrons exceeds eight. In δ-TiN 1⫺x a maximum in microhardness is found for the composition δ-TiN 0.67 , corresponding to 7.3 valence electrons. For δ-HfN 1⫺x a smooth increase in microhardness with increasing nitrogen content is observed, probably as a result of the difference in electronic states due to 5f electrons. The changes in interatomic bonding appear as changed elastic constants (40). The Blackman diagram in Fig. 5 shows results for one particular choice of ratios: y ⫽ C 12 /C 11 and x ⫽ C 44 /C 11 represent ratios of interatomic force constants because y and x are mass-density (volume) independent (41). Lines radiating from the upper left correspond to various Zener anisotropies, A ⫽ 2C 44 /(C 11 ⫺ C 12), from 0.5 to 12. Curved lines correspond to various quasi-isotropic Poisson ratio values from ⫺0.1 to 0.4. The transition metal carbides with an NaCl-type crystal structure suggest a strong ionic bonding component. Figure 6 shows the three-dimensional surface representing the Young’s modulus of TiB 2 single crystal as a function of crystallographic direction, indicating that the elastic constants of TiB 2 single crystals are more isotropic and stiffer than previously considered (42). The Young’s modulus E and hardness H of TiN films measured by a depth-sensing nanoindentation technique and the shear modulus G obtained by measuring the velocity of the acoustic surface wave by Brillouin light scattering are shown in Fig. 7 (43). For x ⫽ 0 (pure titanium) both measured values of Young’s shear modulus agree well with the standard value for titanium, indicating that the film quality is rather good and that the small discrepancy might also be due to other effects, e.g., a different morphology of the films and/or texture. Both Young’s modulus and hardness increase with increasing [N]/[Ti] ratio in a similar fashion. The plot of the hardness versus Young’s modulus shows a linear relationship, which would be due to the fine polycrystalline structure. Mutual alloying and doping improve the mechanical properties. Hardness values of the TiC-VC system with carbon-to-metal ratios close to 0.84 obtained for various cooling rates in a floating-zone process indicated that the variation in hardness of pure VC 0.84 obtained by chang-

Figure 5 The plot of reduced cubic-symmetry elastic stiffness shows groupings according to bonding types (41). A, Alkali metals; B, fcc metal; C, covalent compounds; D, bcc transition metals; E, oxides; F, alkali; G, NaCl-type carbides.

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Figure 6 Three-dimensional surface representing Young’s modulus of TiB2 in different crystallographic directions according to the elastic constants. (From Ref. 42.)

Figure 7 The shear modulus as derived from Brillouin light scattering, Young’s modulus, and the microhardness obtained by ultra load indentation measurements as a function of the N/Ti ratio in TiNx films. (From Ref. 43.)

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ing the cooling rate is related to the vacancy domain size. The observed trend in hardness of the alloys is for higher values for TiC-rich than VC-rich alloys and higher values for both alloys than for the parent carbides (44). Composite materials are of interest from an engineering standpoint, with potential applications in the areas of turbine blades, ball bearings, cutting tools, etc. Directionally solidified lamellar ZrC-ZrB 2 and Chinese-script ZrC-TiB2 eutectics with a phase spacing of 1.85 µm in a floating-zone method exhibited superior mechanical properties compared with the individual constituents (45). Notably high values of microhardness (24.02 GPa) and fracture toughness (5.44 MN/m 3/2) were found for the ZrC-ZrB 2 eutectic. The fracture toughness (KIc) is an important selection criterion for brittle materials used in engineering applications. Value of K ic obtained by different techniques vary greatly. The indentation strength (IS), chevron notched beam (CNB), and indentation fracture (IF) methods are common techniques that were compared with the recently standardized single-edge precracked beam (SEPB) method (46). The SEPB method was more difficult to apply, but it represents the most rigorous method for K ic determination because it uses few assumptions and requires a direct measurement of crack length. Transition metal nitride superlattices, including TiN/VN (47), and TiN/(V0.6 Nb0.4)N (48), exhibit Vickers hardness values as much as 2.5 times those for homogeneous nitrides (Fig. 8). Single-crystal superlattices eliminate possible polycrystalline film structure effects in the hardness measurements. TiN/VN superlattices, with a 2.4% lattice mismatch between the layers, exhibit pronounced peaks at Λ ⬃ 5 nm, which would be due, at least in part, to the ‘‘supermodulus’’ effect, i.e., increases by a factor of 2–4 of the elastic moduli at specific values of Λ. For TiN/(V0.6Nb 0.4)N superlattices, with lattice matching of ⬃0.2%, the hardness increase was smaller and a pronounced peak was not observed. However, the elastic constants of C 44 for TiN/ V0.6 Nb 0.4 N and TiN/NbN superlattices from Brillouin scattering measurements (49) exhibited no anomalies over the wavelength range investigated, so elastic anomalies are not responsible for the large hardness enhancements in nitride superlattices. The hardness value for the TiN/ (V0.6 Nb 0.4)N lattice-matched superlattice agrees with that for TiN/VN superlattices, so coherency strains do not play a major role in enhancing the hardness of these nitride superlattices. Transition metal carbides and nitrides have attracted considerable attention as catalysts because of their availability in high specific surface area form with reasonably clean surfaces (50). They have been shown to have exceptionally high activity in reactions involving hydrogen

Figure 8 Vickers hardness of nitride superlattice structures as a function of superlattice period λ. (From Ref. 47, 48.)

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transfer, such as hydrogenation, hydrogenolysis, isomerization, hydrodesulfurization (HDS), and hydrodenitrogenation (HDN) of hydrocarbons (50,51). They also show excellent hydrogenation activity in the treatment of quinoline and coal-derived liquid. Their catalytic activities in hydroprocessing indicate tolerance of sulfer (51).

ACKNOWLEDGMENTS A number of the figures have been taken from the literature. The author would like to thank the authors and publishers of these materials for permission to reproduce them here, especially the American Institute of Physics (Fig. 5 (Ref. 41), Fig. 6 (Ref. 42), Fig. 7 (Ref. 43), and Fig. 8 (Ref. 47 and 48)), Elsevier Science Ltd. (Fig. 1 (Ref. 9) and Fig. 2 (Ref. 15)), and John Wiley & Sons, Ltd. (Fig. 4 (Ref. 39)).

REFERENCES 1. WS Williams. Transition metal carbides, nitrides, and diborides for electronic applications. JOM J Miner Met Mater Soc 49:38, 1997. 2. H Ihara. Electronic structures of the transition metal carbides and borides studied by X-ray photoelectron spectroscopy and band calculation. Researches of Electrotechnical Laboratory No. 725, 1977. 3. LG Van Uitert. A comparison of melting point relations for metals, tetrahedral semiconductors, and metal carbides and nitrides with rocksalt structure. J Appl Phys 52:5547, 1981. 4. AI Gusev. Disorder and long-range order in non-stoichiometric interstitial compounds, transition metal carbides, nitrides and oxides. Phys Status Solidi (b) 163:17, 1991. 5. LW Shacklette, WS Williams. Scattering of electrons by vacancies through an order-disorder transition in vanadium carbide. J Appl Phys 42:4698, 1971. 6. CH de Novion, B Beuneu, T Priem, N Lorenzellii, A Finel. Defect structures and order-disorder transformations in transition metal carbides and nitrides. In: R Freer, ed. The Physics and Chemistry of Carbides, Nitrides and Borides. Dordrecht: Kluwer Academic Press, 1990, p 329. 7. T Epoicier. Application of transmission electron microscopy to the study of transition metal carbides. In: R Freer, ed. The Physics and Chemistry of Carbides, Nitrides and Borides. Dordrecht: Kluwer Academic Press, 1990, p 297. 8. AI Gusev, AA Remple. Order-disorder phase transition channel in niobium carbide. Phys Status Solidi [a]93:71, 1986. 9. W Lengauer, S Binder, K Aigner, P Ettmayer, A Guilloiu, J Debuigne. Solid state properties of group IVb carbonitrides. J Alloys Compounds 217:137, 1995. 10. P Ettmayer, A Vendl. Phase equilibria and crystal structures of transition nitrides. In: RK Viswanadham, DJ Rowcliffe, J Gurland, eds. Science of Hard Materials. New York: Plenum, 1983, p 47. 11. T Lundstro¨m. Transition metal borides. In: VI Matkovich, ed. Boron and Refractory Borides. Berlin: Springer, 1977, p 351. 12. C Bulfon, AL Jasper, H Sassik, P Rogl. Microhardness of Czochralski-grown single crystals of VB 2. J Solid State Chem 133:113, 1997. 13. KE Spear, P McDowell, F McMahon. Exerimental evidence for the existence of Ti 3B 4 phase. J Am Ceram Soc 69:C4, 1986. 14. T Lundstro¨m. In: DJ Rowcliffe, ed. Proceedings of International Conference on the Science of Hard Materials. New York: Plenum, 1983, p 219. 15. T Lundstro¨m, B Lo¨nnberg, I Westman. A study of the microhardness in homogeneity ranges of NbB 2 and TaB 2. J Less Common Met 96:229, 1984. 16. S Otani, T Tanaka, Y Ishizawa. Electrical resistivity in single crystals of TiC x and VC x . J Mater Sci 21:1011, 1986.

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17. FA Modine, MD Foegelle, CB Finch, CY Allison. Electrical properties of transition-metal carbides of group IV. Phys Rev B 40:9558, 1989. 18. WS Williams. Resistivity as tool for characterizing point defects in nonstoichiometric metallic ceramics. Mater Res Soc Symp Proc 411:169, 1996. 19. AA Rempel, AI Gusev. Heat capacity of niobium carbide in different structural states. Phys Status Solidi (a) 113:353, 1989. 20. LC Dy and WS Williams, Resistivity, superconductivity, and order-disorder transformations in transition metal carbides and hydrogen-doped carbides. J Appl Phys 53:8915, 1982. 21. H Ihara. Non-oxide superconductors. J Ceram Soc Jpn Int Ed 95:C-229, 1987. 22. CA Brookes, JB O’Neill, BAW Redfern. Anisotropy in the hardness of single crystals. Proc R Soc Lond A322:73, 1971. 23. HJ Hannink, DL Kohlstedt, MJ Murray. Slip system determination in cubic carbides by hardness anisotrophy. Proc R Soc Lond A326:409, 1972. 24. DL Kohlstedt. The temperature dependence of microhardness of the transition-metal carbides. J Mater Sci 8:777, 1973. 25. DJ Rowcliffe, WJ Warren. Structure and properties of tantalum carbide crystals. J Mater Sci 5:345, 1970. 26. Y Kumashiro, Y Nagai, H Kato, E Sakuma, K Watanabe, S Misawa. The preparation and characteristics of ZrC and TaC single crystal using an r.f. floating-zone process. J Mater Sci 16:2931, 1981. 27. DJ Rowchiffe, GE Hollox. Plastic flow and fracture of tantalum carbide and hafnium carbide at low temperatures. J Mater Sci 6:1261, 1971. 28. Y Kumashiro, A Itoh, T Kinoshita, M Sobajima. The micro-Vickers hardness of TiC single crystals up to 1500°C. J Mater Sci 12:595, 1977. 29. G Morgen, MH Lewis. Hardness anisotropy in niobium carbide. J Mater Sci 9:349, 1974. 30. Y Kumashiro, E Sakuma. The Vickers micro-hardness of non-stoichiometric niobium carbides and vanadium carbide single crystals up to 1500°C. J Mater Sci 15:1321, 1980. 31. DJ Rowchiffe, GE Hollox. Hardness anisotropy, determination mechanisms and brittle-to-ductile transition in carbides. J Mater Sci 6:1270, 1971. 32. E Breval. Microplasticity at room temperature of single-crystal titanium carbide with different stoichimetry. J Mater Sci 16:2781, 1981. 33. RHJ Hannink, MJ Murray. Comment on ‘‘Slip and microhardness of IVa and VIa refractory materials.’’ J Less Common Met 60:143, 1978. 34. FR Chien, RJ Clifton, SR Nutt. Stress-induced phase transformation in single crystal titanium carbide. J Am Ceram Soc 78:1537, 1995. 35. FW Vahldiek, SA Mersol. Slip and microhardness of VIa refractory materials. J Less Common Met 55:265, 1977. 36. K Nakano, T Imura, S Takeuchi. Hardness anisotropy of single crystals of VIa-diborides. Jpn J Appl Phys 12:186, 1973. 37. K Nakano, I Higashi. The hardness of NbB 2 single crystals. J Less Common Met 67:485, 1979. 38. W Lengaueer, P Ettmayer. Physical and mechanical properties of cubic δ-VN 1⫺x . J Less Common Met 109:351, 1985. 39. P Ettmayer, W Lengauer. Nitrides:Transition metal solid-state chemistry. In: Encyclopedia of Inorganic Chemistry. New York: Wiley, 1994, p 2498. 40. Y Kumashiro, H Tokumoto, E Sakuma, A Itoh. The elastic constants of TiC, VC, and NbC single crystals. In: RR Hashiguchi, Y Mikoshiba, eds. International Friction and Ultrasonic Attenuation in Solids. Tokyo: Tokyo University Press, 1977, p 395. 41. HM Ledbetter, S Chevacharoenkul, RF Davis. Monocrystal elastic constants of NbC. J Appl Phys 60:1614, 1986. 42. PS Spoor, JD Maynard, MJ Pan, DJ Green, JR Hellmann, T Tanaka. Elastic constants and crystal anisotropy of titanium diboride. Appl Phys Lett 70:1959, 1997. 43. X Jiang, M Wang, K Schmidt, E Dunlop, J Haupt, W Gissler. Elastic constants and hardness of ionbeam–sputtered TiN x films measured by Brillouin scattering and depth-sensing indentation. J Appl Phys 69:3053, 1991.

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44. RHJ Hannink, MJ Murray. Effects of cooling rate on the microstructure and hardness of TiC-VC alloys. Scr Metall 9:1271, 1975. 45. CC Sorrell, VS Stubican, RC Bradt. Mechanical properties of ZrC-ZrB 2 and ZrC-TiB 2 directionally solidified eutectics. J Am Ceram Soc 69:317, 1986. 46. SD Conzone, WR Blumenthal, JR Varner. Fracture toughness of TiB 2 and B 4C using the singleedge precracked beam, indentation fracture, chevron notched beam and indentation strength methods. J Amer Ceram Soc 78:2187, 1995. 47. U Hermersson, S Todorova, SA Barnett, J-E Sundgren, LC Markert, JE Greene. Growth of singlecrystal TiN/VN strained-layer superlattices with extremely high mechanical hardness. J Appl Phys 62:481, 1987. 48. PB Mirkarimi, L Hultman, SA Barnett. Enhanced hardness in lattice-matched single-crystal TiN/ V0.6 Nb 0.4 N superlattices. Appl Phys Lett 57:2654, 1990. 49. PB Mirkarimi, M Shinn, SA Barnett, S Kumar, M Grimsditch. Elastic properties of TiN/(VxNb 1⫺x)N superlattices measured by Brillouin scattering. J Appl Phys 71:4955, 1992. 50. ST Oyama. Introduction to the chemistry of transition metal carbides and nitrides. In: S.T. Oyama, ed. The Chemistry of Transition Metal Carbides and Nitrides. Glasgow: Blakie Academic & Professional, imprint of Chapman & Hall, 1996, p 1. 51. S Ramanathan, ST Oyama. New catalysts for hydroprocessing: transition metal carbides and nitrides. J Phys Chem 99:16365, 1995.

3 Bulk Crystal Growth Yukinobu Kumashiro Yokohama National University, Hodogaya-ku, Yokohama, Japan

I.

INTRODUCTION

According to the classification based on the state of aggregation of the starting materials, these compounds are obtained by liquid-phase, solid-phase, gas-phase, and solution processes and combinations of these processes. Evaporation-condensation is a physical vapor deposition (PVD) method in which a metal is evaporated in an atmosphere of rarefied in active gas. In chemical vapor deposition (CVD) the types of deposits are films, whiskers, bulk crystals, and powders. Powders are made by growth of nuclei following homogeneous nucleation, and whiskers and bulk crystals are formed by heterogeneous nucleation on the substrate. Plasma reactants offer potential advantages for powder preparation: a fast reaction time due to high temperatures and rapid cooling rates leading to a high degree of supersaturation and homogeneous nucleation. Carbide and nitride powders are conventionally prepared by the carboreduction of oxide powder with subsequent nitridation in a nitrogen atmosphere or carborization in an inert gas. Diboride powders are synthesized by carbothermal reduction, where boron needs to form the boride and carbon aids in the removal of oxygen. These processes require a high temperature and a long heating time. Fine powders of these compounds are prepared by the thermite method by reduction with Mg. New processes for the production of powders have been developed. Molecular precursor methods for preparing nitrides are currently being explored. A precursor processible to metal boride is obtained by dispersing a metal source in a boron carbide polymeric precursor. Electrochemically prepared polymeric precursors have been used for the formation of pure nitride and carbide powders. Direct formation of carbides and diborides by mechanical alloying of metal powder and carbon or boron powder is also an effective method for synthesizing nanocrystalline powders. Self-propagation high temperature synthesis (SHS) or combustion synthesis is of interest for making a wide variety of powders and sintered bodies, which involves highly exothermic chemical interactions in combustion mode. The products are generally in the form of powder blocks or powders, which are comminuted, and the resulting powders are used in fabricating components by conventional powder metallurgy. The ideal production process would combine the synthesis and densification steps in a one-step process. New techniques for simultaneous densification of products in SHS are explosive consolidation or dynamic compaction, hot forging, and shock-induced reaction synthesis. These compounds are known to be difficult to sinter to high density because of the small 19

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diffusion coefficient of the constituent atoms. Hot pressing and hot isostatic pressing techniques are usually essential. Additives to the specimen such as Ni, Co, and Al play an important role in promoting densification via liquid-phase sintering. The preparation of single crystals of these refractory compounds is fairly difficult because of their high melting point—3000°C or above. The largest crystals were obtained by liquidphase and solid-phase methods; it is much more feasible to prepare larger single crystals of carbides by these methods than by gas-phase and solution processes. Crystal growth in closed tubes, involving chemical reactions and gas transport referred to as chemical vapor transport (CVT), requires a temperature gradient to be described as two successive thermodynamic systems. The purest crystals (e.g., with purity of the order of 99.98 wt %) have been obtained by the liquid-phase method and somewhat less pure ones (e.g., of 99.5 wt %) have been prepared by the solution method, where the impurities in the crystals are the solvent metal. Large single crystals of carbides and diborides are obtained by the radio frequency (RF) floating-zone process, but those of nitrides are limited by sold-phase methods. Plasma-arc heating provides not only high temperature but also the use of light element–containing gases (CO2, CH4, N2, and NH3 gas) as components of the plasma-generating gas, which serves for the compensation of carbon and nitrogen losses in carbides and nitrides, respectively. In this chapter, the preparation of powders, fabrication of polycrystalline specimens, and growth of single crystals are reviewed in relation to crystal characterization.

II. POWDERS A gas evaporation method in which a carbon rod vertically touches the top surface of a metal block in a vacuum chamber produces ultrafine particles of various carbides (1). As the electric current is increased until the carbon rod changes from red heat to white heat in a helium or argon atmosphere, the metal block melts and molten metal climbs up along the surface of the carbon rod. Spherical or trigonal smoked TiC with a diameter of about 50 nm can be most easily obtained (1). In the CVD process the reactants are gaseous, volatile liquids, or solids with reaction temperature. The carbide, nitride, and diboride specimens were prepared using TiCl4, ZrCl4, HfCl4, NbCl4, NbCl5, VCl4, CH4, C3H8, CCl4, NH3, N2, B2H6, and BCl3 at various temperatures and gas pressures. Ultrafine nitrides such as TiN, VN (2), and NbN (3) were prepared using MCl4-NH3-H2-N2 systems at temperatures above 800°C. The properties of NbN powders depended on the reaction temperature, mixing temperature of NbCl4 and NH3, and gas composition ratio ([NH3]/[NbCl4]). The process consisted of the initial formation of NbCl4-NH3 adduct particles (NbCl4 ⋅ nNH3) in the low temperature (⬍800°C) zone of the reactor and their subsequent thermal decomposition to NbN particles in the high temperature zone (ⱖ800°C). The NbN powders consisted of particles with sizes less than 50 nm and showed a superconducting transition temperature of 14.1 K. Polycrystalline TiB2 powders with 10-nm crystallites (4) and nanosized TiC powders (5) were synthesized by CO2 laser–induced pyrolysis of TiCl4-B2H6 and TiCl4-hydrocarbon. The TiC nanopowder showed high reactivity on air exposure as evidenced by the surface oxidation of the particles. Let us consider the various plasma processes for producing powders. One process involves the reaction between metal halides and reactive gases, which have been widely used in ordinary CVD processes. The compositions of the products are controlled linearly by those of the reactants (6). Titanium diboride powder consisting of submicrometer-sized crystals of equiaxed and tabular forms with only small amounts of crystal intergrowth was produced in an arc plasma

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by the reaction of titanium tetrachloride and boron trichloride gases in the presence of excess hydrogen (6). In another process, pure metallic powders are used as starting materials. The metallic powders are vaporized completely in a plasma region and react directly with reactive gases with an RF plasma torch (30 kW, 4.0 MHz) (7). The compositions of the products were correlated with the [N2]/[Ti] molar ratio. Thermodynamic equilibrium compositions for the Ti-N2-Ar system calculated up to a temperature of 6000 K show nine gaseous species [Ar, Ar⫹, Ti(g), Ti⫹, N2, N, N⫹, e⫺, TiN(g)] and two condensed species [Ti(c), TiN(c)] (Fig. 1). Ti(c) cannot be present, so a low flow rate of nitrogen is sufficient to produce TiN particles from the gas mixture. The condensation temperature of TiN(c) is 2760 K, indicating that solid particles of TiN would grow from the vapor phase directly, because the melting temperature is about 3220 K. The mole concentrations of N, Ti⫹, e⫺, and TiN(g) at the condensation temperature would play important roles in determining the nucleus centers at the beginning of a homogeneous nucleation. There exists an optimal molar ratio of [N2]/[Ti] for making stoichiometric TiN. Each particle is a single crystal, and the preferential growth form is a cube bounded by (100) planes. Adiabatic expansion through a converging-diverging nozzle could be used as an alternative means to produce the high rates of temperature change required to preserve metastable products; here the reactants are heated in a plasma and then expanded through a converging-diverging nozzle to freeze in the desired products (8). The velocity of the gas increases continually from the inlet in a nozzle, reaches the sonic point near the throat, and becomes supersonic in the diverging section. The average rate of cooling in a supersonic nozzle is of the order of 107 K/s, which allows use of TiO2 and C as reactants for the production of TiC (8).

Figure 1 Thermodynamic equilibrium diagram for the Ar-Ti-N system under 1 atm. (From Ref. 7.)

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Using liquid synthesis, Powell et al. (9) produced ultrafine powders of NbC and NbN by conversion of an Nb-bearing spray-dried powder in hydrogen-methane and ammonia atmospheres at temperatures as low as 800 and 700°C, respectively. The solution prepared by slowly dissolving NbCl5 powder in high-purity ethanol formed a new dissolved compound [NbCl2(OC2H5)3] and HCl gas. Conversion of the spray-dried powders to NbC was achieved at temperatures from 800 to 1050°C in a mixed atmosphere of hydrogen and methane, and that to the NbN was achieved at temperatures of 700–1000°C using an ammonia atmosphere. The powder processed at 700, 800, and 850°C had the structure of δ-NbN, but it gradually converted to the stable ⑀-NbN phase from 900 to 1000°C. The powders consisted of 5–10-µm balls subdivided into 10–100-nm microcrystallites. The Tc of the NbC powder produced at 850°C was approximately 6.8 K with a transition width of 1.5 K. The electrochemical preparation of polymeric precursors (10–12) involves anodic dissolution of a metal electrode in a single-compartment electrochemical cell containing an electrolyte solution consisting of liquid NH3 and NH4X (X ⫽ Br or Cl). Following evaporation of the solvent and calcination of the resulting powder at temperatures between 375 and 1100°C, such nitrides as NbN, TiN, VN, and ZrN were produced (12). The NbN precursor requires anodic dissolution of the metal anode, where Nb5⫹ reacts directly with liquid NH3 by ammonolysis to form the ceramic precursor. Precursor calcined in pure Ar at 600 and 800°C is superconducting despite a high level of Br contamination; calcination at 1000°C removes much of the Br, but with a reduction of Tc. Metallic tantalum and titanium were electrochemically dissolved in an organic electrolyte containing n-propylamine (13,14). Metal (M) is oxidized at the anode. At the cathode, NH2R is reduced and the corresponding anion and gaseous hydrogen are formed. Part of the titanium occurs as Ti3⫹, which might be formed either directly at the electrodes or by reduction of Ti4⫹ by hydrogen, and tantalum occurs as Ta5⫹. In the course of the electrolysis and drying, the viscosity of the solution formed amorphous products with the empirical formulas TaC19.3H3.3N5.87 and TiC3.94H8.24N1.14. The former product calcined in anhydrous ammonia and argon at 1000°C showed the cubic phase of TaC. Calcination of the latter precursor in an atmosphere of anhydrous ammonia resulted in the formation of a gold-colored titanium nitride–titanium carbide solid solution with a comparatively low carbon content, about 5%. When the calcination was carried out in nitrogen, Ti(C,N) solid solutions containing large amounts of carbon were obtained. Calcining at comparatively low temperatures led to products with poor crystallinity. An alternative method for the synthesis of nitride powder at a lower reaction temperature than 1300°C was performed using methane as a reducing agent in the nitridation of zirconia prepared by a sol-gel technique (15). Anhydrous ammonia was used as the nitrogen source and methane was used as the reducing agent at a reaction temperature of 1323 K. Molecular precursor methods (16) also produce transition metal nitrides, where the conversion of the pentamer [(tBuCH2)2 TaN]5 and ammonia to cubic TaN0.8 proceeds via precipitate 1/n[TaC1.41H3.90N1.90]n and amorphous TaN. Precursors other than (tBuCH2)3Ta CHtBu and NH3, which provided [(tBuCH2)2TaN]5, such as Ta(NMe2)5 and NH3 (Me2N)3 Ta NtBu and NH3, afforded TaN0.8 with low quality (16). A precursor processible to a metal diboride is obtained by dispersing a metal source such as TiO2 or ZrO2 in a boron carbide polymeric precursor, i.e., decaborane-dinitrile polymer. When these mixtures are heated to ⬎1450°C the corresponding diborides are formed in high chemical yields (⬎90% based on metal) (17) with very low levels of carbon, hydrogen, oxygen, and nitrogen. The oxygen contents decrease at higher temperatures. The powders formed at lower temperatures have a small grain size, but larger crystals with an average size of ⬃2–5 µm were obtained upon heating at 2000°C. Direct formation of carbides and diborides by mechanical alloying of metal powder and

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carbon or boron powder produces nanocrystalline powders (18–21), where the powder particles are repeatedly fragmented and cold welded to result in the intimate mixing of reactant particles on the nanoscale (22). The average grain size of TiC was about 9–11 nm after 27 h of milling (20). The large negative heat of formation of TiC not only provides a driving force to reaction but also favors the reaction by increasing the diffusivity of C atoms. Ball milling of titanium hydride in air for 30 h causes simultaneous dehydrogeneration and nitrogenation of the titanium hydride to result in nearly stoichiometric TiN with good stability (23). For some highly exothermic reactant systems, spontaneous compound formation occurs by a mechanically induced selfpropagating reaction, the mechanism of which is analogous to that of thermally ignited selfpropagating high-temperature synthesis (SHS) (22). When mechanically activated mixtures of Nb and C powders with 50–80 mol % C ground in a planetary ball mill were transferred into a graphite crucible and exposed to air, they ignited spontaneously and SHS took place to produce almost stoichiometric NbC (24). Solid nitrogen driven by mechanical alloying is a promising method for preparing nanocrystalline nitrides, where surface-induced dissociation of molecular nitrogen and chemisorption of nitrogen onto clean metal surfaces created by milling play an important role (25). After 60 h of milling, the fully developed structure of TiN with a very fine grain size of 9 nm is obtained. The grain size of as-milled ZrN powders was found to be 14 nm. Hf will behave in the same way. However, Ta2N is the only dominant phase formed in the whole milling process (26). The heat of formation of Ta2N (⫺271 kJ/mol) is larger than that of TiN (⫺252 kJ/mol), demonstrating that the formation of Ta2N is thermodynamically more favorable than the formation of TaN. A method for producing submicrometer (0.1 µm), low-oxygen-content nonagglomerated TiC powders involved the carbothermal reduction of carbon-coated titanium diboride (TiO2) (27), where carbothermal synthesis proceeded via the purification of titanium oxycarbide toward pure titanium carbide. The carbon coating process provided a high contact area of the reactants to produce a TiC powder with uniform shape by synthesis at 1550°C for 4 h. Rapid preparation of TiN, TiC, and TiCxNy powders from mixtures of TiO2 and graphite powders became possible with an arc imaging furnace (28). TiO2 was reduced completely and single-phase TiN with fine grains of ⬃1 µm diameter was synthesized within 30 s. The reaction between TiO2, carbon, and nitrogen was completed to form TiCxNy in a period of time shorter than 30–120 s. The other transition metal (Nb, Ta, and V) nitride and carbide powders (29) were synthesized in a short heating time (⬃30 s) using a mixture of transition metal oxides and graphite in 1 atm of nitrogen or argon flowing gas. Many diboride powders were prepared by a carbothermic reduction process (30). NbB2 powders with particles of size 40–50 nm with a carbon residue of 2.65% were synthesized from fine precursor particles prepared from Nb2O5, H3BO3, and cornstarch as starting materials under optimal conditions (31). An intermediate reaction at 1400°C produced ZrB2 powder by the reduction of ZrO2 with B4C and carbon with respect to both thermodynamical calculation and experimental observation (32). Excess boron is added to compensate for the boron loss caused by the volatile intermediate product B2O3 in order to prepare high-purity ZrB2 powder. The higher processing temperature decreases the oxygen and carbon contents of the product powder but increases the particle size. Borothermic reduction was confirmed at a lower temperature, and the carbothermic reduction occurred at a higher temperature (33), which favors the production of high-purity powders. TiB2 and ZrB2 powders were also synthesized by mechanochemical treatment of titania and zirconia powders with amorphous boron followed by a relatively low-temperature annealing (1100°C) (34). The occurrence of polymorphic transformations has been observed with milling time for both systems, together with a decrease upon annealing of the temperature of the boro-

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thermic reduction reactions with increased milling time. The reaction paths are different for TiB2 and ZrB2, with TiBO3 and Ti2O3 formed as intermediate compounds in the case of the borothermic reduction of titania, whereas in the zirconia-boron system a direct borothermic reduction of zirconium oxide is observed. Mitamura and coworkers (35–41) have synthesized fine powders of carbides, nitrides, and diborides (particle size 30–100 nm) by means of the thermite method by reduction with Mg; metal oxides were used as a source, and CH4 gas, N2 gas, and amorphous boron were used as light element sources. The preparative process is shown in Fig. 2. The synthesis conditions for single-phase powders depend noticeably on the molar ratio of Mg to metal oxide, temperature, and heating rate. The powder product was washed with (0.05–1) M HCl to remove by-product, washed with water and ethanol, and then finally recovered centrifugally. In the case of carbide (35–37), Mg plays the important role of continuously feeding C into the reaction group through the Mg-Mg2C3-Mg cyclic reaction. The Mg2C3 decomposes easily so that reduction by Mg is not inhibited, and formation and decomposition of Mg2C3 improve the carbonization of the reduced product of metal by supplying the C source. Metal oxides are not completely reduced in an N2 gas stream because Mg3N2 is formed by a reaction of the N2 gas and Mg (N source and reducing metal), lessening the activity of Mg as a reducing metal. Then nitride powder (38,39) is obtained by nitridation of metal at a temperature at which the decomposition of Mg3N2 occurs after completing the reduction of metal oxide with Mg. The reaction of Mg with amorphous B occurred to form MgB2, which decomposed into MgB4 and Mg (40,41). MgB2 did not interfere with the formation of diboride because it decomposed above 750°C, but MgB4 interfered with the boridation of metal above 850°C. It is most important to suppress the formation of MgB4 by controlling the reaction temperature below 850°C. TiN powders were also produced by reacting NaCN, sodium cyanide, at 1000°C with several Ti compounds: TiO2 (42), TiP2O7, (TiO)2P2O7, NaTi2(PO4)3, and Na4(TiO)(PO4)2 (43). Combustion synthesis (44) is an efficient method for making a wide variety of materials such as carbides (45,46), borides (47), and nitrides (48,49) and is superior to conventional methods with respect to higher purity and more reactivity (Fig. 3a). When the SHS reaction is carried out with powders containing ‘‘nonvolatile’’ contaminants, significant amounts of these impurities remain in the product (50). The initial reactant mixtures (chemical composition, shape and size of reactant particles, and shape, size, and density of samples) and combustion conditions (composition and pressure of the environment, initial temperature of the compact, the method and intensity of combustion initiation, or additional external effects) determine the properties of synthesized materials (45–49). Three different modes of combustion behavior, steady-state burning, oscillatory burning, and spin burning, were noted in the synthesis of various materials, and the differences in the burning behavior were attributed to the heat losses and to the exothermicity of the reaction (44). Combustion velocities are influenced by the theoretical maximum density and particle sizes of Ti and C (51). Synthesis of TiC consists of an initial diffusional reaction of liquid Ti and C at the combustion front, mainly occurring during the passage of the combustion front, and an additional reaction leading to completion within 400 ms after melting of Ti metal, confirmed by real-time diffraction using synchrotron radiation (52). Utilization of a very high surface area carbon for the synthesis of TiC leads to a very low surface area carbide (53). The apparent reactivity of titanium with graphite powder was higher than with amorphous carbon black powder. The reaction between graphite and liquid titanium was accomplished mainly on the surface of the thinly fissured layer where the carbon diffusion through TiC is the rate-controlling process. The reaction occurring in the bulk titanium phase produces the sintered grain structure, and that occurring in the inter- and intraparticle pores of carbon produces the agglomerated fine particles (54). The SHS method is used with mixtures of TiO2, Mg, and C to prepare TiC powder. The

Figure 2

The preparative processes in the thermite method (35–41). (Courtesy of Prof. T. Mitamura, Saitama Institute of Technology.)

Bulk Crystal Growth 25

Figure 3 Schematic representation of various SHS processes including high-pressure self-combustion sintering as a combination of SHS and highpressure technique (79–81).

26 Kumashiro

Bulk Crystal Growth

27

TiC/MgO product is leached by hydrochloric acid to remove the MgO and to obtain TiC with ⬎99.9% purity and a uniform particle size of 0.3–0.4 µm (55). Although SHS of diborides was performed in an argon atmosphere (56), it is possible to initiate and sustain it in a vacuum using the plane wave propagation mode of combustion reactions between particles mixed corresponding to the composition TiB2 (57). The synthesis wave propagation underwent considerable volume expansion, so that a spongelike structure of the reactant TiB2 was obtained. When combustion synthesis was carried out in air, some TiN formation was also observed (58). The product of combustion of Ti under nitrogen at 1 atm is a mixture of titanium nitride and two solid solutions of nitrogen in titanium (primarily α and β-transformed α). The relative abundance of the latter phases depended on the degree of melting of titanium and the initial relative density of the sample (59,60). The influence of nitrogen pressure on the combustion wave velocity and the degree of conversion to NbN indicated that the dominant nitride phase was Nb4N3 at low pressures (⬍2.7 atm), but at higher pressures the major phase in the surface layer was NbN (61). The conversion increased rapidly from about 35 to 70%. Further increase in the pressure produced a much less significant increase in conversion, approaching an asymptotic value of 75% at the highest experimental pressure, 13.6 atm, related to the formation of a surface layer. The relative thickness of the surface layer continues to grow as the pressure increases beyond this value, ultimately increasing by a factor of 3 as the pressure reaches the maximum of 13.6 atm. Nitrogen and Ta in the combustion wave form the intermediate product TaN with a single phase if the process is quenched after the combustion wave has passed (44). If the sample is heated by the combustion wave in nitrogen, repeated combustion takes place with the formation of the TaN phase. It should be noted that experiments at ambient nitrogen pressure (⬃40 atm) produce a hexagonal modification of TaN, but those at high pressures (⬃3000 atm) yield a cubic one. The cubic modification is synthesized by the combustion of Ta in liquid nitrogen (44). The TaN was also synthesized by shock compression (62). Shock compression recovery experiments with a porous sample of tantalum nitride with a hexagonal structure were performed in the impact velocity range up to 1.5 km s⫺1. The recovery rate of the B1-type phase increased with increasing porosity. Almost 100% recovery was achieved for a powder of 70% porosity on impact by a 2-mm-thick tungsten plate with velocities above 1.4 km s⫺1. The shock-synthesized B1-type tantalum nitride has good stoichiometry compared with combustion-synthesized ones. The synthesis of refractory ceramics via rapid solid-state metathesis (SSM) reactions between solid metal halides and alkali (or alkaline earth) metal main group compounds (e.g., Li3N or MgB2) is combustion-like synthetic technique (63). Rapid, highly exothermic reactions can reach high temperatures (⬎1000°C) in a very short time (⬍1 s) with careful choice of the precursors. The desired product is easily separated from the salt by-products and any unreacted starting materials by washing with alcohol and/or water. Metal chlorides with a high oxidation state provide sufficient volatility and reactivity to result in rapid, exothermic reactions with lithium nitride or sodium azide. A mixture of finely divided ZrCl4 and Li3N is ignited with a heated filament to produce superconducting ZrN in a molten LiCl flux, while the reaction front containing reactive species moves quickly through the sample. Partial substitution of Li3N by NaN3 reduces the amount of undernitrided material in favor of the stoichiometric cubic mononitride. The reaction mode in the diborides varies with the metal halide used. An alkaline earth boride, MgB2, is used as the boron source (64). Generally, group V chlorides lead to rapid selfpropagating reactions, whereas group IV counterparts (TiCl3, ZrCl4, and HfCl4) require prolonged external heating (⬎650°C) in evacuated silica tubes to produce a complete reaction.

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III. POLYCRYSTALLINE SPECIMENS It is very difficult to obtain fully dense specimens by conventional sintering unless very fine nanocrystalline powders (65) or ‘‘in-flight plasma powder treatment’’ is used (66). Complete densification of a titanium diboride powder by pressureless sintering occurred when a powder with high purity and submicrometer particle size was produced by an arc-plasma method (6). Considerable changes of chemical composition took place during the introductory plasma treatment of titanium carbide powders involving the formation of carbon site vacancies and the dissolution of oxygen atoms on the surface of the particles, which gave rise to greater shrinkage at the initial stage of the sintering process due to diffusional transfer of atoms through the vacancies at temperatures lower than 1700°C. The sintering behavior is affected by the amount of oxygen in the starting powder and the type and content of metal dopants. Additives to TiN such as Ni or Co (67) play an important role in promoting densification and cause the precipitation of a second phase at the grain boundary, resulting in a reduction of grain size in comparison with additive-free TiN. Dense TiB2 bodies (⬎94% of theoretical density) were obtained at temperatures as low as 1500°C using nickel as the sintering additive under vacuum and in an argon atmosphere (68). The addition of carbon strongly reduced the density and oxygen content and inhibited grain growth, so that the exaggerated grain would be enhanced by surface diffusion in a titanium oxide–rich layer on the TiB2 grains. Dense ZrB2 has been produced from powder mixtures of B6Si and ZrO2 or ZrSi4 by the thermal explosion mode in an SHS process through the formation of a thin glass phase along the ZrB2 grain boundaries (69). The simultaneous synthesis and the use of an additive to provide the liquid phase in the combustion process is also essential to promote densification of the products. Addition of Ni to the initial Ti and C powder mixture pellets produced a maximum density of ⬃75% of the theoretical density after SHS reaction by filling of the pores by Ni during the SHS reaction (70). The microwave sintering method (2.45 GHz, 6 kW) is suitable for rapid densification above 2000°C. An enhanced sintering ‘‘microwave effect’’ occurs with 2.45-GHz processing with an inert gas atmosphere as compared with conventional sintering, so that the microwave sintering of TiB2 –3 wt %CrB2 occurs at lower temperatures (200°C lower) and yields material with improved hardness, grain size, and fracture toughness (71). Hot pressing or hot isostatic pressing techniques are usually applicable for the densification of ceramics (72), and the synthesis and simultaneous sintering of ceramics can be accomplished directly from the constituent elements in a period of seconds without external heating for a longer time. The activation energy of ZrC hot pressing (73) was in better agreement with that of carbon diffusion. Hot-pressed NbB2, fabricated without additives contains pores both at the grain boundaries and within the grains and cracks along the grain boundaries (74). TiN additions are effective in preventing grain growth and improve the mechanical properties by reducing porosity and grain size. The effect of Al as an additive to TiN in hot press sintering indicated that the formation of an intermetallic compound, TiAl3 (melting point 1340°C), was the major factor in densification, so that densification started at 1300–1400°C (74). A high-pressure self-combustion sintering (HPCS) process is a combination of SHS and a high-pressure technique (Fig. 3c and d). Forced consolidation techniques that involve small time scales, such as high-speed forging, would be preferable to techniques that require substantially more time, such as hot pressing or hot isostatic pressing (HIP). A dense TiB2 compact with a relative density of 95% and a microhardness of 20 GN/m2 is easily fabricated in a few seconds with electric ignition at one end of a powdered mixture of the constituent elements under 3 GPa by means of a cubic anvil press (76). High-density and high-hardness TiB2 and TiB2-based materials are obtained by SHS under uniaxial compression (77). Miyamoto and Koizumi (78) and Miyamoto (79) have attempted to apply gas pressure using HIP (Fig. 3d). Two

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ignition electrodes were installed in the HIP equipment, and the conventional glass encapsulation technique for HIP was adopted to prevent gas penetration into the green compact. Nearly fully dense ceramics and ceramic composites of TiB2, TiCx, and TiC ⫹ Ni have been obtained from their elemental powders under an Ar gas pressure of 100 MPa by the gas pressure combustion sintering method. Some alterations in HPCS would be necessary to obtain monophase nitride (80,81), with an Nb metal plate embedded in the combustion agent of Nb ⫹ NbN powders and the agent burned at nitrogen pressures above 3 MPa (Fig. 3d). The Nb plate is converted to an NbN ceramic plate by the nitriding, mainly because of the reaction heat of the combustion agent. When the Nb metal is thin, less than 100 µm thick, the plate is completely nitrided NbN0.88 with a Tc of 16.4 K in a few minutes. The B1 NbN is a high-temperature phase in equilibrium above 1300°C, so that the high-temperature phase is quenched by the rapid propagation of combustion. With thick Nb metal, NbN and Nb2N layers are formed at the surface. New techniques for simultaneous densification of the products are explosive consolidation (82) or dynamic compaction (83–87), hot forging (88–90), and shock-induced reaction synthesis (91,92). These techniques have been used to produce TiC and TiB2 with greater than 96–98% of theoretical density and microhardness values equal to or greater than those of commercially available hot-pressed materials. Their fracture properties indicate an improvement in intergrain bonding. In the SHS/DC technique, hot and porous ceramic bodies formed during the SHS reactions are consolidated to high density by the action of a pressure wave generated by the detonation of a high explosive and/or the impact of an explosively driven flyer plate. Under appropriate conditions, near fully dense TiB2, TiC (83), and HfC (84) ceramics could be prepared. The effects of the powder characteristics, inert diluent, impurities, delay time, C/M ratio, and ratio of the explosive mass to the metal driving plate mass on the synthesis and compaction were clarified. The C/Ti ratio significantly alters the structure of the product TiC. The ideal composition for TiC made by the SHS/DC technique has a C/Ti ratio of 0.95 to 0.90, and sufficient density is achieved without significantly reducing the microhardness (95). TiB2 specimens prepared by the SHS/DC method using boron powder containing 1–5% carbon had higher densities and less cracking than those prepared using purer boron powder (0.2% carbon), so less pure boron powders were employed in the production of dense TiB2 ceramics (94). The grain boundary strength of the TiB2 and TiC prepared by the SHS/DC process was relatively weak because of the rapid heating, compression, and cooling in the process (95). The process of shock compression loading places a material in a highly unusual combination of states. Very high pressures and significant increases in temperature for a few microseconds cause deformation and forced relative mass motion of individual particles, exposure of fresh surfaces, and cleansing of existing surfaces that lead to interparticle bonding. The passage of a shock wave triggers an exothermic, self-sustaining reaction between elemental powder mixtures of Ti and B and of Ti and C (91) to produce compact ceramics. Almost crack-free compacts with better than 96% density and hardness of ⬃2000 kg/mm2 have been produced (91). The SHS process was used to produce ceramic composite materials (81) consisting of titanium carbide (TiC) and an intermetallic alloy of the nickel-aluminum (Ni-Al) system (95). The materials were produced by rapidly heating a mixture of elemental titanium (Ti), carbon (C), Ni, and Al powders in a graphite die up to the ignition temperature. By applying mechanical pressure during or immediately following the combustion reaction, products with greater than 99% of theoretical density were obtained. It is possible to synthesize simultaneously composites composed of both TiB2 and TiN phases from elemental powders of Ti, B, and BN by SHS (96). Both TiN and TiB2 phases had small grain sizes, less than 1µm, due to the pinning effect of TiN grains. Boron nitrides can be used as solid nitrogen sources to fabricate desired composites, including nitrides, where nitrogen turns into the green mixtures in the form of decomposition compounds and makes it possible to overcome the problem of permeation while increasing the

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amount of bonded nitrogen (97). TiB2 /TiC0.5N0.5 composites were fabricated by controlling the ratio and adjusting the combustion parameters of the initial reactants of Ti, B4C and BN. The self-propagating reaction process is expected to be an excellent method for producing functional gradient material (FGM) (98) whose interlayers form a compositional gradient. TiB2Cu composites were fabricated with stepwise compact interlayers of Ti, Cu, and B mixed powders. The maximum temperature of the product was calculated for the adiabatic reaction, and the reaction propagating regions were obtained for Ti-2B-TiB2-Cu mixed powder.

IV. SINGLE CRYSTALS Single-crystal whiskers of similar refractory carbides [TiC (99–105), ZrC (106), and HfC (107,108), nitrides [TiN (109–111) and HfN (107)], and diboride [NbB2 (112) have been grown by the CVD method. A number of authors have reported investigations of the catalystic effect of impurities on the growth of whiskers by the vapor-liquid-solid (VLS) mechanism in high temperature ranges. In the lower temperature region, ZrC (106) and HfC (107) whiskers are considered to grow by the vapor-solid (VS) mechanism and NbB2 whiskers (112) by radial growth with a comparable rate by a VS mechanism. Also, NbC whiskers were synthesized by heating of Nb2O5 powder and carbon black in the graphite crucible at an argon atmosphere of 1 MPa to a temperature in excess of 1100°C (113). Sodium fluoride and sugar were added to initiate the reaction and supply an active carbon source. According to the VLS mechanism, the major factor inhibiting the growth of TiC whiskers is capture of part of the Ni-Ti-C alloy by the growing whiskers (103). TiC whiskers could be grown by the VLS mechanism in a lower temperature range from 1270 to 1370 K (114). In this method TiC, the product of the gaseous reaction, is first transferred from the vapor to the liquid eutectic alloy Ni-Ti on a nickel substrate, diffuses through the liquid toward the liquid-solid interfaces, and finally, on saturation, is precipitated on the interface as whiskers. Crystal qualities of whiskers were examined by field ion microscopy (FIM), electron diffraction and high-resolution lattice imaging, and X-ray topography. Figure 4 shows an FIM image of an HfC whisker with twofold symmetry (107). Transmission Berg-Barrett topographs (115) of a tapered 〈111〉 TiC whisker are shown in Fig. 5. Several intense broad lines for grooves and faint sharp lines for edges are observed to run along the growth axis. The image contrast of the whisker edge is considered to be formed by the lattice distortion around the whisker edge. The whisker tips surrounded by several facets are imaged with intense enhancement. The image contrast at the tips would be due mainly to lattice distortion caused by segregated impurities, although an electron probe microanalysis (EPMA) test failed to detect possible impurities because of the small content. The included impurities at the tip are considered to take part in the whisker growth. Kamiya et al. (116) reported on the preparation of TiN fibers (presumably polycrystalline) by nitridation with NH3 of TiO2 fibers prepared by a sol-gel method; for a 5-h exposure to NH3, the nitriding reaction started at 900°C and was complete at 1100°C. Microcoiled fibers of TiC were prepared by vapor-phase metallizing of microcoiled fibers with full preservation of the coiling morphology of the source coiled carbon fibers (117). TiC1.0 coils were obtained at 1100– 1200°C for 1.5 h. The bulk resistivity of the coiled TiC fibers sharply decreased with the bulk density and was 10⫺2 S⫺1 cm at 1.4 g cm⫺3. When sodium titanium bronze (STB), NaxTiO2, was reacted with NaCN formed at 1000°C, the TiN had the morphology of needles or whiskers (118). The presence of Ti3⫹ in the bronze enhanced the initial concentration of Ti in NaCN. The yields of TiN whiskers were always close to 100%, so whisker formation did not involve a volatile Ti species. Dai et al. (119) reported the synthesis of nanoscale structures based on nanotubes, in which

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Figure 4 Neon field-ion micrograph of HfC whisker. The twofold symmetry of the image shows that the growth orientation is along the 〈110〉 axis (107). (Courtesy of Dr. M. Futamoto, Central Research Laboratory, Hitachi Ltd., Kokubunji, Tokyo.)

the tubes are converted to carbide rods by reaction with volatile oxide and/or halide species. Transmission electron microscopy (TEM) images of the product obtained from the reaction of TiO and carbon nanotubes at 1375°C show both straight and smoothly curved, solid rodlike structures that are distinct from the irregularly curved and hollow carbon nanotube reactant. The TiC nanorods were single crystals with a very low density of stacking faults. The diameters of the rodlike products were similar to those of the carbon nanotubes, 2–30 nm, and the lengths

Figure 5 The 220 topographs of a TiC 〈111〉 direction whisker (115). (Courtesy of Prof. K. Hamamura, Polytech College, Tokyo.)

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typically exceeded 1 µm. TEM and electron diffraction studies of stoichiometric TiC single nanorods showed a smooth regular sawtooth with 〈110〉 axis and irregularly faceted nanorod with 〈111〉 axis morphologies. The reaction of Nb metal and I2 with carbon nanotubes at 730°C yields superconducting polycrystalline NbC nanorods because of the low reaction temperature. The data can be explained in part by a mechanism involving template-mediated growth. CVD is the most suitable technique for preparing highly dense, thick, and oriented plates. Octahedral single crystals (⬃1.5 mm) were deposited on a graphite substrate from a vapor phase consisting of TiCl4-CCl4-H2 in the temperature range 1200–1600°C (105). Titanium carbide (TiCx, x ⫽ 0.6–1.0) (117), titanium diboride (121,122), and titanium nitride (TiNx, x ⫽ 0.74– 1.0) (123) plates were prepared using various gases at various deposition temperatures (Tdep) and total gas pressures (Ptot) of 4 to 40 kPa. The Tdep was in the range 1673–1873 K for TiCx, 1323–1773 K for TiB2, and 1373–1873 K for TiNx. The preferred orientation of the plate varied mainly with Ptot. The deposition rates showed a strong gas molar ratio and the maximum rate was found at a certain ratio. This maximum peak shifted to a lower gas molar ratio for TiN. The stoichiometries for TiNx and TiCx were controlled by the deposition conditions. The activation energies for the formation of plates are 41–50 kJ/mol for TiB2 and 86–95 kJ/mol for TiCx, indicating that the diffusion of the gaseous species through the boundary layer is rate determining. The activation energy for TiNx is 80 kJ/mol in the lower temperature range, so that the deposition reaction of NH3 gas would be associated with the rate-controlling step. However, the diffusion process would predominate to form a large amount of powder (mainly NH4Cl) in the gas. Nonstoichiometry may be controlled over wide ranges, and the deposition region of nonstoichiometric TiNx becomes smaller at higher Tdep values (124). Although the calculations and experiments have the same trend—i.e., x values increase with increasing source gas molar ratio m N/Ti (⫽[NH3]/[TiCl4])—there is a significant discrepancy between the calculated and experimental m N/Ti values for the deposition of nonstoichiometric TiNx plates, which suggests the formation of intermediate species (such as imides or amides) in the gas phase. The thermodynamic approach (125) was used to calculate the gas-phase composition in equilibrium with the solid and the theoretical efficiencies of deposition at equilibrium. The chemical compatibility of the substrate with the gas phase in the first stages of the deposition, to define the pressure-temperature-composition ranges of stability of various solid phases in multicomponent gas-solid systems, are shown for TiC (Fig. 6) together with the curves obtained for values of P 0TiCl4 equal to 10⫺2, 10⫺1, and 0.5 atm. The minimum possible value of C/Ti increases when P 0TiCl4 increases, which is the complete ‘‘CVD phase diagram’’ for Ti-C solids deposited from TiCl4-CH4-H2. Isostoichiometric curves are also reported in the deposition domain of the pure ZrxC1⫺x solid solution (126). For equilibrium, the deposited phase (ZrC ⫹ C, ZrC, ZrC ⫹ Zr) and composition of the pure solid solution may be easily varied by adjusting the input partial pressure of CH4 at a constant ZrCl4 feed. At 1900 K, the field of interest is located in the following range (atm units): 5 ⫻ 10⫺3 ⬍ P 0CH4 ⬍ 10⫺2 and 6 ⫻ 10⫺2 ⬍ P 0ZrCl4 ⬍ 10⫺1. Both the suitability of a system for transport and the transport direction can be predicted in the CVT method (127). Iodine was the most popular transport agent. TeCl4 was the best transport agent (TA). In particular, TiB2 single crystals of known atomic ratio (128) were investigated in relation to the influence of the transporting agent. Two groups of TAs were selected: (a) a group with T2 ⬎ T1 (I2, BI3) in which the efficient chemical species are BX3 and TiX4 and (b) a group with T2 ⬍ T1 (TeCl4, BBr3) in which the transport is due principally to BX3 and TiX3. The T1 and T2 ranges were 1050–1255 K and 1105–1225 K, respectively. The transport by TeCl4 should occur in a reverse temperature gradient (1250–1120 K). The amount of transported diboride was three times as important as in I2 and BI3. The TiB2 crystals are well-formed hexagonal-based prisms well developed along the three crystallographic directions, ranging from 1 to

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Figure 6 Phase fields for solid species deposited at equilibrium in the Ti-C-H-Cl system, showing the iso-concentration curves in the titanium carbide single-phase domain. (From Ref. 125.)

3 mm in size, and the faces of these crystals have spirals typical of vapor-phase growth. The B/Ti atomic ratio varies from 1.89 to 1.94 for I2, BBr3, and TeCl4 and increases as the atomic ratio of boron to titanium in the gas phase increases. Correlation with the gas-phase composition should lead to a value of about 1.96 for BBr3. Thermodynamic computations give the partial pressures of all the gaseous compounds present in the system; the ratio of the ‘‘boron’’ partial pressure to the ‘‘titanium’’ (combined forms) partial pressure in the gas phase in equilibrium with the growing crystals varies when going from I2 to BBr3. Next, we would like to introduce the flux method. Several attempts have been made to prepare some of carbides and diboride crystals with the aid of metal flux solvents (129). Nakano et al. (130) prepared TiB2, ZrB2, and HfB2 from molten Fe solutions. Cobalt, nickel, and aluminum fluxes were also used to obtain TiB2 single crystals (128,129). As for carbide crystals, the growth of TaC (133,134) and HfC (134) from Fe solutions has been reported. Higashi et al. (135) grew single crystals of diborides and carbides of TiB2, ZrB2, HfB2, NbB2, TaB2, TiC, and TaC by using molten Al as a solvent to demonstrate that Al is a suitable solvent for the growth of diborides and carbides. The molten solutions were kept at 1500–1550°C for 10 h except for TaC, which was kept at 1300°C for 50 h. They cooled to 600°C at the rate of 10°C/h. Metals dissolve in the Al melts at the initial stage of heating of materials and then gradually react with B (or C) to produce powdery crystals. The crystals mostly subside to the bottom of the crucible,

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with only the very small ones dissolving in the Al melt even at the maximum temperature. While the molten mixtures are kept at this temperature, the melt becomes supersaturated, and they grow into crystals in the lower temperature regions of the crucible, while the powdery products supply the solute materials for further crystal growth (135). The amounts of solvent atoms incorporated in these crystals range from 0.02 to 0.1 wt %. As-grown crystals with welldeveloped prismatic and pyramidal planes had the shape of a needle-like hexagonal prism. Many shallow and sharp pits corresponding to local defects such as impurities are observed in the (0001) and (101¯0) planes. Chan and Kauzlarich (136) discovered a novel synthetic route for making TaC and NbC single crystals in the course of studying the superconducting phase of Lu2Cl2C2⫺x. TaC and NbC single crystals can be prepared by reacting Ta or Nb and C in an LnCl3 (Ln ⫽ Y, Lu) flux at 1000–1150°C for 14 days. The revised eutectic temperature of 1270°C instead of 1680°C for the published phase diagrams of the quasi-binary system TaC-Co makes it impossible to use alumina crucibles, so TaC0.98 single crystals have been grown from a Co flux using intermittent stirring and a modified Czochralski technique (137). The furnace unit (Fig. 7) consisted of a water-cooled aluminum cast housing that could be evacuated to 0.4 torr. The graphite heater is surrounded by a heat shield of graphite wool. The experiment was performed with He gas as a protective atmosphere at a slight overpressure against atmosphere. The crucible was rotated in order to avoid concentration gradients in the melt with resulting constitutional supercooling and spurious nucleation. After the melt was homogenized at 1600°C, it was slowly lowered to the pulling temperature. The seed was brought near the melt surface to reach the temperature of the surroundings (⬃ 1 h). Then it was dipped in the flux and pulling began with intermittent stirring. A cooling rate of 5°C/day produced the largest cubic TaC (⬃ 7 mm) with (100) faces. Next, a solid-phase process for carbides and nitride will be mentioned. Good single crystals

Figure 7 Furnace unit with crystal pulling system. (From Ref. 137.)

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for several carbides were obtained by Fleischer and Tobin (138,139) using liquid-state carburization at high temperatures. Reactions of liquid Ti, Zr, Hf, V, Nb, and Ta with graphite thimbles produce the transition metal monocarbides. Carbon gradients in the carbides produced by direct reaction were largely eliminated by extended homogenizing anneals (⬃100 h) at temperatures 100 to 200°C below the carbide-carbon eutectic temperatures. The resulting grain structures were fine and uniform in HfC; larger and nonuniform in TiC, ZrC, NbC, and TaC; and very coarse and irregular in VC. The conversion of the polycrystalline carbides to single crystals and grain size refinement were examined by uniaxial loading experiments. Sufficient strain was developed by deforming these carbides in the temperature range 2000 to 2500°C to recrystallize them on subsequent annealing at higher temperatures. The recrystallized grain size was a function of the amount of plastic strain. Strain levels near the critical strain encouraged very large grains, i.e., single crystals of TiC, ZrC, HfC, NbC, and TaC without lineage structure. The main problems would be long annealing times at very high temperatures, cracking, and difficulties of seeding particular orientations. Growing nitride single crystals with the δ-phase turned to be extremely difficult, because the cubic phase can be produced only in a very narrow range of temperatures, pressures, and concentrations. Scheerer (140) tried to prepare NbN by diffusion of N into Nb and NbN1⫺x at temperatures higher than 2000°C, so nitriding niobium single crystals over a period of several days by direct or indirect heating in a tungsten crucible to 1600 up to 2000°C at a nitrogen pressure of 20 bar is a workable possibility for preparing δ-NbN0.89 single crystals with a superconducting transition temperature of 14.5–15 K. Christensen et al. (141) prepared single crystals of δ-NbN by a zone annealing technique. A niobium rod of 99.99% purity was annealed in a nitrogen atmosphere at a pressure of 2 MPa and a temperature of approximately 2100°C for 100 h to convert it to γ-NbN. Single crystals of γ-NbN with volumes of 0.5–1 cm3 were cut from the rod and were zone annealed at 2 MPa nitrogen gas and 2300°C for 100 to 150 h to produce δ-NbN0.93. This method was applied to prepare other transition metal nitrides. A hafnium rod of 99.9% purity was made by zone melting in helium, and the rod was then annealed in a nitrogen atmosphere at high pressure to give a single crystal of δ-HfN0.93 (142). The RF floating-zone process is suitable for growing large single crystals. Packer and Murray (143) examined zone melting of TiC, ZrC, VC, and NbC by RF heating employing an eddy current concentrator under pressure of an argon atmosphere (Fig. 8). The concentrator consisted of two main parts: a cylinder with a single longitudinal slit and a U-shaped insert that is situated inside the split cylinder so as to bridge the slit halfway along its length. Currents induced in the cylinder by the work coil must be conducted through the insert, whose thickness is a principal factor determining the length of the molten zone. Some attention was given to the shape of the concentrator insert to maximize the stability of the molten zone for crystal growth. Single crystals of VC with compositions of VC0.34–0.77 and of NbC with compositions around NbC0.84 were readily grown (144), but high pressure was necessary to obtain stoichiometric NbC and TiC single crystals. TaC has been melted, but it has not been possible to form a stable zone in the material. This method was not widely used, but the RF floating-zone method developed by Haggerty and Lee (145,146) became popular and was used to prepare most carbide and diboride single crystals, 6–10 mm in diameter and 30–100 mm in length (147). First, the conventional RF floating method will be reviewed (Fig. 9). The sintered specimen was heated gradually to its melting point. During solidification the specimen was pulled up continuously at constant rate. It was rather difficult to keep the molten zone stable during crystal growth owing to overflow of the melt and puncturing of the coils by arcing between the coil and the melt or between one coil turn and another. An outer polycrystalline rim was observed at both ends of the single crystals, which is attributed to the light elements being prone to diffuse outward through molten region during crystal growth, so that the vacancies introduced into the

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Figure 8 Schematic diagram of the floating zone apparatus using an eddy current concentrator. (From Ref. 143.)

structure coalesce to produce the clusters that form grain boundaries (148). There would exist an optimal pressure for growing such refractory carbides, depending on the dissociation pressure of the specimen, the viscosity of the melt, and both heat and mass losses caused by convection (148,149). Single crystals of VC (150), NbC (151), ZrC (152), and TaC (152) were grown under appropriate pressures of 0.3 and 1.0 MPa, respectively. Above this, both the rates of transportation of evaporated species and heat from the surface of the specimen, accompanied by convection flow of gas, would become larger (150). An increase in density of convection flow over the specimen surface, therefore, is found at higher gas pressure. The C/Ti ratio along the radial direction (Fig. 10) indicated that in the case of lower ambient pressure the C/Ti ratio is constant, corresponding to TiC1.00⫾0.02 over the whole region, compared with the case of higher ambient pressure. Then the temperature gradient toward the inner side from the surface in the growing specimen at 17 atm becomes larger than at 3 atm. In the phase diagram of the Ti-C system, the carbon vacancies increase with temperature, resulting in a decrease in carbon content from S to B in Fig. 10. The increase in carbon content from B to A is due to the diffusion of vacancies toward region B from the inner part with constant composition. In the case of 3 atm, the temperature gradient across the specimen would be expected to be lower because of small heat loss from its surface. Larger etch pit densities of VC0.88 than of VC0.83 form the subgrain boundaries characterized by the presence of substructure such as antiphase boundaries due to the formation of an ordered compound (150). The hardness of NbC decreases with carbon content and the hardness anisotropy of NbC0.8 is less pronounced than that of NbC0.9 (Fig. 11), which would be due to (a) deviation from stoichiometry of the crystal and (b) ordering of carbon vacancies. A high-resolution electron microscopy (HREM) study gives very detailed information about defect order

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Figure 9 Diagram of the zone melting arrangement. Broken lines indicate the shape of the molten zone (148–152).

within carbides (153–158), such as conservative and/or nonconservative antiphase boundaries (APBs), domain boundaries, and interfaces between differently ordered superstructures. A ˚ ) of the 〈110〉 lattice of an multibeam image recorded at a relatively large thickness (⬎100 A NbC0.88 annealed specimen (157) shows two sets of {111} face-centered cubic (fcc) planes are ˚ ). The ordering of domains along the [11¯1] and [11¯ 1¯] cubic directions resolved (d{111} ⬃ 2.58 A is confirmed: the superlattice fringes that appear in the precipitates correspond to a doubling of

Figure 10 C/Ti ratio determined by EPMA with scanning along the radial direction. (From Ref. 149.)

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Figure 11 Hardness anisotropy of {100} plane of NbC0.8 and NbC0.9. (From Ref. 150.)

˚ ⫽ 2d{111} (d1 is the distance between nearest this {111} matrix distance, that is, d1 ⫽ 5.15 A ‘‘vacancy-containing’’ carbon layers of the {111} cubic family). Matching of the experimental HREM micrograph with images simulated by ‘‘multislice’’ calculation (Fig. 12) demonstrates that the ordering of carbon vacancies would induce a detectable difference in intensity for white dots, which represent the 〈110〉 carbon columns, with the atomic rows that are fully occupied in lower contrast than those with an occupancy factor of 2/3, but the metallic sublattice is not observed. Crystal growth experiments with TiN and ZrN rods (159) using the floating-zone process with a nitrogen pressure of 18.8 atm did not produce large single crystals by expansion before melting, showing cavities and a fairly thick and powdery surface layer, while those with group V nitrides (147,150,151) produced δ- and β-phases with lamellar structures. The transverse and longitudinal cross sections of NbN crystals show lamellar structures caused by the eutectic of NbN-Nb2N. These structures arise from low interfacial energy of a highly coherent interface {111}NbN //{0001}Nb2N. The dislocation-pit arrays, arising from δ-NbN, cross over the lamellar structure in transverse cross section with a density of ⬃ 105 /cm2. A single colony eutectic structure can be described as an eutectic ‘‘single crystal’’ that reflects the X-ray Laue pattern (150,151). The overall chemical composition of the zone-melted specimens close to VN0.65 in zone melting of sintered rods of δ-VN in an ambient nitrogen gas pressure of 1 MPa changed the composition range from VN0.84 to VN1.0 in subsequent zone annealing at 2000°C and 2 MPa (160). The structures of vanadium and niobium diboride crystals (161) resemble those of tantalum diboride grown by the floating-zone method (162). Widmansta¨tten-type precipitates found in

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Figure 12 Matching the experimental HREM micrographs (top row) with simulated images (bottom row) for both disordered (left) and ordered (right) NbC0.83 phases. Dark atoms: Nb, grey atoms: C in bottom ˚ defocus and 180 row. The superimposed simulation has been obtained from Nb6C5 structure at ⫺800 A ˚ A thickness. [001]-monoclinic C ordered phase//. [110]fcc azimuth. (Courtesy of Dr. T. Epicier, Charge´ de Recherches CNNS, France.)

melt-grown group IV diboride (146) single crystals were not observed in group V diboride single-crystal grains, indicating that the second phase, with a composition slightly different from that of the diboride matrix, is difficult to precipitate owing to the wide homogeneity range of the group V diboride phase. VB2 vaporizes congruently, so diboride is easy to obtain as a single phase, whereas TaB2 and NbB2 vaporize incongruently near their melting points, so boron deficiency and Ta3B4 or Nb3B4 or lower borides result instead of single phases. The periphery had polycrystalline structures, especially in the case of niobium and tantalum diborides, where MB2 and M3B4 phases were observed; however, the inner part was single crystalline. Cracks were observed in the single-crystal region and attributed to the thermal stresses arising from the high temperature gradients. Lang X-ray topography of a thin section (VB2 single crystal) parallel to the (1¯100) plane showed distinct dislocation images along the [0001] direction (Fig. 13), generated by prismatic slip caused by the high thermal stresses in the growth process. The occurrence of straight dislocation lines would be attributed to the high Peierls potential of the dislocations. The (0001) plane of the diborides had a high etch pit density of nearly the same order as that of the (101¯1) plane, whereas the (101¯0) and (112¯0) planes had low etch pit densities. The etch pit densities were much higher for basal and pyramidal planes than for prismatic planes, suggesting that prismatic slip of TaB2 single crystals predominates at high temperatures. Next we would like to discuss controlling the composition of the melt to obtain single crystals with uniform composition. The traveling solvent float zone (TSFS) technique (163) was applied to grow TiC (164,165), ZrC (166), HfC (167), VC (168), NbC (169), and TaC (170)

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Figure 13 Lang topography of a VB2 thin section parallel to the (1¯100) plane. The direction of the diffraction vector (g ⫽ 112¯0) is indicated by an arrow and is 1.0 mm on the topograph. (From Ref. 161.)

single crystals. Figure 14 illustrates the TSFS technique for the growth of TiC single crystals (165). A 〈100〉 seed crystal was set on the lower shaft. An initial molten zone was formed by melting the seed crystal together with a carbon disk put on the crystal because the feed rod had too low a density to initiate the melting. The carbon disk was used to control the composition of the initial molten zone so as to produce zone leveling conditions on initial melting, C/Ti ⫽ 1.3. The composition of the feed rod was controlled at C/Ti ⫽ 0.98 to compensate for the composition change due to evaporation during a zone pass. In preparation from a commercial

Figure 14 A modified zone leveling method (164–175).

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powder the growth rate was decreased to 0.5 cm/h to avoid cellular growth due to the impurity W (0.05–0.5 wt %), which makes the growth difficult and decreases the crystal quality. The visible misorientations between the grains were higher than 1°. The W impurity cannot be removed by evaporation or zone refining because of its low vapor pressure and its distribution coefficient (k ⬎ 1) (171). Therefore, a starting material without W impurity was prepared from Ti metal and carbon by an SHS method (Fig. 3b) (172,173). Crystals prepared at a slow rate were subjected to a strong thermal stress, caused by a steep temperature gradient (maximum 200°C/mm) along the crystal rod for a long time. The crystals can be prepared at a higher rate using an SHS rod. The growth rate was 1.5 cm/h, and the feed rod was melted into the molten zone at a rate of 3.5 cm/h to compensate for its low density (172,173). The crystal quality was improved to such an extent that the cleavage plane was like a mirror plane without subgrain boundaries. A crystal rod of V8C7 with a slight gradient composition was prepared around a composition (C/V) of 0.875 (174) and had the highest residual resistance ratio, 19.4, among the reported values. Furthermore, a microcomputer (CPU) and two digital voltmeters (DVMs) were attached to the RF generator (200 kHz, 40 kW) for automatic growth (175) to detect the shape of the molten zone and to provide a zone pass more stable than in the case of manual growth. Subgrain boundaries of diboride single crystals have been removed by controlling the molten-zone composition (Fig. 15). The growth rate of diboride crystals was determined in the process of removing the flux at the growing interface (176–178). Single crystals of TiB2, which evaporates at a 50 times higher rate than TiC, were prepared by increasing the growth rate up to 9 cm/h (176). All the crystals grew almost normal to the c-axis of the hexagonal crystal lattice. The existence of a preferential growth direction is favorable for increasing the optimal growth rate. The molten zone had a higher boron content, B/Ti ⫽ 2.6, than a stoichiometric composition because of violent evaporation during growth. The crystal grew by removing the excessive boron acting as a flux at the growing interface. High-quality ZrB2 crystals that have the same growth temperature, 3270°C, as TiB2 were obtained at a rate of 3 cm/h (177). The molten zone had an excess of zirconium because of the evaporative loss of boron. HfB2 melts congruently at 3380°C, the highest value among the diborides. High-quality HfB2 crystals (178) were obtained at a rate of 2–3 cm/h, using a feed rod with B/Hf ⫽ 2.1–2.15 whose molten

Figure 15 Etching pattern of TiB2 (101¯0) single crystal (176). The diameter is 10 mm. (Courtesy of Dr. S. Otani, National Institute for Inorganic Materials, Tsukuba, Ibaragi.)

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zone had an excess of hafnium. The differences in flux among TiB2, ZrB2, and HfB2 influence growth rates. The growth rate of TiB2 is higher when the molten zone is controlled to have excess boron, which has a lower mass number than metals such as Zr and Hf. The growth rate increases with increasing growth temperature, indicating that the growth rate is determined in the process of removing the flux at the growing interface. The high growth rate of 9 cm/h for TiB2 crystals is due to the boron flux and high growth temperature. Furthermore, helium ambient gas causing convection in the molten zone is useful for increasing the growth rate (176–178). Argon ambient gas contains more inclusions, so the growth rate must be decreased compared with that in helium gas to remove them. The heating powder of an SHS rod was several percent less than that of a sintered rod used as the feed rod (179). This is due to low thermal conductivity caused by the low density of the SHS rod, which is an advantage of using SHS rods. The crystal has a stoichiometric composition. Plasma-arc heating provides crystal growth of refractory materials. A schematic diagram of the plasma torch method (180) is shown in Fig. 16. The growth of a single crystal starts with fusing the end plane of a seed crystal by a plasma jet. A rod of the carbide, 3–10 mm in diameter, is then transported from the side and fused in the plasma jet so that the drops of melt fall into a cone-shaped void punched in a single-crystalline ingot of the tungsten bath and provide steady feeding. If drops of carbide are added to the melt bath by means of input of the charge rod to the plasma arc and if the velocity of lowering the tungsten substrate is properly chosen, crystallization will start at the peak of the cone to form a few crystallization centers. Competitive growth of a restricted number of grains takes place in the cone-shaped bath so as to form a single crystal practically throughout the volume. The technique permits us to obtain sufficiently large single

Figure 16 Schematic diagram of the plasma torch method. (From Ref. 180.)

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crystals of high-melting carbides (20 mm or more in diameter): subboundaries of the first order, with a disorientation not greater than 10, and an etch pit density of 104 –105 cm⫺2. Czochralski growth of single crystals has been carried out using an arc-melting technique (181) with a tri-arc Czochralski furnace (Fig. 17), which consists of an upper cathode and a lower anode insulated from each other by glass ring. The upper body includes three ball and socket joints for the electrodes, a central ball and socket for the water-cooled seed rod, and three windows for observation. Arc melting on a well-cooled hearth permits Czochralski growth without a hot crucible. The circumference of the melt is heated by three arcs, and the crystal is pulled from the center of the melt with a water-cooled seed rod. The charge is contained in a hollow water-cooled copper hearth fitted with a piston so that the melt can be continuously fed. The seed is dipped into the melt and raised rapidly to form a neck in the growing crystal in order to favor a single growth front. Tungsten studs mounted in the seed holder were used for starting crystallization to produce a VB2 single crystal (182). After a diameter of 2–3 mm was reached, the crystal growth proceeded constantly with a high pulling speed of about 30 mm/h. An arc-induced floating-zone technique (Fig. 18) was adopted to grow refractory materials (183,184). Mackie and Hinrichs (184) have successfully prepared single crystals of ZrCx up to 3 mm in diameter and 6 cm in length using a travel speed in the range of 10–30 cm/h under the inert gas. Two pieces of sintered ZrC rod were supported vertically between two molybdenum clamps with their free ends touching. A sharpened electrode (or stinger) made of sintered ZrC was held in a horizontal position on a screw-driven stage that could be moved up or down.

Figure 17 Schematic drawing of a tri-arc Czochralski furnace. (From Ref. 181.)

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Figure 18 Schematic drawing of the arc-induced floating zone method used for LaB6. (From Ref. 183.)

As the stinger was brought near the sintered rods, an arc could be initiated and sustained between the rods and the stinger. The molten zone was moved along the rod by moving the stinger stage. A 75% Ar–25% He mixture is effective in suppressing evaporation, as argon is about ten times as effective as helium. A new process was developed using a well-focused RF plasma flow for the crystal growth of nitrides in which escape of nitrogen is suppressed by the plasma gas pressure (185–188). The characteristics of the RF plasma for the crystal growth of nitrides with high dissociation pressures are described. The plasma generator is an annular planar jet composed of four sections (Fig. 19). Four quadrant plasma guns [1] are combined into an annular shape, and a grounded electrically conductive specimen [4] is set up facing the annular opening of the plasma gun with a spacing [3] of 0.5–1.0 mm. By applying an RF potential to the electrode [5] from the RF supply through the cooling water inlet pipe [8] an RF discharge is initiated between the tip portion [5b] of the electrode [5] and the specimen [4]. The discharge is then pushed along by the gas flow to establish a steady and stable plasma flow. The flow of gas between the electrode plate [14] and the wall [2] serves to direct the plasma on both the upper and lower sides onto the specimen [4]. The electrical behavior measured with a new ammeter is sensitive to both gas composition and ambient pressure in Ar-N2 atmospheres. The experiment with VN0.83 rod was performed under optimal conditions: the RF voltage

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Figure 19 Sketch of the annular plasma generator: [1] plasma gun; [2] discharge chamber; [3] opening; [4] specimen; [5] discharge electrode; [5] convex part of the discharge chamber; [7] insulating spacer; [8,9] water inlet and outlet pipes; [10] electrode supporting plate; [11] insulating adapter; [12] RF supply; [13] gas inlet pipe; [14] electrode plate; [15] spacer; [16] screw (185–188).

decreases with increasing RF current, the discharge changes from glow to arc, and the rod is melted in the arc region. The current waveforms indicate that the higher the plasma impedance, the higher the anode efficiency, with good matching between output and plasma impedances. To compare the nitrogen content, the VN0.83 rod was also melted by RF induction heating under nitrogen pressures of 10 atm. The RF plasma is focused onto the surface of the specimen by the gas flow and the specimen is subsequently melted by the heat capacity of the plasma. The composition of the crystal obtained by the plasma method is almost equivalent to that obtained by RF induction heating at 10 atm in nitrogen, which demonstrates the utility of RF plasma melting for nitride crystal growth.

V.

CONCLUSION

In the past two decades, well-characterized crystals have been obtained by various unique methods and advanced technologies. Nanostructured powder with a high surface area would be of interest as a material for catalysis. The heavy collision of balls in mechanical alloying proceeds gradually during milling as the repeated fragmentation and coalescence process continuously brings unreacted material into contact. In the case of solid-nitrogen systems, the nitrogen absorbed on the surface layer is subsequently moved by the successive collisions into deeper surface layers (25). In the mechanically induced self-propagating reaction mode, once a portion of the elemental powder mixture reacts during milling, the heat liberated by the exothermic reaction propagates and ignites the unreacted portion until the bulk of the elemental powder mixture is converted to the product (22). The nanorod represents an important building block for nanostructures. Nanorods would be useful as reinforcements in metal and ceramic matrix composites as well as ideal structures with which to pin vortices in high-temperature superconductors (119). Whiskers represent attractive reinforcing additives for metal and ceramic matrix compositions to impart more strength to the ceramic object. The superior performance of titanium carbide reinforcements is found in two different forms, discontinuous fiber and hollow microspheres, by controlled morphology carbide synthesis where titanium and carbon precursors combine in specially designed graphite

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(189). The process can also produce other carbides (Hf-, Ta- and Zr-). The existence of an impurity droplet on the top of the whisker supports the VLS mechanism, which is confirmed by X-ray topography (115). Electrochemical methods for synthesizing nitride precursors afford a significant level of control over characteristics of powders, i.e., high surface area, small particle sizes, and high purity. To take full advantage of the molecular precursor method, the relationship between complex and solid phases should be clarified through analysis of intermediate stages of conversion. The key requirements of the polymer components in polymeric precursor methods are that they are stable and processible and contain both the boron needed to form the metal boride and carbon to aid in the removal of oxygen. The polymer precursor technique would be applicable to nitride. New materials such as ultrafine powders could be produced by the RF plasma process, in which the products can be metastable with regard to stoichiometry and phase structure. The key to the formation of these products is a rapid rate of cooling, ⬃106 K/s, which ‘‘freezes in’’ the desired stoichiometries and phases. NbN with B1 phase is in a high-temperature equilibrium form above 1300°C and is usually not easily synthesized. The rapid cooling effects of a plasma or combustion reaction have the effect of quenching the high-temperature phase. The SHS method is expected to be developed as a process for producing new materials from composite powders and solid solutions that are difficult to prepare by conventional synthesis methods. By varying the combustion synthesis parameters, the properties of the product can be tailored to meet specific application needs. The combustion-consolidation method makes it possible to change the metal composition in the ceramic matrix because the initial arrangement of compositional constituents of the green body remains in the product due to the rapid wave propagation of the combustion reaction. The cylindrical shock wave technique is unique among processes for crystal growth at high speed from the gas phase far from equilibrium conditions at high temperatures and high pressures (190). Because thermodynamic self-cooling takes place as a result of an adiabatic wave front, the high-temperature ultrasupersaturated gas generated condenses within a few microseconds. Then fine crystals with various growth forms grow at high speeds from the gas phase under extremely nonequilibrium conditions. As a result of the detonation of explosive surrounding the steel container, shock waves generated by detonation in the gas in the container converge on the axis of the sample. A ‘‘Mach-disk’’ region at ultrahigh pressure (⬃100 GPa) and high temperature (⬃5000 K) is calculated. CVD and CVT in multicomposition gas-solid systems are complex processes in which many factors can affect the deposition mechanism and the final composition and structure of the materials. A thermodynamic approach gives information about the optimal conditions for the synthesis of specified solid phases, but the uncertainties of thermodynamic data and significant departure from equilibrium should be kept in mind. The floating-zone technique eliminates many problems of contamination arising from holding specimens in a container and makes it possible to grow large single crystals of carbides and diborides, but the crystals contain subgrain boundaries. The crystal quality could be improved by controlling the molten-zone composition. Furthermore, the crystal purity was increased by more than one order of magnitude by using a self-combustion rod. In automatic growth, the feed rate is controlled by small changes in the zone shape to decrease variation in the zone shape during a zone pass, which is related to growing single crystals with high quality. Since single crystals of high chemical and known structural perfection have been available, grain boundaries and structural defects in a grain would be eliminated and their intrinsic transport properties would be fully clarified. The well-characterized nitride single crystals are limited to diffusion of nitrogen to metal

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single crystals at high temperatures. These crystals should serve to measure many uncertain characteristics because it is difficult to obtain large single crystals by other methods. The diffusion and layer growth behavior in the transition metal–boron system are different from those in the corresponding carbide and nitride systems (191). Various diffusion layers are formed, with which it would be difficult to prepare diboride single crystals. In the plasma zone melting method it is necessary to focus the plasma flame stably, so many sophisticated techniques are required. In addition to plasma processes, the laser technique is a promising method for the preparation of powders and single crystals. In particular, a laserheated floating zone process using a CO2 laser (192) is suitable for preparing filamentary single crystals of carbides and diborides for high-brightness electron emission sources.

ACKNOWLEDGMENTS A number of figures have been taken from the literature. The author would like to thank the authors and publishers of these materials for permission to reproduce them here, especially, Kluwer Academic Publishers (Fig. 1 (Ref. 7)), The Electrochemical Society, Inc. (Fig. 6 (Ref. 125)), IOP Publishing Limited (Fig. 8 (Ref. 143)), and Elsevier Science (Fig. 4 (Ref. 107), Fig. 5 (Ref. 115), Fig. 7 (Ref. 137), Fig. 11 (Ref. 150), Fig. 13 (Ref. 161), Fig. 14 (Ref. 175), Fig. 15 (Ref. 176), Fig. 16 (Ref. 180), Fig. 17 (Ref. 181), Fig. 18 (Ref. 183), Fig. 19 (Ref. 186)).

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146. JS Haggerty, DW Lee. Plastic deformation of ZrB2 single crystals. J Am Ceram Soc 54:572, 1971. 147. J Billingham, PS Bell, MH Lewis. The crystal growth of transition metal interstitial compounds by floating zone technique. J Cryst Growth 13/14:693, 1973. 148. Y Kumashiro, A Itoh, S Misawa. TiC single crystals prepared by the radio frequency floating zone process. J Less Common Met 32:21, 1973. 149. Y Kumashiro, A Itoh, S Misawa. TiC single crystal preparation by floating zone technique under low ambient gas pressure. Jpn J Appl Phys 15:921, 1976. 150. Y Kumashiro, E Sakuma, Y Kimura, H Ihara, S Misawa. The preparation of single crystals of refractory carbides and nitrides. J Cryst Growth 52:591, 1981. 151. Y Kumashiro, E Sakuma, Y Kimura, H Ihara, S Misawa. The preparations of NbN and NbC single crystals by radio-frequency floating zone process. J Less Common Met 75:187, 1980. 152. Y Kumashiro, Y Nagai, H Kato, E Sakuma, K Watanabe, S Misawa. The preparation and characteristics of ZrC and TaC single crystals using a rf floating-zone process. J Mater Sci 16:2930, 1981. 153. K Hiraga. Vacancy ordering in vanadium carbides based on V6C5. Philos Mag 27:1301, 1973. 154. MH Lewis, J Billingham. Long-period order in vanadium carbide. Philos Mag 29:241, 1974. 155. T Epicier, Y Kumashiro. A contribution to the experimental study of the crystallography and ordering phenomena in some transition-metal carbides: Part II: Applicability of high-resolution electron microscopy to the study of ordered defects in vanadium carbide single crystals. Adv Ceram 23: 677, 1987. 156. T Epicier, Y Kumashiro. A first HREM observation of the ordered carbon sublattice in a transitionmetal carbide (VC1⫺x). Philos Mag Lett 55:171, 1987. 157. T Epicier, Y Kumashiro. Conventional and high resolution transmission electron microscopy of NbC⬃0.88 single crystals. J Less Common Met 146:17, 1989. 158. T Epicier. Application of transmission electron microscopy to the study of transition metal carbides, nitrides and borides. In: The Physics and Chemistry of Carbides, Nitrides and Borides. R Freer, ed. Dordrecht: Kluwer Academic, 1990, p 297. 159. AN Christensen. The crystal growth of the transition metal compounds TiC, TiN and ZrN by a floating zone technique. J Cryst Growth 33:99, 1976. 160. AN Christensen, P Roehammer. The crystal growth of δ-VN by floating zone annealing techniques. J Cryst Growth 38:281, 1977. 161. K Nakano, K Nakamura, Y Kumashiro, E Sakuma. Single crystal growth of VB2 and NbB2. J Cryst Growth 32:602, 1981. 162. K Nakano, Y Kumashiro, E Sakuma. Single-crystal growth of tantalum diboride. J Less Common Met 65:27, 1979. 163. S Kimura, I Shindo. Single crystal growth of YIG by the floating zone method. J Cryst Growth 41:192, 1977. 164. F Yajima, T Tanaka, H Bannai, H Kawai. Preparation of TiCx single crystal with homogeneous compositions. J Cryst Growth 47:493, 1979. 165. S Otani, S Honma, T Tanaka, Y Ishizawa. Preparation of TiCx single crystals with maximum carbon content by a floating zone technique. J Cryst Growth 61:1, 1983. 166. S Otani, T Tanaka, A Hara. Preparation of ZrCx single crystals with compositions by floating zone technique. J Cryst Growth 51:164, 1981. 167. S Otani, T Tanaka. Preparation of HfC single crystal by a floating zone technique. J Cryst Growth 51:381, 1981. 168. Y Hou, S Otani, T Tanaka, Y Ishizawa. Preparation of VC single crystals by a floating technique. J Cryst Growth 68:733, 1984. 169. S Otani, T Tanaka, Y Ishizawa. Preparation of NbCx single crystals by a floating zone technique. J Cryst Growth 62:211, 1983. 170. S Otani, T Tanaka, Y Ishizawa. Preparation of TaC single crystals by a floating zone technique. J Cryst Growth 55:431, 1981. 171. S Otani, T Tanaka, Y Ishizawa. Effect of W doping on the growth of TiC crystal by the floating zone method. J Cryst Growth 92:359, 1988. 172. S Otani, T Tanaka, Y Ishizawa. Preparation of TiC single crystals from a self-combustion rod by the floating zone method. J Cryst Growth 83:481, 1987.

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173. S Otani, T Tanaka, Y Ishizawa. Growth conditions of high purity TiC single crystal using the floating zone method. J Cryst Growth 92:8, 1988. 174. S Otani, T Tanaka, Y Ishizawa. Preparation of V8C7 single crystal by floating zone technique. J Cryst Growth 99:1005, 1990. 175. S Otani, Y Ishizawa. Single crystals of carbides and borides as electron emitters. Prog Crystal Growth Charac 23:153, 1991. 176. S Otani, Y Ishizawa. Preparation of TiB2 single crystals by the floating zone method. J Cryst Growth 140:451, 1994. 177. S Otani, Y Ishizawa. Preparation of ZrB2 single crystals by the floating zone method. J Cryst Growth 165:319, 1996. 178. S Otani, MM Korsukova, T Mitsuhashi. Preparation of HfB2 and ZrB2 single crystals by the floatingzone method. J Cryst Growth 186:582, 1998. 179. S Otani, Y Ishizawa. Floating zone growth of TiB2 single crystals using SHS rods. Int J SelfPropagating High Temp Synth 3:93, 1994. 180. EM Savitsky, GS Burkhanov. Growth of single crystals of high melting metal alloys and compounds by plasma heating. J Cryst Growth 43:457, 1978. 181. TB Reed, ER Pollard. Tri-arc furnace for Czochralski growth with a cold crucible. J Cryst Growth 2:243, 1968. 182. C Bulfon, A L-Jasper, H Sassik, P Rogl. Microhardness of Czochralski-grown single crystals of VB2. J Solid State Chem 133:113, 1997. 183. JD Verhoeven, ED Gibson, MA Noak, RJ Conzemius. An arc floating zone technique for preparing single crystal lanthanum hexaboride. J Cryst Growth 36:115, 1976. 184. W Mackie, CH Hinrichs. Preparation of ZrCx single crystals by an arc melting floating zone technique. J Cryst Growth 87:101, 1988. 185. Y Kumashiro, A Itoh, E Sakuma, S Misawa. Plasma jet generator for r-f plasma zone melting. J Phys E13:1271, 1980. 186. Y Kumashiro, A Itoh, E Sakuma, S Misawa. An apparatus for r-f plasma zone melting. J Cryst Growth 32:495, 1981. 187. Y Kumashiro, N Yazawa, S Misawa, A Itoh. Apparatus for r-f plasma zone melting. J Phys E16: 747, 1983. 188. Y Kumashiro, N Yazawa, S Misawa, A Itoh. RF plasma zone melting apparatus. Plasma Chem Plasma Process 3:249, 1983. 189. HS Crouch, S Wright. TiC reinforcements with controlled morphology. Ceram Bull 70:1131, 1991. 190. K Yamada. Crystal growth of tungsten carbide plates by condensation of high-temperature ultrasupersaturated gas. J Am Ceram 73:2103, 1990. 191. J Brandato¨tter, W Lengauer. Multiphase reaction diffusion in transition metal–boron systems. J Alloys Compos 262/263:390, 1997. 192. K Takagi, M Ishii. Growth of LaB6 single crystals by a laser heated floating zone method. J Cryst Growth 40:1, 1977.

4 Thin-Film Preparation Konosuke Inagawa Chiba Institute for Super Materials, ULVAC Japan, Ltd., Tsukuba, Ibaraki, Japan

I.

INTRODUCTION

In general classification, a surface treatment consists of a thin-film preparation (i.e., deposition or coating) on a substance and a modification of a top surface thereof. The techniques involved in the surface treatment are divided into two types, wet and dry processes. The former include electroplating, chemical plating, anodic oxidation, and conversion coating. The latter comprise physical vapor deposition (PVD), chemical vapor deposition (CVD), ion implantation, ion nitriding, ion carburizing, etc. Of these many processes, PVD and CVD have proved most suited to preparation of thin films of refractory materials, i.e., ceramics such as carbides, nitrides, and borides, because only these two methods produce films of excellent quality, sufficiently high purity, and high density with stoichiometric composition. PVD is a fundamental process that relies on a solid-liquid-gas or solid-gas-solid phase transformation to deposit a very thin film with uniform thickness over a wide area. PVD technology has progressed historically starting with vacuum evaporation, followed by sputtering to utilize the energy of charged particles, and more recently ion plating to use the charge and chemical activity of charged particles. In the preparation of a ceramic thin film, PVD encompasses many methods, including direct evaporation, reactive evaporation, reactive ion plating, direct sputtering, reactive sputtering, and dynamic mixing. CVD utilizes the solidification generated by a decompositive reaction from a gas phase. Its characteristic is the low-temperature synthesis of refractory materials. The main CVD techniques for depositing ceramic films are thermal CVD carried out at normal or lower pressure and plasma CVD utilizing a discharge. In this section, preparation and characterization of carbide, nitride, and boride films will be described. The oxide will be discussed briefly if the occasion demands.

II. CONDITIONAL PARAMETERS FOR DEPOSITING THIN FILMS A.

General Aspects

The characteristics of the thin films deposited by PVD and CVD are greatly influenced by the substrate temperature, deposition rate, and gas pressure. Moreover, in some cases, other conditions such as plasma power play a part. The grain size and texture of a deposited film grown with increasing substrate temperature result in good crystallinity of the film. The lower the 55

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Table 1 Pressure, Substrate Temperature, and Deposition Rate in PVD and CVD Processes Method PVD process Vacuum evaporation Sputtering Ion plating Ion beam deposition CVD process Thermal CVD Plasma CVD Laser CVD Metal organic CVD

Operating pressure (Pa) a

Ultimate pressure (Pa)

Substrate temperature (°C)

10 ⫺7 –10 ⫺2 10 ⫺1 –10 10 ⫺1 –5 10 ⫺6 –10 ⫺4

10 ⫺9 –10 ⫺4 10 ⫺7 –10 ⫺4 10 ⫺5 –10 ⫺3 10 ⫺7 –10 ⫺5

Arbitrary Arbitrary Arbitrary Arbitrary

10–10 5 1–10 10–10 3 10–10 3

10 ⫺4 –10 ⫺2 10 ⫺7 –10 ⫺5 10 ⫺7 –10 ⫺5 10 ⫺6 –10 ⫺4

ⱖReaction temperature 200–600 200–400 ⱖReaction temperature

Deposition rate (nm/s) ⬃10 3 ⬃10 ⬃10 3 ⬃1 ⬃10 ⬃10 0.2–0.3 ⬃10

Pa ⫽ 7.50 ⫻ 10 ⫺3 torr. Source: Itoh, 1986.

a

deposition rate and pressure, the denser the film obtained and the smoother its surface. In practical film formation, the characteristics and properties are decided by the complicated relation among the pressure, substrate temperature, deposition rate, etc. as they occur in each applied method.

B.

Effect of Pressure on PVD and CVD Films

Table 1 gives the distinctive gas pressures, substrate temperatures, and deposition rates used in the preparation of PVD and CVD films (1). It is clear that the ultimate pressure before deposition and the operating pressure in PVD are lower than those in CVD. In each method, the film characteristics such as impurities and defects are strongly influenced by the gas pressure. This very significant factor may be called the ‘‘vacuum character.’’ The relationship of the characterization of thin films and the vacuum character is shown in Fig. 1 (1). Besides pressure, of course,

Figure 1 Characterization of thin-film material. (From Itoh, 1986.)

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Figure 2 Schematic representation of the influence of residual gas pressure. (From Namba, 1971.)

surface cleanness of the substrate, substrate temperature, deposition rate, exciting energy, applied substrate voltage, etc. are important process parameters. The effect of pressure is as follows. The lower the ultimate pressure, the higher the purity of the deposited film, although the extent of the impurity involved differs a little according to the method employed. Moreover, the operating pressure affects the morphology of the film. Namba (2) showed that any vacuum-deposited film grows more densely with a smoother surface in a lower surrounding pressure, as shown in Fig. 2. As for sputter deposition, Thornton (3) showed the relation of the film morphology to substrate temperature and discharge gas pressure as illustrated in Fig. 3. Wan et al. (4) evaluated the film deposited by ion plating with their figure of merit of morphology (FOM) introduced by arranging morphologic characteristics of the film as a function of gas pressure, ion bombardment power, deposition rate, and substrate temperature. From these considerations, it may be postulated that a low deposition pressure in PVD improves the film growth morphology, with a dense bulk with less defects and a smooth surface. Similarly, in CVD a dense film with crystallinity is deposited with lower supersaturation.

III. PREPARATION OF CERAMIC FILMS A.

Direct Evaporation

Direct evaporation with a ceramic used as an evaporant material has been carried out since the 1950s. However, the technique encounters two problems. One is partial dissociation of the starting ceramic, resulting in a discrepancy in the chemical composition between the deposited film and the evaporant material. This is one of the reasons for a reduction in the quality of the film. For instance, TiC, ZrC, TiB 2, ZrB 2, (TiC-ZrC), (TiC-TiB 2), and (TiC-TiB 2-Co) films were directly deposited by electron beam heating using each of the ceramic materials (5). In the case of the TiC film, a micro Vickers hardness in the range of 945 to 1615 kg/mm 2 was obtained. This was considerably lower than that of the bulk, 3200 kg/mm 2. It is just too difficult to obtain excellent properties with direct evaporation. Another problem is that the evaporation source

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Figure 3 Microstructure zone diagram for metal films deposited by sputtering. T is the substrate temperature, and T m is the melting point of the coating material in degrees absolute. (Reprinted with permission from J. A. Thornton, Journal of Vacuum Science & Technology A3:3059, 1986. Copyright 1986 American Vacuum Society.)

needs to be of high power density to evaporate the ceramic because of the high melting point involved. In some cases, safely becomes a factor in operating it for a long time. To solve these problems, reactive evaporation, reactive ion plating, etc. were developed, as explained in the following. B.

Reactive Evaporation

Figure 4 shows a schematic of reactive evaporation in which a metal such as Ti, Zr, Si, or Al is evaporated using an electron beam source, a resistance heater, etc., while a reactive gas such as C 2 H 4, C 2 H 2, N 2, or NH 3 is simultaneously introduced into the vacuum chamber, resulting in the formation of carbide and nitride films of the metal concerned. The ultimate pressure before introduction of the reactive gas needs to be kept sufficiently low to avoid any bad effect from residual gas, as the operating pressure during deposition is pretty low, 4 ⫻ 10 ⫺4 to 1.3 ⫻ 10 ⫺2 Pa. At a fixed substrate temperature, when the frequency ratio of reactive gas molecules and metal atoms incident on the substrate, Γ, attains an adequate value, Γ 0, a stoichometric composition is obtained, and there is little composition change in the range above Γ 0. Several carbides and nitrides such as TiC, SiC, TiN, ZrN, and AlN can easily be prepared at deposition rates of 0.006 to 0.018 µm/min, which are not so large. In this so-called reactive evaporation, the reactive gas is introduced to improve upon the discrepancy in chemical composition in direct evaporation. C.

Reactive Ion Plating

Reactive ion plating is a deposition process in which a part of the evaporated atoms and reactive gas is ionized and energetically neutralized by a gas discharge. These activated particles enable the ceramic film to form on the substrate at a high deposition rate. Reactive ion plating consists

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Figure 4 Schematic of reactive evaporation.

of hollow cathode discharge (HCD) ion plating, cathodic arc ion plating, activated reactive evaporation, radio frequency (RF) ion plating, etc. Using these methods, many ceramic films such as carbides—TiC, ZrC, HfC, VC, NbC, TaC, WC, TiC-Ni, VC-TiC, CrC, SiC, Ti (C, N), etc.—and nitrides—TiN, Ti 2 N, ZrN, NbN, HfN, TaN, CrN, AlN, Si 3 N 4, cBN (cubic boron nitride), (Ti, Al) N, (Ti, Zr) N, (Ti, Nb) N, (Ti, Hf) N, etc.—have been deposited. Reactive ion plating has the desirable characteristics of a much higher deposition rate than reactive evaporation, a high density with little porosity of the deposited film and strong adhesion of the deposited film to the substrate. Reactive ion plating technology is applied in the field of structural materials as a protective coating, to promote wear resistance, heat resistance, corrosion resistance, and lubricant properties as thick films of a few to a few tens of micrometers can be formed quickly at a high deposition rate. Let us move on to HCD ion plating as an example of ceramic film formation. A schematic illustration is shown in Fig. 5. A high-current electron beam attracted from a hollow cathode strikes an evaporant in the water-cooled hearth, heating and evaporating it. Ionization occurs as the evaporating atoms collide with the electrons. The ionization efficiency of the evaporating atoms in the HCD process is high, 40 to 70%. In TiC film deposition, C 2 H 2 gas is introduced into the chamber together with Ar gas to maintain an HCD discharge, and N 2 gas is introduced in the case of TiN. Cointroduction of C 2H 2 and N 2 forms a TiC 1⫺x N x film. Because the operating pressure is quite high, about 1.3 ⫻ 10 ⫺1 Pa, the throwing power of the deposited film on the substrate is good. The maximum deposition rate of the film formed on a flat substrate is about 2 µm/min in a production machine. Generally, in reactive ion plating the characteristics of the deposited film are strongly affected by the voltage applied to the substrate because of the great quantity of ions impinging on the substrate. Figure 6 shows the relation between the micro Vickers hardness of a TiC film and the applied substrate bias voltage. The hardness increases rapidly with a negative bias volt-

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Figure 5 Schematic of HCD ion plating.

Figure 6 Variation of micro Vickers hardness with substrate bias voltage for a TiC film deposited by the HCD process. Inconel 625 substrate; substrate temperature 500°C; 10 µm thick; 25-g load.

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Figure 7 Variation of internal stress with substrate bias voltage for TiC film.

age up to ⫺20 to ⫺50 V and decreases after reaching the maximum value at around ⫺70 V. The maximum value of the hardness is 4000 kg/mm 2. This is larger than in the bulk. As shown in Fig. 7, the internal stress of the deposited film, which is largely compressive, indicates the same substrate bias dependence as the hardness. It should be pointed out that the film peels off in some cases when the internal stress is very large, so attention must be paid to this in the deposition of a thick film. It is therefore important to control the substrate bias voltage to accommodate an object that is of high hardness or requires strong adhesion. Moreover, the lattice constant, the full width at half-maximum (FWHM), and the preferred orientation are affected by the substrate bias voltage as shown in Figs. 8 and 9. In RF ion plating and RF sputtering, a large change in the characteristics of the film deposition is generated at ⫺100 to ⫺300 V, which is much higher in than HCD ion plating. This fact suggests that the HCD process involves a larger ion quantity than that found in RF ion plating and RF sputtering. It is considered that such changes in film characteristics are caused by the following: (a) incorporation of gas molecules into the film, (b) incorporation of impurities, and (c) the peening effect of ions, with their effects differing depending on the process. Results of scratch tests to investigate the adhesion of TiN films deposited by HCD ion plating are shown in Fig. 10 (6). The critical load at which the film peels off increases with

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Figure 8 Variation of lattice constant and full width at half-maximum with substrate bias voltage for TiC film. Determined from the 220 line.

increasing deposition temperature in each substrate of a cemented carbide (WC-Co) and a highspeed steel (SKH 9). D.

Sputtering

Direct or reactive sputtering is employed to produce ceramic films in a sputtering process. Using a ceramic target such as carbide, nitride, or boride, many ceramic films are deposited by direct sputtering for practical use in industry. However, there are some problems. The first is the need to hand manufacture the expensive ceramic target. The second is the discrepancy in chemical composition between the film and target, a problem similar to that in direct evaporation using a ceramic evaporant. Moreover, it is undesirable from the standpoint of industrialization that the sputtering yield of the ceramic target is smaller by nearly one figure than that of a metal target. To overcome these disadvantages, reactive sputtering is applied to ceramic film deposition. Figure 11 is a schematic of reactive sputtering. We can use most metals and semiconductors as the reactive sputtering target and CH4, C 2 H 2, or CO as the reactive gas for carbides and N 2 or NH 3 for nitrides. The reactive gas is introduced into a discharge gas, Ar, at a rate of 1 to 50%. Carbide films of TiC, VC, TaC, WC, SiC, Fe 3C, etc. and nitride films of TiN, ZrN, NbN, TaN, Si 3N 4, AlN, Ta 2N-TaN, (Ti, Al) N, etc. are deposited by reactive sputtering. Table 2 shows examples of the ceramic films prepared by direct and reactive sputtering. As shown in Fig. 12, in reactive sputtering, the deposition rate decreases gradually (to about 0.09 µm/mm) with increasing reactive gas pressure until a critical value, P C1, after which it decreases rapidly and at higher pressures decreases only slightly (about 0.02 µm/mm). In the case of decreasing pressure, the critical value P C2, that is, the pressure at which there is a rapid increase of the deposition

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Figure 9 Influence of substrate bias voltage on relative intensity of X-ray diffraction line for TiC film.

rate, is lower than P C1, hence a hysteresis loop is seen. This phenomenon is attributed to the ceramic formation, which has a low sputtering yield, on the target surface reacting with the reactive gas. The term reactive sputtering is also used when the reactive gas is introduced to combat a deficiency of the volatile gas composition in direct sputtering. Magnetron sputtering is employed to increase the deposition rate above that in conventional sputtering when the deposition rate is relatively low. The magnet is set behind the target as shown in Fig. 13. The discharge plasma is confined and enhanced surrounding the magnetic field generated on the target, resulting in an increase of the deposition rate. The deposition rate in magnetron sputtering can be increased nearly ten fold. E.

Chemical Vapor Deposition

CVD is the deposition process in which a ceramic film is formed through the reaction of raw gases introduced on the heated substrate. There are three main types of reaction, hydrogen reduction, thermal decomposition and solid-phase diffusion. Some examples of ceramic films prepared by CVD are given in Table 3. Figure 14 shows a schematic diagram of equipment used to prepare a TiC film by thermal CVD. A TiCl 4 gas is conveyed in a carrier gas, H 2, and after mixing with CH 4 is introduced into a deposition system. The reaction is generally carried

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Figure 10 Influence of substrate temperature on critical load of TiN film deposited using HCD ion plating. Deposition rate 0.08 µm/min; substrate bias voltage ⫺20 V; 2.1 µm thick; micro Vickers hardness 1650 kg/mm 2 under 10-g load. (From Oishi, 1990.)

Figure 11 Schematic of reactive sputtering.

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Table 2 Examples of Carbide, Nitride, and Boride Films Prepared by Direct and Reactive Sputtering Carbide TiC ZrC HfC VC NbC TaC Cr 3 C 2, Cr 7 C3 Cr 23 C 6 Fe 3C SiC MoC 2 WC, W 2C TiC-TiN TiC-VC Ti-Si-C (Fe, Mn) 3C

Nitride

Boride

TiN ZrN HfN VN NbN TaN CrN Fe 4N AlN Si 3 N 4 TiN-Ti (Ti, V)N (Ti, Al)N (Ti, Cr)N (Si, Al)N

TiB 2 ZrB 2 HfB 2 VB 2 NbB 2 TaB 2 WB 2 MoB 2

Figure 12 Schematic illustration of variation of deposition rate with reactive gas pressure in reactive sputtering.

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Figure 13 Schematic of magnetron sputtering cathode.

Table 3 Examples of Carbide, Nitride, and Boride Films Prepared by CVD Material Carbide TiC

SiC

Nitride TiN Si 3N 4 (Si-N) AlN BN

Boride TiB 2 NbB2 TaB2 SiB14

Deposition method

Raw gas

Synthesis temperature (°C)

Thermal CVD Plasma CVD Laser CVD Thermal CVD Thermal CVD Thermal CVD Thermal CVD Plasma CVD Plasma CVD Plasma CVD

TiCl 4, CH 4, H 2 TiCl 4, CH 4, H 2 TiCl 4, CH 4, H 2 SiCl 4, C 3H 8, H 2 SiH 4, CH 4 CH 3 SiCl 3 (CH 3) 2 SiCl 2 SiF 4, CF 4, H 2 Si(CH 3) 4 SiH 4, CnHm

950–1050 400–900 — 1200–1500 1300 1300–1400 1100–1365 140–600 140–600 140–600

Thermal CVD Plasma CVD Thermal CVD Plasma CVD Plasma CVD Thermal CVD Plasma CVD Thermal CVD Thermal CVD Plasma CVD Plasma CVD

TiCl 4, N 2, H 2 TiCl 4, N 2, (NH 3) SiCl 4, NH 3, H 2 SiH 4, N 2, (He, Ar) SiH 4, NH 3, (He, H 2) AlCl 3, N 2, H 2 AlCl 3, N 2, H 2 BCl 3, NH 3, (NH 4Cl), H 2 B 2 H 6,NH 3 BCl 3, NH 3, (Ar) B 3N 3 H6

850–1050 250–1000 850–1050 25–500 25–500 900–1000 ⬃1000 1000–1400 700–1250 300–700 300–700

Thermal CVD Plasma CVD Thermal CVD Thermal CVD Thermal CVD

TiCl 4, BCl 3, H 2 TiCl 4, BCl 3, H 2 NbBr 5, BBr 3, H 2 TaBr 5, BBr 3, H 2 SiBr 4, BBr 3, H 2

850–1100 480–650 1500 1500 927–1327

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Figure 14 Schematic representation of thermal CVD for depositing a TiC film.

out at normal pressure or at a reduced pressure of (6.6–13) ⫻ 10 3 Pa. To achieve uniform thickness and good microstructure in any part of the furnace, reduced pressure is more desirable than normal pressure. The TiC film is prepared at a substrate temperature of 950 to 1050°C according to the following reaction: TiCl 4 ⫹ CH 4 → TiC ⫹ 4HCl The deposition rate is about 0.033 µm/min. The merits of film deposition by the thermal CVD process are as follows: (a) the film has good crystallinity because of the reaction at high temperature, (b) the film adheres strongly to the substrate owing to interdiffusion, and (c) it is possible to form a film even on a substrate of complicated shape. In thermal CVD, however, the types of substrates are generally restricted to those whose mechanical strengths are maintained despite the high temperature of 800 to 1500°C. But a reheat treatment after deposition at high temperature spreads the substrate material to be used in thermal CVD. In plasma CVD, the film is deposited by utilizing an excited reactive species in a thermally nonequilibrium state. This species is generated by electron collision with gas molecules in a discharge plasma. The reaction is accelerated even more at a lower substrate temperature because of the presence of excited atoms and molecules, radicals, ions, etc. The reaction temperature in plasma CVD is much lower than in thermal CVD, as seen in Table 3. The substrate temperature of TiC deposition can be decreased to less than 500°C, at which the deposition rate is about 0.045 µm/min. Carbide films of TiC, ZrC, HfC, TaC, WC, W 2C, SiC, B 4C, etc.; nitride films of TiN, HfN, AlN, Si 3 N 4, BN, etc.; and boride films of TiB 2, NbB 2, TaB 2, SiB 4, etc. are deposited by the two CVD processes.

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Figure 15 Schematic of dynamic mixing for TiN film formation.

F.

Dynamic Mixing

Recently, dynamic mixing, which is a combination of ion implantation and vacuum evaporation, has been applied for the preparation of ceramic films. Ion implantation is advantageous for surface modification of the material, in addition to its use in semiconductor processes in which ions such as B, P, and As are implanted into Si and GaAs in impurity doping. It takes about 100 times the quantity of ions used in a doping process to perform a surface modification. Therefore, in many cases a large quantity of ions are implanted into a substrate with a large surface without mass separation generated in an ion source. Figure 15 depicts schematically a process for depositing a TiN film using dynamic mixing, carried out by a simultaneous operation of Ti evaporation and nitrogen ion implantation. The ceramic film deposited by dynamic mixing shows excellent adhesion because of the presence of a mixed layer formed between the film and substrate. Ceramic films such as TiN, ZrN, AlN, (Ti, Al) N, cBN, and TiC are prepared by this method.

IV. CHARACTERISTICS AND APPLICATIONS OF CERAMIC FILMS The ceramic films prepared by PVD and CVD are applied in two fields in accordance with their characteristics. One is surface treatment (or surface modification), in which the mechanical, chemical, and decorative characteristics of ceramic films are utilized for protective coatings in

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the field of structural materials. The other utilizes the functional characteristics such as the electrical and optical properties of ceramic films. In this section, all of the carbide, nitride, and boride films mentioned above except for oxide films, which are largely applied in the optical field, are discussed. A.

Wear-Resistant Films

1. Wear Property of Ceramic Films Hard coated films are available that resist abrasive wear because of their high hardness and resistance to plastic deformation. Moreover, if a film is chemically stable, it is durable to both adhesive and corrosive wear. In addition to the preceding properties, a lowering of friction with any sliding material and chemical stability at high temperature are important conditions in the selection of a wear-resistant film. Ceramics satisfy these requirements to a certain extent. In high-speed cutting under severe load, the temperature of the cutting edge of the tool becomes high due to friction with the workpiece, diffusion and oxidation, etc. This results in serious wear. It is necessary that a wear-resistant film be coated so that it will not diffuse with atoms of the work material or oxidize but will be chemically stable. Figure 16 shows a diagram of the free energy of formation of ceramic materials, which represent values of the chemical stability (7). The smaller the free energy of formation, the more chemically stable the ceramic material is. Generally, the free energy of formation becomes small with enhanced thermal stabil-

Figure 16 Free energy of formation for ceramics. (From Kikuchi, 1981.)

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ity in the order carbide, nitride, and oxide. Because hardness is an important factor in resistance to abrasive wear, it is necessary that hardness be maintained when the temperature of the film substance is high. Microhardness values for ceramic materials at elevated temperatures are shown in Fig. 17 (8). In terms of both the free energy of formation and the hardness at elevated temperature, HfN is considered to be the most excellent wear-resistant material. In practical cutting, it has been shown that HfN films are superior to TiN films, which are mostly used now (8). For wear-resistant films, TiC, TiN, Ti(C, N), (Ti, Al)N, and Al 2O 3 are mainly used, with TiN being the most common. The endurance of these films against abrasive wear is high, in the order of TiC, Ti(C, N), TiN, and Al 2 O 3, whereas against adhesive wear it is in the reverse order. For instance, a comparison of the tool life of cemented carbide inserts coated with TiC and Al 2O 3 films produced by thermal CVD is shown in Fig. 18 (9). In low-speed cutting, the life of a TiC-coated tool is longer than that of an Al 2 O 3-coated one, whereas the Al 2 O 3 film shows excellent wear resistance in high-speed cutting, in which the tool is subject to a higher temperature. Figure 19 shows the cutting performance of cemented carbide inserts coated with various nitride films (10). The best performance is seen with the (Ti, Al)N film–coated insert. 2. Practical Application Table 4 shows the general application of PVD and CVD ceramic films in the field of structural materials, including their wear resistances (11). As an application of PVD, reactive ion plating

Figure 17 Hardness at elevated temperature for ceramics. (From Leverenz, 1977.)

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Figure 18 Tool life of cemented carbide insert coated with ceramic film using thermal CVD. (From Takatsu, 1983.)

has been employed to prepare TiN, TiC, Ti(C, N), and (Ti, Al)N films a few micrometers thick on cutting tools made of high-speed steel for such uses as end milling, hobbing, and drilling. Use of these materials dates back to 1977 except for (Ti, Al)N, which came 10 years later. More recently, cemented carbide has found use as a substrate. The life of a ceramic film–coated cutting tool is two to five times that of an uncoated one. The application of thermal CVD for TiC coating on cemented carbide tools began in 1969. Now, the utilization of a single layer of TiC, TiN, and Al 2 O 3 is decreasing slowly, while mulilayering is increasing. Two-layer coatings of

Figure 19 Flank wear versus cutting time of cemented carbide insert coated with ceramic film using cathodic ion plating. Work material low-carbon steel S 50C; cutting speed 170 m/min; feed 0.25 mm/ rev; depth of cut 0.1 mm; dry cutting. (From Ikeda and Satoh, 1993.)

Source: Inagawa, 1993.

Acoustic property Gas barrier Transparency

Corrosion resistance High strength Oxidation resistance Corrosion resistance Low outgassing Wear resistance Low atomic number Plasma erosion resistance Radiation resistance Color, wear resistance Corrosion resistance

BN, Si 3 N 4 SiC

TiN, TiC, CrN, BN TiC C TiN, Ti(C, N, O), (Ti, AL)N ZrN, CrN, Cr(N, C, O) DLC Diamond, DLC SiO x, Al 2 O 3

Vacuum equipment and parts Nuclear reactor Nuclear fuel Personal ornaments Daily commodities Oscillation plate Packaging material

SiC, Si 3 N 4, Al 2 O 3, MoSi 2

Semiconductor parts Die for high temperature Structural material Hearth Composite material

UO 2 Cemented carbide Quenched and tempered steel, stainless steel, Ti alloy Al 2 O 3 plate, Ti plate PET film

Mo, Inconel

Stainless steel, Al alloy

Carbon, quenched and tempered steel, sintered Si 3 N 4, sintered SiC Carbon, SiO 2 Carbon fiber

TiC, TiN, Ti(C, N) (Ti, Al)N, W 2 C

Mold

Wear resistance Seizure resistance Corrosion resistance Oxidation resistance

Substrate Cemented carbide Quenched and tempered steel, stainless steel, Ti alloy, Al alloy, PET film Plastic lens Cemented carbide Quenched and tempered steel

Film TiC, TiN, Ti(C, N), (Ti, Al)N CrN, Cr 7 C 3, Al 2 O 3, SiO 2 W 2 C, TiB 2, diamond Diamond-like carbon

Cutting tools, machine parts Electric parts, optical parts

Application

Ceramic Films Prepared by PVD and CVD That Are Applicable in the Field of Structural Materials

Wear resistance

Property

Table 4

72 Inagawa

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Ti(C, N)/TiC/substrate (henceforth substrate details are omitted), TiN/TiC, and Al 2 O3 /TiC and three-layer coatings of TiN/Ti(C, N)/TiC and TiN/Al 2 O 3 /TiC are widely used. In special cases more than 10 layers can be coated. The total film thickness, for instance, of four layers of the TiN/Al 2 O 3 /TiC/Ti compound is 8 to 10 µm. In addition to cutting tools, the sliding parts of many components of various machines are coated with wear-resistant ceramic films. Also, hard ceramic films are utilized in many kind of molds for such applications as sheet metal forming, cold forming, powder forming, die casting, and injection molding because of their good release properties and to assist maintenance of specular surfaces. TiN films prepared by reactive ion plating; (Ti, Al)N films prepared by reactive sputtering; TiC, Ti(C, N), and TiN/Ti(C, N)/TiC films prepared by thermal CVD; W 2C films made by low-temperature CVD at 300 to 500°C; and TiN, TiC, and Ti(C, N) films made by plasma CVD are all applied to the surfaces of molds. 3. Emerging Materials for High Hardness Cubic boron nitride (cBN) is a very promising material that, after diamond, displays the highest hardness, excellent thermal conductivity, and important characteristic properties such as high electrical insulation and chemical and thermal stability. The cBN film can be deposited on a cemented carbide insert using activated reactive evaporation with a gas activation nozzle. Figure 20 shows the relation between the micro Vickers hardness (10 g load) of a BN film and its

Figure 20 Micro Vickers hardness of BN film deposited using activated reactive evaporation with a gas activation nozzle. Load 10 g. (Reprinted from Ref. 12 with permission from Elsevier Science.)

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chemical composition ratio N/B (12). The hardness of a cBN film about 1.5 µm thick is very high, 5500–6300 kg/mm 2, as high as that of converted compact cBN. For practical uses, it is necessary to establish much stronger adhesion of the cBN film to the substrate. An interesting mechanical characteristic has also been obtained in a superlattice film and in a multilayer coating. Figure 21 shows the relation between the Knoop hardness and the lamination period, λ, of a TiN/AlN superlattice film deposited on cemented carbide using cathodic arc ion plating to a total thickness of more than 1.3 µm (13). The hardness depends a great deal on the period and at λ ⫽ 2.5 nm has a maximum value about 1.6 times that of TiN film. This tendency is similar to that of a TiN/VN epitaxial superlattice film, whose micro Vickers hardness has a maximum value of 5560 kg/mm 2 (14). A TiN/AlN superlattice film–coated cemented carbide end mill and insert display excellent performance in high-speed cutting. Also, a multilayer film such as TiC/TiB 2 and TiN/TiC, for instance, of 1000 layers with a total thickness of 5 µm, deposited using magnetron sputtering, shows a distinct improvement in mechanical properties such as hardness, friction coefficient, and wear resistace (15). A superhard Ti-B-C film with a micro Vickers hardness of 7200 kg/mm 2 was obtained by reactive DC magnetron sputtering with a TiB 2 target and CH 4 gas introduced (16). The implication of the very high hardness is that carbon atoms are included interstitially in the TiB 2 lattice. The latest exciting development in hard coating is the synthesis of β-C 3 N 4 a new material with the same structure as the well-known β-Si 3 N 4. Theoretical calculations suggest that β-C 3 N 4 has extremely high hardness (comparable to or greater than that of a diamond of 10,000 kg/ mm 2) and a low friction coefficient (17,18). Preparations of β-C 3 N 4 films are being attempted employing a wide variety of methods such as magnetron sputtering (19), cathodic arc ion plating (20), ion beam–assisted sputtering (21), ion implantation (22), laser ablation (23), and plasma

Figure 21 Variation of Knoop hardness with lamination period for TiN/AlN superlattice film prepared using cathodic arc ion plating. Load 50 g. (From Nakayama, Stetoyama, and Yoshioka, 1994.)

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CVD (24). Results so far have not shown the anticipated hardness. Active investigation will no doubt continue toward realizing the potential of β-C 3 N 4. B.

Oxidation- and Corrosion-Resistant Films

The behavior of ceramics with good oxidation and corrosion resistance has been studied by exposing the films in air to elevated temperatures and dipping them into acid solution, respectively. Figure 22 shows a comparison of the weight gain, i.e., the oxidation rate, of TiC, TiN, (Ti, Zr, Al)N, (Ti, Al)N films in hot air (25). The ceramic films were deposited on stainless steel substrates using reactive magnetron sputtering. The (Ti, Al)N film showed the best oxidation resistance, beginning to oxidize at a temperature of 700 to 750°C, nearly 200°C higher than TiN film. A protective layer of amorphous Al 2 O 3 formed at the top surface of the (Ti, Al)N film, preventing further oxidation of the sample. Next, Fig. 23 shows the weight reduction of TiN and CrN films dipped in a 10% hydrochloric acid solution (26). The films were deposited on stainless steel substrates using cathodic arc ion plating. The weight loss of the coated samples is smaller than that of the uncoated sample. In particular, the corrosion resistance of the CrN film is noted to be superior to that of the TiN film, as a Cr 2 O 3 layer is more stable than a TiO 2 one in regard to each protective layer formed in a corrosive solution. C.

Decorative Film

Most metals, with the exception of Au and Cu, are colorless, whereas ceramics exhibit various colors. TiN, ZrN, HfN, and TaC are all gold with small differences in color tone, Be 2C is red, NbN is bright brown, WN is brown, and MnN is black. Reflectance spectra of materials having a gold color are shown in Fig. 24 (27). The TiN x film was prepared using reactive ion plating. The reflectance curve of the sample with an about 0.1-µm-thick Au coating to raises the bright-

Figure 22 Oxidation property of ceramic film deposited using reactive magnetron sputtering. (Adapted with permission from W. D. Mu¨nz, Journal of Vacuum Science & Technology A4:2717, 1986. Copyright 1986, American Vacuum Society.)

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Figure 23 Corrosion property of stainless steel SUS 304 coated with TiN and CrN films using cathodic arc ion plating. (From Kohno, Ikenaga, and Ichimura, 1993.)

ness, after TiN x deposition is similar to that of an electroplated Au alloy. Other colors such as whitish gold, pinkish gold, brown gold, and gray are realized by the simultaneous introduction of H 2, O 2, C 2 H 2, etc. in addition to the reactive gas N 2. As a decorative film with wear and corrosion resistance, the TiN-based one is utilized for personal ornament; in stationery; and in commodities such as watch cases and bands, spectacle frames, scissors, shaving edges, and cooking knives. Also, CrN (gray) and Cr 2 N (white) films deposited using reactive ion plating and (Ti, Al)N films (brown) prepared by reactive magnetron sputtering have found practical use.

Figure 24 Reflection spectrum of TiN group film showing gold deposited using reactive ion plating. (From Yamazaki, 1986.)

Thin-Film Preparation

D.

77

Electrical Applications

1. Resistance Film For ceramic resistor use, cermet and Ta 2N films have been used since the time of the early hybrid integrated circuits (ICs). A cermet film is produced by mixing a metal and ceramic, for instance, Cr-SiO, Cr-MgF 2, and Au-SiO. The Cr-SiO (SiO 25–90%) film is generally used because of its stable properties and its specific resistance of 3.1 ⫻ 10 ⫺4 to 4.3 ⫻ 10 ⫺3 Ω cm. Ta 2N resistance film is prepared using reactive sputtering. Figure 25 shows the relation of the N 2 partial pressure and crystal structure, specific resistance, and temperature coefficient of resistance (TCR) (28). Under general sputtering conditions, a Ta film shows a β-phase (tetragonal structure); however, an α-phase (body-centered cubic) forms at a high substrate temperature and in the low gas pressure of a discharge. A film involving a Ta 2N phase is appropriate for a resistor, because its specific resistance is large and its TCR is close to zero. The properties of little scatter and only a small variation over time are beneficial. In addition to Ta 2N, the electrical properties of (Ti, Al)N, (Ta, Al)N, (Ti, Si)N, Ta(N, O), AlN, TiN, and ZrN have been investigated and some of these are applied to thin-film resistors and heaters. 2.

Diffusion Barrier and Insulation Films

Many oxide films are utilized in semiconductor ICs, along with a few nitrides. TiN film is prepared by sputtering and CVD for use as a diffusion barrier in metallization. A CVD Si 3 N 4 film is used for an insulator in dynamic random-access memory (DRAM). Si 3 N 4 film is largely applied in gate insulators for metal-oxide-semiconductor (MOS) transistors, insulators for capacitors, interlayer insulators between interconnecting materials, surface passivation uses, etc. 3. Surface Accoustic Wave Devices Oxides such as LiNbO 3, SiO 2, and especially ZnO film are usually used for surface accoustic wave devices that operate utilizing the piezoelectric effect. Also, AlN films are applied in these devices. These films are generally formed using RF magnetron sputtering.

Figure 25 Variation of specific resistance and temperature coefficient of resistance with N 2 partial pressure for TiN film deposited using reactive sputtering. (From Kinbara, 1984.)

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4. Superconducting Films Preparing superconducting films is a fundamental technique for creating electronic devices based on the Josephson effect, such as switching devices and magnetic and optical sensors. As a superconductor has perfect diamagnetism, a superconducting current will flow through a surface layer 30 to 200 nm thick, i.e., the magnetic penetration depth. It is therefore sufficient for utilization to ensure about the same thickness, and a thin film proves to be the most suitable form. Ceramic superconducting films are divided into three classes, B1-type compounds, ternary compounds, and high-temperature oxide superconductors. The B1-type (NaCl-type structure) compound superconductors consist of nitrides and carbides with 5A, 6A, and 7A transition metals, such as TiN, ZrN, HfN, VN, NbN TaN, MoN, WN, TiC, ZrC, HfC, VC, NbC, TaC, MoC, WC, NbN 1⫺x C x , hex-MoN, and hex-MoC. Regarding the thin-film material, it is notable that NbN and NbN 1⫺x C x (x ⫽ 0.08 and 0.15) have superconducting critical temperature, T c , values of 17.3 and 17.8 K, respectively. The deposition method used is almost always sputtering or CVD. The properties of films deposited by the former method are superior. A highly reliable Josephson device was realized with an NbN film. Ternary compound superconductor films such as BaPb 1⫺x Bi x O 3, Ba 1⫺xK x BiO 3, and Ba 1⫺xRh x BiO were prepared using sputtering, molecular beam epitaxy (MBE), and laser ablation, and a maximum T c of 25 K was achieved. Since the high-temperature oxide superconductor was discovered in 1986, research and development on it have been largely carried out with the aim of finding the highest critical temperature, critical magnetic field, and critical current. YBa 2 Cu 3 O 7, Bi 2 Sr 2 CaCu 2 O 8, Bi 2 Sr 2 Ca 2 Cu 3 O 10, HgBa 2 CaCu 2 O 10, and Tl 2 Ba 2 Ca 2 Cu 3 O 10 films were deposited by various methods such as vacuum evaporation, sputtering, laser ablation, ionized cluster beam (ICB) and CVD, with a maximum T c of 122 K being obtained. E.

Miscellaneous

A TiN film formed by reactive ion plating is used to produce low outgassing of the inner walls of vacuum chambers and parts for vacuum equipment. It is considered that two functions contribute to the low outgassing rate of TiN film. One is the barrier effect against H 2 gas dissolved in the wall material. The other is the low adsorption and/or desorption of each gas component in air. In magneto-optical disks, Si 3 N 4 and AlN films produced by sputtering are applied to protect against oxidation of the magnetic layer and enhance the magnetic Kerr rotation angle. In the medical field, for dental restoration, TiN films produced by reactive ion plating are serving in pratical applications to prevent wear and corrosion.

REFERENCES 1. Itoh A. Characterization and evaluation of ceramic coatings. Bull Ceram Soc Jpn 21:502, 1986. 2. Namba Y. Growth of evaporated Bi film and its cross-sectional structure. Oyo Buturi (Appl Phys) 40:639, 1971. 3. Thornton JA. The microstructure of sputter-deposited coatings. J Vac Sci Technol A4:3059, 1986. 4. Wan CT, Chambers DL, Carmichael DC. Effect of processing conditions on characteristics of coatings vacuum deposited by ion plating, Proceedings of 4th International Conference on Vacuum Metallurgy, 1974, pp 231–237. 5. Bunshah RF, Nimmagadda R, Dunford W, Movchan BA, Demchishin AV, Chursanov NA. Structure and properties of refractory compounds deposited by electron beam evaporation. Thin Solid Films 54:85, 1978.

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6. Oishi M. On the preparation of wear resistance hard films by physical vapor deposition. J Surf Fin Soc Jpn 41:1125, 1990. 7. Kikuchi N, Itaba S. Application of ceramic coatings for cutting tool. Bull Ceram Soc Jpn 16:170, 1981. 8. Leverenz RV. Hafnium nitride coating for cutting tools, Proceedings of Symposium on New Developments in Tool Materials, Chicago, 1977, pp 1–5. 9. Takatsu S. CVD on tool materials. Zairyo Gijutsu (Mater Technol) 1:78, 1983. 10. Ikeda T, Satoh H. High-temperature oxidation and wear resistance of Ti-Al-N hard coating formed by PVD method. J Jpn Inst Met 57:917, 1993. 11. Inagawa K. Recent development in preparation and applications of super hard films. J Jpn Soc Prec Eng 59:373, 1993. 12. Inagawa K, Watanabe K, Saitoh K, Yuchi Y, Itoh A. Structure and properties of c-BN film deposited by activated reactive evaporation with a gas activation nozzle. Surf Coat Technol 39/40:253, 1989. 13. Nakayama A, Setoyama M, Yoshioka T. Preparations and evaluations of TiN/AlN superlattices by arc ion plating. J Vac Soc Jpn 37:929, 1994. 14. Helmersson U, Todorova S, Bernett SA, Sundgren J-E, Markert LC, Grren JE. Growth of singlecrystal TiN/VN strained-layer superlattices with extremely high mechanical hardness. J Appl Phys 62:481, 1987. 15. Holleck H, Schier V. Multilayer PVD coatings for wear protection. Surf Coat Technol 76–77:328, 1995. 16. Knotek O, Breidenbach R, Jungbut F, Loffer F. Surf Coat Technol 43/44:107, 1990. 17. Liu AY, Cohen ML. Prediction of new low compressibility solids. Science 245:841, 1989. 18. Liu AY, Cohen ML. Structural properties and electronic structure of low-compressibility materials: β-Si 3 N 4 and hypothetical β-C 3N 4. Phys Rev B 41:10727, 1990. 19. Marumo Y, Yang Z, Chung YW. Optimization of properties of carbon nitride and CN x /TiN coatings prepared by single-cathode magnetron sputtering. Surf Coat Technol 86–87:586, 1996. 20. Chhowalla M, Alexandrou I, Kiely C, Amaratunga GAJ, Aharonov R, Fontana RF. Investigation of carbon nitride films by cathodic arc evaporation. Thin Solid Films 290–291:103, 1996. 21. Hammer P, Baker MA, Lenardi C, Gissler W. Ion beam deposited carbon nitride films: Characterization and identification of chemical sputtering. Thin Solid Films 290–291:107, 1996. 22. Xie EQ, Jin YF, Wan ZG, He DY. Formation of C-N compounds by N-implantation into diamond films. Nucl Instrum Methods B 135:224, 1998. 23. Soto R, Gonza´lez P, Redondas X, Parada EG, Pou J, Leo´n B, Pe´rez-Amor M, da Silva MF, Soares JC. Growth and characterization of carbon nitride films prepared by laser ablation. Nucl Instrum Methods B 136–138:236, 1998. 24. Dekempeneer EHA, Meneve J, Smeets J, Kuypers S, Eesels L, Jacobs R. Structural, mechanical and tribological properties of plasma-assisted chemically vapor deposited hydrogenated C x N 1⫺x : H films. Surf Coat Technol 68/69:621, 1994. 25. Mu¨nz WD. Titanium aluminium nitride films: A new alternative to TiN coatings. J Vac Sci Technol A4:2717, 1986. 26. Kohno M, Ikenaga M, Ichimura H. Properties and industrial application of arc ion plated films. J Surf Fin Soc Jpn 44:708, 1993. 27. Yamazaki T. Golden TiN film prepared by ion plating. Boundary 2(9):42, 1986. 28. Kinbara A. Sputtering Gensho (Sputtering Phenomena). Tokyo: University of Tokyo Press, 1984, p 210.

5 Electronic Structure Adolf Neckel Institute for Physical Chemistry, University of Vienna, Vienna, Austria

I.

INTRODUCTION

The high interest in the electronic structure of the refractory hard metals, among which primarily the monocarbides, mononitrides, and diborides of the transition metals of the fourth and fifth groups of the periodic table are understood, arises from the unusual combination of properties that characterizes these compounds. Because of its very similar properties, tungsten monocarbide, WC, has also been included in this review. These substances exhibit, on the one hand, ultrahardness and high melting points, characteristics typical of covalently bonded compounds. On the other hand, they also display metallic properties, such as high electric and thermal conductivity. Some of the compounds of this class of substances are superconductors with transition temperatures as high as 18 K (niobium nitride, 17.3 K; niobium carbonitride, NbC 0.3 N 0.7, 18 K). The monocarbides and mononitrides of the elements Ti, V, Zr, Nb, Hf, and Ta* crystallize in the sodium chloride (B1 type) structure, which is found mostly with ionic compounds. For WC the hexagonal form (α-WC) is the stable modification, whereas WC crystallizing in the B1 structure (β-WC) is a metastable form. Transition metal monocarbides and mononitrides will be designated by the formula MX. The transition metal diborides (MB2) crystallize in the AlB2 structure (C32 type), in which hexagonal-close-packed M layers alternate with graphite-like B layers. The transition metal monocarbides and mononitrides typically exhibit wide homogeneity regions, caused by the formation of vacancies, mainly on the nonmetal sites and, to a much lesser extent, also on the metal sites. Because the vacancies have a strong influence on the physical and chemical properties of the substances, a large number of theoretical and experimental investigations have been devoted to the study of the electronic structure of vacancycontaining transition metal carbides and nitrides. The aim of this chapter is to present a short overview of the electronic structure—mainly based on theoretical approaches—of the foregoing classes of substances. However, it must be clearly stated that numerous experimental methods have produced significant findings about the electronic structure. Only the mutual supplementing and cross-checking of theory and experiment can provide an in-depth understanding of electronic structure. Both tools are equally important. A heightened interest, awakened especially by the properties of the transition metal carbides

* TaN crystallizing in the sodium chloride structure is a metastable phase. 81

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and nitrides and the great number of investigations dedicated to the elucidation of the electronic structure and the bonding mechanism of this class of substances, has led to several review articles (1–6). The book by Gubanov et al. (7) and Johansson’s comprehensive review article (8) on the electronic and structural properties of transition metal carbide and nitride surfaces deserve special mention. The relations between electronic structure and cohesive properties will be dealt with in Chap. 6. It is impossible to present the whole field and its related literature in this chapter. Rather, typical results and characteristics will be discussed for representative examples. A comprehensive bibliography can be found in the book by Gubanov et al. (7).

II. ELECTRONIC STRUCTURE OF STOICHIOMETRIC TRANSITION METAL MONOCARBIDES AND MONONITRIDES Most calculations have been performed for stoichiometric phases MX, which constitute model compounds. The real crystals used for the experimental investigations, however, almost always show deviations from ideal stoichiometry and crystal defects. A.

Electronic Structure and Bonding Mechanisms: Early Ideas and Calculations

The unusual combination of properties gave rise to early speculations about the bonding mechanism in these substances. Ha¨gg (9) studied compounds of the transition metals with the elements H, C, N, and O from a crystallographic point of view as early as 1931. He found a relationship between the ratio (r X /r M ), where r X is the radius of the nonmetal atom X and r M the radius of the metal atom M, and the crystal structure of the compound. He observed that compounds for which the ratio (r X /r M ) is smaller than 0.59 frequently crystallize in a structure having the same metal sublattice as the corresponding pure metal and that the MM distances are only slightly larger than those in the pure metal. Ha¨gg concluded from these findings that the nonmetal atoms occupy only the voids in the metal lattice and do not contribute to the stability of the compounds. He coined the name ‘‘interstitial compounds’’ for this class of substances, which is still in use. Consequently, he assumed that only the MM bonds are essential for the stability of these compounds. Rundle (10) revised this view and inferred a weakening of the MM bonds from the slight increase of the MM distances in the compounds compared with the MM distances in the corresponding pure metals. He assumed that MX bonds are also formed and that these are responsible for the hardness and brittleness of these substances. The importance of π bonds between nonmetal p orbitals and metal d orbitals (of t 2g symmetry) was stressed by Krebs (11). Pauling (12) held the view that the octahedral coordination of six metal atoms about each carbon or nitrogen atom involves resonance among six positions, because a carbon or nitrogen atom can form only a maximum of four covalent bonds. The first band structure calculation for TiC, TiN, and TiO was performed by Bilz (13). He used a simplified linear combination of atomic orbitals (LCAO) method and considered only the MX bonds as the important ones. From his results he inferred a charge transfer from the metal to the nonmetal atom. A completely opposite point of view was adopted by Costa and Conte (14). These authors ignored the MX bonds and considered only the MM bonds. According to their calculations, a transfer of electronic charge from the nonmetal to the metal atom should occur. Lye and Logothetis (15), using optical data to adjust the parameters in their

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semiempirical LCAO band structure calculation for TiC, came to similar conclusions. These authors considered both TiC and TiTi bonds. Their results, however, could not be confirmed by later calculations or experiments. Ern and Switendick (16) performed the first ab initio band structure calculation for TiC, TiN, and TiO using the augmented plane wave (APW) method. Their calculation was based on a crystal potential that was derived from a superposition of atomic or ionic electron densities. Because the authors did not carry their calculations to selfconsistency, their results depended on the assumed atomic configuration. Later, however, Neckel et al. (17–19) showed that the main features of the findings of Ern and Switendick agreed with those obtained by the self-consistent APW method. B.

Electronic Structure: Computational Methods

A great number of electronic structure calculations have been performed since the early band structure calculations, mentioned in Sect. II.A. In principle, two different groups of methods have been applied: cluster methods and band structure methods. In the cluster approach only a small part of the crystal, a cluster, is considered. Quantum chemical methods developed for the study of molecules or complexes are used to compute the electronic structure of the cluster. The crystalline surrounding of the cluster can also be taken into account by using an embedded cluster scheme. The main advantage of the cluster methods is their simplicity. They are, by their nature, particularly appropriate for calculating properties caused by the interaction between nearest-neighbor atoms. The limited size of the cluster can sometimes lead to unrealistic results (‘‘cluster effects’’). Within the range of their applicability, however, cluster methods frequently provide results that are in good agreement with band structure calculations or the experiment. A description of the methods for calculating the electronic structure of clusters and for computing properties of solids on the basis of cluster models can be found in Ref. 7 and in the literature cited therein. The band structure methods are based on the concept of an infinite, ideal crystal. A band structure represents the electron states as a function of energy and wave vector. Band structure methods implicitly take into account the translational symmetry of the crystal. Therefore, they can also be applied for the calculation of properties that cannot properly be obtained by means of cluster methods. Extreme examples are the topology of the Fermi surface and the dispersion of the energy bands, i.e., the dependence of the energy of the electron states on the wave vector k. In general, band structure calculations require more computational effort than cluster methods. Furthermore, one has to bear in mind that in band structure methods several approximations are also used. One of the most important features is the fact that band theory is a one-electron approach. The basis of the one-electron treatment of ground state properties forms the density functional theory (DFT) of Hohenberg and Kohn (20) and Kohn and Sham (21) and the local density approximation (LDA) (21,22). Essential for the quality of the results is the self-consistency (SC) of a band structure calculation. Starting from an assumed electron density, which is usually obtained by superposition of the electron densities of the constituent atoms, the Coulomb potential is computed by solving Poisson’s equation. The exchange-correlation potential, which is essential in a one-electron band structure method and which includes all many-body effects on the ground state properties, can also be computed from the electron density. The one-electron Schro¨dinger equation is solved for the sum of these two potentials using one of the many available schemes. The solutions of the Schro¨dinger equation yield the energy eigenvalues of the electron states for special wave vectors k and the corresponding wave functions. By summing the squares of the wave functions of the occupied electron states a new electron density is obtained, which forms the basis of a new iteration. This procedure is repeated until certain convergence criteria are fulfilled. Reliable values for the amount of s-, p-, and d-like character

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of the wave functions and consequently for the configuration of each atom in the compound can be derived only from self-consistent band structure calculations. Self-consistency is also an inevitable prerequisite for the calculation of the charge transfer between the constituent atoms of the compound. Various methods for the calculation of band structures have been devised. The augmented plane wave (APW) method (23,24) and the Green’s function (GF) method of Korringa, Kohn, and Rostocker (KKR) (25–28) were used for most of the early calculations of the band structures of transition metal compounds. A common approximation in both methods is the use of the socalled muffin tin potential. In this approximation it is assumed that the crystal potential is spherically symmetric within nonoverlapping spheres around the atomic sites and constant in the region between the atomic spheres. Various forms of the exchange-correlation potential have been proposed in the literature (29–35). Fortunately, the results of band structure calculations frequently do not depend much on the choice of the exchange-correlation potential. However, differences up to about 25 mRyd can occur when different exchange-correlation potentials are applied. Linearized band structure methods were developed in the 1970s: the linearized augmented plane wave (LAPW) method (36), the linear combination of muffin-tin orbitals (LMTO) method (37), the augmented spherical wave (ASW) method (38), and some others. In the LAPW method a warped muffin tin potential is frequently used, in which the real shape of the crystal potential in the interstitial region between the atomic spheres is taken into account. In the LMTO and ASW approaches the atomic sphere approximation (ASA) is frequently applied, in which— contrary to the muffin-tin approximation—overlapping atomic spheres are used. The crystal potential in the spheres is again assumed to be spherically symmetric. The sum of the atomic sphere volumes must be equal to the total volume of the unit cell. No interstitial space remains. The main advantage of the linearized methods is a considerable reduction is computing time. This reduction is achieved by the introduction of further approximations, which, however, influence the quality of the results only slightly in most cases. The introduction of these techniques has extended the applicability of band structure methods to considerably more complex crystal structures. A detailed description of the linearized methods can be found in the articles by Andersen et al. (39), Andersen (40), Skriver (41), and Nemoshkalenko and Antonov (42). In the 1980s, methods were introduced that permit dealing with a crystal potential of completely general shape (‘‘full-potential’’ methods). The full-potential linearized augmented plane wave (FLAPW) method was developed by Wimmer et al. (43) in 1981. Another version of the FLAPW method was elaborated by Blaha et al. (44,45). A full-potential linear muffin tin orbital method has also been introduced (46,47). Relativistic effects have to be taken into account for compounds containing transition elements with higher atomic numbers; the 5d transition elements (Hf, Ta, W) are of particular concern in the present review. A fully relativistic treatment requires the solution of the Dirac equation instead of the Schro¨dinger equation. However, in many cases, it is sufficient to use a scalar relativistic scheme (48) as an approximation. In this technique, the mass-velocity term and the Darwin s-shift are considered. The spin-orbit splitting, however, is neglected. In this approximation a different procedure must be used to calculate the radial wave functions, but the nonrelativistic formalism, which is computationally much simpler than solving Dirac’s equation, is retained. Only the most important band structure methods have been mentioned in this section. The repertoire of techniques is by no means exhausted by the present description; for example, reference should be made to the pseudopotential methods (49–51). Angle-integrated and angle-resolved photoemission experiments provide an efficient source for the experimental elucidation of band structures. Angle-integrated photoemission in-

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vestigations primarily permit the determination of the relative positions of the energy bands and the approximate shape of the density of states. From angle-resolved photoemission (ARP) experiments, however, detailed information about a band structure can be extracted. ARP studies facilitate the exact determination of the position and the dispersion of energy bands. In connection with the evaluation and interpretation of ARP spectra, numerous band structure calculations, frequently to high energies, have been performed. These calculations will not be covered in this chapter, as they are included in the article by Johansson (See Ref. 8, and references therein).

C.

Band Structures of the Stoichiometric Monocarbides and Mononitrides of Ti, V, Zr, and Nb

The graph of the energy E of the electron states as a function of the wave vector k along a certain path in the first Brillouin zone (BZ) represents an energy band. E(k) is a multivalued function of k, the branches being numbered by a band index in order of increasing energy. A branch of E(k) corresponding to a certain band index represents a band of closely spaced energy levels. The form of E(k) throughout all branches (bands) is called the band structure of the crystal. As already mentioned, the transition metal monocarbides and mononitrides crystallize in the sodium chloride (B1 type) structure (Fig. 1). The first BZ for a face-centered cubic (fcc) lattice, the translational lattice for the B1 structure, is displayed in Fig. 2. The labeling of symmetry points in the BZ normally follows the notation (Γ, ∆, X, . . . .), introduced by Bouckaert et al. (52). The electron states in the compounds can be classified as follows: 1. Core states, which lie energetically deep and are not directly involved in the bonding. They can be treated as atomic-like and calculated using the self-consistent crystal potential. They show no dispersion of the energy in k space. 2. Semicore states, with relatively low energies, which show only a slight energy dispersion in k space. They are usually not displayed in the band structure. 3. Valence states, which show a strong energy dispersion in k space and are displayed in the band structure. Various band structure calculations for the title compounds have been performed (see Ref. 7). The present discussion is based mainly on the results obtained by means of the SC APW method by Neckel et al. (17–19) for TiC, TiN, VC, and VN; Schwarz et al. (53) for VC; Schwarz et al. (54) for ZrC and ZrN; and Schwarz (55,56) for NbC and NbN and on the results of

Figure 1 Cubic unit cell of the B1 type structure (sodium chloride structure).

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Neckel

Figure 2 First Brillouin zone (BZ) for a face-centered cubic (fcc) translational lattice.

additional calculations for TiC and TiN by Schwarz and Blaha (22,57) using the SC LAPW method and by Herzig et al. (58), who applied the SC FLAPW method. Blaha and Schwarz (59) also performed a band structure calculation for VN by means of the full-potential LAPW method. The authors compared the band structures, densities of states, and partial charges obtained by this method with the results of the earlier APW calculations (17,19), in which the muffin-tin approximation was used. The main differences between the two methods were outlined. It was found that the non-muffin-tin effects in this highly coordinated compound are very small. Price and Cooper (60) calculated the electronic structure, total energies, and equilibrium lattice constants for TiC with B1 structure and for various prototype superlattice structures by means of the full-potential LMTO method (37). The band structures of this class of compounds show great similarities. The main features will be discussed on the basis of band structures of TiC and TiN (Figs. 3 and 4), but the arguments apply equally to the band structures of the other compounds. 1. The band structures are characterized by an energetically low-lying band, which is derived from the nonmetal 2s state. The wave functions of the states of this band display almost exclusively s symmetry. This band will be designated the ‘‘s band.’’ 2. Separated by an energy gap from the s band, three overlapping bands occur, which are derived from the nonmetal 2p states. These three bands originate from the threefold degenerate state at the k point Γ labeled Γ15. The wave functions of the states of these bands are primarily characterized by p symmetry, but they also contain a significant contribution from d symmetry, due to the interactions of the nonmetal 2p orbitals with the transition metal nd orbitals. The amount of d character generally decreases from the carbide to the nitride. These three overlapping bands will be denoted ‘‘p bands.’’ 3. Progressing to higher energies, five overlapping bands are found that originate from the states Γ′25 and Γ12 . These bands are mainly derived from the transition metal nd states but also exhibit some p character. These bands will be called ‘‘d bands.’’ In the lower energy range the d bands overlap the p bands. The upper limit of the p bands can be defined in such a way that they contain exactly six electrons per unit cell.

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Figure 3 Band structure of TiC, calculated by means of the full-potential LAPW method. The energy (Ryd) refers to the mean value of the potential in the region between the atomic spheres as energy zero. The Fermi energy, indicated by a horizontal line, is at 0.64172 Ryd. (From Ref. 58.)

4. The next band above the d bands originating from the state Γ1 can be derived from the transition metal (n ⫹ 1)s state. This band is characterized by highly delocalized states with prevailing s and p symmetry and will be denoted the M-s band. Contrary to the situation in the pure transition metals, where the broad (n ⫹ 1)s band overlaps the narrow nd bands, in the carbides and nitrides the (n ⫹ 1)s band is shifted to higher energies above the Fermi energy due to the repulsive interaction with the nonmetal s band. Passing from the carbides to the nitrides, the nonmetal s band is lowered in energy and increasingly localized. Because of these effects, the repulsion between the nonmetal s and the transition metal (n ⫹ 1)s band (M-s band) is reduced and, consequently, the M-s band, particularly the state Γ1, is shifted to lower energies. The band structures of the four compounds ZrC, ZrN (54), NbC, and NbN (55,56) were calculated using the nonrelativistic SC APW method. Weinberger (61) has proved that the neglect of relativistic effects for the 3d and, to a lesser extent, the 4d transition metal carbides (and nitrides) is essentially justified. This author calculated relativistic energy bands along the [100], and [110], and [111] directions in the BZ for VC and NbC. The calculations were based on self-consistent nonrelativistic APW crystal potentials and were performed by means of the relativistic KKR method (27,28). These calculations show that, in taking into account relativistic effects, only small changes occur. Some degeneracies are lifted by the spin-orbit splitting, which is found to be of the order of 5 mRyd in the case of VC and of the order of 10 to 20 mRyd in the case of NbC.

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Figure 4 Band structure of TiN, calculated by means of the full-potential LAPW method. The energy (Ryd) refers to the mean value of the potential in the region between the atomic spheres as energy zero. The Fermi energy, indicated by a horizontal line, is at 0.77582 Ryd. (From Ref. 58.)

Figures 5 and 6 show the band structures of ZrC and ZrN, respectively. The band structures are similar to those of TiC and TiN. One can recognize the s band (originating from the state Γ1), the p bands (originating from the state Γ15), and the d bands (originating from the states Γ′25 and Γ12). The M-s band, which lies above the d bands in the 3d compounds, is found to lie in ZrC and ZrN at much lower energies. The states of the bands at higher energies are highly delocalized and represent a mixture of different symmetries. In addition to the band structure calculations for NbC and NbN already mentioned, LMTOASA band structure calculations for NbC are available from Rajagopalan et al. (62) and for NbN from Palanivel et al. (63). The electronic structure and other electronic properties, such as the superconducting transition temperature, of NbN (and also VN, TaN, CrN, MoN, and WN) were calculated by Papaconstantopoulos et al. (64). The band structures of NbC and NbN are principally analogous to the structures of the monocarbides and mononitrides discussed previously. The band structure of NbN for two different crystal structures, namely the hexagonal and the NaCl structure, was calculated by Alekseev and Tatarchenko (65) using the LMTO method. From their calculations it follows that NbN in the hexagonal structure has semimetallic properties, whereas in the NaCl type structure it has metallic ones. D.

Densities of States and Partial l-like Densities of States for the Stoichiometric Monocarbides and Mononitrides of Ti, V, Zr, and Nb

The density of states (DOS) is defined as the number of electron states in a unit interval of energy per unit cell and can be computed by a simple histogram technique. As this procedure

Figure 5 Band structure and density of states, N(E ), of ZrC. The energy scale is shown twice: to the left in Ryd with respect to the muffin-tin zero V 0, to the right in eV with respect to the Fermi energy E F. N(E ) is given in states of both spin directions per Ryd and unit cell. (From Ref. 54. Reproduced with the permission of the Springer Verlag,  Springer Verlag.)

Figure 6 Band structure and density of states, N(E ), of ZrN. The energy scale is shown twice: to the left in Ryd with respect to the muffin-tin zero V 0, to the right in eV with respect to the Fermi energy E F. N(E ) is given in states of both spin directions per Ryd and unit cell. (From Ref. 54. Reproduced with the permission of the Springer Verlag,  Springer Verlag.)

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requires the calculation of the energy eigenvalues for a great number of k points, more efficient techniques have been devised, such as schemes involving gradients (66) or the more commonly used tetrahedron method (67). An LCAO interpolation scheme, following Slater and Koster (68), was applied because in the early APW calculations for TiC, TiN, VC, and VN (17–19) and for NbC and NbN (55,56) the energy eigenvalues could be calculated for only a limited number of k points. Starting from the X-s, X-p, and M-d orbitals as basis functions, the necessary interaction integrals in the LCAO scheme were determined by a nonlinear least squares fit to APW energies. Having determined the LCAO interaction integrals, the energy eigenvalues for the states being derived from the corresponding basis functions for a great number of k points can be computed. Later (69,70), the basis of the LCAO interpolation scheme was extended to include M-s and M-p functions and applied to ScN, ScP, TiN, and ZrN. Klein et al. (71) also used an LCAO interpolation scheme with an extended basis set to calculate energy eigenvalues for NbC, HfC, and TaC. With the advent of the computationally much faster linearized methods, the computation of reliable densities of states has become much easier. These techniques allow the calculation of energies for a great number of k points in an energy band. The DOS is then obtained by means of the tetrahedron method (67). Examples for DOSs are given in Figs. 5 and 6, which display the band structures of ZrC and ZrN, together with the corresponding DOSs, calculated on the basis of LAPW results (54) by means of the tetrahedron method (67). The band structure is reflected in the DOS. Typical for this class of compounds is the minimum in the DOS at the energy where the number of valence electrons per unit cell equals eight. Therefore, the Fermi energy, E F, for ZrC, which has eight valence electrons per unit cell, lies at this minimum, whereas for ZrN, which has one more valence electron, E F lies in the lower part of the Zr-d bands. For the discussion of the chemical bonding or for the interpretation of experimental results, e.g., X-ray emission or photoelectron spectra, partitioning the DOS into its components, corresponding to different angular momentum quantum numbers l, is very useful. Although in the LCAO interpolation scheme no wave functions appear, because only the interaction integrals are fitted, the modulus of each LCAO eigenvector component determines the weight with which the corresponding orbital contributes to the wave function of a given state. The partial l-like DOS can be obtained by weighting every state with the square of the modulus of the corresponding LCAO eigenvector component. In this way the DOS can be divided into partial l-like densities of state, g lt (E ). (The superscript t refers to the atom t on which the corresponding orbital is centered). The partial l-like density of states specifies the number of electron states corresponding to the angular momentum quantum number l per unit energy interval and unit cell. In the band structure methods that use the concept of an atomic sphere (muffin-tin sphere), a wave function in an atomic sphere is represented by the product of a radial function and an angle-dependent function Y ml (spherical harmonic). By weighting the total DOS by the square of the contribution of the partial functions with a specific l value to the total wave function of each state, a local (site projected) l-like partial DOS is obtained. The total DOS, g(E ), is thus spatially divided according to g(E ) ⫽ gout (E ) ⫹

冱 g (E ) t l

(1)

t, l

into local partial l-like DOSs, g tl (E ), corresponding to the atomic sphere t. The g out (E ) is the contribution of the interstitial space between the muffin-tin spheres. If a transition metal is octahedrally coordinated by the ligands (nonmetal atoms) X, the d electron states of the transition metal atom are split into orbitals (dxy, dxz, d yz) of t2g symmetry and orbitals (d z2 , d x2⫺y 2) of eg symmetry. Correspondingly, the partial d-like DOS can be split into a t2g and an eg component. The partial t2g- and eg-like DOSs are valuable for a discussion of the chemical bonding.

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The LCAO partial l-like DOSs for the compounds TiC, TiN, VC, and VN are displayed in Figs. 7 and 8. From these diagrams it can be gathered—as already discussed in the context of the band structures—that the energetically low-lying X-s band exhibits nonmetal s character. In passing from the carbides to the nitrides, this band is energetically lowered and becomes noticeably narrower, indicating an increased localization of the wave functions of these states at the nonmetal atom site. Separated from the X-s band by an energy gap and extending to the minimum of the DOS, the X-p bands follow. As can be seen from the partial l-like DOSs, the crystal wave functions of the states of the X-p bands exhibit not only X( p) symmetry but also M(d ) symmetry. This is demonstrated by the strong contribution of a partial d-like DOS. Above the minimum of the DOS the M-d bands are found, in which the M(d )-like DOS is predominant but which also contain a small contribution of X( p)-like DOS. Figures 9 and 10 exemplify the partition of the LCAO partial d-like DOS into its components of t 2g and eg symmetry. In the X-p bands of TiC, VC, and VN the eg component is somewhat smaller than the t2g component, whereas in TiN the opposite behavior is found. In the M-d bands the t 2g component predominates in all compounds. With increasing number of valence electrons in the sequence TiC–TiN, VC– VN the Fermi energy is shifted to higher energies in the M-d bands. The partial l-like DOSs of the M-4s band are not included in these figures. A similar situation is encountered for NbC and NbN. The LCAO partial l-like DOSs, shown in Fig. 11, for these two compounds were calculated by Schwarz (55,56). The X-s band is lowered in energy going from the carbide to the nitride. In the X-p bands (between 0.25 and 0.65 Ryd), in which the X( p)-like DOS prevails, a considerable contribution of Nb(d )-like DOS is found for NbC, which is significantly reduced in NbN. At higher energies the Nb(d )-like DOS predominates. The LAPW total and local partial l-like DOSs for TiC and TiN are displayed in Figs. 12 and 13. Figure 14 shows the partition of the LAPW local partial d-like DOSs of TiC and TiN into the t2g and eg manifolds, respectively (4,72). There exist some differences between the

Figure 7 LCAO partial l-like densities of states, g tl (E ), in units of states of both spin directions per Ryd and unit cell for TiC (top) and TiN (bottom). The energy (Ryd) refers to the muffin-tin zero V 0 of the APW calculation. Dotted curves, g Xs (E ); broken curves, g pX(E) (with X ⫽ C, N); full curves, g Tid (E ). (From Refs. 17 and 18. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

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Figure 8 LCAO partial l-like densities of states, g tl (E ), in units of states of both spin directions per Ryd and unit cell for VC (top) and VN (bottom). The energy (Ryd) refers to the muffin-tin zero V 0 of the APW calculation. Dotted curves, g Xs (E ); broken curves, g Xp (E ) (with X ⫽ C, N); full curves, g Vd (E ). (From Refs. 17 and 18. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

Figure 9 Partition of the LCAO partial d-like DOS, g Tid (E ), into the components with t 2g (full curves) and e g (broken curves) symmetry for TiC (top) and TiN (bottom) in units of states of both spin directions per Ryd and unit cell. (From Refs. 17 and 18. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

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Figure 10 Partition of the LCAO partial d-like DOS, g Vd (E ), into the components with t 2g (full curves) and e g (broken curves) symmetry for VC (top) and VN (bottom) in units of states of both spin directions per Ryd and unit cell. (From Refs. 17 and 18. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

Figure 11 LCAO partial l-like DOS, g tl (E ), in units of states of one spin direction per Ryd and unit cell for NbC (top) and NbN (bottom). Dotted curves, g Xs (E ); broken curves, g Xp (E ) (with X ⫽ C, N); full curves, g Nb d (E ). The energy (Ryd) refers to the muffin-tin zero of the original APW calculation. (From Ref. 56. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

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Figure 12 LAPW total, g(E ), and local partial l-like densities of states, g tl (E ), for TiC in units of states of both spin directions per Ryd and unit cell, calculated by means of the full-potential LAPW method. g(E ),———; g Cs (E ),⋅ ⋅ ⋅ ⋅; g Cp (E ),---; g Tid (E ),-⋅-⋅-.(From Ref. 58.)

Figure 13 LAPW total, g(E ), and local partial l-like densities of states, g tl (E ), for TiN in units of states of both spin directions per Ryd and unit cell, calculated by means of the full-potential LAPW method. g(E ),———; g Ns (E ),⋅ ⋅ ⋅ ⋅; g Np (E ),---; g Tid (E ),-⋅-⋅-.(From Ref. 58.)

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Figure 14 Partition of the LAPW local partial d-like DOS, g Tid (E ), into the components with t 2g (full curves) and e g (broken curves) symmetry for TiC (top) and TiN (bottom) in units of states of both spin directions per Ryd and unit cell. (From Ref. 72. Reproduced with the permission of Prof. P. Blaha, Techn. University of Vienna.)

LCAO partial l-like DOSs and the LAPW local partial l-like DOSs (4), because the LCAO partial l-like DOSs refer to the whole unit cell, whereas the LAPW local partial l-like DOSs refer to specific muffin-tin spheres. As an example of this difference, the partition of the d-like DOS of TiC in the range of the p bands may be mentioned. According to the LCAO calculation the t 2g component of the partial d-like DOS is higher than the eg component, as can be inferred from Fig. 9. However, the local partial t 2g-like DOS obtained by means of the LAPW method is smaller than the eg component, as can be gathered from Fig. 14. E.

Bonding Mechanisms for the Stoichiometric Monocarbides and Mononitrides of Ti, V, Zr, and Nb

The exceptional combination of properties that is a characteristic feature of this class of compounds has its root in the bonding mechanism. The electronic structure calculations reveal that all three main types of chemical bonding (ionic, covalent, and metallic) occur in these substances. 1. Charge Distribution From band structure calculations utilizing the muffin-tin approximation, the distribution of the charges of the valence electrons over the muffin-tin spheres and the interstitial region between t the spheres can be calculated: qout is the charge in the interstitial region, q tot the total charge t residing in the muffin-tin sphere t, and the partition of q tot yields the local (inside muffin-tin

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sphere t) partial (l-like) charges q lt. The partial charges thus defined satisfy the following equation: N val ⫽ q out ⫹

冱q

t tot

⫽ q out ⫹

t

冱冱q t

t l

(2)

l

where N val is the total number of valence electrons. A systematic comparison in terms of the valence electron charge distribution for the eight compounds ZrC, ZrN, NbC, NbN, TiC, TiN, VC, VN was performed by Schwarz et al. (54) and is presented in Tables 1 and 2. Such a comparison provides insight into the charge transfer and, consequently, into the ionic bonding component. Each type of the considered energy bands contains N b electrons: the X-s bands 2, the X-p bands 6, and the M-d bands (N val ⫺ 8) electrons. To establish a common basis for the comparison, all partial charges have been normalized, according to q¯ lt ⫽ q lt /N b

(3)

where q¯ t represents the charge contribution corresponding to one electron in that band. For the X-s band the values of the total charges q¯ t, and for the X-p and the M-d bands, only the values of q¯ tl for the most important components are listed. The lattice constants decrease monotonically in the sequence of the compounds in Table 1, and, as a consequence, there is a great variation in the unit cell volume, Ω, and in the volumes of the three different regions of the unit cell, as listed at the bottom of Table 1. To account for these variations a mean l-like valence electron density, f lt, per valence band and valence electron has been defined f lt ⫽ q¯ lt /Ω t

(4)

Table 1 Local Partial APW Charges, q¯ tl , According to Eqs. (2) and (3) in Percent a M(4d )X Compound N val d-bands

p-bands

s-band

˚) a(A Ω M(a3 0) ΩX Ω out Ω

M(3d )X

ZrC

ZrN

NbC

NbN

TiC

TiN

VC

VN

8

9

9

10

8

9

9

10

M d X p out

q¯ (39) (27) q¯ (28) q¯ 23 q¯ dM 39 q¯ pX q¯ out 31 M 14 q¯ tot X 65 q¯ tot q¯ out 21 4.685

41 23 30 16 50 26 11 75 14 4.585

41 27 25 28 33 31 15 62 23 4.471

48 23 24 21 46 27 11 73 16 4.400

26 40 28 12 65 23 4.328

60 14 22 17 53 24 9 76 15 4.242

62 17 17 32 35 27 13 62 25 4.182

68 13 16 20 50 24 8 75 17 4.140

61.8 32.3 79.6

60.2 28.8 73.6

52.6 28.8 69.4

52.0 26.2 65.5

41.3 30.8 64.7

40.4 27.8 60.5

37.8 27.4 58.2

37.3 26.2 56.5

173.7

162.6

150.8

143.7

136.8

128.7

123.4

120.0

˚ ); Ω, volume of the unit cell and its N val , number of valence electrons in the respective band; a, lattice constant (in A partition into the volumes of the metal sphere, Ω M, the nonmetal sphere, Ω X, and the region outside the spheres, Ω out. All volumes in atomic units (a 0)3. Source: From Ref. 54. Reproduced with the permission of the Springer Verlag,  Springer Verlag. a

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Table 2 Local Partial APW Electron Densities, f tl , According to Eq. (4) in Units of 10⫺4 Electrons per Atomic Unit (a 0) 3 M(4d )X Compound N val d-bands

f f f

p-bands

s-band

˚) a(A

M d X p out

f dM f pX f out M f tot X f tot out f

M(3d )X

ZrC

ZrN

NbC

NbN

TiC

TiN

VC

VN

8

9

9

10

8

9

9

10

(63) (84) (35) 37 121 39 23 201 26 4.685

68 80 41 27 174 35 18 260 19 4.585

78 94 36 53 115 45 29 215 33 4.471

92 88 37 40 176 41 21 279 24 4.400

63 130 43 30 211 36 4.328

148 50 36 42 191 40 22 273 25 4.242

164 62 29 85 128 46 34 226 43 4.182

182 50 28 54 191 42 21 286 30 4.140

Source: From Ref. 54. Reproduced with the permission of the Springer Verlag,  Springer Verlag.

In order to reveal the main trends in the chemical bonding from Tables 1 and 2, the figures in these tables have been analyzed (54) according to three points of view: 1. Changes in passing from the carbide MC to the nitride MN. In the nonmetal sphere, the charges q¯ Xtot in the X-s band as well as the charges q¯ Xp in the X-p bands increase, whereas the charges q¯ dM and q¯ out in the X-p bands decrease. This behavior indicates a higher degree of localization and a reduced interaction between the X-p and M-d states within the N sphere. In the M-d bands the opposite effect is observed: the charges q¯ Xp are diminished, whereas the charges q¯ dM are slightly increased, indicating a reduction of the X( p)-M(d ) interaction. 2. Changes in passing from M(n,d)X to M(n,d ⫹ 1)X (both metals in the same period of the periodic table). The charges q¯ dM in the X-p and M-d bands increase only slightly. Because the volumes Ω M decrease, the mean electron densities f dM increase more strongly. This effect reflects the stronger localization of the M(n,d ⫹ 1) wave functions. The values for the charges q¯ pM remain almost constant in the M-d bands, whereas they decrease in the X-p bands. This decrease goes parallel with the reduction of the volumes Ω X, yielding nearly constant values for f Xp. 3. Changes in passing from M(3d)X to M(4d)X. The most pronounced changes are observed in the M-d bands. The charges q¯ dM and—to a much higher extent due to the larger volumes Ω M —the mean electron densities f Md decrease. This effect is caused by the greater delocalization of the 4d wave functions compared with the 3d wave functions. Furthermore, a stronger M(d )-X( p) interaction can be inferred from the fact that the corresponding q¯ Md and q¯ Xp (or f Md and f Xp values) are more similar in the case of the M(4d ) than of the M(3d ) compounds. 2. Radial Charge Densities: Charge Transfer An ionic contribution to the binding mechanism is caused by the transfer of electronic charge from one atom (muffin-tin sphere) to another one, resulting in an electrostatic contribution to the binding energy. A charge transfer can be defined only with respect to a suitable chosen

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reference state. Frequently, the spherically averaged radial electron density σ tsuperposed (r), obtained by the superposition of the atomic electron densities of the corresponding neutral atoms, placed on the positions of the atoms, is chosen as reference state. (σ tsuperposed (r) ⫽ 4πr 2 ρ¯ (r), where r is the distance from the center of atomic sphere t and ρ¯ (r) the spherically averaged electron dent sity). σ superposed (r) is often used as the initial density in an SC band structure calculation. The charge transfer density ∆σ t (r) is defined as the difference between the radial electron density, t (r), obtained from a self-consistent band structure calculation, and the superposed atomic σ crystal t (r), radial electron density, σ superposed t t ∆σ t (r) ⫽ σ crystal (r) ⫺ σ superposed (r)

(5)

In Fig. 15 the difference ∆σ t(r) is plotted versus the distance r from the center of the atomic sphere t for TiC, TiN, VC, and VN. R X and R M are the radii of the atomic spheres around the nonmetal X site and the metal M site, respectively. ∆σ t(r) is positive (except for a very small region near the atomic nucleus) in the nonmetal sphere, indicating an increase in electronic charge in this region of the crystal compared with the electronic charge in a hypothetical crystal of noninteracting neutral atoms, and negative in the metal sphere. The total amount of transferred electronic charge, ∆Q t , obtained by integrating ∆σ t(r) over the respective atomic sphere t according to Eq. [6] depends on the atomic sphere radius Rt, which is not uniquely defined. ∆Q t ⫽

冮

R

O

t

∆σ t(r′) dr′

(6)

However, as can be gathered from Fig. 15, for a different choice of the atomic sphere radii, R t, there will always be an increase of electronic charge within the nonmetal sphere and

Figure 15 The difference, ∆σ t (r), between the radial charge density of the crystal, σ tcrystal (r), and the superposed atomic radial charge density, σ tsuperposed (r), in the muffin-tin sphere t plotted versus the distance r from the center of the muffin-tin sphere t in atomic units [see Eq. (5)]. Full curves, nonmetal sphere; broken curves, metal sphere. R X and R M are the radii of the respective muffin-tin spheres around the nonmetal atom X (X ⫽ C, N) and around the metal atom M (M ⫽ T, V), respectively. (From Refs. 18 and 19. Reproduced with the permission of the Berichte der Bunsen-Gesellschaft,  Berichte der BunsenGesellschaft.)

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a decrease within the metal sphere, compared with the hypothetical crystal of noninteracting neutral atoms. Values for the charge transfer ∆Q t (in electrons per atomic sphere) based on the atomic sphere radii used by Neckel et al. (17,18) and Schwarz (55) are listed in Table 3. The charge transfer is about the same for all compounds of the group of substances considered and does not follow the simple electronegativity rules, from which a higher charge transfer, ∆Q t, in the nitrides MN than in the carbides MC would be expected. However, a complex mechanism is responsible for the actual charge transfer. The higher electronegativity of the nitrogen atom causes a stronger localization of the 2p states of the nitrogen atom. This effect should cause an increase of charge in the nitrogen sphere. In the metal sphere two opposite effects occur: the Fermi energy is shifted to higher energies in the range of the d bands on passing from the carbide MC to the nitride MN. Therefore, the additional electron of the nitrogen atom occupies states in the d bands, whose wave functions are localized predominantly in the metal sphere, leading to an increase of charge, q Md,d bands , in the metal sphere in the range of the d bands. On the other hand—due the lower energy and to the higher localization of the 2p states of the nitrogen atom—the N( p)-M(d ) interaction is reduced, resulting in a decrease of the charge, M q d,p bands , in the metal sphere in the range of the p bands. This complex mechanism results in the charge transfer ∆Qt being about the same in the carbides and nitrides. 3. Valence Electron Densities Calculations of the valence electron densities (VEDs) by means of the LAPW method for TiC, TiN, and TiO (57), for TiC (73), and for VN (59,74), as well as by means of the FLAPW method for TiC and TiN (58), form the basis for an extensive discussion of the mechanism of chemical bonding in these substances. The theoretical electron densities (EDs) were compared Table 3 Charges and Charge Transfer in Different Regions of the Crystal for TiC, TiN, VC, VN, NbC, and NbN a Substance Metal sphere M Metal sphere radius R M Total APW charge Q Mcrystal Atomic superposed charge Q Mat ∆Q M ⫽ Q Mcrystal ⫺ Q Mat Nonmetal sphere X Nonmetal sphere radius R X Total APW charge Q Xcrystal Atomic superposed charge Q Xat ∆Q X ⫽ Q Xcrystal ⫺ Q Xat Region between the atomic spheres Total APW charge q out crystal Atomic superposed charge q atout out ∆q out ⫽ q out crystal ⫺ q at a

TiC

TiN

VC

VN

NbC

NbN

Ti 2.1444 19.8589 20.2164 ⫺0.3575 C 1.9449 5.8448 5.4118 0.4330

Ti 2.1290 19.8540 20.1782 ⫺0.3242 N 1.8789 6.9803 6.5235 0.4568

V 2.0807 20.9246 21.2137 ⫺0.2891 C 1.8706 5.6544 5.3018 0.3526

V 2.0722 20.8705 21.1482 ⫺0.2777 N 1.8394 6.8779 6.4718 0.4061

Nb 2.3244 38.846 39.125 ⫺0.639 C 1.9001 5.680 5.240 0.440

Nb 2.3146 38.499 39.075 ⫺0.576 N 1.8428 6.834 6.268 0.566

2.2963 2.3718 ⫺0.0755

2.1657 2.2983 ⫺0.1326

2.4210 2.4845 ⫺0.0635

2.2516 2.3800 ⫺0.1284

2.834 2.635 0.199

2.667 2.657 0.010

Q tcrystal, q out crystal , charge (number of electrons) in the muffin-tin sphere t and the region outside the muffin-tin spheres, respectively, in the crystal; Q tat , q out at , charge (number of electrons) in the muffin-tin sphere t and in the region outside the muffin-tin spheres, respectively, of a lattice with superposed, noninteracting neutral atoms; ∆Qt, charge transfer (number of electrons) in sphere t with respect to the superposed atomic charges (∆Q t ⫽ Q tcrystal ⫺ Q tat); ∆qout , charge transfer (number of electrons) in the region outside the atomic spheres with respect to the superposed atomic charges out (∆qout ⫽ q out crystal ⫺ qat ); R t , radius of the muffin-tin sphere t (au). Source: Data from Refs. 17, 18, and 55. Reproduced with the permission of the Institute of Physics Publ.

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Figure 16 Valence electron densities (VEDs) of TiC, TiN, and VN in the (110) plane. (a) Theoretical ˚ 3. Labeled contour lines must be divided VEDs; (b) experimental VEDs. Contour intervals 0.2 electron/A by 10 to obtain electrons per cubic angstrom. The end points of the plots correspond to 0, 0, 0; 0.5, 0.5, 0; and 0, 0, 1. (From Ref. 74. Reproduced with the permission of Academic Press, Inc.,  Academic Press, Inc.)

with experimental ones for TiC and TiN (75) and VN (76), obtained from X-ray diffraction measurements. For this comparison, however, the experimental data had to be refined. The sample of titanium carbide investigated had the composition TiC 0.94 with 6% vacancies. Further˚ had to be more, a static displacement of the Ti atoms adjacent to the vacancies by about 0.1 A considered. Dunand et al. (75) and Kubel et al. (76) developed a model that takes into account various factors and permits an extrapolation of the raw X-ray data to those of an ideal crystal. Good agreement between the theoretical and the extrapolated VED has been found in general. In particular, the nonspherical electron density distribution around the metal sites and the density distribution around the nonmetal sites agree well, whereas the magnitudes of the 3d maxima

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Figure 17 VEDs in the (100) plane for TiC (left) and TiN (right). For the contour lines a logarithmic ˚ 3. (From Ref. 58.) grid has been used. x i ⫽ x 02i/3, x 0 ⫽ 0.2 e/A

were found to be higher in the experiment. A comparison between theoretical and (extrapolated) experimental VEDs of TiC, TiN, and VN in the (110) plane is presented in Fig. 16. It should be mentioned here that theoretical EDs provide much more information and therefore have an important advantage over experimentally determined EDs. Only the total ED is experimentally available, whereas through theory the total ED can be partitioned into the contributions from respective energy bands. The results obtained in these investigations for the VEDs of TiC, TiN, TiO, and VN are visualized in Figs. 17 and 18 and can be summarized as follows: 1. The VED around the nonmetal sites is essentially spherically symmetric, as expected for p states in an octahedral crystal field, which does not lift the degeneracy of the

˚ ⫺3 (numbers are in these Figure 18 (Left) VED of TiO in the (100) plane. Contour intervals 0.1 e/A ˚ 3. (From Ref. 57. Reproduced with the units). Note the cutoff for the VED of the O atom at 1.7 e/A permission of John Wiley & Sons, Inc.,  John Wiley & Sons, Inc.) (Right) VED of VN in the (100) ˚ 3. Labeled contours must be divided by 10 to obtain electrons per cubic plane. Contour intervals 0.2 e/A ˚ 3. (From Ref. 59. Reproduced with the angstrom. Note the cutoff for the VED of the N atom at 3.0 e/A permission of the American Physical Society,  American Physical Society.)

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p states. The three 2p orbitals ( px , py, pz ) are equally occupied. The VED increases from the carbide to the nitrides. (Note the cutoff of the VEDs for the O and N atom in Fig. 18.) The VED around the metal atom site remains about constant in the cases of TiC and TiN but increases in VN. 2. The octahedral crystal field at the metal site splits the d orbitals into t 2g- and e g-type orbitals. Therefore, the contribution to the VED caused by the d orbitals can also be partitioned into a t 2g- and e g-like component. The t 2g (dxy, d xz, d yz) orbital lobes point toward the nearest metal atoms and consequently the t 2g-like VED shows maxima in these directions in the vicinity of the atomic position. The e g (d x2⫺y2 , dz2) orbital lobes point toward the nearest nonmetal neighbours, causing maxima in the e g-like VED in the directions to nearest nonmetal atoms. The VED around the metal sites deviates from spherical symmetry. Most remarkable is the change in the symmetry of the nonspherical component in the series TiC, TiN, TiO, VN (TiO is included here in the discussion, because it allows a clear recognition of the trend caused by changing the nonmetal atom). As can be gathered from Figs. 17 and 18, which present the VEDs in the (100) plane, the e g-like VED prevails in TiC. In TiN a slight excess of t 2g-like VED can already be observed, whereas in VN, as well as in TiO, the t 2g-like component predominates. The VEDs for the four compounds MX (with M ⫽ Zr, Nb and X ⫽ C, N) have been calculated by Schwarz (4), again using the LAPW method. The main difference between the 4d metals (Zr, Nb) and the 3d metals (Ti, V) is the existence of an additional nodal surface in the VED of the former, leading to a spatially more diffuse electron density distribution. The VED in the interstitial region in the crystal is relatively high, as can be seen from Fig. 19, where the valence electron density ρ(r) for TiC, ZrC, and NbC (4) is plotted along the [100] direction (the direction between next-nearest neighbors) and the [110] direction (the direction between nearest atoms of the same kind). The additional node in the radial wave function in the case of the 4d metals (Zr,Nb), compared with the 3d metals, can be clearly seen. Otherwise, the VEC in the interstitial region is nearly the same. From this fact and the nonvanishing DOS at the Fermi energy (see Sec. II.D), the presence of a metallic bonding component can be inferred. 4. Covalent Bonding The covalent bonding component is of essential importance for the understanding of the bonding mechanism. The local partial l-like charges and the partial l-like DOSs allow only a rough estimate of this bonding component. Much more detailed information can be obtained from valence electron densities (VEDs) and the VEDs of special states. The simple molecular orbital (MO) concept for diatomic molecules can be applied to describe the covalent bonds between adjacent atoms in the crystal. By a linear combination of atomic orbitals (LCAO) on neighboring atoms, bonding or antibonding MOs can be constructed. Applying this description to the case of the transition metal carbides and nitrides, several types of covalent bonds can be formed. The transition metal atoms participate in covalent bonds mainly by their d electrons, which are split by the octahedral crystal field, generated by the nearest nonmetal neighbours, into the t 2g and the eg manifold. To illustrate the various types of covalent bonds occuring in transition metal carbides and nitrides, Herzig et al. (58) selected, in the band structures of TiC and TiN, representative k points that are characterized by a particular type of covalent interaction in more or less pure form. For the selected states, VEDs were computed using the results of full-potential LAPW band structure calculations. Each of Figs. 20–26 shows, in the top panel, a schematic representation of a special bond type and, in the bottom panel, the VED in a definite crystal plane for a

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Figure 19 Total valence electron density, ρ(r), in the [100] direction from the carbon atom C to the metal atom M (M ⫽ Ti, Zr, Nb) and in the [110] direction between the metal atoms (full curves) and the carbon atoms (broken curves). (From Ref. 4. Reproduced with the permission of Critical Reviews in Solid State and Materials Sciences, CRC Press LLC.,  Critical Reviews in Solid State and Materials Sciences, CRC Press LLC.)

selected state that contains this particular type of bond. [The states are characterized by their energy and their main components of the local partial l-like charges, q t l, in the respective atomic spheres, t, in percent. For the contour lines in the VED plots a logarithmic grid is used. Each third contour line corresponds to a doubling of the electron density. In the schematic representation of the atomic orbitals positive and negative regions of the orbitals are distinguished by their tint. Figures 20–26 are taken from Herzig et al. (58).] In order to obtain the required cubic symmetry of the VED the sum over the star of k has to be formed. It cannot be avoided that some of the chosen k points also contain other types of covalent bonds besides the considered one. To reduce this ‘‘mixing’’ of bond types as far as possible, in some cases the cubic crystal has been considered as artificially tetragonal to separate orbitals in the xy plane from those in the xz and yz planes. (The legends to the figures for the VEDs indicate whether the crystal has been considered as cubic or as artificially tetragonal.) As already discussed by Neckel et al. (19), three main types of covalent bonds can be distinguished in the transition metal monocarbides and mononitrides. The orbital lobes of the transition metal e g orbitals (d x2⫺y2 , dz2) point toward the neighboring nonmetal atoms. These orbitals can form pd σ bonds with 2p orbitals of the neighboring nonmetal atoms. This bond type is depicted in Fig. 20, which shows the interaction of a metal d x2⫺y2 orbital (center) with px and py orbitals, respectively, of neighboring nonmetal atoms. The orbital lobes of the t 2g orbitals (dxy, d xz, d yz) extend toward the neighboring metal atoms. These orbitals can form pd π bonds with 2p orbitals of neighboring nonmetal atoms. Figure 21 shows the interaction of a metal d xy orbital (center) with px and py orbitals of neighboring nonmetal atoms.

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Figure 20 (Top) Schematic representation of the formation of pd σ bonds in the (001) plane by the interaction of a transition metal d x 2⫺y 2 orbital (center) with px and py orbitals of neighboring nonmetal atoms. (Bottom) VED for the state N (tetragonal description, corresponds to L′ 3 in cubic description), at 0.42722 Ryd (occupied), in the (001) plane of TiC. q tl: 37.9% C( p), 36.4% Ti(d ). (From Ref. 58.)

The t 2g orbitals can also form dd σ bonds with the t 2g orbitals of the nearest metal atoms. This bond type is represented in Fig. 22, which shows metal (d xy)–metal (d xy) σ bonds. A similar illustration of the three main types of covalent bonds by VED plots has been given by Schwarz and Blaha (22). Besides these main types of covalent bonds, other covalent interactions can occur, which probably play a minor role. Some of the possible types are mentioned in the following. Inspection of the local partial l-like DOSs shows that in the nonmetal s band states occur that have simultaneously nonmetal s and a small amount of metal e g (d x2⫺y2 , d z2) character. From this fact it can be concluded that in the energy range of the nonmetal s band sdσ bonds occur. To illustrate this type of interaction, in Fig. 23 sd σ bonds between a metal d x2⫺y2 orbital (center) and the s orbitals of neighboring nonmetal atoms are shown. The d orbitals of the transition metal atoms can participate in different types of metal-

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Figure 21 (Top) Schematic representation of the formation of pd π bonds in the (001) plane by the interaction of a transition metal d xy orbital (center) with p x and p y orbitals of neighboring nonmetal atoms. (Bottom) VED for the state ⌺ 3 (cubic description), at 0.55980 Ryd (occupied), in the (001) plane of TiC. q tl : 25.2% C( p), 1.4% C(d ), 1.7% Ti( p), 38.1% Ti(d ). (From Ref. 58.)

metal bonds. The d z2 orbital of a metal atom can interact with the d z2 orbitals of neighboring metal atoms in the (110) and (110) planes, respectively, to form metal (d z2)–metal (d z2) σ bonds as shown in Fig. 24. Also metal-metal π bonds can be formed. Figure 25 shows the interaction of d x2⫺y2 orbitals of neighboring metal atoms in the (001) plane leading to metal (d x2⫺y2)–metal (d x2⫺y2) π bonds. In a similar way the d z2 orbitals of neighboring metal atoms in the (100) and (010) planes can interact forming π-like bonds as depicted in Fig. 26. Other types of covalent bonds, e.g., δ bonds, and bonds involving metal s and p orbitals, can also be imagined. Not all of the bond types mentioned are found in the occupied energy range. 5. Discussion of the Bonding Mechanism The discussion of the bonding mechanism in this section is based on TiC, TiN, TiO, and VN as representative examples. Inspection of the partial l-like DOSs and of the partition of the

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Figure 22 (Top) Schematic representation of the formation of dd σ bonds in the (001) plane by the interaction of a transition metal d xy orbital with d xy orbitals of neighboring transition metal atoms. (Bottom) VED for the state Γ′25 (tetragonal description, corresponds to Γ′25 in cubic description) at 0.72835 Ryd (occupied), in the (001) plane of TiN. q tl: 2.3% N(d ), 71.9% Ti(d ). (From Ref. 58.)

partial l-like charges into the contributions of the respective energy bands shows that, in the p bands, the X( p)-like charge prevails and the M(d )-like charge is the minor component. In the d bands the opposite situation is encountered. Such behavior is to be expected when a covalent X( p)-M(d ) interaction is present. In the simple MO description of heteronuclear diatomic molecules MX two atomic orbitals of appropriate symmetry form a bonding and an antibonding MO. The bonding orbital tends to concentrate on the atom with the lower energy orbital, in the present case the X-2p orbital. The antibonding MO tends to resemble the higher energy atomic orbital, in the present case the M3d orbital. The energy separation between the M-3d orbital and the X-2p orbital increases in the sequence X ⫽ C, N, O (keeping M constant), leading to a diminishing M(d )-X( p) interaction and consequently to an increase of the X-2p character [X(2p)-like charge] and to a decrease of the M-3d character [M(3d )-like charge] in the bonding MO. In the antibonding MO the opposite

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Figure 23 (Top) Schematic representation of the formation of sd σ bonds in the (001) plane by the interaction of a transition metal d x 2⫺y 2 orbital (center) with s orbitals of neighboring nonmetal atoms. (Bottom) VED for the state X (tetragonal description, corresponds to X 1 in cubic description) at ⫺0.08921 Ryd (occupied), in the (001) plane of TiC. q tl : 60.3% C(s), 1.2% Ti(s), 12.4% Ti(d ). (From Ref. 58.)

behavior is observed. From this point of view, the characteristic minimum in the DOS, which always occurs at approximately eight valence electrons, could be regarded as separating the bonding from the antibonding X( p)-M(d ) interactions. The strongest X( p)-M(d ) interactions are found in TiC, because the atomic orbitals involved have nearly equal energies and the wave functions overlap effectively. The X( p)-M(d ) interactions decrease passing to TiN and further to TiO. In VN these interactions are slightly stronger than in TiN. This behavior can be understood if one takes into account that the V-3d orbitals lie about 0.8 eV lower than the Ti-3d orbitals and are therefore energetically nearer to the N-2p orbitals. For a closer examination of the types of covalent bonds occurring in the p and d bands, respectively, not only the partition of the partial d-like DOS into the e g and t 2g components but also the partial l-like charges as well as the VEDs have to be considered.

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Figure 24 (Top) Schematic representation of the formation of dd σ bonds in the (110) plane by the interaction of a transition metal d z2 orbital with d z2 orbitals of neighboring transition metal atoms in the same (001) plane. (Bottom) VED for the state Γ 12 (tetragonal description, corresponds to Γ 12 in cubic description) at 0.81497 Ryd (0.03915 Ryd above E F ) in the (110) plane of TiN. q lt: 3.8% N(d ), 81.4% Ti(d ). (From Ref. 58.)

In TiC only the p bands are occupied and the p- and the d-like DOSs are of comparable size. Both the LCAO partial d-like DOSs (Fig. 9) and the LAPW local partial d-like DOSs (Fig. 14) show that the e g and the t 2g components are of almost equal magnitude (although the two schemes lead to somewhat different results, as mentioned in Sec. II.D). As can be gathered from Fig. 17, the maxima in the VED near the Ti atoms point toward the next nearest C neighbors, indicating the predominance of e g orbitals. From the partial e g-like DOS and from the clear e g-like VED it can be concluded that pd σ bonds prevail. In TiC only the states that correspond to bonding pd σ bonds are occupied, whereas all antibonding pd σ states remain empty. The occurrence of the t 2g component leads to the assumption that pd π and some dd σ bonds are also present. In the p bands of TiN the partial d-like DOS is reduced compared with TiC. The e g component is somewhat higher than the t 2g component. The occurrence of pd σ bonds has, therefore, to be assumed. The t 2g states will form predominantly pd π bonds because many N-2p states are available in the p bands. In the occupied range of the d bands the partial d-like DOS has exclusively t 2g character. Because the number of N-2p states is small in this energy range, mainly

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Figure 25 (Top) Schematic representation of the formation of dd π bonds in the (001) plane by the interaction of a transition metal d x2⫺y2 orbital with d x2⫺y2 orbitals of neighboring transition metal atoms. (Bottom) VED for the state X (tetragonal description, corresponds to X 5 in cubic description) at 0.89386 Ryd (unoccupied), in the (001) plane of TiN. q tl: 3.1% N(d ), 87.4% Ti(d ). (From Ref. 58.)

dd σ bonds will be formed. The results of these considerations are confirmed by the VED of TiN (Fig. 17), which shows a slight excess of the t 2g-like component. In the p bands of TiO the admixture of partial d-like DOS is small, so very little pd bonding occurs. The main covalent bonding contribution is brought about by the dd σ bonds in the occupied range of the d bands. In the titanium compounds considered, the covalency decreases from the carbide to the oxide. The ionicity—actually the localization of the charge on the nonmetal atom—increases in that direction, whereby the charge transfer remains almost constant, as already discussed in Sec. II.E.2. The behavior of VN lies between that of TiC and that of TiN. A charge analysis (59) reveals that in the p bands 2.88 electrons with p symmetry are found in the N sphere and 1.30 electrons with d symmetry in the V sphere. From the latter 0.74 electrons exhibit e g character.

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Figure 26 (Top) Schematic representation of the formation of π-like transition metal (d z 2)–transition metal (d z 2) bonds by the interaction of transition metal d z 2 orbitals in the (100) plane. (Bottom) VED for the state Γ 12 (tetragonal description, corresponds to Γ 12 in cubic description) at 0.81497 Ryd (0.03915 Ryd above E F ) in the (100) plane of TiN. q tl:3.8% N(d ), 81.4% Ti(d ). (From Ref. 58.)

Accordingly, the e g component of the local partial d-like DOS predominates the t 2g component. From these facts the presence of pd σ bonds in the range of the p bands can be inferred. A small amount of pdπ bonding may also be present. In the occupied part of the d bands the local partial p-like DOS is small (0.24 p electrons in the N sphere). Only about 8% of the d electrons (1.35 d electrons in the V sphere) possess e g symmetry. This situation leads to the prevailing formation of dd σ bonds. In the total VED the contribution of the d bands predominates, so that the total VED has t 2g character, as can be seen from the VEDs in the (110) plane (Fig. 16) and in the (100) plane (Fig. 18). These conclusions concerning the bonding in VN are corroborated by an analysis of the VED (74). In Fig. 27 the total VED of VN is split into the contributions of the (s ⫹ p) bands (eight electrons) and the occupied part of the d bands (two electrons). In the (s ⫹ p) bands the VED has e g character (Fig. 27, bottom). The maxima near the V atom point toward the neighboring N

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˚ ⫺3. Figure 27 VEDs in the (100) plane of VN. (Note the cutoff of the VED for the N atom at 3.0 e/A (Top) Total VED; (middle) contribution of the occupied part of the d bands (two electrons); (bottom) contribution of the s and p bands (eight electrons). (From Ref. 74. Reproduced with the permission of Academic Press, Inc.,  Academic Press, Inc.)

atoms, indicating the presence of pd σ bonds. In the d bands (Fig. 27, middle), however, the maxima near the V atoms point toward the neighboring V atoms, indicating the presence of dd σ bonds. For the compounds ZrC, ZrN, NbC, and NbN a bonding situation qualitatively similar to that of the corresponding compounds with the 3d metals Ti and V can be expected for the p bands as judged by the partial charges (Table 1). This view is also supported by the calculated VEDs (4). Because the M-4d wave functions are more diffuse than the M-3d wave functions, the overlap with the X-2p wave functions will be more efficient and a stronger bonding M(d )X( p) interaction will result. In the d bands, however, the situation seems to differ from that with the M-3d compounds. The partial p-like charges q¯ Xp , and particularly the f Xp values (Tables 1 and 2), in the d bands are higher for the M-4d compounds, which leads to the assumption that the M(d )-X( p) interactions are stronger.

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6. Metallic Bonding Component From the nonvanishing DOS at the Fermi energy and from the relatively high electron density in the interstitial region between the muffin-tin spheres (see Sec. II.E.3), metallic behavior can be expected.

F.

Electronic Structure of the Stoichiometric Monocarbides and Mononitrides of Hf and Ta

1. Band Structures: Densities of States For the band structure calculations for the monocarbides and mononitrides of the transition elements Hf and Ta the application of relativistic methods is necessary, as demonstrated by Weinberger et al. (77,78). These authors used the self-consistent relativistic KKR method (27,28) to calculate the band structures of HfC and TaC (77) as well as those of HfN and TaN (78). Further band structure calculations for HfC and TaC (71,79) and TaN (64,80) have been reported in the literature. Total and local partial l-like DOSs for HfC and HfN were calculated by Schadler and Monnier (81) by means of the relativistic KKR-GF method. The same approach was used by Schadler et al. (82) to calculate the total and local partial l-like DOSs for TaC. As an example, the energy bands of HfC, obtained by Weinberger et al. (77), for the directions [111] (Γ-Λ-L), [100] (Γ-∆-X ), and [110] (Γ-⌺-K ) in the first BZ are displayed in Fig. 28. Also shown in this figure are the nonrelativistic bands in the direction [100] (Γ-∆-X ). In the following the notation l j (l, angular momentum quantum number; j, total angular momentum quantum number) is used, instead of the relativistic quantum number κ, to characterize an electron state. If both values of j, namely j ⫽ 1 ⫾ 1/2 , apply, the superscript in the symbol l j is dropped. The relativistic band structure of HfC is characterized by the following bands: a broad C-2s band, originating at the state Γ ⫹6 (⫺0.1496 Ryd); broad C-2p bands, originating at the states Γ 6⫺ (0.8533 Ryd); and Γ ⫺8 (0.8640 Ryd). The states of the C-2p bands contain, besides p character, an appreciable amount of d character (up to 20% of the charge of a state) due to the interaction between the C-2p and the Hf-5d orbitals. Originating at the states Γ ⫹8 (0.9892 Ryd), Γ 7⫹ (1.0083 Ryd), and Γ 8⫹ (1.2048 Ryd), the very broad Hf-5d bands follow. Most interesting is the fact that the Hf-4f 7/2 bands, originating at the states Γ ⫺6 (0.3852 Ryd), Γ ⫺7 (0.4010 Ryd), and Γ 8⫺ (0.4017 Ryd), cut through the C-2p bands in the [111] direction. The Hf-4f 5/2 bands, originating at the states Γ 8⫺ (0.2708 Ryd) and Γ 7⫺ (0.2721 Ryd), lie about 0.13 Ryd below the Hf-4f 7/2 bands. The Fermi energy lies at 0.8165 Ryd. A comparison of the relativistic and nonrelativistic band structures reveals that the relativistic C-2s and C-2p bands are much broader than the nonrelativistic ones. The relativistic Hf-4f 5/2 and Hf-4f 7/2 bands are split. The mean value of the f-like Γ 7⫺ states lies 0.149 Ryd below the energy of the corresponding nonrelativistic Γ 2⫺ state. The relativistic band structure of HfN (78) is characterized by a N-2s 1/2 band at the bottom of the valence band region. This band lies well below the very narrow Hf-4f bands. Above the Hf-4f bands, and nearly touching the Hf-4f 7/2 band, the N-2p bands are found. They are separated by a small indirect gap from the Hf-5d,6s band complex. The Fermi energy cuts through the Hf-5d bands. The relativistic band structure of TaC (77) is characterized by overlapping C-2p and Ta5d bands. The Ta-4f bands lie well below the C-2s band (Fig. 29). For TaN one has to bear in mind that the modification crystallizing in the NaCl structure is a metastable phase. In the phase diagram of the Ta-N system, two hexagonal phases exist near the equiatomic composition: ⑀-TaN, crystallizing with the CoSn structure, and δ-TaN, crystallizing with the WC structure.

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Figure 28 Self-consistent relativistic energy bands for HfC along the [111], [100], and [110] directions and nonrelativistic energy bands along the [100] direction in the first Brillouin zone. Fermi energy at 0.8165 Ryd. (From Ref. 77. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

⑀-TaN has the stoichiometric composition and no range of homogeneity, and δ-TaN exists in the composition range from TaN 0.8 to TaN 0.9 . The most significant feature of the relativistic band structure of B1 TaN is the overlap of the N-2s 1/2 band with the Ta-4f 5/2 band in the [111] and [110] directions of the first BZ. In this energy range there are states that exhibit s-like character in the N sphere and f 5/2-like character in the Ta sphere, indicating an interaction between the corresponding orbitals. At higher energies the N-2p bands are found, which touch a Ta-5d band at the X point. The Fermi energy lies slightly above the lowest states of the Ta-6s 1/2 band. 2. Radial Charge Densities: Charge Transfer Weinberger et al. (77) computed for HfC and TaC as well as for HfN and B1 TaN (78) the following quantities by means of the self-consistent, relativistic KKR method: (a) partial l j-like charges in a special atomic sphere P for selected electron states; (b) partial l j-like charges in a special atomic sphere P corresponding to the occupied region of the valence bands; (c) l j-like radial charge densities in a special atomic sphere P. From the large amount of information obtained in these calculations only a few points that are of special interest for the understanding of the bonding mechanism can be mentioned. From the listed partial l j-like charges of special states it can be seen that in HfC there is an f 5/2-like state with a significant s 1/2-like partial charge in the carbon sphere. Also, f 7/2-like states with some p-like partial charge in the carbon sphere can be found. From this fact it can be

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Figure 29 Self-consistent relativistic energy bands for TaC along the [111], [100], and [110] directions and nonrelativistic energy bands along the [100] direction in the first Brillouin zone. Fermi energy at 0.8749 Ryd. (From Ref. 77. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

concluded that f electrons take part, at least to a minor extent, in the chemical bonding. The l jlike radial charge densities, σ Pl j (r), in the metal and nonmetal spheres are displayed in Fig. 30 for HfC and in Fig. 31 for TaC. Furthermore, the difference between the self-consistent radial crystal charge density, σ P(r), and the relativistic radial charge density, σ Psuperposed (r), obtained by the superposition of the charges of the constituent atoms has been calculated and is displayed for HfC in Fig. 32 and for TaC in Fig. 33. By comparing Fig. 32 with Fig. 30 it can be seen that, in the Hf sphere of HfC, there is an increase of electronic charge, relative to the radial charge density of the superposed atoms, which is caused by Hf(s 1/2)-, Hf( p 1/2)-, and Hf( p 3/2)like charge densities. Charge is lost in the region where the d-like charges prevail. In total, these two contributions compensate each other so that the total charge in the Hf sphere remains almost constant. The charge in the C sphere of HfC increases by about 0.5 electrons. A similar situation is encountered in TaC, where only a small amount of charge (about 0.2 electrons) is lost in the Ta sphere and about 0.55 electrons are gained in the C sphere. The corresponding calculations for HfN and TaN yield similar results. The charge in the metal spheres remains almost constant compared with the charge obtained by the superposition of the charges of the neutral atoms, whereas the charge in the N sphere of HfN increases by about 0.52 electrons and in the N sphere

Figure 30 l j-like radial charge densities, σ lPj (r), for HfC within the Hf sphere (a, b) and the C sphere (c) plotted versus the distance r from the center of the respective muffin-tin sphere. RHf and RC are the atomic sphere radii of the Hf and the C sphere, respectively. The quantum number κ is replaced by the more familiar notation l j . (From Ref. 77. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

Figure 31 l j-like radial charge densities, σ lPj (r), for TaC within the Ta sphere (a, b) and the C sphere (c) plotted versus the distance r from the center of the respective muffin-tin sphere. R Ta and R C are the atomic sphere radii of the Ta and the C sphere, respectively. The quantum number κ is replaced by the more familiar notation l j . (From Ref. 77. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

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Figure 32 Differences between the total radial charge density, σ P (r), and the superposed relativistic P (r), within the Hf sphere (curve A) and the C sphere (curve B) for atomic radial charge density, σ superposed HfC plotted versus the distance r from the center of the respective sphere. (From Ref. 77. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

Figure 33 Differences between the total radial charge density, σ P(r), and the superposed relativistic P atomic radial charge density, σ superposed (r), within the Ta sphere (curve A) and the C sphere (curve B) for TaC plotted versus the distance r from the center of the respective sphere. (From Ref. 77. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

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of TaN by about 0.43 electrons. This insignificant loss of charge in the metal spheres is in contrast to the behavior of the first-row transition metal carbides and nitrides, where a larger loss of electronic charge is observed. The main contribution to the chemical bonding is provided by the nonmetal (2p)–metal (5d ) interaction in the range of the nonmetal p bands. Also, metal (5d )–metal (5d ) interaction can be expected, particularly in the Ta compounds. In addition to the binding components already mentioned, contributions to the chemical bonding result—particularly in the case of TaC— from interactions between nonmetal s states and metal s, p, and d states. G.

Electronic Structure of Tungsten Monocarbide WC

Tungsten monocarbide has been included in the present overview because its properties greatly resemble those of the fourth and fifth group transition metal monocarbides. Whereas the fourth and fifth group transition metal monocarbides (TiC, ZrC, HfC and VC, NbC, TaC) crystallize in the B1 structure, the monocarbides of the transition elements of the sixth group (Cr, Mo, and W) with B1 structure are scarcely stable. CrC does not exist. This fact was qualitatively explained by Zhukov et al. (6) and also follows from the analysis of thermodynamic parameters of metastable carbides by Guillermet and Grimvall (83). A molybdenum carbide phase (αMoC 1⫺x) with B1 structure shows a homogeneity range, large carbon deficiency (composition about MoC 0.7), and is stable only at temperatures above 1960°C. Tungsten monocarbide with B1 structure (β-WC) exists only at temperatures above about 2525°C and also exhibits substoichiometry. The stable modification of tungsten monocarbide, WC, at room temperature crystallizes l in a hexagonal structure (α-WC) with the space group symmetry D 3h (P6m2). This structure consists of alternating simple hexagonal layers of W and C atoms with the stacking sequence ABAB. . . . The nearest neighbor coordination of both the W and the C atom is trigonal prismatic, in contrast to the B1 structure, where each site is octahedrally coordinated. The structures of hexagonal WC and its first BZ are displayed in Fig. 34. Of special importance is the high catalytic activity of hexagonal WC for the chemical reactions that are usually catalyzed by Pt or Pd (84,85). Self-consistent, scalar relativistic energy band calculations for hexagonal WC in bulk and thin-film forms were performed by Mattheiss and Hamann (86) by means of the LAPW method.

Figure 34 (a) Crystal structure of hexagonal WC. (b) First Brillouin zone for the hexagonal translational lattice corresponding to the hexagonal WC structure. (From Ref. 91. Reproduced with the permission of the American Physical Society,  American Physical Society.)

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The band structure results for WC obtained by these authors agree qualitatively with those of previous studies (87,88). Zhukov and Gubanov (89) used the LMTO-ASA method, including the most important relativistic corrections, i.e., the Darvin and mass-velocity terms, to calculate the electronic structure of B1 and hexagonal WC [as well as of body-centered cubic (bcc) W and W 2 C]. Scalar-relativistic pseudopotential local orbital calculations (49,50) for cubic WC were carried out by Liu and Cohen (90) and for hexagonal WC by Liu et al. (91). The electronic structure of cubic and hexagonal WC was also investigated by Price and Cooper (60). These authors also performed similar calculations for TiC, crystallizing in the B1 structure, in the hexagonal WC structure, and in other prototype superlattice structures. The electronic structures of TiC and WC crystallizing in the cubic and the hexagonal modifications were compared. The main goal of these studies was to elucidate the role played by the two additional valence electrons of tungsten compared with titanium in stabilizing the different crystal structures. From the work of Zhukov and Gubanov (89) and Price and Cooper (60) it follows that the band structure of cubic WC shows the typical features of the band structures of the fourth and fifth group transition metal monocarbides. For cubic WC the Fermi energy is located in a region of the d bands, where antibonding C(2p)-W(5d ) states or W(5d )-W(5d ) bonds with either nonbonding or antibonding character prevail, tending to destabilize the B1 structure. Liu and Cohen (90) show that the instability of cubic WC arises from the occupation of antibonding states in the region of the d bands. The electronic structure of hexagonal WC shows a different behavior, as can be seen from the total DOS and the partial l-like DOSs (Fig. 35). The C-2s band (between ⫺14 eV and ⫺10 eV in Fig. 35) has preserved its shape and character. In the following peaks, up to about 2 eV below the Fermi level, the contributions from the C-2p and W-5d states are almost equal. In the next two peaks just below and above the Fermi energy the W-5d character predominates.

Figure 35 Total density of states of WC and the partial contributions to the density of states from orbitals of different angular symmetry centered on C and W sites (partial l-like DOSs). Energies are measured relative to the Fermi level, which is indicated by the dashed line. (From Ref. 91. Reproduced with the permission of the American Physical Society,  American Physical Society.)

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Most remarkable is the shift of some states from the d bands to lower energies. The eight C2p and W-5d bands are apparently split symmetrically in a bonding and an antibonding manifold. The Fermi energy lies at the minimum of the DOS, where eight valence electrons occupy the bonding states leaving the antibonding states unoccupied. The bonding states represent a mixture of states with C-2p and W-5d character, as can be concluded from the partial l-like DOSs (see Fig. 35). About half the energy bands at or below the Fermi energy have predominantly C-2p and W-5d character, respectively. This means that the valence charge is nearly equally distributed between the C and the W atom, leading to a net charge transfer from W to C, which, according to Liu et al. (91), amounts to about 1.4 electrons. In contrast to the transition metal monocarbides with B1 structure, where the bonding-antibonding C( p)-M(d ) bands are distributed in almost the same ratio (3 :5) as the atomic p and d states, the ratio of the bonding to the antibonding bands is 4 :4 in the case of hexagonal WC. In spite of the fact that the environment of a C or W atom is no longer octahedral in the hexagonal form, the C( p)-W(d ) interaction still persists. It can be assumed therefore that the strength and stability of hexagonal WC can also be attributed to the formation of strong CW bonds. Calculations of the VED (86,91) prove the existence of nearest neighbor CW bonds. The VEDs in the W and C planes do not indicate pronounced interplanar directional bonds but show a large background charge, especially in the W planes. Liu et al. (91) explained the bonding in hexagonal WC by stating that the addition of C atoms to bcc W generates strong WC bonds while leaving some metallic W bonding intact. The Fermi surface of hexagonal WC is that of a semimetal, consisting of small pockets of electrons and holes (86).

III. ELECTRONIC STRUCTURE OF NONSTOICHIOMETRIC TRANSITION METAL CARBIDES AND NITRIDES OF THE FOURTH AND FIFTH GROUPS OF THE PERIODIC TABLE WITH B1 STRUCTURE A.

Introduction

The cubic transition metal monocarbides and mononitrides exhibit wide homogeneity ranges corresponding to the composition MX x , where, for example in titanium monocarbide, x ranges from about 0.48 to about 0.99 depending on the temperature (92). Substoichiometry (x ⬍ 1) of these phases is caused by vacancies at the nonmetal subattice sites. Mononitrides may also contain several percent metal vacancies, e.g., TiN x , whose composition range extends from TiN 0.41 to TiN 1.08. For some nitrides vacancies exist on both sublattices (metal and nitrogen) even at the stoichiometric composition MN. The vacancies may be randomly distributed over the nonmetal sites of the B1 structure. Frequently, some short-range order between the nonmetal atoms and the vacancies occurs. However, one also encounters long-range-ordered vacancies forming a superlattice, e.g., V8 C 7 , Nb 6 C 5. A general overview of the defect structures and orderdisorder transformations in transition metal carbides and nitrides can be found in the review articles by de Novion et al. (93), de Novion and Landesman (94,95) and Gusev and Rempel (96). The vacancies affect the properties of the nonstoichiometric monocarbides and mononitrides (97) significantly. A remarkable feature of the defect structures is the occurrence of static displacements of the metal atoms adjacent to a nonmetal vacancy. Various experimental studies of these compounds, such as measurements of the Debye-Waller factors (98), elastic diffuse neutron scattering (93,99,100), ion channeling (101), extended X-ray absorption fine structure (EXAFS) (102), and X-ray diffraction measurements (75,103,104), have proved the existence of atomic static displacements. It has been found that the main displacement is always a shift of the neighboring ˚. metal atoms away from the vacancy by, typically, 0.05 A

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Theoretical Methods Applied for the Investigation of the Influence of Vacancies on the Electronic Structure of Transition Metal Carbides and Nitrides with B1 Structure

The remarkable effects caused by vacancies on the properties of carbides and nitrides have given rise to numerous experimental and theoretical studies. In the present overview we will concentrate on theoretical approaches only, although experimental results are imperative as a basis for testing theoretical models and methods. A complete list of references of computations on nonstoichiometric carbides and nitrides can be found in the book of Gubanov et al. (7). An essential problem in the theoretical investigations of the electronic structure of the substoichiometric materials is a proper description of the vacancy-containing phases. Various concepts and models have been devised to treat the vacancy problem. Essentially four different types of approaches can be distinguished. The influence of the vacancies on the electronic structure can be studied by means of cluster models, with vacancies replacing the central atom and/or ligand atoms. Because the metal-nonmetal interaction furnishes an essential contribution to the chemical bonding in the transition metal monocarbides and mononitrides, the occurrence of vacancies will affect mostly the electronic structure of the atoms that surround the vacancy. Cluster surface effects can be minimized by choosing the cluster size relatively large and by applying suitable boundary conditions (105–108). The cluster approach, in combination with the scattered wave Xα method, was used as early as 1976 by Schwarz and Ro¨sch (109) to study the electronic structure of NbC x . These authors chose a 䊐 C Nb 6 V12 Nb 8 cluster (䊐 C is the carbon vacancy) to model the effect of vacancies in NbC x. This cluster represents the first three coordination shells around a vacancy. Ries and Winter (110) applied a modification of the self-consistent multiple scattering Xα method to investigate the electronic structure of a nonmetal vacancy in NbC x and VN x . As a first step the electron density and the potential of a cluster having perfect order and consisting of 53 atoms with a nonmetal atom at its center were computed. The calculation was repeated for a cluster with a vacancy at the position of the central atom. By use of group theoretical means, these authors were able to treat clusters up to 200 atoms. The influence of vacancies in the nonmetal and in the metal sublattice on the electronic structure of TiC x and TiO x was studied by Gubanov et al. (111) by applying the discrete variational (DV) method (112) in the ‘‘embedded cluster’’ scheme (105,106). In these calculations the effect of a C vacancy was modeled by the cluster 䊐 C Ti 6 C 12 Ti 8 and that of a Ti vacancy in TiCx by the cluster 䊐 Ti C 6 Ti 12 C 8. The same approach was also used by Novikov et al. (113) to study the influence of various shifts of the Nb atoms surrounding the vacancy in a 䊐 C Nb 6 C 18 cluster. Kucherenko et al. (108) calculated the electronic structure of a 䊐 N Ti 6 N 12 cluster by means of the self-consistent scattered wave Xα-method. Cluster calculations taking into account the static displacements of the metal atoms surrounding the vacancy applying the ‘‘Complete Neglect of Differential Overlap, Version 2’’ (CNDO/2) method were performed for VN x by Ska´la and Cˇapkova´ (114) and for TiC x and TiN x by Cˇapkova´ and Ska´la (115). The main drawback of the cluster approach is its inability to yield well-defined valence bands. Calculations for smaller clusters may not be entirely free from cluster-surface effects, and the results for a system with only one vacancy may not be valid for substoichiometric compounds with many vacancies. The second approach involves conventional band structure calculation methods, assuming an ordered array of vacancies. Such calculations, which are based on extended unit cells containing one or more vacancies, allow the investigation of compounds with higher vacancy concentrations. Furthermore, the changes in interatomic interactions caused by the vacancies can be taken into account by the self-consistency process. From band structure calculations, valence

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electron densities, for example, can be derived, which provide insight into the bonding situation. An obvious disadvantage of the method is that only compounds with special compositions (e.g., 25% ordered vacancies) can be treated. Redinger et al. (116,117) as well as Herzig et al. (118) performed self-consistent APW band structure calculations for a model substance Ti 3[4]Ti [6]X3 䊐X , X being C (116,117) and N (118), respectively. The hypothetical ordered structure corresponds to the composition TiX 0.75. The chosen model structure (Fig. 36) is derived from the cubic unit cell of the B1 structure containing four formula units TiX by replacing the nonmetal atom at the center of the unit cell by a vacancy 䊐 X . Due to the existence of the vacancy two different types of Ti atoms occur, which are designated by their respective number of coordinating nonmetal atoms. The Ti [6] atoms at the corners of the unit cell are octahedrally coordinated by six nonmetal atoms as in the stoichiometric compound TiX. The second type of Ti atoms, designated by Ti [4], occupy the centers of the cube faces. They are quadratically surrounded by four X atoms. Based on this model structure, band structures, DOSs, local partial l-like DOSs, and VEDs in special crystallographic planes were calculated for TiC 0.75 (116,117) and TiN 0.75 (118). The same model structure was also employed by Benco (119), who performed band structure calculations for VN 0.75 (and VN) by means of the extended Hu¨ckel method. This author also performed a molecular orbital calculation for the cluster V14N 12 䊐 N . The LMTO method was used by Zhukov and Gubanov (120) and Zhukov et al. (121) to calculate the band structures and some characteristics of the ground state of TiC 0.75, VC 0.75 (120) and TiN 0.75, VN 0.75 (121). These authors also estimated the lattice constants, bulk moduli and cohesive energies, and the energies of vacancy formation. The results of the APW and LMTO calculations, which will be discussed in Sec. III.D, show great similarities to each other. The assumed periodic long-range order of the vacancies leads to sharp structures in the DOSs, which are probably not realistic. The third group of methods starts from an alloy problem. This approach is based on the assumption that the vacancies are randomly distributed over the nonmetal lattice sites, leading to a loss of translational symmetry. If one also wants to apply a conventional band structure calculation method in such a case, some sort of averaging has to be carried out in order to retain the translational symmetry for the non-long-range-ordered crystal. The first calculations along this line were performed for VC x by Zbasnik and Toth (122) and Neckel et al. (123) and for VC x , ZrC x, and NbC x by Ihara (124), using a special version of the so-called virtual crystal approximation (VCA). If, for the band structure calculations, the

Figure 36 Cubic unit cell for the TiX 0.75 model structure. (䊉) X atoms (X ⫽ C, N); (䊊) vacancy; ( ) Ti [4] atoms; ( ) Ti [6] atoms; (---) (100) plane, section 1; (⋅ ⋅ ⋅) (100) plane, section 2; (-⋅-⋅-) (110) plane; (———) (111) plane. (From Ref. 117. Reproduced with the permission from Elsevier Science,  Elsevier Science.)

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APW method is used, the averaging is achieved by replacing the logarithmic derivative of the nonmetal wave function at the nonmetal muffin-tin radius in the Hamiltonian matrix elements for the stoichiometric compound by the average of the logarithmic derivatives of the nonmetal and the vacancy wave functions in the case of the substoichiometric phases. However, these calculations proved to be unsatisfactory in many respects, mainly because they did not take into account the changes in the local symmetry of the metal atoms adjacent to the vacancy. Another possible method for solving the true alloy problem and calculating the electronic structure of substoichiometric compounds is the ‘‘tight binding coherent potential approximation’’ (TB-CPA) method, which was used by Klima for TiC x (125) and TiN x (126) and by Klein et al. (71) for NbC x , TaC x , and HfC x . In this method the tight-binding Hamiltonian for the stoichiometric compound is replaced by a translationally symmetric effective Hamiltonian with complex eigenvalues and average scattering properties for the substoichiometric crystal. The average scattering amplitudes for the valence electrons at the nonmetal sublattice sites are determined self-consistently assuming random distribution of the vacancies over the nonmetal sites. However, these calculations (125,126,71) failed to yield ‘‘vacancy states’’ or a ‘‘vacancy band,’’ a point that will be discussed later. This failure is probably due to the assumption that the potential in a vacancy sphere tends to infinity. Also, the DOS and its dependence on the vacancy concentration in the region in the neighborhood of the Fermi energy is probably wrong because the vacancy-induced states are not properly accounted for. If the effective scattering amplitudes at the nonmetal sublattice sites are not determined self-consistently but set equal to the arithmetic mean of the nonmetal and the vacancy t-matrix, the ‘‘average T-matrix approximation’’ (ATA) follows. This approximation, combined with the Korringa-Kohn-Rostocker (KKR) method, was used by Huisman et al. (127) to study the mechanism of the vacancy stabilization in titanium carbide and titanium oxide. According to the calculations of these authors, stabilizing vacancy states occur in the minimum of the DOS between the nonmetal p and the metal d bands, increasing the DOS in this energy range. Klima et al. (128) applied the KKR coherent potential approximation (CPA) and the KKR– Green’s function (GF) method to study the electronic structure of substoichiometric phases. The KKR-CPA treats the case of completely randomly arranged vacancies and avoids some of the deficiencies occurring in the TB-CPA calculations of Klima (125,126) and Klein et al. (71). In this approach the physical properties of an alloy are derived from the effective Green’s function ˆ c (E ). The CPA-GF corresponds to an ordered lattice of complex, energy-dependent, effective G potentials replacing the varying potentials in the alloy. In the KKR-CPA the effective Green’s ˆ c (E ) is defined by function G ˆ c (E ) ⫽ xG ˆ Ac ⫹ (1 ⫺ x)G ˆ Bc G

(7)

ˆ Ac and G ˆ Bc describe a single impurity atom A where, in the single-site approximation, the GFs G and B, respectively, in an otherwise perfect effective lattice, and x stands for the concentration of atoms A in a binary alloy A x B 1⫺x . A detailed description of this technique can be found in the paper by Klima et al. (128). The KKR-CPA has the advantage of treating as special cases all interesting systems: the stoichiometric crystal MX, a single vacancy in an otherwise perfect crystal MX, and the alloy MX x . By this approach the electronic structures of TiN x (128) of TiC x , TiN x , VC x, and VN x (129) and of ZrC x, ZrN x , NbC x , and NbN x (130) were studied. Several calculations were devoted to the study of the influence of a single, isolated vacancy on the electronic structure of an otherwise perfect crystal. It is assumed that the results obtained by investigating a single vacancy are also characteristic for crystals with somewhat higher vacancy concentrations. Ivanovsky et al. (131) considered an isolated vacancy as an impurity and proposed a self-consistent solution for this problem. These authors started from the LMTO procedure and the KKR-GF equations and developed an LMTO-GF method, which they applied to the calculation of the electronic structure of TiC, TiN, TiO, VC, VN, and VO containing

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isolated vacancies in both the nonmetal and the metal sublattice. They supplemented their investigations by cluster Xα discrete variation (DV) calculations. A TB calculation for a single carbon vacancy in NbC was performed by Pecheur et al. (132). The perturbation caused by the vacancy was introduced by the Green’s function method. The changes in the overlaps of the metal and nonmetal wave functions caused by the vacancy were taken into account. A resonant peak associated with the vacancy appears in the DOS minimum between the C-2p and the Nb-4d bands lying 1.5 eV below E F. It is assumed that this peak will also persist at higher vacancy concentrations. The electronic structure of an isolated carbon vacancy in NbC was also investigated by Pickett et al. (133) using the SC muffin-tin Green’s function method. These authors found an s-like vacancy induced peak in the DOS 2.6 eV below E F and a weaker p-like peak at 1.74 eV below E F. C.

Band Structures of Substoichiometric Transition Metal Carbides and Nitrides MXx (x ⬍ 1)

In the case of long-range-ordered vacancies, the translational symmetry of the crystal is retained and, therefore, a conventional band structure calculation can be performed. As a typical example, the band structure of the ordered model substance TiC 0.75 (Ti 3[4]Ti [6]C 3䊐 C ), whose unit cell is depicted in Fig. 36, will be discussed. The band structure of this model substance was calculated by Redinger et al. (116), using the SC APW method. In Fig. 37 the band structure of ordered TiC 0.75 (Fig. 37b) is compared with the band structure of stoichiometric TiC (Fig. 37a). In order to facilitate comparison, the band structure of TiC is drawn for a cubic unit cell containing four formula units, but it is otherwise entirely equivalent to the band structure of TiC displayed in Ref. 17. The larger real space unit cell for Ti 4 C 4 corresponds to a smaller BZ, having only onequarter of the volume of the BZ for the ordinary fcc unit cell containing one formula unit. The energy bands of TiC are backfolded into this smaller BZ and a complex-looking band structure with 4 C-2s (instead of 1) and 12 C-2p (instead of 3) valence bands results. Many of the energy states are degenerate in the symmetry directions displayed in Fig. 37a. Because of the lower symmetry of the model compound Ti 3[4] Ti [6] C 3 䊐 C , some of these degeneracies are lifted. Instead of only 3 C-2s and 9 occupied C-2p bands—which one would expect because a formula unit contains three carbon atoms—13 or even 14 energy bands appear below the Fermi energy. Inspection of the partial charges of some of the additional energy states near the Fermi level reveals that they are mainly formed by Ti [4]-3d z 2 orbitals. (For the designation of the orbitals of the Ti [4] atoms a local coordinate system has been used, which is oriented in such a way that the z-axis points from the Ti [4] atom toward the vacancy and the x- and y-axes toward the neighboring C atoms.) The additional states also exhibit a remarkable amount of charge (about 20%) in the vacancy sphere. These ‘‘vacancy states,’’ as they are called, are marked in Fig. 37b by small circles. If the carbon atom at the (1/2 , 1/2 , 1/2 ) lattice site of the cubic unit cell is missing, the Ti [4]-3d z2 (Ti [4]-3d xz, 3d yz) orbitals cannot form dpσ (dp π) bonds. This situation leads to ‘‘dangling’’ d bonds. The overlap of these Ti [4]-3d orbitals in the region of the vacancy sphere results in a certain amount of charge in the vacancy sphere. The ‘‘vacancy band’’ can therefore be better understood as a metal d band that is lowered in energy to the region of the Fermi level. The lowering of d bands by the introduction of a nonmetal atom vacancy at the site (1/2 , 1/2 , 1/2 ) of the cubic unit cell can be explained by simple electrostatic crystal field arguments. As is well known (see also Secs. II.E.3 and II.E.4), the five d orbitals of a transition metal atom are split in an octahedral crystal field into the three energetically lower lying t 2g orbitals and the two energetically higher e g orbitals. Because the e g orbitals point directly toward the (negatively charged) ligands, the electrons in these orbitals are more strongly repelled than the electrons in the t 2g orbitals, which point along the bisectors of the angles between the directions toward the ligands. This situation still holds for the Ti [6] atoms in the model structure. However, the Ti [4]

Figure 37 Band structure of stoichiometric TiC (a) and ordered TiC 0.75 (b). The energy (Ryd) refers to the constant muffin-tin potential between the muffin-tin spheres. The band structure of TiC(17) has been backfolded into the smaller Brillouin zone corresponding to the cubic real space unit cell shown in Fig. 1. So-called vacancy states are circled in (b). (From Ref. 116. Reproduced with the permission from Elsevier Science,  Elsevier Science.)

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Figure 38 Energetic splitting of the d levels in electrostatic fields of Oh and D4h symmetry. (From Ref. 117. Reproduced with the permission from Elsevier Science,  Elsevier Science.)

atoms in the model structure are surrounded quadratically by only four nonmetal atoms and therefore experience a crystal field of D 4h symmetry. The five d states are now split into orbitals of symmetry a 1g (d z2), e g (d xz, d yz), b 2g (d xy), and b1g (d x2⫺y 2). The pattern of the orbital splitting in a quadratic crystal field is displayed in Fig. 38. In this case we can also attribute the energetic sequence of the orbitals to the different degrees of repulsion that the electrons occupying these orbitals experience by the ligands. For the electrons in the d z2 orbital, which points directly toward the neighboring vacancies, this repulsion is greatly reduced compared with the octahedral enviroment. To a lesser extent this situation also holds for the electrons in the d xz and d yz orbitals. Therefore these electronic states are lowered in energy with respect to the corresponding states in an octahedral crystal field. This mechanism leads to an energetic lowering of d bands with appropriate symmetry into the region at the top of the p bands and the bottom of the d bands. However, one also has to take into consideration that in a molecular orbital description the number of Ti(3d z 2)-C(2p) σ bonds and Ti(3d xz , 3d yz)-C(2p) π bonds between the respective Ti [4]-3d and C-2p states is reduced due to the missing carbon atoms. The Ti [4]-3d orbitals not participating in bonds are destabilized and shifted from the region of the p bands to a position just below or at the bottom of the d bands. On the other hand, the loss of carbon partners will shift Ti-3d states involved in antibonding Ti(3d )-C(2p) interactions in the stoichiometric compound downward, leading qualitatively to the same result as the crystal field description. A similar calculation as for ordered TiC 0.75 was performed for ordered TiN 0.75 (Ti 3[4]Ti [6]N 3 䊐 N ) by Herzig et al. (118). In this case again, energy bands containing vacancy states appear in the region of the minimum of the DOS between the p and d bands of the stoichiometric compound. D.

Total Densities of States and Local Partial l -like Densities of States of Substoichiometric Transition Metal Carbides and Nitrides MXx (x ⬍ 1)

The effect of the introduction of vacancies on the DOS can be seen from Fig. 39, which shows a comparison of the DOSs of stoichiometric TiC and ordered TiC 0.75 (Ti 3[4] Ti [6] C 3 䊐 C ) calculated

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Figure 39 Total DOS (———), local interstitial DOS (---), and local vacancy DOS (⋅ ⋅ ⋅) for stoichiometric TiC and ordered TiC 0.75 in units of states per Rydberg, per spin, and cubic unit cell. (The cubic unit cell for TiC contains four formula units.) The curves are adjusted to coincide in the bottom of the C-2s band. The Fermi level of TiC 0.75 is chosen as energy zero. (From Ref. 116. Reproduced with the permission from Elsevier Science,  Elsevier Science.)

by means of the SC APW method. The main components of the local partial l-like DOSs (Ti[4]and Ti [6]-3d, C-2p, and C-2s) are displayed in Fig. 40. [The presence of three equivalent Ti[4] atoms and only one Ti [6] atom in the unit cell of Ti 3[4] Ti [6]C 3 䊐 C causes the statistical weight of the local partial Ti[4](3d )-like DOS to be three times larger than that of the local partial Ti [6](3d )like DOS.] Inspection of Figs. 39 and 40 reveals that the reduced number of C-2s and C-2p states in the substoichiometric compound, leading to a reduction of possible interactions with Ti-3d states, results in a clearly recognizable decrease of the local partial Ti [4](3d )-like DOS in the range of the p bands where the Ti(3d )-C(2p) interactions mainly occur. The lower number of Ti(3d )-C(2p) and Ti(3d )-C(2s) bonds causes a narrowing of the corresponding bands by approximately 0.03 Ryd. The most remarkable feature in the DOS of Ti 3[4]Ti [6]C 3 䊐 C is, however, the appearance of two additional narrow peaks in the region of the minimum of the DOS between the p and d bands of the stoichiometric compound. These two peaks are mostly formed by Ti [4]3d states but also contain a noticeable contribution of the vacancies. The vacancy partial l-like DOS in the peak just below E F exhibits predominantly s symmetry, whereas the vacancy partial l-like DOS in the peak above E F shows mainly p symmetry with respect to the center of the vacancy sphere. Figure 41 displays the local vacancy DOS for TiC 0.75 with its s and p components. The charge in the vacancy sphere is caused by the tails of the 3dz2 wave functions of the surrounding six Ti [4] atoms, which reach into the vacancy sphere. The s or p symmetry re-

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Figure 40 Main local partial l-like DOSs, g tl(E ), for stoichiometric TiC and ordered TiC 0.75. The same units and conventions as for Fig. 39 are employed. (-⋅-) C(2s)-like DOS; (⋅ ⋅ ⋅) C(2p)-like DOS; (———) Ti(3d )- and Ti [6] (3d )-like DOS; (---) Ti [4] (3d )-like DOS. (From Ref. 116. Reproduced with the permission from Elsevier Science,  Elsevier Science.)

Figure 41 Local partial l-like DOSs, g tl (E ), in the vacancy sphere of ordered TiC 0.75 in units of states per Rydberg, per spin, and cubic unit cell. (———) Total local vacancy DOS; (⋅ ⋅ ⋅) vacancy s-like DOS; (---) vacancy p-like DOS. (From Ref. 116. Reproduced with the permission from Elsevier Science,  Elsevier Science.)

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sults by viewing the wave functions from the center of the vacancy sphere. The s symmetry of the wave functions can be considered as resulting from Ti [4] (3d z 2)-Ti [4](3d z 2) bonding and the p symmetry as resulting from Ti [4](3d z 2)-Ti [4] (3d z 2) antibonding interactions across the vacancy. A similar situation is found for ordered TiN 0.75 (Ti [6]Ti 3[4]N 3 䊐 N ). In Fig. 42 the total DOSs for stoichiometric TiN and ordered TiN 0.75 are compared. The first and the second peak in the total DOS, formed mainly by N-2s states (s band) and N-2p states ( p bands), respectively, show reduced width and reduced magnitude in the substoichiometric compound because a smaller number of N-2s and N-2p states is available. Most remarkable is the appearance of two peaks (‘‘vacancy peaks’’) in the lower part of the d bands of the substoichiometric compound, which are formed predominantly by Ti [4]-3d states of d z 2 and d xz, d yz symmetry. The energetically lower peak is situated below E F, the higher one exactly at E F. Both peaks contain an appreciable amount of vacancy partial l-like DOS. As in the substoichiometric carbide, the vacancy partial l-like DOS exhibits s symmetry in the lower peak and p symmetry in the higher peak (compare Fig. 47). In Fig. 43 the local partial N(2s)-, N(2p)-, Ti [6](3d )-, and Ti [4] (3d )-like DOSs of TiN 0.75 are displayed. In the p bands not only the N(2p)-like but also the Ti [4] (3d )-like DOS is greatly reduced, indicating less N(2p)-Ti(3d ) bonding in the substoichiometric nitride. The LMTO-ASA method was applied by Zhukov and Gubanov (120) and Zhukov et al. (121) to calculating the band structures and total and local partial DOSs of TiC 0.75, TiN 0.75, VC 0.75,

Figure 42 Total DOS, g(E ), for stoichiometric TiN and ordered TiN 0.75 in units of states per Rydberg, per spin, and cubic unit cell. (The cubic unit cell contains four formula units.) The curves are adjusted to coincide in the bottom of the N-2s band. The Fermi level of TiN 0.75 is chosen as energy zero. (From Ref. 118. Reproduced with the permission of Academic Press, Inc.,  Academic Press, Inc.)

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Figure 43 Main local partial l-like DOSs, g tl (E ), for ordered TiN 0.75. The same units as for Fig. 42 are used. The Fermi energy is chosen as energy zero. (---) N(2s)-like DOS; (-⋅-) N(2p)-like DOS; (⋅ ⋅ ⋅) Ti [6] (3d )-like DOS; (———) Ti [4] (3d )-like DOS. (From Ref. 118. Reproduced with the permission of Academic Press, Inc.,  Academic Press, Inc.)

and VN 0.75 using the same supercell model as was employed for the APW calculations (116– 118). These investigations also show the appearance of vacancy-induced states in the substoichiometric compounds in the region of the minimum of the DOS of the stoichiometric compounds. As an example, the total DOS of ordered VC 0.75 is displayed in Fig. 44. The two additional peaks in the DOS of VC 0.75 just below E F are induced by the vacancy states. The local partial l-like DOS of these two peaks has mainly V-3d character in the V [4] spheres. In the vacancy sphere, however, the local partial l-like DOS exhibits s character in the lower peak and p character in the higher peak. Both peaks lie below E F and are therefore occupied. The number of

Figure 44 Total densities of states, N(E ), for (a) stoichiometric VC and (b) ordered VC 0.75, calculated by the LMTO method. (From Ref. 7, page 102. Reproduced with the permission of Cambridge University Press,  Cambridge University Press.)

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Figure 45 Total densities of states g(E ), of TiC x phases calculated by the KKR-CPA method. The concentrations x are indicated in the figures. (Adapted from Ref. 129. Reproduced with the permission of the American Physical Society,  American Physical Society.)

electrons in the vacancy states of VC 0.75 (8.78 electrons per unit cell) is significantly greater than the corresponding number (1.78 electrons per unit cell) for TiC 0.75. From this effect the authors (120) conclude that the stability of the vacancies in VC 0.75 is higher than in TiC 0.75. Calculations of the DOSs based on the assumption of a random distribution of vacancies and nonmetal atoms over the nonmetal atom sublattice sites of the B1 structure were performed for TiN x by Klima et al. (128); for TiC x , TiN x , VC x , and VN x by Marksteiner et al. (129); and for ZrC x , ZrN x , NbC x by Marksteiner et al. (130) using the KKR-CPA method. In these calculations the total DOSs and the main contributions to the local partial l-like DOSs [metal t 2g , metal e g , non metal t 1u ( p-like), vacancy a 1 (s-like), and vacancy t 1u ( p-like) DOS] were calculated for many vacancy concentrations, covering the whole range of existence of these phases. As typical examples the KKR-CPA DOSs for TiC x (x ⫽ 1.00, 0.94, 0.875, 0.76) are displayed in Fig. 45. The DOSs derived from the KKR-CPA calculations correspond well to the DOSs obtained by the SC APW method (118) as can be gathered from Fig. 46, in which the total DOS for ordered TiN 0.75 is compared with the total DOS from the KKR-CPA calculation. The sharp peaks obtained for the ordered structure are smoothed in the case of the random distribution of the vacancies. The very sharp peak at E F with a high DOS is probably an artifact due to the highly symmetric long-range-ordered model structure. In Fig. 47 the local partial l-like DOSs in the vacancy sphere of ordered TiN 0.75 are compared with those obtained by the KKR-CPA method. As with the total DOS (Fig. 46), the KKR-CPA DOS, particularly the peak at E F, is much more diffuse than the DOS for the ordered structure. (The greater intensity of the KKR-CPA DOS peaks is caused by the fact that the DOS curves for the vacancy do not refer to the corresponding APW atomic sphere but to a larger volume.) For both calculations the first vacancy peak is almost exclusively formed by vacancy s states, whereas the second one contains an appreciable number of p states. The general trends of the KKR-CPA DOSs for the preceding substoichiometric phases MX x can be summarized as follows: 1. All sharp peaks are smoothed compared with the ordered compounds and the DOSs become less structured with increasing vacancy concentration.

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Figure 46 Total density of states, g(E ), for ordered TiN 0.75 (118) calculated by the SC APW method (———) compared with the total density of states for TiN 0.75 (128, 129) calculated by the KKR-CPA method (---). The same units as for Fig. 42 are used. (From Ref. 118. Reproduced with the permission of Academic Press, Inc.,  Academic Press, Inc.)

Figure 47 Total vacancy density of states and vacancy l-like densities of states, g l䊐, for ordered TiN 0.75 calculated by the SC APW method (a) and for TiN 0.75 calculated by the KKR-CPA method (b). The same units as for Fig. 42 are used. (———) Total vacancy DOS; (⋅ ⋅ ⋅) vacancy s-like DOS; (---) vacancy plike DOS. (From Ref. 118. Reproduced with the permission of Academic Press, Inc.,  Academic Press, Inc.)

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2. The DOS peaks originating mainly from nonmetal 2s and 2p states lose intensity. This effect is not surprising because there are fewer nonmetal electrons present. 3. Additional peaks (vacancy peaks) appear near the minimum of the DOS of the stoichiometric compound (except for ZrCx). 4. The peaks above E F with mainly metal d character are not strongly affected by the introduction of vacancies. 5. The Fermi energy with respect to the muffin-tin zero is generally lowered with increasing vacancy concentration (except for ZrC x). The relativistic KKR-CPA method was also employed to study the electronic structure of substoichiometric HfC x and HfN x (81) and TaC x (82). The main difference in the electronic structure of the substoichiometric phases HfC x and TaC x compared with the stoichiometric compounds HfC and TaC is a backflow of charge from the carbon atoms to the hafnium and tantalum atoms, respectively, with increasing vacancy concentration. This finding is in agreement with an earlier observation following from a TB CPA calculation (71) in which the DOSs and the Bloch spectral functions of NbC x , HfC x, and TaC x (0.7 ⱕ x ⱕ 1.0) were determined. In contrast to the behavior of HfC x and TaC x , in substoichiometric HfN x both the hafnium and the nitrogen atom lose electrons to the vacancy. A remarkable further result is that no significant vacancy contribution to the DOS of TaC x is found. The existence of vacancy-induced states in substoichiometric transition metal carbides and nitrides was confirmed experimentally by various methods. Ho¨chst et al. (134) were the first to observe a structure in the X-ray photoelectron spectroscopy (XPS) valence band spectrum of NbC 0.85, which they attributed to vacancy-induced states. Several investigations were devoted to the study of the influence of vacancies on X-ray photoelectron spectra (135–139) and ultraviolet photoelectron spectra (138,140,141). A comprehensive discussion of this subject, including angle-resolved photoemission spectra, can be found in the review article by Johansson (8). Xray emission spectroscopy (107,108,142–144), X-ray absorption spectroscopy (102), and optical spectroscopy (145,146) were employed to investigate vacancy-induced electronic states. Changes of the DOS in the unoccupied energy region were observed by energy loss spectroscopy (147–149).

E.

Bonding Mechanisms in Substoichiometric Transition Metal Carbides and Nitrides MXx (x ⬍ 1)

The bonding mechanisms can be best derived from valence electron density and difference electron density plots. The ordered model compounds TiC 0.75 and TiN 0.75 (Ti [6] Ti 3[4] X 3 䊐 x) may serve as representative examples. The three main types of covalent bonding ( pd σ, pd π, and dd σ) known from the stoichiometric compounds also occur in the ordered phases TiC 0.75 and TiN 0.75 but with distinct modifications. In addition, new types of interaction appear. As already mentioned, the d z 2 and d x 2⫺y 2 orbitals of the Ti [4] atoms are no longer equivalent in the square crystal field of the four nonmetal atom neighbors. The Ti [4]-3d z 2 orbitals extend toward the vacancy and cannot form pd σ bonds with the X-2p orbitals. Therefore, the number of pd σ bonds is reduced compared with the stoichiometric compounds. More information can be gained from Tables 4 and 5, which list the splitting of the Ti(3d )-like charge into its components. The Ti [4]-3d z 2 and Ti[4]-3d xz, 3d yz components are greatly reduced in the p bands of the substoichiometric compounds but furnish the biggest contributions to the DOS in the vacancy band. From the reduction of the number of Ti [4]-3d z 2 states in the p bands of the substoichiometric compounds it can be concluded that the number of pd σ bonds is reduced. In a similar way, the

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Table 4 Partition of the Ti(3d )-like Charge in TiC and Ordered TiC 0.75 (All Charges Are Given in Electrons per Atomic Sphere) TiC 0.75

TiC

Ti [4] Bands p Vacancy Occupied valence

Ti [6]

Ti

d z2

d x2⫺y2

d xy

(d xz ,d yz )

eg

t 2g

eg

t 2g

0.09 0.22 0.33

0.39 0.01 0.44

0.21 0.03 0.24

0.26 0.31 0.57

0.80 – 0.89

0.69 0.07 0.76

0.84

0.78

0.94

0.78

Source: From Ref. 116. Reproduced with the permission from Elsevier Science,  Elsevier Science.

decrease of Ti [4]-3d xz, 3d yz states indicates a reduction of pd π bonds. The pd σ and pd π bonds in which Ti [6] atoms take part are not significantly altered by the introduction of vacancies. Whereas the number of titanium-nonmetal bonds is diminished in the substoichiometric compounds, the Ti(3d )-Ti(3d ) bonds gain importance. Three types of Ti(3d )-Ti(3d ) interactions can be distinguished in the model compounds: 1. The introduction of vacancies leads to a new type of Ti(3d )-Ti(3d ) interaction. Inspection of the VED in the (100) plane of three typical vacancy states of ordered TiN 0.75, displayed in Fig. 48, reveals that there is a distortion of the VED around the Ti [4] atoms toward the vacancy. The increase of VED in the direction from the Ti [4] atoms toward the vacancy can be considered as an indication of the formation of a weak bonding interaction of s symmetry viewed from the vacancy sphere (bonding d z2-䊐 x-d z2 interaction). Energetically these states lie in the first ‘‘vacancy peak’’ of the DOS. The corresponding antibonding states (of p symmetry in the vacancy sphere) are found in the second vacancy peak. These states are partly occupied in the nitride but not in the carbide. Interactions via the vacancy can also occur between two Ti [4]-3d z 2 orbitals oriented at right angles to each other. 2. The second type of covalent Ti(3d )-Ti(3d ) bonds is formed between Ti [4] -3d xz , 3d yz orbitals of Ti [4] atoms surrounding a vacancy. Because the number of pd π bonds in which Ti [4]-3d xz, 3d yz orbitals are involved is reduced in the substoichiometric compounds, the Ti [4]-3d xz and 3d yz orbitals can form better overlapping (stronger) Ti [4]Ti [4] dd σ bonds. These bonds are oriented along the edges of the octahedra formed by the Ti [4] atoms surrounding a vacancy (‘‘octahedral bonds’’). This type of bond

Table 5 Partition of the Ti(3d )-like Charge in TiN and Ordered TiN 0.75 (All Charges Are Given in Electrons per Atomic Sphere) TiN 0.75 Ti Bands p d ⫹ vacancy Occupied valence

TiN

[4]

Ti

[6]

Ti

d z2

d x2⫺y2

d xy

(d xz ,d yz)

eg

t 2g

eg

t 2g

0.04 0.33 0.38

0.24 0.01 0.27

0.10 0.09 0.19

0.13 0.51 0.64

0.55 0.01 0.61

0.38 0.41 0.79

0.58 0.01 0.65

0.46 0.58 1.05

Source: From Ref. 118. Reproduced with the permission of Academic Press, Inc.,  Academic Press, Inc.

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Figure 48 Valence electron densities for the ‘‘vacancy band’’ states Γ 1, ∆ 1, and X l in the (100) plane, ˚ 3. (From Ref. 118. Reproduced with the section 2 (see Fig. 36) of ordered TiN 0.75 in units of 10 ⫺2 e/A permission of Academic Press, Inc.,  Academic Press, Inc.)

can be realized from the electron density plot for a special state (X 3 symmetry) in the (111) plane of ordered TiN 0.75 (Fig. 49). In the substoichiometric nitride more bonding states forming octahedral bonds are to be found than in the corresponding carbide, because in TiC 0.75 these states lie partly above the Fermi level. Therefore, the stabilization of the Ti [4] octahedra is more pronounced for the substoichiometric nitride than for the substoichiometric carbide. 3. The interaction between the Ti [4] and Ti [6] atoms also changes on passing from the stoichiometric to the substoichiometric compounds. The Ti [4]-3d xy orbitals can form dd σ bonds with Ti [6]-t 2g orbitals, entirely analogous to the dd σ bonds in the stoichiometric compounds. Inspection of the difference of the VED between the ordered substoichiometric and the stoichiometric compounds reveals that the VED in the Ti [6]-Ti [4] direction increases in the case of the carbide but decreases in the case of the nitride. Therefore, it can be assumed that the Ti [6]-Ti [4] dd σ bonds are strengthened in the carbide and weakened in the nitride.

Figure 49 Valence electron density for the state X 3 of ordered TiN 0.75 in the (111) plane (see Fig. 36) ˚ 3. (From Ref. 118. Reproduced with the permission of Academic Press, Inc.,  Acain units of 10 ⫺2 e/A demic Press, Inc.)

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The preceding conclusions about the chemical bonding are mainly based on the results obtained for a hypothetical model structure. From the fact that both the long-range order and the random distribution of the vacancies yield similar DOSs, it can be assumed that the general description of the electronic structure of the substoichiometric phases is essentially correct. F.

Metal-Deficient Transition Metal Carbides and Nitrides of the Fourth and Fifth Groups of the Periodic Table with B1 Structure M y X ( y ⬍ 1)

Metal vacancies occur almost exclusively in transition metal nitrides. Gubanov et al. (111) studied the electronic states of a Ti vacancy in TiC by means of the cluster Xα DV method. Local DOSs of a single vacancy in TiC, VC, ZrC, TiN, and VN were calculated by Ivanovsky et al. (131). The influence of metal vacancies on the electronic structure of zirconium nitride (Zr 0.75N and Zr 0.8 N 0.8) was studied by Marksteiner et al. (150) using the KKR-CPA method. The DOSs of the metal-deficient nitrides Ti 0.75N, Zr 0.75N, and Hf 0.75N, assuming a model structure that can be described by the formula M 3 䊐 MN [6] N 3[4] (M ⫽ Ti, Zr, and Hf), were calculated by Schwarz et al. (151,152) using the ASW method. The calculations yield a slight overlap between the N2p bands and the Zr-4d bands indicating metallic behavior of Zr 3N 4 whereas experimentally (153) it is found that Zr 3N 4 is an insulator. If neon is implanted in the vacancy, the resulting insulator NeZr 3N 4 has a lattice spacing that perfectly matches that of the superconductor ZrN. A Josephson junction constructed from these two isostructural and isochemical substances should have a perfect match at the interface.

IV. ELECTRONIC STRUCTURE OF TRANSITION METAL CARBONITRIDES OF THE FOURTH AND FIFTH GROUPS OF THE PERIODIC TABLE Transition metal monocarbides MC and mononitrides MN form solid solutions MC x N 1⫺x . Some of them are of great technical importance, e.g., as hard coatings. Weinberger (154–156) employed the relativistic KKR-ATA method to study the electronic structure of TiC xN 1⫺x , TiC x O 1⫺x , TiN x O 1⫺x , and HfCxN 1⫺x . Petru and Klima (157) used the KKR-CPA method to investigate the electronic states in TiC xN 1⫺x (x ⫽ 0.4 and 0.6). The DOSs of the solid solutions NbC x N 1⫺x (x ⫽ 1.0, 0.75, 0.5, 0.25, 0.12, and 0) were calculated by Nikiforov and Kolpachev (158) using the cluster version of the local coherent potential approximation. The calculated DOS at the Fermi level correlates with the dependence of the superconducting transition temperature on the carbon concentration x. (In the solid solutions NbC x N 1⫺x the highest value, about 18 K, of the superconducting transition temperature for transition metal carbides and nitrides is found.) The band structures and cohesive energies of titanium carbonitrides Ti 4C 4⫺nN n , with n ⫽ 0, 1, 2, 3, and 4 (corresponding to TiC xN 1⫺x , x ⫽ 1, 0.75, 0.5, 0.25, and 1) were calculated by Zhukov et al. (159) employing the SC LMTO ASA method. The results were used to analyze available electromagnetic, thermodynamic, and elastic properties of the compounds. Gustenau-Michalek et al. (160) performed SC LAPW calculations for the three ordered model structures Ti 4C 3N (TiC 0.75N 0.25), Ti 2CN (TiC 0.5N 0.5), and Ti 4CN 3 (TiC 0.25N 0.75). The total DOSs for these three ordered compounds are displayed in Fig. 50. The lowest lying valence band is formed by N-2s states (‘‘N-2s band’’). After a gap of about 0.2 Ryd the corresponding ‘‘C-2s band’’ follows. A further gap separates the ‘‘N-2p bands,’’ which overlap the slightly higher lying ‘‘C-2p bands.’’ After a minimum in the DOS the ‘‘Ti-3d bands’’ follow. The VEDs in the (100) plane for the three model structures together with the VEDs of the pure compounds TiC and TiN are displayed in Fig. 51. The maxima of the VED in the Ti spheres are much more pronounced in the directions toward the carbon atoms than toward the nitrogen atoms, indicating that the covalent TiC bonds are stronger than the TiN bonds. The successive

Figure 50 Total densities of states, DOS, for Ti 4C 3N (left), Ti 2CN (middle), and Ti 4CN 3 (right) in units of states per Rydberg and unit cell. The Fermi energies are indicated by vertical lines. (From Ref. 160. Reproduced with the permission from Elsevier Science,  Elsevier Science.)

˚ 3. The atom in the center Figure 51 Valence electron densities in the (100) plane of TiC, Ti 4C 3N, Ti 2CN, Ti 4CN 3, and TiN (from left to right) in units of 10 ⫺1 e/A is Ti in all cases. The number of C atom neighbors of a Ti atom is indicated in the square bracket of the superscript of the respective Ti atom. (From Ref. 160. Reproduced with the permission from Elsevier Science,  Elsevier Science.)

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replacement of C atoms by N atoms leads to a weakening of the covalent titanium-nonmetal bonds and an increased ionicity of the bonds. At the same time the TiTi dd σ bonds are strengthened. In pure TiN the maxima of the VED around the Ti atoms are directed toward the neighboring Ti atoms (t 2g-like VED). If the TiC and TiN bonds are considered separately, almost no influence of the C/N ratio on the strength of the particular titanium-nonmetal bonds is found. Schadler and Monnier (81) considered not only the effect of the nonmetal atom substitution but also the presence of vacancies in the solid solutions Hf(C xN 1⫺x)y . To handle this problem in the frame of the relativistic KKR approach for y ⬍ 1, a three-component CPA method had to be developed. Total and local DOSs for HfC 0.8, Hf 0.9 C 0.37 N 0.53, HfC 0.42 N 0.58, and HfN 0.8 were calculated.

V.

ELECTRONIC STRUCTURE OF M 2X PHASES

In the phase diagrams of the fifth and sixth group transition metals with carbon subcarbides M 2C (V 2C, Nb 2C, Ta 2C, Mo 2C, W 2C) appear. In the metal sublattice of these compounds there is one octahedral interstitial site per metal atom. One half of the interstitial sites is occupied by carbon atoms, the other half of the interstitials is vacant. The stable high-temperature modification is the L′3 type structure with a random distribution of carbon atoms in half of the octahedral interstitial sites. An exception is β-W 2C which crystallizes in the orthorhombic ξ-Fe 2N structure. At lower temperatures ordering of the carbon atoms occurs, partly associated with a distortion of the metal sublattice. Ivanovsky et al. (161) performed LCAO MO calculations for clusters of the type MX 3M 12 (M ⫽ V, Nb; X ⫽ C, N) to study the electronic structure of V 2X and Nb 2X. A remarkable finding is that in these compounds not only metal-carbon bonds but also metal-metal bonds form the main covalent bonding components. In contrast, in the monocarbides mostly covalent metal-carbon bonds are found in the occupied energy region. In the TiN system two phases with a composition near TiN 0.5 are found, δ′-Ti 2N and ε-Ti 2N. δ′-Ti 2N has a long-range-ordered defect structure. This structure can be derived from the sodium chloride (B1) structure by assuming a long-range order of the vacancies on the ˚ ) along the fourfold nitrogen sublattice and by shifting the titanium atoms (by about 0.123 A tetragonal axis away from the adjacent vacancy in this axis (space group I4 1 /amd). The tetragonal unit cell of δ′-Ti 2N is displayed in Fig. 52. δ′-Ti 2N is a metastable phase and transforms into the stable, tetragonal ε-Ti 2N phase, which crystallizes in the antirutile structure (space group P4 2 /mnm) displayed in Fig. 53. As can be seen from Figs. 52 and 53, in both δ′- and ε-Ti 2N each N atom is surrounded by a slightly distorted octahedron of Ti atoms. Band structures, total DOSs, local partial l-like DOSs, and VEDs for these two phases were calculated by Eibler (162) by means of the SC LAPW method. The total DOSs for both ε- and δ′-Ti 2N are shown in Fig. 54. For both structures the energetically lowest lying peak is formed by N-2s states (‘‘N-2s band’’). Separated by an energy gap of about 0.6 Ryd, the six ‘‘N-2p bands’’ follow. These bands originate predominantly from N-2p states but also contain a contribution of Ti-3d states. The N-2p bands overlap only slightly with the lowest ‘‘Ti-3d band.’’ A pronounced minimum in the DOS (at about ⫺0.24 Ryd for ε-Ti 2N and ⫺0.22 Ryd below E F for δ′-Ti 2N) separates the ‘‘N-2p bands’’ from the ‘‘Ti-3d bands.’’ The main difference in the DOSs between ε- and δ′-Ti 2N is found at the bottom of the Ti-3d bands. Two peaks, d 1 and d 2, separated by a sharp minimum at ⫺0.11 Ryd below E F, characterize the DOS of the lower part of the Ti-3d bands of ε-Ti 2N. In δ′-Ti 2N, however, only one peak at about ⫺0.1 Ryd appears at the bottom of the Ti-3d bands. The Fermi level for ε-Ti 2N is located in the DOS minimum above the peak d 2, and the Fermi level for δ′-Ti 2N lies in the ascent of the main peak of the Ti-3d bands just above a minimum in the DOS. A shift of the Fermi level to this minimum and assuming a rigid band

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Figure 52 Tetragonal unit cell of δ′-Ti 2N with crystallographic axes X, Y, and Z. Empty circles, Ti atoms; full circles, N atoms; squares, N vacancies. The shift of the Ti atoms adjacent to a vacancy is indicated by arrows. (From Ref. 162. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

model would lead to a titanium nitride with the composition Ti 2N 0.98, very close to the composition Ti 2N. A thorough discussion of the results obtained furnishes a qualitative explanation for both the occurrence of the metastable δ′-Ti 2N structure and the stability of the ε-Ti 2N phase. In δ′Ti 2N the t 2g orbitals of the Ti atoms surrounding a vacancy can form octahedral dd σ bonds, as discussed in the context of the electronic structure of ordered TiN 0.75. The t 2g states involved in octahedral bonding are lowered in energy and form the peak in the DOS at the bottom of the Ti-3d bands. This peak is separated from the remaining part of the Ti-3d bands. In contrast to the results for the ordered model structure of TiN 0.75, the tails of the Ti-e g orbitals (Ti-3d z 2 orbitals in the model structure for TiN 0.75) reaching into the vacancy overlap only very slightly. Therefore, no significant Ti(d )-Ti(d ) interaction across the vacancy occurs. This behavior may be due to the shift of the Ti atoms away from the vacancy, thus reducing the overlap and the amount of charge in the vacancy. The VED plot of ε-Ti 2N in the (001) plane shows the presence of strong pd σ bonds between

Figure 53 Unit cell of ε-Ti 2N with crystallographic axes X, Y, and Z. Empty circles, Ti atoms; full circles, N atoms (From Ref. 162. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

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Figure 54 Densities of states of (a) ε- and (b) δ′-Ti 2N in states of one spin direction per Rydberg and unit cell. For δ′-Ti 2N the local vacancy DOS is indicated by the dash-dotted curve. (From Ref. 162. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

each N atom and its two nearest (apical) Ti atoms (Fig. 55). The Ti 2N units are aligned in the [110] direction in the basal plane. Adjacent, parallel Ti 2N units only interact in the [110] direction at right angles to the orientation of the Ti 2N units via weak TiTi dd σ bonds formed by Ti-e g states. The VED plot of δ′-Ti 2N in the (001) plane is displayed in Fig. 56. As can be seen from this figure, the N atoms form pd σ bonds with the four Ti atoms surrounding each N atom ˚ out of the (001) plane.) in the (001) plane. (Note that the Ti atoms are shifted by ⫾ 0.123 A The transformation of δ′-Ti 2N into ε-Ti 2N allows the Ti-e g orbitals to form not only strong

Figure 55 Valence electron density in the (001) plane of ε-Ti 2N. Contour lines on a linear mesh in units ˚ 3. (From Ref. 162. Reproduced with the permission of the Institute of Physics Publ.,  Institute of 10⫺1 e/A of Physics Publ.)

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Figure 56 Valence electron density in the (001) plane of δ′-Ti 2N. Contour lines on a linear mesh ˚ 3. (From Ref. 162. Reproduced with the permission of the Institute of Physics Publ., in units of 10 ⫺1 e/A  Institute of Physics Publ.)

NTi pd σ bonds but also TiTi dd σ bonds in the basal plane between the strongly bound ‘‘molecular’’ Ti 2N units. The corresponding states are stabilized and form the subband d 1 at the bottom of the Ti-3d bands. This effect is presumably the main reason for the stabilization of the ε-Ti 2N structure with respect to the δ′-Ti 2N structure. A quantitative confirmation of the higher stability of the ε-phase was furnished by Eibler (163), who calculated the total energies of ε- and δ′-Ti 2N by volume minimization using the FLAPW method (43). Figure 57 shows the total energies of ε- and δ′-Ti 2N plotted as a function of the volume of the unit cell. At 0 K, the ε-phase is found to be more stable than the δ′-phase by 9.35 kJ/mol and has a 2% smaller equilibrium volume, indicating stronger bonding. The experimental volumes are higher by 1.8% for both phases. This deviation is characteristic for all band structure calculations based on the local density approximation (LDA).

Figure 57 Total energies of δ′- and ε-Ti 2N plotted versus the volume of the respective unit cell. (From Ref. 163. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

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VI. ELECTRONIC STRUCTURE OF TRANSITION METAL DIBORIDES MB 2 OF THE FOURTH AND FIFTH GROUPS OF THE PERIODIC TABLE Many transition metal diborides MB 2 (M ⫽ Sc, Ti, V, Cr, Mn, Y, Zr, Nb, Mo, Hf, Ta) crystallize in the C 32 (AlB 2) structure with the space group P6/mmm. The translational lattice of this structure is a simple hexagonal lattice. The boron atoms form graphite-like layers that are separated by hexagonal closed-packed metal layers. The center of a hexagonal boron ring lies both directly above and below each metal atom. The structure is displayed in Fig. 58. The unit cell contains one metal and two boron atoms. The properties of the transition metal diborides with C 32 structure resemble those of the transition metal monocarbides and mononitrides. The diborides also have high melting points, hardness, chemical stability, and metallic conductivity. Perkins and Sweeney (165) performed an LCAO-TB calculation for TiB 2. A remarkable result is the close grouping of the Ti-3d bands. The Fermi level lies within this group of Ti-3d states and splits the Ti-3d bands into lower (bonding) and upper (antibonding) states. Also, graphite-like features are found in the band structure. The band structure and the total DOS of ZrB 2 was calculated by Ihara et al. (166) using the APW method. According to these authors, the bonding mechanism in ZrB 2 can be explained as a combination of the graphitic bonding model of boron network and the hcp-metal bonding model of zirconium. Similar results have been obtained by Johnson et al. (167), who employed the KKR method to study the electronic structure of ZrB 2. Armstrong (168) used the LCAO MO method to calculate the band structures and total DOSs for the transition metal diborides MB 2 (M ⫽ Sc, Ti, V, Cr, and Mn). Trends in the electrical conductivity and spin susceptibility were evaluated. The solid-state calculational procedure was supplemented by cluster calculations using a cluster (M 18B 36) comprising 54 atoms. These investigations led to the following trends: The metal-metal bonding in the metal

Figure 58 Two projections of the AlB 2-type structure. The top view is down the z-axis with the metal atoms at z ⫽ 0 and the boron atoms at z ⫽ 1/2. The bottom view is a projection of the x ⫺ z plane with the metal atoms at y ⫽ 0 and the positions of the two boron atoms at y ⫽ 1/3 and 2/3. a 0, c 0, lattice constants. (From Ref. 164. Reproduced with the permission from Elsevier Science,  Elsevier Science.)

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plane reaches a maximum at VB 2. The interlayer metal-metal bonding is small for ScB 2 and TiB 2 but reaches large values for VB 2, CrB 2, and MnB 2, corresponding to the enhanced 3d orbital population. Metal-boron bonding increases along the series from ScB 2 to MnB 2. The boron-boron bonding in the hexagonal boron plane, however, is strongest for ScB 2 and decreases gradually from ScB 2 to MnB 2. The bonding between the boron layers is weak. The electronic structure of the transition metal diborides MB 2 (M ⫽ Sc, Ti, V, Cr, and Mn) was also investigated by Burdett et al. (169) employing band structure calculations of the extended Hu¨ckel type. The bonding mechanism was discussed, and it was concluded that the interactions of the metal orbitals with those of the planar, graphite-like net of boron atoms and with those of other metal atoms are both important in influencing the properties of the diborides. The authors offer an explanation for the experimentally observed variation in the heat of formation of the diborides, which depends, according to their calculations, on the extent of occupation of the metal-boron orbitals. The SC LMTO ASA method was used by De-Cheng Tian and Xiao-Bing Wang (170) to calculate the band structure and total and partial l-like DOSs for TiB 2. Figure 59 shows the total DOS of TiB 2. The peak A arises from the B-2s states, and the broad peak B originates from the B-2p and Ti-3d states, which overlap strongly. The Fermi level lies exactly in a pronounced minimum (pseudogap) of the DOS. [A similar minimum at the Fermi level was also found by Ihara et al. (166) for ZrB 2.] The authors regard this minimum as caused by a competing effect of a Ti-3d resonance and the strong bonding interaction between the B-2p and Ti-3d states. The DOS above the Fermi level (peak C) can be put down to nonbonding Ti-3d states. The authors stress that the covalent metal-boron bonding is a least as important as other types of bonding. The fact that the Ti-3d and the B-2p states belong to different layers proves the importance of the interlayer bonding. Therefore, TiB 2 cannot be regarded as a true interlayer compound, because there is a strong interaction between the metal and the boron layers. The calculations of De-Cheng Tian and Xiao-Bing Wang (170) were extended by Xiao-Bing Wang et al. (171) to a series of transition metal diborides MB 2 (M ⫽ Sc, Ti, V, Cr, Mn, Y, Zr, Nb, Mo, Hf, and Ta) using the same computational approach. The total DOSs for VB 2, ZrB 2, NbB 2, HfB 2, and TaB 2 are displayed in Fig. 60. The DOS curves for the different compounds show great similarity. (Also compare the DOS of TiB 2, Fig. 59.) The boron sublattice, which has the planar graphite-like structure, is reflected in the DOS by the lowest lying peak (peak A). All diborides are characterized by a pronounced minimum (pseudogap) of the DOS. The broad peak

Figure 59 Total density of states, TDOS, (left scale) and integrated density of states, IDOS, (right scale) of TiB 2. Fermi energy at 0.04 rydberg. The Fermi energy is indicated by a vertical dashed line. (From Ref. 170. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

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Figure 60 Total densities of states, DOS, of VB 2, ZrB 2, NbB 2, HfB 2, and TaB 2 in units of states per Rydberg and unit cell. The Fermi energies are at 0.08 Ryd (VB 2), 0.04 Ryd (ZrB 2), 0.14 Ryd (NbB 2), 0.04 Ryd (HfB 2), and 0.16 Ryd (TaB 2. (From Ref. 171. Reproduced with the permission of the Institute of Physics Publ.,  Institute of Physics Publ.)

below the minimum (peak B) is caused by the overlapping transition metal d and the boron 2p orbitals, leading to strong covalent transition metal(d )–boron(2p) bonds. The DOSs have nonvanishing values at E F, indicating that the diborides possess metallic properties. The peak above the minimum of the DOS (peak C) originates from nonbonding transition metal d states. The authors stressed that, besides the interaction of the transition metal d orbitals with the boron 2p orbitals and the interactions between the transition metal orbitals, the boron-boron interaction is also of importance. Furthermore, the variation of the chemical stabilities of the investigated transition metal diborides was analyzed and it was found that the observed trends can be understood in terms of a band-filling concept of the bonding states. The electric field gradients at the boron and metal sites for various transition metal diborides MB 2 (M ⫽ Ti, V, Cr, Zr, Nb, Mo, and Ta) were calculated by Schwarz et al. (172) by means of the full-potential LAPW method as embodied in the Wien 95 code (45) in a scalar relativistic version.

ACKNOWLEDGMENTS Figures and tables in this article are reproduced with permission from the authors of the corresponding papers and from the following publishers who own the copyright on the respective figures and tables: Academic Press Inc., American Physical Society, Berichte der Bunsen-Gesellschaft, Cambridge University Press, Critical Reviews in Solid State and Materials Sciences

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(CRC Press LLC), Elsevier Science, Institute of Physics Publ., Springer Verlag, and John Wiley & Sons, Inc. This assistance is gratefully acknowledged. The author would like to express his thanks to Prof. Peter Herzig for many valuable discussions.

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101. R Kauffmann, O Meyer. Determination of static displacements around non-metal vacancies in NbN 1⫺c and TiC 1⫺c . Solid State Commun 51:539, 1984. 102. V Moisy-Maurice, CH de Novion. An application of Ti-K X-ray absorption edges and fine structures to the study of substoichiometric titanium carbide TiC 1⫺x . J Phys Fr 49:1737, 1988. 103. TH Metzger, J Peisl, R Kaufmann. X-ray determination of local atomic displacements around carbon vacancies in NbC 1⫺c single crystals. J Phys F Metal Phys 13:1103, 1983. 104. M Morinaga, K Ohshima, J Harada, S Otani. X-ray determination of the atomic displacements in NbC 0.72. J Appl Crystallogr 19:417, 1986. 105. DE Ellis, GA Benesh, E Byrom. Molecular cluster studies of binary alloys: LiAl. Phys Rev B 16: 3308, 1977. 106. DE Ellis, GA Benesh, E Byrom. Self-consistent embedded-cluster model for magnetic impurities: Fe, Co, and Ni in β′-NiAl. Phys Rev B 20:1198, 1979. 107. M Gupta, VA Gubanov, DE Ellis. Chemical bonding and X-ray emission spectra analysis for niobium carbide, nitride and oxide. J Phys Chem Solids 38:499, 1977. 108. YN Kucherenko, LM Sheludchenko, VZ Khrinovsky, VV Nemoshkalenko. Study of the electron states in nonstoichiometric titanium nitrides by the X α-scattered-wave method. J Phys Chem Solids 45:319, 1984. 109. K Schwarz, N Ro¨sch. Effects of carbon vacancies in NbC on superconductivity. J Phys C Solid State Phys 9:L433, 1976. 110. G Ries, H Winter. Electronic structure of vacancies in refractory compounds and its influence on T c . J Phys F Metal Phys 10:1, 1980. 111. VA Gubanov, AL Ivanovsky, GP Shveikin, DE Ellis. Vacancies and the energy spectrum of refractory metal compounds: TiC and TiO. J Phys Chem Solids 45:719, 1984. 112. A Rosen, DE Ellis, H Adachi, FW Averill. Calculations of molecular ionization energies using a self-consistent-charge Hartree-Fock-Slater method. J Chem Phys 65:3629, 1976. 113. DL Novikov, AL Ivanovsky, VA Gubanov. The influence of carbon vacancies and local atomic displacements on the electronic structure of niobium carbides. Phys Status Solidi (b) 139:257, 1987. 114. L Ska´la, P Cˇapkova´. Nitrogen vacancy and chemical bonding in substoichiometric vanadium nitride. J Phys Condens Matter 2:8293, 1990. 115. P Cˇapkova´, L Ska´la. Chemical bonding and lattice relaxation in substoichiometric titanium carbide and nitride. Phys Status Solidi (b) 171:85, 1992. 116. J Redinger, R Eibler, P Herzig, A Neckel, R Podloucky, E Wimmer. Vacancy induced changes in the electronic structure of titanium carbide—I. Band structure and density of states. J Phys Chem Solids 46:383, 1985. 117. J Redinger, R Eibler, P Herzig, A Neckel, R Podloucky, E Wimmer. Vacancy induced changes in the electronic structure of titanium carbide—II. Electron densities and chemical bonding. J Phys Chem Solids 47:387, 1986. 118. P Herzig, J Redinger, R Eibler, A Neckel. Vacancy induced changes in the electronic structure of titanium nitride. J Solid State Chem 70:281, 1987. 119. Lˇ Benco. Chemical bonding in stoichiometric and substoichiometric vanadium nitride. J Solid State Chem 110:58, 1994. 120. VP Zhukov, VA Gubanov. The study of the energy band structures of TiC, VC, Ti 4C 3 and V 4C 3 by the LMTO-ASA method. J Phys Chem Solids 48:187, 1987. 121. VP Zhukov, VA Gubanov, O Jepsen, NE Christensen, OK Andersen. Calculated energy-band structures and chemical bonding in titanium and vanadium carbides, nitrides and oxides. J Phys Chem Solids 49:841, 1988. 122. J Zbasnik, LE Toth. Electronic structure of vanadium carbide. Phys Rev B 8:452, 1973. 123. A Neckel, P Rastl, K Schwarz, R Eibler-Mechtler. Berechnung der Bandstrukturen nichtsto¨chiometrischer Vanadiumcarbide VCx . Z Naturforsch 29a:107, 1974. 124. H Ihara. Electronic structures of the transition metal carbides and borides studied by x-ray photoelectron spectroscopy and band calculation. Res. Electrotechn. Laboratory, Tokyo, Report No. 775, 1977; Chem Abstr 89:155195d, 1978, Phys Abstr 82:15074, 1979. 125. J Klima. Density of states of substoichiometric TiC 1⫺x . J Phys C Solid State Phys 12:3691, 1979. 126. J Klima. Density of states of substoichiometric TiN 1⫺x . Czech J Phys B 30:905, 1980.

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152. K Schwarz, AR Williams, JJ Cuomo, JHE Harper, HTG Hentzell. Zirconium nitride—a new material for Josephson junctions. Phys Rev B 32:8312, 1985. 153. P Prieto, L Gala´n, JM Sanz. Electronic structure of insulating zirconium nitride. Phys Rev B 47: 1613, 1993. 154. P Weinberger. On the electronic structure of transition metal carbonitrides, carboxides, and oxinitrides I. Phys Status Solidi (b) 97:565, 1980. 155. P Weinberger. On the electronic structure of transition metal carbonitrides, carboxides, and oxinitrides II. Phys Status Solidi (b) 98:207, 1980. 156. P Weinberger. On the electronic structure of transition metal carbonitrides, carboxides, and oxinitrides III. Phys Status Solidi (b) 98:591, 1980. 157. J Petru, J Klima. The KKR CPA study of electron states in TiC xN 1⫺x . Z Phys B Condens Matter 73:213, 1988. 158. IY Nikiforov, AB Kolpachev. Electronic structure of niobium nitrocarbides. Phys Status Solidi (b) 148:205, 1988. 159. VP Zhukov, VA Gubanov, O Jepsen, NE Christensen, OK Andersen. Calculated electronic properties of titanium carbonitrides TiC xN 1⫺x . Philos Mag B 58:139, 1988. 160. E Gustenau-Michalek, P Herzig, A Neckel. Titanium carbonitrides, Ti(C,N): Electronic structure and chemical bonding. J Alloys Compounds 219:303, 1995. 161. AL Ivanovsky, VA Gubanov, EZ Kurmaev. Study of the electronic structure of hexagonal vanadium and niobium carbides and nitrides by cluster MO LCAO method. Zh Neorg Khim (USSR) 30:2969, 1985. 162. R Eibler. Electronic structure of ε-Ti 2N and δ′-Ti 2N. J Phys Condens Matter 5:5261, 1993. 163. R Eibler. Energetics of titanium nitrides of composition Ti 2N. J Phys Condens Matter 10:10223, 1998. 164. KE Spear. Chemical bonding in AlB 2-type borides. J Less Common Met 47:195, 1976. 165. PG Perkins, AVJ Sweeney. An investigation of the electronic band structures of NaB 6, KB 6, TiB 2, and CrB. J Less Common Met 47:165, 1976. 166. H Ihara, M Hirabayashi, H Nakagawa. Band structure and X-ray photoelectron spectrum of ZrB 2. Phys Rev B 16:726, 1977. 167. DL Johnson, BN Harmon, SH Liu. Self-consistent electronic structure of the refractory metal ZrB 2, a pseudographite intercalation compound. J Chem Phys 73:1898, 1980. 168. DR Armstrong. The electronic structure of the first-row transition-metal diborides. Theor Chim Acta (Berl) 64:137, 1983. 169. JK Burdett, E Canadell, GJ Miller. Electronic structure of transition-metal borides with the AlB 2 structure. J Am Chem Soc 108:6561, 1986. 170. De-Cheng Tian, Xiao-Bing Wang. Electronic structure and equation of state of TiB 2. J Phys Condens Matter 4:8765, 1992. 171. Xiao-Bing Wang, De-Cheng Tian, Li-Long Wang. The electronic structure and chemical stability of the AlB 2-type transition-metal diborides. J Phys Condens Matter 6:10185, 1994. 172. K Schwarz, H Ripplinger, P Blaha. Electric field gradient calculations of various borides. Z Naturforsch 51a:527a, 1996.

6 Lattice Vibrations, Heat Capacity, and Related Properties Go¨ran Grimvall Royal Institute of Technology, Stockholm, Sweden

I.

INTRODUCTION

The discussions in this chapter will pay particular attention to relations that are relevant for diatomic solids in either the NaCl-type crystal structure, as exemplified by TiC and TiN, or in the AlB 2-type crystal structure, as exemplified by TiB 2. A nonmagnetic metal has contributions to its heat capacity C p from the excitation of lattice vibrations (phonons) and conduction electrons. The vibrational part C vib can be expressed in the phonon density of states F(ω). Similarly, the vibrational entropy S vib , the corresponding Helmholtz energy Fvib ⫽ Uvib ⫺ TSvib , etc. are expressed in F(ω). The low-frequency part of F(ω) is uniquely given by the single-crystal elastic coefficients cij, for instance, by the three quantities c11 , c12 , and c44 for a solid with cubic lattice symmetry. The elastic coefficients c ij, when properly averaged, yield the engineering elastic constants of a polycrystalline material, i.e., the bulk modulus K, the shear modulus G, and Young’s modulus E. The phonon density of states also yields other quantities, such as the vibrational displacement that enters the Debye-Waller factor. Because the forces that determine the phonon frequencies ω are related to the bonding in the solid, there are connections between the properties just mentioned and other cohesion-related quantities, such as the cohesive energy and the melting temperature. This chapter briefly outlines the theoretical connection between these properties and then gives an application to refractory transition metal carbides, nitrides, and borides. The role of electronic excitations is also briefly exposed. Most of the general relations in the following sections are well known and can be found in a monograph by the present author (1) and in many textbooks. Therefore they are usually given without references to original work.

II. THE DEBYE AND SOMMERFELD MODELS OF THE HEAT CAPACITY Often the vibrational heat capacity Cvib of a solid is described by the Debye model, with a Debye temperature θ D. The electronic part Cel is usually described by the Sommerfeld model in which the heat capacity is linear in the temperature T. Thus, Cp ⫽ Cvib ⫹ Cel ⫽ CD (T/θ D) ⫹ γT

(1) 153

154

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In the low-temperature limit, C vib varies as T 3, and the Debye-model heat capacity per mole takes the form CD ⫽ rLk B

冢冣

12π 4 T 5 θD

3

(2)

Here r is the number of atoms per formula unit (i.e., r ⫽ 2 for TiC and r ⫽ 3 for TiB 2), L is Avogadro’s number, and k B is Boltzmann’s constant. In the electronic contribution at low temperatures, and per mole, γ⫽

2π 2 2 k BN(E F ) (1 ⫹ λ el-ph ) 3

(3)

where N(E F ) is the electron density of states at the Fermi level E F, per spin and mole. [Many sources let N(E F) refer to both electron spin directions. Then the prefactor 2 in Eq. (3) should be absent.] In Sommerfeld’s original theory, the so-called enhancement factor 1 ⫹ λ el-ph was not included. It is caused by many-body electron-phonon interactions, and its existence was not fully understood until the 1960s. The magnitude of λ el-ph typically varies between 0.2 and 1.5, with no simple correlation with the chemical composition of the solid. For transition metals and their compounds λ el-ph is often between 0.4 and 1.0, and λ el-ph ⬇ 0.9 may be a good estimate for several of the materials of interest here (2). Thin films often have a larger λ el-ph ; for example, λ el-ph ⬇ 1.46 ⫾ 0.10 was reported for NbN films by Kihlstrom et al. (3). In Eq. (3) a further enhancement due to interactions with spin fluctuations may be present in nearly magnetic solids; see Rietschel (4) for VN. Some data on θ D and another Debye temperature θ S, to be defined later, are given in Tables 2 and 5. Figure 1 gives the coefficient γ in Eq. (3) but without the enhancement factor (1 ⫹ λ el-ph ); i.e., it shows the ‘‘band structure’’ γ that is obtained from N(E ) in electron band structure calculations.

III. LOW-FREQUENCY PART OF THE PHONON DENSITY OF STATES A.

Sound Velocity and Debye Temperature

The Debye temperature θ D to be used in the low-temperature limit of the heat capacity is related to the average sound velocity Cav as

冢 冣


6π 2 rL θD ⫽ kB V

1/3

Cav

(4)

Cav is averaged over the longitudinal (s ⫽ 1) and the two transverse (s ⫽ 2, 3) sound velocities Cs(θ,φ) in directions given by the angles θ, φ in the single crystal (dΩ ⫽ sin θ dθ dφ): 3 ⫽ C 3av

3

冱 冮 C (θ,φ) 4π s⫽1

1

3 s

dΩ

(5)

The sound velocities Cs (θ,φ) are uniquely related to the single-crystal elastic constants c ij. In the special case that the single crystal is elastically isotropic we get 3 1 2 ⫽ ⫹ C 3av C 3L C 3T

(6)

Lattice Vibrations and Heat Capacity

155

Figure 1 The coefficient γ in the electronic heat capacity C el ⫽ γT plotted versus the average number of valence electrons per atom for some refractory compounds. γ is obtained through Eq. (3) from the electron density of states N(E ) in ab initio electron structure calculations for 3d metal compounds (5) and for NbN and TaN (2) i.e., without the enhancement factor (1 ⫹ λ el-ph) that is present only at low temperatures (approximately for T ⬍ θ D /3).

The longitudinal (L) and the transverse (T) sound velocities are expressed in the bulk modulus K and the shear modulus G as ρC 2L ⫽ K ⫹

4 G 3

(7)

and ρC 2T ⫽ G

(8)

where ρ is the mass density of the solid. B.

Elastic Properties of Polycrystalline Materials

A polycrystalline material without texture (i.e., without preferred crystal grain orientations) is elastically isotropic, in an average sense. Then the longitudinal and transverse sound velocities are still exactly given by Eqs. (7) and (8), even if the single crystal is not elastically isotropic. Because the number of independent elastic coefficients c ij is at least three, while Eqs. (7) and (8) contain only two elastic parameters K and G, there can be no general and exact algebraic relation between c ij and both of K and G. In fact, there is such an exact relation for K and cubic lattice symmetry only. It takes the form K⫽

c 11 ⫹ 2c 12 3

(9)

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The shear modulus G is limited by upper and lower bounds, G V ⱖ G ⱖ G R , often referred to as the Voigt (V) and Reuss (R) bounds. Then (1) G V ⫽ (c 11 ⫺ c 12 ⫹ 3c 44)/5

(10)

G R ⫽ 5(c 11 ⫺ c 12)c 44 /[4c 44 ⫹ 3(c 11 ⫺ c 12)]

(11)

In the case of hexagonal lattice symmetry (such as for TiB 2) there are five independent elastic coefficients, c 11, c 12 , c 13 , c 33 , and c 44 . Then the polycrystal bulk modulus and shear modulus are bounded by K V ⱖ K ⱖ K R and G V ⱖ G ⱖ G R , with (see, e.g., Ref. 1) KV ⫽

1 [2(c 11 ⫹ c 12) ⫹ c 33 ⫹ 4c 13] 9

(12)

K R ⫽ C 2 /M GV ⫽

1 [12c 66 ⫹ 12c 44 ⫹ M] 30

GR ⫽

5 c 44 c 66 C 2 2 (c 44 ⫹ c 66) C 2 ⫹ 3K V c 44c 66

冤

(13) (14)

冥

(15)

where C 2 ⫽ (c 11 ⫹ c 12 )c 33 ⫺ 2c 213

(16)

M ⫽ c 11 ⫹ c 12 ⫹ 2c 33 ⫺ 4c 13

(17)

c 66 ⫽ (c 11 ⫺ c 12 )/2

(18)

Under certain conditions on overall isotropy, there are narrower but algebraically more complicated bounds usually referred to as the Hashin-Shtrikman bounds (see, e.g., Ref. 1). However, for not too elastically anisotropic single crystals, one is usually satisfied with bulk and shear moduli given by the Voigt-Reuss-Hill approximation, which has the forms K ⬇ KVRH ⫽ (KV ⫹ K R)/2

(19)

G ⬇ G VRH ⫽ (G V ⫹ G R)/2

(20)

We shall see that this is an excellent approximation for the refractory compounds considered in this chapter. Young’s modulus for a polycrystalline material without texture, and expressed in K and G, is exactly given by E⫽

9KG 3K ⫹ G

(21)

and Poisson’s number ν is exactly given by ν⫽

3K ⫺ 2G 2(3K ⫹ G)

(22)

Hence one can choose any two of the four elastic parameters K, G, E, and ν to specify uniquely the other two engineering elastic constants. Because K and G are bounded as shown before, E is also bounded, E V ⱖ E ⱖ E R, by expressions obtained from Eqs. (12)–(15) and (21). There is no analogous bound to ν.

Lattice Vibrations and Heat Capacity

157

Table 1 Elastic Engineering Constants K, G, and E (in GPa) and Poisson’s Number v, as Calculated from the Cited (7) Experimental c ij (in GPa) a Compound

c 11

c 12

c 44

K

TiC ZrC VC 0.83 NbC 0.9 TaC 0.9

513 441 366 413 505

106 60 110 111 73

178 151 192 206 79

242 187 195 212 217

a

G 188 166 163 182 120

⫾ ⫾ ⫾ ⫾ ⫾

1 1 3 2 14

E

ν

448 384 382 425 304

0.19 0.16 0.17 0.17 0.27

The upper and lower limits given for G refer to the upper (Voigt) bound G V and the lower (Reuss) bound G R . G of TaC 0.9 is discussed in the text.

Table 1 gives experimentally determined elastic coefficients c ij and the corresponding engineering elastic constants K from Eq. (9), G ⫽ G VRH from Eq. (20), E from Eq. (21), and ν from Eq. (22). The uncertainties in c ij, and hence in the resulting engineering elastic constants, may be large (see comment later on TaC). Kosolapova (6) cites experimentally determined Young’s moduli E for a large number of refractory compounds. For the compounds considered here, the values given by Kosolapova often differ much (⬎20%) among themselves and also differ from the E values in Table 1. However, the table also serves the purpose of showing how K, G, E, and ν can be obtained from c ij. We next exemplify how the elastic constants are related to the conventional Debye temperature θ D from the low-temperature heat capacity [i.e., θ D(⫺3) in Table 4]. The detailed numerical integration in Eq. (5) yields θ D as shown in the first row of Table 2, using c ij from Table 1 and mass densities ρ calculated from the atomic volumes Ω a [⫽V/(rL)] in Table 5. As an illustration we shall also apply Eqs. (6)–(8) together with Eqs. (19) and (20), which allow a simple calculation of θ D. Anderson (8) suggests that such an approach, with K and G estimated by the VoigtReuss-Hill approximation, gives θ D to within about 2% when A H ⬍ 0.2. Here A H ⫽ (G V ⫺ G R)/ (G V ⫹ G R ) is a measure of the elastic anisotropy. Table 2 summarizes the results for θ D. The results for TaC in Table 1 and 2 motivate a comment. Poisson’s number of TaC differs significantly from that of TiC, ZrC, VC, and NbC. This is in contrast to the regularities these compounds show in the atomic volume Ω a , the entropy Debye temperature θ S, and the related quantity E S (Table 5, Figs. 7–9). Tables 2 and 5 give θ D /θ S ⫽ 1.12 ⫾ 0.05 for TiC, ZrC, VC, and NbC, whereas θ D /θ S ⫽ 0.76 for TaC, which suggests that θ D for TaC obtained here from cij is too low. Comparison with θ D from low-temperature heat capacity measurements could show whether θ D calculated for TaC from c ij is correct, because the two Debye temperatures should be equal. The θ D values reported by Kosolapova (6) are too uncertain to settle the problem. However, θ D from heat capacity data in Roedhammer et al. (9), together with our θ S , gives θ D /θ S ⫽ 1.05 ⫾ 0.09 for TiC, ZrC, VC, and NbC and 1.06 for TaC 0.9. This is strong evidence that the actual c 44 of TaC 0.9 lies outside the experimental uncertainty suggested in the Table 2 Debye Temperatures θ D Calculated Accurately from c ij in Table 1 (First Line) and Calculated Approximately from K and G (Second Line) a

θ D (K) θ D (K) AH a

TiC

ZrC

VC 0.83

NbC 0.9

TaC 0.9

938 940 0.005

697 699 0.006

847 851 0.018

710 713 0.011

418 430 0.12

The parameter A H measures the elastic anisotropy.

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experimental work (10). Suppose that G in Table 1 is too low. Assuming that ν ⫽ 0.17 and an unchanged K ⫽ 217 GPa yields G ⫽ 184 GPa, from which θ D ⫽ 512 K and θ D /θ S ⫽ 0.93. Even that is a bit low and also suggests a larger K. We note that θ D in Table 2 was calculated here with the correct mass density and crystal volume for the nonstoichiometric compounds, but with a normalization of the Debye spectrum assuming stoichiometry (r ⫽ 2). A correct normalization for a compound MX y would reduce θ D by a factor [(1 ⫹ y)/2] 1/3 , that is, by ⬍2% for TaC 0.9, which is negligible in the context of the present discussion. We also note that the heat capacity may be affected by order-disorder effects in nonstoichiometric carbides (11), but not enough to change our conclusions. Very little is known about the single-crystal elastic coefficients c ij for the noncubic refractory diborides. For TiB 2 experimental results are available (7) for c 11 ⫽ 690 GPa, c 33 ⫽ 440 GPa, c 44 ⫽ 250 GPa, and c 12 ⫽ 410 GPa. The value c 13 ⫽ 320 GPa is estimated (7). With these c ij, Eqs. (12)–(18) give K ⫽ 412 ⫾ 24 GPa and G ⫽ 169 ⫾ 11 GPa, where the limits refer to the Voigt and Reuss bounds. Then θ D ⫽ 1000 K, to be compared with our θ S ⫽ 972 K. Lowtemperature heat capacity data (12) give θ D ⫽ 1182 K, after multiplication by 3 1/3 to get the normalization used here. The lack of agreement is typical of the difficulties in determining θ D from experiments on elastic constants or heat capacities.

C.

Effect of Porosity

Many refractory compounds are obtained through sintering, which may give a material with a certain porosity. As an illustration, we assume that the pores are spherical and with a radius that is much larger than the size of an atom; i.e., the pores are macroscopic. Let a volume fraction p of a material be made up of pores, so that the mass density is 1 ⫺ p of the ideal density. The elastic properties of such a material, in the dilute limit that p ⬍⬍ 1, are given by (subscript e refers to the effective properties of the porous material and quantities without subscripts refer to the nonporous material)

冤

3K ⫹ 4G 4G

冤

5(3K ⫹ 4G) 9K ⫹ 8G

Ke ⬇ K 1 ⫺ p

Ge ⬇ G 1 ⫺ p

冥

(23)

冥

(24)

The effective Young’s modulus E e follows from Eq. (21), that is, E e ⫽ 9K e G e /(3Ke ⫹ G e ). As the pores are assumed to be macroscopic, the heat capacity and its directly related properties are not affected. A certain mass of the compound has the same heat capacity, irrespective of the presence of pores. The engineering elastic constants Ke and G e give the sound velocities according to Eqs. (7) and (8), but obviously those sound velocities for porous materials are not to be used in the calculation of a Debye temperature. It is sometimes unclear how well measured elastic constants have been corrected for porosity. Therefore one must be cautious when Debye temperatures of refractory compounds calculated from elastic parameters are compared with Debye temperatures obtained from a fit to low-temperature heat capacity data. Figure 2 shows measured moduli G e and E e for NbC, as given by Toth (13). It also gives the theoretical E e , G e , and Ke that follow from Eqs. (23) and (24), i.e., from an extrapolation of the low-porosity limit for spherical pores, and using the experimental values of Fig. 2 for G and E at zero porosity. Nonspherical pores would give lower values of E e , G e, and K e .

Lattice Vibrations and Heat Capacity

159

Figure 2 Experimental data (symbols, from Ref. 13) for the shear modulus G e and Young’s modulus E e as a function of the porosity. Solid lines give theoretical estimates for G e , E e , and the bulk modulus K e obtained in a model with spherical pores, Eqs. (23) and (24).

IV. PHONON DENSITY OF STATES AND DEBYE TEMPERATURES A.

General Expressions for Thermodynamic Quantities

The lattice vibrations of a solid are often described by citing a Debye temperature. However, the Debye temperature varies with the physical property one considers and with the temperature at which this property is described. Therefore tables with Debye temperatures must always be considered with caution. In the case of solids in which the constituent atoms have a large mass ratio, as is the case in many refractory compounds, it is particularly important to be aware of how different Debye temperatures are defined and used. We therefore give the theoretical background in some detail. Thermodynamic quantities of harmonic lattice vibrations, such as the energy U, heat capacity C, and entropy S, can be expressed in the phonon density of states F(ω), normalized to three per atom, where hω is the energy of a phonon. One has, per mole, U(T ) ⫽ rL

C(T ) ⫽ rL

S(T ) ⫽ rL

冮

ω

冮

ω

max

UE (T;ω) F(ω) dω

(25)

CE (T;ω) F(ω) dω

(26)

S E(T;ω) F(ω)dω

(27)

0

max

0

冮

0

ω

max

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where U E , C E, and SE are the expressions for an Einstein model of the lattice vibrations, i.e., for a single oscillator. One has U E(T;ω) ⫽ hω

冤exp(hω/k1 T) ⫺ 1 ⫹ 21冥

(28)

B

CE(T;ω) ⫽ k B

冢 冣

S E(T;ω) ⫽ k B

冤2khωT coth冢khωT冣 ⫺ ln 冢2 sinh冢2kh ωT冣冣冥

hω kBT

2

exp(hω/k B T) [exp(hω/k B T) ⫺ 1] 2

B

B

(29)

(30)

B

Two high-temperature expansions will be of particular interest, namely C(T) ⫽ rLk B

冮

ω

S(T ) ⫽ rLk B

冮

ω

max

0

0

max

[1 ⫺ (1/12) (hω/k B T) 2 ⫹ (1/240) (hω/k B T) 4 ⫹ ⋅ ⋅ ⋅] F(ω)dω

(31)

[1 ⫹ ln(k B T/hω) ⫹ ⋅ ⋅ ⋅ (1/24) (hω/k B T ) 2 ⫹ ⋅ ⋅ ⋅] F(ω)dω

(32)

The vibrational displacement of atoms will be illustrated here with a solid such as TiC, whose primitive crystallographic cell contains two atoms (labeled 1 and 2), having masses M 1 and M 2 and displacements u 1 and u 2 . Then (1) M 1 〈u 21〉 ⫹ M 2 〈u 22 〉 ⫽ 2

冮

ω

max

[U E(ω;T) /ω 2 ] F(ω)dω

(33)

0

Brackets 〈 〉 denote a thermal average. At high temperatures UE ⬇ k B T, and M 1 〈u 21 〉 ⫹ M 2 〈u 22 〉 ⬇ 2k B T

冮

ω

0

max

ω ⫺2 F(ω)dω

(34)

An interesting case is that the interatomic forces act only between nearest neighbors, in cubic structures, and at high temperatures (i.e., T ⬎ θ D). Then the two displacements are equal and hence independent of the mass ratio M 1 /M 2 (1,14). This counterintuitive result, with equal thermal displacements of the light nonmetal and heavy metal atoms in NaCl crystal–type refractory carbides and nitrides, seems to hold approximately even though the condition on the interatomic forces is not strictly obeyed. This is illustrated in Table 3, which gives the Debye parameter B Table 3 Displacements of Metal and Nonmetal Atoms at Room Temperature, as Given by the Debye Parameter B, Based on Experiments and from an Unpublished Compilation Compound TiC ZrC NbC TiN ZrN NbN Source: From Ref. 15.

B metal (10 ⫺20 m 2 )

B nonmetal (10 ⫺20 m 2)

0.15 ⫾ 0.02 0.21 ⫾ 0.02 0.19 ⫾ 0.02 0.18 ⫾ 0.02 0.23 0.36

0.15 ⫾ 0.02 0.21 ⫾ 0.02 0.18 ⫾ 0.02 0.17 ⫾ 0.02 0.16 0.26

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that enters the conventional Debye-Waller factor exp(⫺M ). Here M ⫽ B sin 2 θ/λ 2 and B ⫽ 8π 2 〈u 2i 〉 with i referring to the metal and nonmetal atom, respectively. Data, based on experiments, are from Ref. 15. B.

Frequency Moments

We define frequency moments ω(n) of the phonon density of states F(ω) as

[ω(n)] ⫽ n

冮

ω

max

0 ω

冮

ω n F(ω)dω (35)

max

F(ω) dω

0

when n ⬎ ⫺3 and n ≠ 0. For n ⫽ 0, ω(0) is defined as

ln ω(0) ⫽

冮

ω

max

0

冮

ω

ln ω F(ω)dω (36) max

F(ω)dω

0

Equation (31) now implies that to leading order in the temperature dependence, the high-temperature heat capacity of harmonic lattice vibrations depends only on the frequency moment ω(2). From Eq. (32) we see that the high-temperature vibrational entropy depends only on the moment ω(0). A certain combination [see Eq. (34)] of the thermal atomic displacements at high temperatures depends on ω(⫺2). Table 4 summarizes these results, together with the case of very low temperatures, which will be discussed in the following section. In the preceding discussions, the phonons were described by their angular frequencies ω. Many works on lattice dynamics instead use the frequency ν ⫽ ω/2π, that is, hν ⫽ hω in our notation. C.

Debye Model for the Phonon Spectrum

It is common practice to approximate the true density of states F(ω) with the Debye model density of states FD(ω), which has an upper cutoff frequency ω D FD (ω) ⫽ 9ω 2 /ω 3D

(37)

Table 4 In the Limit of Low or High Temperatures, Some Important Thermodynamic Quantities Depend Only on a Single Frequency Moment ω(n) or Equivalently on a Single Debye Temperature θ D (n) Thermodynamic quantity

Temperature

Value of n in ω(n), θ D (n)

C vib S vib C vib S vib M 1 〈u 21 〉 ⫹ M 2 〈u 22〉

T→0 T→0 High T (T ⬎ θ D) High T (T ⬎ θ D) High T (T ⬎ θ D)

⫺3 ⫺3 2 0 ⫺2

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Here FD (ω) has been normalized to three per atom. A Debye temperature θ D can be defined through k B θ D ⫽ hω D ⫽ hν D

(38)

If FD (ω) replaces F(ω) in Eqs. (25)–(27) we get the Debye model expression for the heat capacity, C D (T; θ D ), for the entropy, S D (T; θ D ), etc. We next require that a physical property for an actual phonon density of states F(ω) is represented by a Debye model spectrum. For instance, we can let the actual entropy S(T ) be described by S D (T; θ D ) and write S(T ) ⫽ S D (T;θ D )

(39)

The S(T ) on the left-hand side of Eq. (39) could be an entropy S vib,exp (T ) determined from experiments or it could be the result of a detailed model calculation based on a certain F(ω) in Eq. (27). There is a solution θ D to Eq. (39) for each temperature T. We shall call that θ D a ‘‘Debye temperature.’’ Because we represent the property of a system that has 3rL degrees of freedom with a single parameter θ D, it is obvious that we have to pay a price. In this case, the price is that θ D varies with T and also with the physical property that is modeled. (Here θ D refers to the entropy.) One may therefore introduce one Debye temperature θ S that describes the vibrational entropy, another Debye temperature θ C that describes the vibrational heat capacity, etc. The heat capacity Debye temperature θ C would be the solution to C(T ) ⫽ C D(T;θ C)

(40)

where C(T ) is the actual heat capacity of a system. We can also define Debye temperatures θ D (n) such that they correctly reproduce the frequency moment ω(n) of a certain density of states F(ω). One finds that k B θ(n) ⫽

冢 冣 n⫹3 3

1/n

hω(n)

(41)

when n ⬎ ⫺3 and n ≠ 0. For n ⫽ 0, one has k B θ(0) ⫽ exp(1/3) hω(0). Most tables listing Debye temperatures take θ D from a description of the heat capacity in the limit of low temperatures. One can show that this corresponds to the limit n → ⫺3, so that the Debye temperature θ(⫺3) ⫽ θ C (T → 0). This quantity can be defined only through the mathematical limit of T → 0 in Eq. (26), as ω(n) is defined only for n ⬎ ⫺3. The low-temperature limit of the vibrational heat capacity (and the thermal energy and the entropy) only ‘‘probes’’ the low-frequency limit of F(ω), i.e., the long-wavelength limit of the acoustic phonon branches. That part is also given uniquely by the elastic constants, as mentioned before, and we can define an ‘‘elastic limit’’ Debye temperature θ E that also equals θ(⫺3). Debye temperatures obtained from the low-temperature heat capacity and from the elastic constants should thus be equal, but only if the elastic constants are also measured at very low temperatures. Normally, they are measured at room temperature and are somewhat lower than the values at 0 K because of anharmonic effects. Therefore θ E based on room-temperature elastic constants is usually somewhat lower than θ C (T → 0). [One may note that c 12 increases slightly with T from 0 K to 300 K for TiC, VC 0.83 , and NbC 0.83 but c 11 and c 44 decrease; see Kumashiro et al. (16) and Every and McCurdy (7).] The expression (31) for the heat capacity can never exceed the value 3k B per atom because it assumes strictly harmonic vibrations. In contrast, real systems are anharmonic and usually the heat capacity increases with T above the value 3k B . Then Eq. (40) has no physical solution θ D. When the measured C(T ) approaches 3k B per atom, small errors in C(T ) give rise to a large uncertainty in θ C . Therefore the heat capacity Debye temperature θ C (T ) of a real system is meaningful only for, say, T ⬍ θ D. The case of the entropy is different. There is no upper limit

Lattice Vibrations and Heat Capacity

163

for the vibrational entropy, and the equation S vib (T ) ⫽ S D(T;θ S) always has a solution θ S(T ). Further, when anharmonic effects enter S vib they are correctly accounted for, to low order in quantum mechanical perturbation theory, by anharmonic shifts in θ S(T ) (1). Finally, as we shall return to later, the atomic masses enter θ S in a simple multiplicative way. Figure 3 shows the gross features of the phonon density of states F(ν) for TiC, as obtained by Pintschovius et al. (17) from a fit to their experiments using inelastic neutron scattering. (The actual measurements were performed on crystals having the compositions TiC 0.95 and TiC 0.89. We treat the data as if they refer to stoichiometric TiC.) The two more thinly drawn parabolic curves in Fig. 3 are Debye densities of states. These Debye models have cutoff frequencies ν D and corresponding Debye temperatures θ D ⫽ hν/k B. The one with the higher ν D encloses the same area as the experimental F(ν). The parabolic curve with the lower ν D has half of that area, i.e., ν D is smaller by a factor 2⫺1/3 , and it would correspond to a θ D that is also smaller by the same factor. At very low temperatures, the optical branch of the phonon spectrum is not excited. The heat capacity then depends only on the acoustic vibrations, i.e., on the low-frequency part of F(ω). One may then take r ⫽ 1 in Eq. (2) and ignore the carbon or nitrogen atoms (although the mass density ρ must also include the nonmetal atoms) or take r ⫽ 2 and normalize F D and θ D accordingly. Both approaches give the same heat capacity at very low T, but because only a description with r ⫽ 2 is relevant at intermediate and high temperatures, we will adopt the latter definition in this chapter. The two possibilities are mentioned here for the reason that the convention r ⫽ 1 has been used in publications on the thermal properties of refractory carbides and nitrides (9,11,12). Figure 4 shows the solutions θ S (T ) and θ C (T ) to Eqs. (39) and (40) for TiC when the heat capacity and the entropy are taken from recommended experimental data in the JANAF tables (18) of thermodynamic functions. Because the experiments give the sum of vibrational and electronic contributions, an electronic part has been subtracted assuming that γ ⫽ 0.5 mJ/(mol ⋅ K 2) at all T and (for simplicity) without correction for the electron-phonon enhancement. In fact, the enhancement goes to zero with increasing temperature and can be ignored when T ⬎ θ D / 3. [A table with data for TiC at a more dense set of temperatures than in the printed JANAF

Figure 3 The phonon density of states F(ν) for TiC (17), based on neutron scattering data. The two thinly drawn parabolas give Debye model spectra normalized to one and two atoms per formula unit, respectively (see text).

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Figure 4 The entropy Debye temperature θ S(T ) and the heat capacity Debye temperature θ C(T ) for TiC, as obtained from recommended thermodynamic data (18), using Eqs. (39) and (40).

version was obtained from Dr. Malcolm Chase at the National Institute of Standards and Technology (NIST).] At high temperatures (T ⬎ 300 K) the value of θ C becomes physically meaningless, for reasons discussed earlier. Figure 5 shows the entropy Debye temperature θ S (T ) obtained as in Fig. 4 but plotted here up to the melting temperature of TiC. The rather strong temperature dependence of θ S(T ) below about 300 K is due to the fact that we model the vibrational entropy of a complex phonon spectrum by a function of a single parameter (i.e., θ S). At high T and if the vibrations were strictly harmonic, θ S(T ) would asymptotically approach the value θ S ⫽ θ(0). However, anharmonic effects usually cause the vibrational frequencies to decrease with T. This is the reason

Figure 5 The entropy Debye temperature θ S (T ) for TiC, as in Fig. 4 but extended to the melting temperature.

Lattice Vibrations and Heat Capacity

165

for the decrease in θ S(T ) that is seen in Fig. 5 above about 400 K. To low order in quantum mechanical perturbation theory, this decrease is linear in T. At very high temperatures there are higher order anharmonic effects that give rise to a faster temperature dependence. We finally remark that part of the strong decrease in θ C (T ) above 300 K would be suppressed if we had fitted the Debye model to the heat capacity at constant volume, C V(T ), instead of the fit to the experimental C p(T ), which is measured at constant pressure. It is a common misunderstanding that the vibrational heat capacity C V has all anharmonicity suppressed and hence tends to 3k B per atom at high T. This is not true, because there remain the anharmonic effects due to increased vibrational atomic displacements, even when the total volume is kept fixed. Therefore θ C(T ) may not be a well-behaved quantity at very high T, even when it is calculated from CV data. V.

QUANTITIES RELATED TO THE BONDING IN THE SOLID

There are several, more or less well defined, quantities that can be taken as measures of the strength of the bonding in a solid. Refractory transition metal carbides, nitrides, and borides are characterized by a high hardness and a high melting temperature T m. The hardness is a property that in practice depends in a complex way on defect structures and other characteristics of the specific test sample. Therefore hardness is not a quantity that can be uniquely related to a fundamental description of the electronic structure. The melting temperature, on the other hand, is in principle determined only by the electronic structure of the solid and liquid phases, but since the thermodynamic properties of the liquid are so difficult to account for accurately, one cannot reliably calculate Tm from first-principles considerations. This can be contrasted with the cohesive energy E coh and the enthalpy of formation ∆H. Modern first-principles electronic structure calculations (at 0 K) are so advanced that E coh and ∆H, within a not too distant future, can be obtained with an accuracy that matches that of experiments. Already today, they accurately give the trends when chemically similar compounds are compared, for instance, by varying the constituent atoms horizontally or vertically in the periodic table. Such theoretically established trends may predict unknown quantities when there are experimentally determined data for a few compounds that can be used for ‘‘calibration’’ (5,19–21). The electronic structure of refractory compounds is considered elsewhere in this book. In this chapter we shall relate the bonding strength to the lattice vibrations and introduce an entropy-related quantity E S that has the dimension of energy and correlates well with other measures of the bonding strength. The phonon spectrum of a solid depends on the interatomic forces as well as on the atomic masses. For an element, the mass dependence is trivial. All phonon frequencies, and hence also all frequency moments ω(n), vary with the atomic mass M as M ⫺1/2. In a compound with two or several different atomic masses, the vibrational frequencies depend on the interatomic forces and on the masses in a complex way, with two exceptions. In the low-frequency part of the phonon density of states, which is uniquely given by the sound velocities, the vibrational frequencies vary as ρ ⫺1/2 , where ρ is the mass density of the solid. It follows that θ C (⫽ θ S) in the limit of low temperatures has interatomic forces and atomic masses separated in the form of two multiplicative factors. The force-constant part is directly related to the elastic coefficients c ij. Hence the low-temperature limit of the Debye temperature gives a certain average over the interatomic forces, as it is reflected in the sound waves. We shall now introduce another average over the interatomic forces, uniquely related to the entire phonon spectrum. It has been shown (22) that in the logarithmic average ω(0) of the phonon spectrum, the atomic masses enter only as a multiplicative factor (M log ) ⫺1/2. We noted earlier that k B θ S ⬇ hω(0) exp(1/3) at high temperatures. Then one can write k B θ S ⫽
√k S /M log

(42)

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Here k S has the dimension of a force constant and is a certain (complicated) average over all the interatomic forces in the solid, and M log is the logarithmic average of the atomic masses. For instance, M log ⫽ (M TiM C)1/2 in TiC and M log ⫽ (M TiM 2B) 1/3 in TiB 2. Equation (42), with θ S determined from experiments, thus allows us to obtain an ‘‘experimental’’ value for k S . A practical difficulty is that θ S(T ) varies with T. One unique prescription for evaluating k S would be to base it on the value of θ S(T ) taken at T ⫽ θ S. Then the temperature is still low enough that anharmonic effects are moderate, but the temperature is also high enough that the variations of θ S(T ) caused by the precise shape of F(ω) are small. This definition is adopted in most of this chapter. However, in some cases the only entropy information available refers to the standard entropy S°(298.15 K). Taking the corresponding θ S (298.15 K) is also reasonable in a calculation of k S. We see from Figs. 4 and 5 that θ S(T ) is slowly varying over a wide temperature range at intermediate temperatures and therefore gives only a small variation in the corresponding force constant k S . The quantities E coh , ∆H, and k B Tm are three measures of the bonding strength that all have the physical dimension of energy. To enable a comparison with bonding strengths extracted from θ S, we multiply k S by a length squared. One could define such a length in different ways. Here it will be obtained as Ω 1/3 a , where Ω a is the average volume per atom in the compound, i.e., the total volume of a crystallographic unit cell divided by the number of atoms in that cell [Ω a ⫽ V/(Lr) in Eq. (4)]. This definition has the advantage that it makes no explicit reference to the crystal structure. Now a cohesion-related quantity E S can be defined as E S ⫽ k S Ω a2/3

(43)

The E S has several attractive features. It is uniquely related to the vibrational entropy at high temperatures but still does not depend on atomic masses. Hence E S depends only on the electronic structure in the solid. Further, E S behaves in a regular way and is often approximately constant when chemically similar compounds are compared. The standard entropy S° of a compound is often better known than other thermodynamic quantities, which makes E S a readily available quantity. Extrapolations or interpolations of experimentally determined E S may provide an accurate way to obtain otherwise unknown Debye temperatures and gives a link (although approximate) to elastic parameters. VI. COMPARISON OF BONDING-RELATED QUANTITIES In this section we compare several of the bonding-related quantities we have introduced, with particular attention to trends in the periodic table. Table 5 summarizes some important data. Debye temperatures depend on the atomic masses as well on the electronic structure, as the latter is reflected in the interatomic forces. In addition to considering trends in the entropy Debye temperature θ S (determined at T ⬇ θ S ), we consider trends in the related quantity E S, which is not affected by the atomic masses. We will also consider the cohesive energy E coh (per atom) for a compound AX, defined by E coh ⫽ ⫺

1 (E AX,cryst ⫺ E A,atom ⫺ E X,atom) 2

(44)

where E AX,cryst is the total energy of the compound AX, and E A,atom and E X,atom are the total energies of atoms of the elements A and X. Hence E coh is the energy required to separate the solid AX into atoms A and X. We shall now demonstrate, in a number of figures, how various bonding-related quantities covary and show regular behavior with the position of the chemical elements in the periodic table. Figure 6 shows how the entropy Debye temperature θ S varies with the transition metal

Lattice Vibrations and Heat Capacity

167

Table 5 The Entropy-Related Debye Temperature θ S , the Corresponding Force Constant k S and Energy E S , Average Volume per Atom Ω a , and Cohesive Energy E coh Compound ScC TiC VC CrC ScN TiN VN CrN ZrC HfC NbC TaC ZrN HfN NbN TaN TiB2 ZrB2 HfB2

θ S (K)

kS (N/m)

Ωa (10 ⫺30 m 3 )

ES (Ry) a

654 805 745 664 755 710 631 535 650 581 634 551 582 521 539 489 972 834 741

283 442 391 314 407 372 303 220 398 445 382 403 345 386 298 343 477 436 426

13.144 10.110 9.058 8.700 11.429 9.521 8.869 8.921 12.962 12.494 11.164 11.064 11.958 11.529 10.591 10.217 8.566 10.234 9.883

7.23 9.48 7.79 6.09 9.47 7.67 5.96 4.34 10.07 10.99 8.75 9.18 8.28 9.04 6.59 7.41 9.16 9.43 9.00

a 1 Ry ⫽ 2.18 ⫻ 10⫺18 J. Source: Data from Refs. 5, 19, 20, and 23.

Figure 6 The entropy Debye temperature θ S (from Refs. 5, 19, 20, and 23; see Table 5) for transition metal carbides, nitrides, and oxides.

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Figure 7 The entropy-related quantity E S , the cohesive energy E S , and the melting temperature T m for transition metal carbides (filled symbols) and nitrides (unfilled symbols) in the NaCl-type crystal structure. Data as in Figs. 8–10.

for carbides, nitrides, and oxides in the NaCl-type structure. Figure 7 gives a similar plot for the cohesive energy E coh, the quantity E S, and the melting temperature T m, for some carbides (filled symbols) and nitrides (open symbols). Figure 8 shows that E S varies with the metallic element for carbides, nitrides, and oxides in a regular way, when plotted as a function of the average number of valence electrons n e per atom in the compound. E S is a measure of the bonding strength and may correlate well with the melting temperature, as shown in Fig. 9. The origin of this relation is analogous to that of the well-known Lindemann melting rule. As in the latter case, one does not expect a universally obeyed relation between E S and Tm. It works best for elements and binary compounds, where the interatomic forces can be well described by simple nearest-neighbor interactions. Figure 10 shows a similar plot for the correlation between E S and E coh. It is not as good as that between E S and Tm. This is not unexpected because E S and T m depend on the interatomic forces characteristic of the condensed compound AX and E coh measures the forces when AX is taken all the way from the condensed phase to separated atoms. Further plots relating E S , E coh , Tm, and other cohesion-related quantities have been published for 3d, 4d, and 5d transition metal carbides and nitrides (5,19–21,23–26) and AlB 2 structure–type transition metal diborides (27,28). The parameter γ in Fig. 1 is directly proportional to N(E ). Thus, with reference to a rigidband electron structure, Fig. 1 can also be viewed as giving an approximate variation of N(E ) with the electron energy E. TiC and ScN have a Fermi level falling at a minium in N(E ) that separates the lower lying bonding electron states from antibonding states of higher energy. The high cohesive strength of these compounds is thus explained by the full utilization of the bonding electron states (21). The decreases in θ S and E S seen for ScC in Figs. 6–8 are immediately explained by the fact that the bonding electron states are not completely filled for ScC.

Lattice Vibrations and Heat Capacity

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Figure 8 The phonon-related energy E S , for solids in the NaCl-type crystal structure, and in energy units of Ry (1 Ry ⫽ 2.18 ⫻ 10⫺18J), plotted versus the average number n e of valence electrons per atom in the compound (n e ⫽ 4 for pure C; 5 for N; 3 for Ti, Zr, Hf; 4 for V, Nb, Ta, etc.). Data from Refs. 5, 19, 20, and 23; see Table 5.

Figure 11 correlates the entropy-related force constant k S with the hardness of some refractory compounds. Because the hardness is measured in the unit of pressure (i.e., having the dimension of force constant per length), we correlate hardness with k S /a, where a is the measured lattice parameter.

VII. CONCLUSIONS This chapter has focused on properties related to the interatomic forces in solids, in particular as they are reflected in the phonon spectrum and in the elastic constants. A phonon spectrum is often crudely characterized by a Debye temperature. The concept of a Debye temperature may give a convenient and accurate description of the vibrational spectrum, provided that the Debye temperature is properly defined. Different physical phenomena depend on different averages over the phonon spectrum and hence cannot be described by the same Debye temperature.

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Figure 9 The melting temperature T m plotted versus the phonon-related energy E S for solids in the NaCltype crystal structure. Unfilled symbols refer to compounds that decompose or change crystal structure before melting. Melting points are from Ref. 18 or, if not given there, from Ref. 29 or 6. T m for TaC is exceptionally uncertain.

Figure 10 The experimental cohesive energy E coh (data from Refs. 5, 19, and 20; see Table 5) plotted versus the phonon-related energy E S for solids in the NaCl-type crystal structure and in energy units of Ry (1 Ry ⫽ 2.18 ⫻ 10⫺18 J). The straight lines are only guides for the eye. They refer to 4d and 5d transition metals from groups IV (Zr, Hf) and V (Nb, Ta) in the periodic table, respectively, and 3d elements from group V (V) and from group IV (Ti) plus Sc from group II and Cr from group V.

Lattice Vibrations and Heat Capacity

171

Figure 11 The hardness of some refractory compounds plotted versus k S /a, where k S is the force constant obtained from θ S through experimental vibrational entropy data. Adopted from Ref. 30.

We have paid particular attention to the entropy Debye temperature θ S, not only because it is the relevant parameter to represent the entropy (and hence the Gibbs energy) but mainly because it is physically well defined, often readily available from thermodynamic data, smoothly varying with temperature and chemical composition, and has a simple dependence on the atomic masses and the electronic structure of the solid. In this chapter we have also considered in some detail the elastic properties, in particular the relation between the elastic coefficients c ij describing a single crystal and the engineering elastic constants describing a polycrystalline material, i.e., Young’s modulus E, the shear modulus G, the bulk modulus K, and Poisson’s number v. The effect of porosity and nonstoichiometry is also dealt with. In addition to a general theoretical treatment of properties related to lattice vibrations, this chapter gives some experimental data for refractory materials. Much of the available experimental information is uncertain, with conflicting results reported by different research groups and using different experimental techniques. In assessments of such experimental information for a particular material, it may be helpful to employ the theoretically and empirically well-founded correlations that have been discussed here. This was exemplified is some detail for TaC, suggesting a new value for the shear modulus G.

REFERENCES 1. G Grimvall. Thermophysical Properties of Materials. Amsterdam: North-Holland, 1986. 2. DA Papaconstantopoluos, WE Pickett, BM Klein, LL Boyer. Electronic properties of transition-metal nitrides: The group-V and group-VI nitrides VN, NbN, TaN, CrN, MoN, and WN. Phys Rev B31: 752, 1985. 3. KE Kihlstrom, RW Simon, SA Wolf. Tunneling α 2 F(ω) from sputtered thin-film NbN. Phys Rev B32:1843, 1985. 4. H Rietschel. Importance of spin fluctuations for the thermodynamic properties of superconducting V and VN. Phys Rev B24:155, 1981. 5. J Ha¨glund, G Grimvall, T Jarlborg, A Ferna´ndez Guillermet. Band structure and cohesive properties of 3d-transition metal carbides and nitrides with the NaCl-type structure. Phys Rev B43:14400, 1991. 6. TY Kosolapova, ed. Handbook of High-Temperature Compounds: Properties, Production, Applications. New York: Hemisphere, 1990.

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7. AG Every, AK McCurdy. Second and higher order elastic constants. In: Landolt-Bo¨rnstein New Series. Vol 29a. Berlin: Springer-Verlag, 1992. 8. OL Anderson. A simplified method for calculating the Debye temperature from elastic constants. J Phys Chem Solids 24:909, 1963. 9. P Roedhammer, W Weber, E Gmelin, KH Rieder. Low temperature specific heat and phonon anomalies in transition metal compounds. J Chem Phys 64:581, 1976. 10. RW Bartlett, CW Smith. Elastic constants of tantalum monocarbide, TaC 0.90 . J Appl Phys 38:5428, 1967. 11. AI Gusev, AA Rempel, VN Lipatnikov. Heat capacity of niobium and tantalum carbides NbCy and TaC y in disordered and ordered states below 300 K. Phys Status Solidi (b) 194:467, 1996. 12. BD Hanson, M Mahnig, LE Toth. Low temperature heat capacities of transition metal borides. Z Naturforsch 26a:739, 1971. 13. LE Toth. Transition Metal Carbides and Nitrides. New York: Academic Press, 1971. 14. C Huiszoon, PPM Groenewegen. Irrelevance of atomic masses for Debye-Waller B values in the limit of high temperatures. Acta Crystallogr A28:170, 1972. 15. G Grimvall, J Rundgren. Unpublished. 16. Y Kumashiro, H Tokumoto, E Sakumura, A Itoh. The elastic constants of TiC, VC, and NbC single crystals. In: RR Haseguti, N Mikoshiba, eds. Internal Friction and Ultrasonic Attenuation in Solids, Proceedings of the 6th International Conference. Tokyo: Tokyo University Press, 1977, p 295. 17. L Pintschovius, W Reichhardt, B Scheerer. Lattice dynamics of TiC. J Phys C 11:1557, 1978. 18. MW Chase, CA Davies, JR Downey, DJ Frurip, RA McDonald, AN Syverud, eds. JANAF Thermochemical Tables. 3rd. ed. J Phys Chem Ref Data 14(suppl. 1), 1985. 19. A Ferna´ndez Guillermet, J Ha¨glund, G Grimvall. Cohesive properties of 4d-transition-metal carbides and nitrides in the NaCl-type structure. Phys Rev B45:11557, 1992. 20. A Ferna´ndez Guillermet, J Ha¨glund, G Grimvall. Cohesive properties and electronic structure of 5dtransition-metal carbides and nitrides in the NaCl structure. Phys Rev B48:11673, 1993. 21. J Ha¨glund, A Ferna´ndez Guillermet, G Grimvall, M Ko¨rling. Theory of bonding in transition-metal carbides and nitrides. Phys Rev B48:11685, 1993. 22. G Grimvall, J Rose´n. Vibrational entropy of polyatomic solids: Metal carbides, metal borides, and alkali halides. Int J Thermophys 4:139, 1983. 23. A Ferna´ndez Guillermet, G Grimvall. Cohesive properties and vibrational entropy of 3d transitionmetal compounds: MX(NaCl) compounds (X ⫽ C, N, O, S), complex carbides, and nitrides. Phys Rev B40:10582, 1989. 24. A Ferna´ndez Guillermet and G. Grimvall, Cohesive properties and vibrational entropy of 3d-transition metal carbides, J Phys Chem Solids 53:105, 1992. 25. A Ferna´ndez Guillermet and G Grimvall, Correlations for bonding properties and vibrational entropy in 3d-transition metal compounds with application to the CALPHAD treatment of a metastable CrC phase, Zeitschrift fu¨r Metallkunde 81:521, 1990. 26. G Grimvall, Vibrational entropy of metal nitrides, High Temp-High Press 17:607, 1985. 27. A Ferna´ndez Guillermet and G Grimvall, Bonding properties and vibrational entropy of transition metal MeB 2 (AlB 2 ) diborides, J Less-Common Metals 169:257, 1991. 28. G Grimvall and A Ferna´ndez Guillermet, Phase stability properties of transition metal diborides, American Institute of Physics Conference Proceedings 231:423, 1991. [Tenth International Symposium on Boron, Borides and Related Compounds, Albuquerque, 1990] 29. I Bahrin. Thermochemical Data of Pure Substances. Weinheim: VCH Verlag, 1989. 30. G Grimvall, M Thiessen. The strength of interatomic forces. Institute of Physics Conference Series 75:61, 1986, (2nd International Conference on Science of Hard Materials, Rhodes, 1986).

7 Electrical and Thermal Conductivity and Related Transport Properties at Low Temperatures Go¨ran Grimvall Royal Institute of Technology, Stockholm, Sweden

I.

INTRODUCTION

This review deals mainly with the electrical and thermal conductivities at temperatures T from 0 K to room temperature. It is the region where the lattice vibrations must be described by quantum mechanics, and the phonon spectrum determines much of the temperature dependence of the transport properties. The absolute magnitudes of the electrical and thermal conductivties depend crucially on a consideration of the quantum mechanical matrix elements for the scattering of electrons and phonons. They are difficult to calculate, not only for the refractory systems of interest here but for most solids. Theories of conduction properties therefore contain parameters, some of which are fairly well known while others are quite uncertain. An additional difficulty in the present chapter is the lack of extensive and accurate experimental data on well-defined specimens for many of the compounds of interest. Williams (1) reviewed electrical conduction in the solids treated here, with an account of how the accuracy and relevance of experimental data have gradually been improved. He also gave references to many early reviews of transition metal carbides, nitrides, and borides. Another review of the electrical properties of these and related systems is that of Wang et al. (2). The present work presents standard theories of transport properties, and as we proceed connection is made mainly to carbides, nitrides, and borides of the transition metals of group IV (Ti, Zr, Hf) and group V (V, Nb, Ta) in the periodic table. In particular, we shall discuss the extent to which the simple textbook relations may have to be modified in order to describe, e.g., refractory compounds. The theoretical arguments leading to many of the general results cited in this chapter are discussed in more detail, e.g., in two monographs by the present author (3,4). References to such well-known relations will usually not be explicitly given but can be found in these two books and in many of the papers referred to in the chapter. Those papers also give more experimental information. Some additional experimental data on the systems of interest, and on many related systems, are found in the compilation by Kosolapova (5).

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II. ELECTRICAL CONDUCTION A.

Ideal Resistivity

A standard textbook result for the electrical conductivity is σ ⫽ ne 2 τ el /m

(1)

where n is the number of conduction electrons (charge carriers) per volume, e is the electron charge, m is an effective electron mass, and τ el is the average electron lifetime between scattering events. The important part of this relation is the lifetime. In a pure and defect-free crystalline material, τ el is limited by the thermal motion of the atoms, i.e., by the electron-phonon interaction. The corresponding resistivity ρ (⫽1/σ) is sometimes called the ideal resistivity, and we shall denote it ρ el-ph . (There is also an electron-electron scattering term, which in most cases is negligible, and in systems with magnetic moments there is an additional contribution to the electrical resistivity.) At high enough temperatures (T ⬎ θ D , where θ D is a Debye temperature), and according to a simple model, the resistivity ρel-ph increases linearly with T, ρel-ph ⫽ αT

(2)

Here we are mainly interested in temperatures T ⬍ θ D . For more than half a century, the BlochGru¨neisen (BG) formula has been used frequently to describe ρ el-ph (T ) at intermediate and low temperatures. It is often given in the form ρ BG ⫽

C1 T

冮

q

D

0

q 5 dq [exp(hCq/k BT) ⫺ 1] [1 ⫺ exp(⫺hCq/k BT)]

(3)

where C 1 is a constant, specific for the metal under consideration, C is the sound velocity, q is a phonon wave number lying between 0 and the Debye cutoff value q D, hCq is a corresponding phonon energy, and kB is Boltzmann’s constant. With z ⫽ hCq/k B T and hCqD ⫽ kBθ D , we rewrite (3) as ρBG ⫽

冢 冣冮 5

C2 T θD θD

θ

D/T

0

冢冣 冢冣

C T z 5 dz ⫽ 2 z (e ⫺ 1) (1 ⫺ e ⫺z ) θ D θ D

5

J5

θD T

(4)

where C 2 is another constant and J5 is the ‘‘transport integral of order 5.’’ At low temperatures we need J5 (∞) ⫽ 124.4. At high temperatures (T ⬎ θ D) we have J 5 ⬇ (1/4) (θ D /T) 4. These two limits imply that ρ BG ⬃ T at high T and ρ BG ⬃ T 5 at low T. The Bloch-Gru¨neisen formula is a special case of a more general expression. Within a variational solution of the Boltzmann equation we can, to a good approximation, write the resistivity ρ el-ph that is limited by the scattering of conduction electrons by phonons as ρ el-ph

冢 冣冮

4π ⫽ ω pl

2

0

ω

max

(hω/kB T) α 2tr F(ω)dω [exp(hω/kB T ) ⫺1] [1 ⫺ exp(⫺hω/kB T )]

(5)

The plasma frequency ω pl has the form (ω pl) 2 ⫽ 4πne 2 /m for a free electron gas, and it can be rigorously generalized to account for a complicated electron band structure. The function α 2tr F(ω) can, somewhat loosely, be regarded as the product of an electron-phonon interaction α 2tr (essentially quantum mechanical matrix elements squared) and a phonon density of states F(ω). The index tr stands for transport property. [There is another electron-phonon coupling

Electrical and Thermal Conductivity

175

α 2 F(ω) that enters the theory of superconductivity and the electron-phonon enhancement of the electronic heat capacity at low T; see Eq. (25).] The maximum phonon frequency is ω max. Let us model α 2tr F(ω) with a power-law expression in ω: α 2tr F(ω) ⫽ C0 ω n

0 ⬍ ω ⬍ ω max

(6)

where C 0 is a constant that depends on the considered material. The Bloch-Gru¨neisen formula (4), with a T 5 behavior at low T, is obtained with n ⫽ 4 in Eq. (6). The orginal motivation of ρ BG was based on several simplifying assumptions. When interpreted in terms of the modern formulation in Eq. (5), they can be stated as follows: take a Debye model for the phonon density of states F(ω), let α 2tr refer only to coupling between electrons and longitudinal phonons, and ignore Umklapp processes. However, we prefer to view the Bloch-Gru¨neisen formula, and its generalizations for n ≠ 4, as models in which the true α 2tr F(ω), including all its complications, is described by Eq. (6). We see that at high T (i.e., when kBT ⬎ hω) any form of α 2tr F(ω) yields ρ ⬃ T, in accord with Eq. (2). At low T we get ρ ⬃ T n⫹1 if, in the low-frequency limit, α 2tr F(ω) ⬃ ω n . It is useful to define a quantity λ tr ⫽ 2

冮

ω

0

max

α 2tr F(ω) dω ω

(7)

Here λ tr is a ‘‘transport’’ electron-phonon coupling parameter. It is a number, typically 0.5–1 for many transition metals, and is closely related to the electron-phonon coupling parameter λ el-ph that appears in the theory of superconductivity; see Eqs. (25) and (26). The high-temperature version of Eq. (5) can then be written ρ el-ph (T ) ⫽

冢 冣 4π ω pl

2

kB λ trT 2h

(8)

where we again recover the general result of Eq. (2). However, most materials show deviations from linearity in T at high temperatures. The coupling constant λ tr depends on ⬍ω ⫺2⬎, where ⬍ ⬎ denotes a weighted average of the phonon frequencies ω. Because anharmonic effects usually lead to a ‘‘softening’’ of the lattice vibrations, i.e., a decrease in ω, the term ⬍ω ⫺2⬎ will cause λ tr to increase with T. The result is that ρ el-ph(T ) increases more rapidly than linearly in T. Another effect, resistivity saturation, gives a temperature dependence with opposite trend. It is considered in Sec. II.C. The quantity α 2tr F(ω) cannot be obtained directly from experiment, but in superconductors (see Sec. V) a closely related quantity α 2 F(ω) can be measured in tunneling experiments. Tralshawala et al. (6) found that their measured α 2F(ω) in superconducting VN, when inserted for α 2tr F(ω) in Eq. (5), accurately accounted for the temperature dependence of their measured electrical resistivity of VN between 10 and 300 K. Suppose that we want to model α 2tr F(ω) with α 2 F(ω) of Tralshawala et al. (6) with C0 ω n as in Eq. (6). There are three parameters, C 0, n, and the cutoff frequency ω max . We then require that our model α 2tr F(ω) has the same λ tr [see Eq. (7)] as the λ exp that was measured, i.e., C0 ⫽ nλ exp /(2ω nmax). It still leaves us with two fitting parameters, n and ω max . Figure 1 shows a possible model, here with n ⫽ 3. We note that ω max is not necessarily to be identified with the highest frequency in the actual phonon spectrum. The experimental α 2 F(ω) and the generalized Bloch-Gru¨neisen α 2 F(ω) in Fig. 1 obviously are quite different, but when inserted in Eq. (5) they both yield the same high-temperature ρ el-ph (T ). Moreover, the same ρ el-ph at high T would result with another n, provided that ω max and C0 were also changed accordingly. It is clear that a property such as the electrical resistivity, which is

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Figure 1 The electron-phonon coupling function α 2tr F(ω) derived from experiments on VN (6) (thin lines) and a possible representation of α 2tr F(ω) through a generalized Debye-type phonon spectrum, as in Eq. (6) (thick lines).

an integrated quantity over the phonon spectrum, does not depend much on fine structure in that spectrum. This fact is the basis for the ability of Bloch-Gru¨neisen type formulas to account for ρ el-ph (T ). Sometimes a kind of ‘‘Debye temperature’’ θ R is derived from resistivity data through hω max ⫽ kB θ R in Eq. (6). The temperature dependence of other physical properties is also often described in terms of a Debye temperature (see Chap. 6). However, this means that one uses a model with a single parameter (i.e., θ) to describe a temperature dependence that is a function of the entire phonon spectrum and usually also involves other complications related to, e.g., the electronic states. It is obvious that such Debye temperatures should not be equal. They give information only about the magnitude of characteristic phonon frequencies, for a given material and for a certain weighting of its various frequency parts. In the case of θ R, one varies not only θ R but also n, in a fit to experiments. Nevertheless, a quantity θ R is often extracted from ρ(T ). Table 1 gives some θ R values obtained in this way and θ S derived from heat capacity data, so that θ S (see Chap. 6) reproduces the vibrational entropy (10) at T ⬇ θ S.

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177

Table 1 A ‘‘Debye Temperature’’ θ R Obtained by Fitting a Generalized BlochGru¨neisen Expression to the Measured Resistivity at Low and Intermediate Temperatures and an ‘‘Entropy Debye Temperature’’ θ S That Reproduces the Experimental High-Temperature Vibrational Entropy a

θ R (K) θ S (K)

TiC

ZrC

VC

NbC

TaC

TiB 2

b

c

c

c

c

720 d 972

719 805

570 650

587 745

431 634

272 551

a

See Chapt. 6 Modine et al. (7) for TiC 0.95. c Allison et al. (8) for ZrC 0.93, VC 0.88, NbC 0.95, and TaC 0.99. d Williams et al. (9). b

It is interesting to note that in an Einstein model for the phonon spectrum, i.e., when α 2tr F(ω) ⬃ δ(ω ⫺ ω e), ρ/T from Eq. (5) has exactly the same temperature dependence as the phonon heat capacity. In Fig. 2 we illustrate to what extent ρ el-ph /T covaries with the heat capacity C p for TaC. For ρ el-ph Allison et al. (8) found that a generalized Bloch-Gru¨neisen formula with n ⫽ 2 in Eq. (6), i.e., involving the transport integral J3 and hence a T 3 behavior at low T, gives a good fit to their experiments on TaC between 10 and 350 K. We normalize their ρ/T to 1 at high T in Fig. 2 and compare with the experimental heat capacity Cp (10), normalized to the value 3kB per atom that holds for harmonic lattice vibrations at high T. Although the general shapes of the two curves in Fig. 2 are similar, they are obviously governed by different characteristic temperature scales. The resistivity in this case depends to a large extent on the low-frequency part of the phonon spectrum. This is in line with the difference between the Debye temperatures θ R and θ S for TaC given in Table 1, and the other compounds listed there give a closer agreement between ρ(T )/T and C p (T ).

Figure 2 The phonon-limited electrical resistivity plotted as ρ el-ph (T )/T of TaC, based on experiments by Allison et al. (8) and normalized to 1 at high temperatures, and the heat capacity C p (10), normalized as C/3k B per atom.

178

B.

Grimvall

Matthiessen’s Rule

Matthiessen’s rule gives the total electrical resistivity ρ tot of (dilute) alloys as ρ tot ⫽ ρ 0 ⫹

冱cρ i

imp i

⫹

i

冱c ρ j

def j

(9)

j

where ρ 0 is the resistivity of the pure and defect-free host (i.e., ρ 0 ⫽ ρ el-ph in most cases), c i is ⫽ dρ tot /dc i is the the concentration (e.g., in atomic percent) of the alloying element i, and ρ imp i corresponding resistivity per impurity concentration. The terms in the last sum refer to static lattice defects j such as grain boundaries, dislocations, and vacancies, and c j measures the amounts of those defects. Typical values for ρ imp in transition metals fall in the range 1–5 i µΩ ⋅ cm/at. % (11). Most of the refractory compounds of interest here are nonstoichiometric, with vacancies on some of the nonmetal lattice sites. These vacancies strongly scatter electrons and can give a dominating contribution to ρ tot , as shown in Fig. 3 for TiCx , ZrCx, VCx, and TaCx . We note that the additional resistivity per atomic % vacant sites is larger than for typical impurities in transition metals. In some cases, the vacancies can form an ordered lattice structure. Shacklette and Williams (12,13) and Otani (14) showed that the ordered compounds V6 C5 and V8 C7 have resistivities that are much lower than in the compounds with the same composition but disordered vacancies; see Fig. 3. Similar work has been done on Nb6 C5 by Dy and Williams (15) and by Lorenzelli et al. (16) on Ti8 C5 . Dy and Williams (15) also studied the effect of hydrogen impurities on the resistivity of NbCx. C.

Resistivity Saturation

If the electron scattering is caused by independent scattering mechanisms, e.g., scattering by phonons, by atomic impurities i (alloying elements or vacancies), and by defects j, the scatteringtime approximation gives

Figure 3 The resistivity ρ of compounds TiC x (16), ZrC x (7), VC x (13,14), and TaC x (17), as a function of x, when the vacant carbon sites are disordered, and the lower ρ as a result of ordering in V6 C5 and V8 C7 (13,14). The curve for disordered VC x is a tentative extrapolation. Data refer to very low temperatures (residual resistivity), except for TaC x , which refers to ⫺196° C.

Electrical and Thermal Conductivity

1 1 ⫽ ⫹ τ el τ el-ph

冱τ ⫹ 冱τ 1

i

i

1

j

179

(10)

j

We see that taking this τ el in (1) gives an expression equivalent to Matthiessen’s rule as in (9). It is instructive to express the electron scattering rate not in terms of scattering times τ but in the corresponding mean free paths ᐉ ⫽ vτ, where v is some properly defined electron velocity at the Fermi energy. (In a model with a spherical Fermi surface, v is the Fermi velocity v F.) Then the equivalent of Eq. (10) is 1 1 ⫽ ⫹ ᐉel ᐉel-ph

冱ᐉ ⫹ 冱ᐉ 1

i

i

1

j

(11)

j

In this picture, a conduction electron travels a distance ᐉ el between two successive scattering events. At low temperatures, and for defect-free and dilute alloys, ᐉ el is much larger than a typical distance between neighboring atoms. If the temperature is increased, the electron-phonon scattering becomes more important and ᐉ el-ph decreases correspondingly. Similarly, if we increase the concentration of alloying atoms in solid solution, ᐉ i will be shorter. But it is obvious that ᐉ el cannot decrease indefinitely, i.e., ρ el cannot be made arbitrarily large, while still maintaining the picture with charge carriers that move between scattering centers. For instance, it would be meaningless to have ᐉ el less than a typical distance a between nearest-neighbor atoms. In fact, ᐉ el must be large compared with the de Broglie wavelength λ associated with a conduction electron for our picture to be valid. For the electrons near the Fermi level, which are responsible for the conduction, λ ⫽ λ F ⬃ 1/a. Using the free electron model, where v ⫽ v F ⫽ (h /m) (3π 2 n) 1/3 , with ᐉ el ⫽ 1/a and n ⫽ 1/a 3 (a typical value), we get σ ⫽ ne 2 ᐉ el /(mvF ) ⫽ e 2 a ⫺2 / h(3π 2 a ⫺3 ) 1/3 ⫽ (3π 2 ) 1/3 e 2 /(ha). This suggests a universal maximum resistivity of the order of ha/e 2 ⬃ 10 2 µΩ ⋅ cm for conduction described by the scattering of electrons (i.e., by the Boltzmann equation). A value of this order of magnitude crudely distinguishes between insulators, where the electrons are localized at a specific atom, and metals, where there are mobile electrons. In nontransition metals and alloys the electron mean free path is usually so large that the standard Boltzmann equation suffices to describe the electrical resistivity. However, both pure transition metals and their alloys and compounds often show a ‘‘saturation’’ of the resistivity when the mean free path becomes short. A further increase in the lattice disorder through more alloying atoms, more static defects, or larger atomic vibrations caused by increased temperature will not have a significant effect on the total resistivity. The temperature dependence of the resistivity ρ in such a material approaching resistivity saturation is sometimes well described by the empirical ‘‘parallel resistor’’ formula due to Wiesmann et al. (18): 1 1 1 ⫽ ⫹ ρ(T ) ρ ideal(T ) ρ max

(12)

Here ρideal (T ) is the resistivity without saturation, e.g., described as in Eq. (1), and ρ max is the limiting value to which the resistivity of a particular material saturates in the extrapolated limit that ρideal(T ) ⬎⬎ ρmax. Resistivity saturation was highlighted in a seminal paper by Mooij (19) in 1973. After several decades, the phenomenon is still poorly understood; see, e.g., work by Nath and Majumdar (20) on transition metal alloys and references therein. Although it may be difficult to notice a correction due to resistivity saturation in data taken for refractory compounds at low temperature, high-temperature measurements clearly reveal its existence. For example, for VN experiments (6) show the effect even below room temperature.

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III. THERMAL CONDUCTION A.

The Wiedemann-Franz Law

The Wiedemann-Franz law, relating the electrical conductivity σ to the electronic contribution κ el to the thermal conductivity in metals, reads κ el ⫽ LTσ ⫽ LT/ρ

(13)

where L is the Lorenz number. Under certain simplifying conditions L is a universal constant, L ⫽ L 0 ⫽ (π 2 /3) (k B /e) 2 ⫽ 2.44 ⫻ 10 ⫺8 WΩK ⫺2. Deviations from the value L ⬇ L 0 may occur as a result of electron band structure effects and, at intermediate and low temperatures, of the inelastic nature of the electron scattering by phonons. At very low temperatures, where impurity scattering dominates, it is often a good approximation to let L ⫽ L 0. As an example, Fig. 4 shows L(T ) for iron, based on an analysis of experimental electrical resistivity and thermal conductivity data (21), with a tentative extrapolation to T ⫽ 0 K assuming that L(0) ⫽ L 0. In order to illustrate further when the Wiedemann-Franz law is valid, we express the thermal conductivity κ el on a form analogous to Eq. (5) for electrical conduction (3,4):

冢 冣冮

1 1 4π ⫽ κ el L 0T ω pl

2

0

⫻

ω

max

0

冦冤

(hω/kBT) [exp(hω/k BT) ⫺ 1] [1 ⫺ exp(⫺hω/kB T)]

冢 冣冥

1 hω 1⫺ 2 2π kBT

2

3 α F(ω) ⫹ 2 2π 2 tr

冢 冣 hω kB T

2

冧

(14)

α F(ω) dω 2

Figure 4 The Lorenz number L(T ) as a function of T for Fe, after Ref. 21 (thick line), and with a tentative extrapolation to L ⫽ L 0 at low T (thin line), where impurity scattering dominates.

Electrical and Thermal Conductivity

181

Here α 2 F(ω) is an electron-phonon coupling introduced later (Sec. V). It is the inelastic nature of the scattering of electrons by phonons that affects the electrical and thermal conductivities differently, and therefore is one reason why in pure specimens L ≠ L 0 at temperatures T ⬍ θ D , where θ D is a characteristic Debye temperature for the solid considered. We see that the Wiedemann-Franz law is valid if we can neglect at term

冢 冣

1 hω 2π 2 kB T

2

[3α 2 F(ω) ⫺ α 2tr F(ω)]

(15)

in the integrand of (14). That is a very good approximation when T ⬎ θ D. When T ⬍⬍ θ D, electron scattering by impurities may dominate the electron-phonon scattering. Then τ el ⫽ τ imp, and L ⬇ L 0 is often a good approximation; see Fig. 4. There are also corrections to the ideal Wiedemann-Franz law caused by electron band structure effects and by a term related to the thermoelectric power, but we refrain from further comments on them in this chapter. B.

Phonon Contribution to the Thermal Conductivity

In metals the major contribution to the thermal conductivity comes from the conduction electrons. But it is an insulator, diamond, that has by far the highest thermal conductivity at room temperature, showing that conduction through phonons is not always small. The total thermal conductivity κ tot is the sum of an electronic part κ el and a phonon (lattice) part κ lat : κ tot ⫽ κ el ⫹ κ lat

(16)

The electronic part was dealt with in the previous subsection. The phonon part is very difficult to model accurately. In a standard textbook model, taken from the theory of thermal conduction in gases, one can formally write κ lat ⫽

1 1 Clat C 2 τ lat ⫽ Clat Cᐉ lat 3 3

(17)

where Clat is the phonon (lattice) heat capacity, C is an average sound velocity, τ lat is an average phonon lifetime, and ᐉ lat ⫽ Cτ lat is the corresponding mean free path. In analogy to the scattering of electrons by independent mechanisms, leading to Eq. (10), we can distinguish between various contributions to τ lat : 1 1 1 1 1 ⫽ ⫹ ⫹ ⫹ τ lat τ size τ def τ ph-ph τ ph-el

(18)

In small and pure systems, and at low temperature, the mean free path of the phonons may approach a characteristic dimension (size) of the specimen. That limits a further increase in τ lat , through the term τ size . Impurities and other lattice defects give a contribution τ def. Both τ size and τ def are temperature independent. The phonon-phonon interaction gives a temperature-dependent τ ph-ph , which at high T and in a simple model varies inversely with the number of excited phonons, i.e., as 1/T. At these temperatures, the heat capacity C lat has approximately the classical DulongPetit value of 3k B per atom. If then τ ph-ph gives the most important contribution to τ lat , Eq. (17) implies that the lattice contribution to the thermal conductivity varies as τ ph-ph , that is, as 1/T. With decreasing T, typically below θ D /2, τ ph-ph increases exponentially in 1/T, which leads to a rapidly increasing κ ph-ph . Eventually τ ph-ph will be so large that τ def or τ size , which are both independent of T, dominates τ lat . Then κ lat has the same temperature dependence as the heat capacity C lat(T ), i.e., varying as T 3 at very low temperatures. This would be the description of κ lat in

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insulators. In metals we must also consider the scattering of phonons by conduction electrons, described by τ ph-el in Eq. (18). Relations (17) and (18) are deceptively simple but present enormous difficulties if one wants more than a crude numerical estimate. A major root of the difficulty is that τ ph-ph requires an average over terms involving the anharmonic phonon-phonon interaction. In fact, attempts at accurate such calculations have been made for only a few solids, mainly alkali halides and solid noble gases. Also, the phonon-electron term τ ph-el is difficult to calculate. Little is therefore known through direct calculation about the magnitude of κ lat in metallic systems. Instead, κ lat is often inferred from measurements of the total thermal conductivity, after subtraction of an electronic part κ el that is obtained from the experimental electrical conductivity and the application of the Wiedemann-Franz law with L ⫽ L o . It is believed that in many transition metals κ lat makes an almost negligible contribution to κ tot, say κ lat ⬇ 0.1 κ el at room temperature. But the refractory compounds dealt with here show a behavior quite different from that of normal transition metals. For instance, measurements by Morelli (22) on TiC 0.95 suggest that the thermal conductivity is dominated by the lattice part, κ el being about 25% of κ tot at 300 K and only about 5% at 100 K; see Fig. 5. Those thermal conductivity data essentially agree with earlier measurements by Radosevich and Williams (23). Some unexpected features arise from the studies of Morelli (22) and Radosevich and Williams (23). The thermal conductivity of TiCx at low T increases with increasing x, i.e., with more vacant carbon sites. This fact shows that phonon scattering by vacancies is rather unimportant, contrary to the case of electron scattering in the electrical conductivity. Instead, the vacancies affect the electron structure through τ ph-el . This is important because τ lat at low T is strongly limited by τ ph-el in TiC. An account of κ lat through a fitting of parameters that describe the various contributions to τ lat in Eq. (18) leaves many uncertainties, not only because of the large number of fitting

Figure 5 The lattice contribution κ lat to the thermal conductivity of TiC 0.93 and the total thermal conductivity κ tot ⫽ κ lat ⫹ κ el . The lattice part κ lat is deduced from the measured total thermal conductivity κ tot by subtracting an electronic part κ el that is calculated from the measured electrical resistivity and assuming the Wiedemann-Franz law with L ⫽ L 0. After experiments by Morelli (22).

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183

parameters but primarily because we have no universally valid and simple theoretical expressions to fit to. Work by Radosevich and Williams (23) illustrates well the difficulties one encounters. Finally, we note that in analogy to the electrical resistivity saturation in systems with strong electron scattering, a saturation may also take place in κ lat when ᐉ lat becomes of the order of the interatomic distance a. There are few measurements of the thermal conductivity of refractory compounds. Williams et al. (24) measured κ(T ) in TiB 2. Radosevich and Williams (25) [see also Williams (26)] measured κ in normal and superconducting NbC. In a conventional superconductor, the thermal conductivity decreases on the transition to the superconducting state. The reason is that the electrons in the superconductor cannot transport heat because they would fall into the forbidden energy gap if they lost energy. (A superconductor is not a ‘‘thermal superconductor,’’ and the Wiedemann-Franz law is not valid.) Contrary to this behavior, κ tot in NbC increased as one passed below Tc . This can be understood from the dominating role of κ lat, which is limited by τ ph-el . In the superconducting NbC the phonon-electron interaction becomes weaker and hence κ lat increases.

IV. CONDUCTION IN INHOMOGENEOUS MATERIALS A.

Two-Phase Materials

Many materials of practical interest consist of two or several phases. An important special case is a porous material, in which the voids can be regarded as a separate phase. The mathematical results given in this section, and in the following section on anisotropic materials, hold equally well for the thermal conductivity κ and the electrical conductivity σ. Suppose that we know the conductivities κ i of each phase i and their volume fractions f i with ∑ f i ⫽ 1. Further, neglect any grain boundary effects. The overall conductivity κ eff is always bounded from above and below by the conductivities of a corresponding material in which the same amounts of the phases are arranged in a series or parallel coupling, as in lamellar or fiber composites. Another, and nontrivial, geometry is one in which the phases are distributed so as to make κ eff isotropic, in a statistical sense. This would be the case in a random distribution of inclusions in a matrix. Then κ eff is bounded from above and below by the Hashin-Shtrikman (27) bounds κ HS⫹ and κ HS⫺. With two phases, i ⫽ 1 and 2, one has κ HS⫺ ⫽ κ 1 ⫹

f2 1/(κ 2 ⫺ κ 1) ⫹ f1 /(3 κ 1)

(19)

Here labels 1 and 2 are chosen so that κ 2 ⬎ κ 1 , and both phases are assumed to have isotropic κ. The upper bound κ HS⫹ is obtained by interchanging the labels 1 and 2 in Eq. (19). One may also try to get a direct estimate κ* of κ eff , rather than limiting κ eff by bounds. There are several schemes to accomplish this. We shall exemplify them with one version of what is called an effective medium theory. In its simplest form it assumes that each individual grain of a phase does not deviate systematically from a spherical shape. Then κ* is the solution to the equation

冢

冣 冢

冣

κ 1 ⫺ κ* κ* ⫺ κ 2 f1 ⫽ f2 κ 1 ⫹ 2κ* κ 2 ⫹ 2κ*

(20)

In the ‘‘dilute limit,’’ i.e., when the volume fraction of the inclusions in a matrix is so low that one may neglect the mutual influence of two neighboring inclusions on the overall properties,

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exact results can be obtained for ellipsoidal inclusions. In the special case of spherical inclusions (phase i) in a matrix (phase m) one has

冤

κ eff ⬇ κ m 1 ⫺ fi

冥

3(κ m ⫺ κ i ) 2κ m ⫹ κ i

(21)

For pores, corresponding to κ i ⫽ 0, Eq. (21) reduces to κ eff ⫽ κ m [1 ⫺

3 fi] 2

(22)

which coincides with the upper Hashin-Shtrikman bound for fi ⬍⬍ 1. There are many, more or less fundamental, relations aiming at a description of conduction in inhomogeneous materials. They come under various names, and some of them are in fact identical, although that may not be immediately apparent. For instance, the Maxwell-Eucken relation cited by Williams et al. (9) and used by them to correct for the presence of Ti 2 O 3 in TiB 2 is identical to the upper Hashin-Shtrikman bound. Generalizations of such relations to three or more phases, to ellipsoidal inclusions, etc. are reviewed in Ref. 3. Relations such as (19) and (20) assume that one can ignore grain boundary effects. That is usually a good approximation, because the region of a grain boundary, where the atomic arrangement and composition differ from those of the bulk phases, has a width of only a few atomic diameters. It could then be viewed as another phase, occupying a very small volume fraction of the composite material, and methods of the type discussed in this section could be applied. However, there are cases in which complications arise, as will be now be exemplified. Both TiB 2 and SiC have thermal conductivities more than five times higher than that of coldpressed titanium. In an experiment (28) particulate composites were made by cold-pressing Ti powder with either TiB 2 or SiC particles, followed by a heat treatment and extrusion. For TiTiB 2 the thermal conductivity of the composite was higher than that of the matrix Ti material, as expected, but in the case of Ti-SiC the conductivity was lower. This result was explained by reactions at the interface between Ti and SiC. The reaction products caused a large (4.6%) volume expansion in the reaction zone, leading to interfacial cracking and poor thermal contact. B.

Average Conductivity in Noncubic Lattice Structures

In a lattice with cubic symmetry the single-crystal conductivity is isotropic. Hence it is also isotropic in a polycrystal, irrespective of the geometric arrangement of the individual grains. This is the case, e.g., for TiC that has an NaCl-type lattice structure. TiB 2 has hexagonal structure, and its single-crystal conductivity is characterized by the conductivities κ c (along the crystallographic c-axis) and κ a (in the plane perpendicular to the c-axis). The effective conductivity κ eff of a polycrystal, of course, must lie between the values κ c and κ a that will be attained when all the single crystals in a specimen have aligned crystallographic c-axes. If the arrangement of grains is such that the conductivity of the specimen is isotropic, κ eff always lies between the bounds 3

冢

1 2 ⫹ κa κc

冣

⫺1

ⱕ κ eff ⱕ

1 (2κ a ⫹ κ c) 3

(23)

For a polycrystal in which the individual grains are more or less spherical and with random crystallographic orientation, the effective conductivity is isotropic. It can be approximated by an effective-medium result κ* (29) that, for hexagonal symmetry, has the form

Electrical and Thermal Conductivity

κ* ⫽

185

1 [κ a ⫹ (κ 2a ⫹ 8κ a κ c) 1/2 ] 4

(24)

The anisotropies κ c /κ a and σ c /σ a for the thermal and electrical conductivities in TiB 2 and related noncubic compounds seem not to be known but are thought to be weak. As a numerical illustration, let us assume that κ c /κ a ⫽ 1.1. Then, from Eq. (23), 1.03125κ a ⱕ κ eff ⱕ 1.03333κ a, while Eq. (24) gives κ* ⫽ 1.03262κ a . Correspondingly, with κ c /κ a ⫽ 1.3 we get 1.08333κ a ⱕ κ eff ⱕ 1.11000κ a and κ* ⫽ 1.09410κ a .

V.

SUPERCONDUCTIVITY

The transition temperature Tc of the traditional superconductors of interest here (as opposed to the more recently discovered high-temperature superconductors) depends on the strength of the electron-phonon interaction parameter λ el-ph . It can be written in the form

λ el-ph ⫽ 2

冮

ω

0

max

α 2 F(ω) dω ω

(25)

We immediately see the similarity to the parameter λ tr of Eq. (7). The electron-phonon coupling function α 2 F(ω) essentially differs from α 2tr F(ω) in that the latter function contains an average over a geometric factor 1 ⫺ cos θ, where θ is the angle between the wave vectors of the initial and final states of an electron in a scattering event. Since the average of 1 ⫺ cos θ is rather close to 1, it may be a good approximation to take λ tr ⬇ λ el-ph . The function α2F(ω) can be measured by tunneling in superconductors; see Tralshawala et al. (6) and Fig. 1 for VN and Kihlstrom et al. (30) for NbN. The quantity λ el-ph enters two important physical relations. It gives the electron-phonon enhancement of the low-temperature electronic heat capacity as Cel ⫽ γT ⫽ γ bandT(1 ⫹ λ el-ph), where γ band T is the heat capacity obtained from the electron band structure without regard to the electron-phonon interaction. The other important relation, of particular interest here, is the connection between λ el-ph and the transition temperature T c. An accurate calculation of T c requires the solution of the Eliashberg equations, which explicitly take into account the shape of α 2 F(ω). In many practical applications one instead obtains Tc from a semiempirical relation containing α 2 F(ω) in the form of the average λ el-ph , Eq. (25). The most frequently used such relation is that due to McMillan (31). It reads

Tc ⫽

冤

冥

θD ⫺1.04(1 ⫹ λ el-ph ) exp 1.45 λ el-ph ⫺ µ*(1 ⫹ 0.62λ el-ph )

(26)

Here θ D is a Debye temperature and µ* is a parameter measuring the strength of the electronelectron interaction. The latter is not very accurately known. For many systems, including transition metals, it is usually assumed that µ* lies in the interval 0.10–0.13. Equation (26) is often used to derive λ el-ph from a known Tc . It could also be used in the reverse direction, to estimate Tc from a λ el-ph that is theoretically calculated or inferred from, e.g., λ tr and resistivity data. The parameters θ D , λ el-ph , and µ* in Eq. (26) that determine Tc do not depend sensitively on lattice defects, but with the large variations in vacancy concentration and specimen state encountered for the compounds reviewed here, there are significant variations in Tc ; see Table 2.

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Table 2 Exemplifying That the Transition Temperature Tc to Superconductivity Depends on the Composition x a Compound NbC NbC x NbC x TaC x TiN ZrN x VN VN x VN x VN x NbN NbN x TaN x a

x

Tc (K)

Reference

0.96 0.92–0.98 0.83–0.97 0.98

10 6–10 2–10 10 6 10 9 4–9 4–9 2–8 16 14–16 8

Shacklette et al.(32) Storms et al. (33) Dy and Williams (15) Dy and Williams (15) Wokulski and Sulkowski (34) Storms et al. (33) Zasadzinski et al. (35) Chen et al. (36) Zhao et al. (37) Ajami and MacCrone (38) Gray et al. (39) Chen et al. (36) Chen et al. (36)

0.98 0.70–0.98 0.64–0.99 0.75–1 0.82–0.95 0.95

Tc also depends on the state of the specimen (mode of preparation).

VI. TRANSPORT PROPERTIES RELATED TO MAGNETISM We shall consider two refractory compounds in which electron scattering due to magnetic effects may appear: TiB 2, which shows a resistivity minimum at low temperatures that has been attributed to the Kondo effects, and VN, in which spin fluctuations have been suggested to affect the resistivity. Measurements of ρ(T ) for TiB 2 by Williams et al. (9) from 4.2 to 300 K showed a resistivity minimum in the range 34–47 K. A normal resistivity term ρ el-ph (T ) could be extracted. It was well described by a Bloch-Gru¨neisen expression varying as T 5 at low T and with θ R ⫽ 720 K. The latter value seems reasonable, when compared with θ S; see Table 1. The Kondo effect is caused by a spin-flip interaction between conduction electrons and localized magnetic moments of impurity atoms. Ni impurities are essential, but there are still several unsolved problems in the interpretation of the Kondo minimum in TiB 2. It has generally been assumed that spin fluctuations in strongly paramagnetic systems contribute a term to the electrical resistivity, as well as a related enhancement of the electronic heat capacity, with a characteristic coupling parameter λ sp in analogy to the quantity λ el-ph introduced in Sec. V. There is not yet a theoretical description that can give a good numerical estimate of the magnitude of the effect. It has sometimes been regarded as an explanation for an extra term, beyond standard descriptions, that has seemed necessary to account for experimental results, e.g., in VN; see Refs. 35, 37, 38, 40 and 41. The Hall coefficient has been studied for a few of the compounds reviewed here. It has helped to distinguish between effects due to changes in the carrier density and effects due to defect scattering in nonstoichiometric compounds; see Modine et al. (7,42) for work on TiC, ZrC, and HfC with varying vacancy concentration; Santoro and Dolloff (17) for similar work on TaC; and Shacklette and Ashworth (43) for the effect of vacancy ordering in VC. VII. EXPERIMENTS ON TRANSPORT IN CARBIDES, NITRIDES, AND BORIDES We end this review by giving references in Tables 3 and 4 to experiments on transport properties in some carbides, nitrides, and borides formed by group IV and V transition metals. The list is

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187

Table 3 Some References to Transport Properties of Transition Metal Carbides: Electrical Resistivity (ρ) and Thermal Conductivity (κ) Compound TiC

ZrC

HfC

VC

NbC

TaC

References

Property

Modine et al. (7) Shacklette and Williams (12,13) Otani et al. (14) Lorenzelli et al. (16) Lei et al. (44) Wokulski and Sulkowski (34) Radosevich and Williams (23) Morelli (22) Modine et al. (7,42) Allison et al. (8) Lei et al. (44) Radosevich and Williams (23) Modine et al. (7) Lei et al. (44) Dy and Williams (15) Allison et al. (8) Otani et al. (14) Shacklette and Ashworth (43) Shacklette et al. (32) Radosevich and Williams (25) Williams (26) Santoro and Dolloff (17) Allison et al. (8) Cooper and Hansler (45)

ρ, Hall coefficient ρ ρ ρ ρ ρ, Ti(C,N) κ κ, thermoelectricity ρ, Hall coefficient ρ ρ κ ρ, Hall coefficient ρ ρ ρ ρ κ, Hall coefficient κ (T ⬎ Tc ; T ⬍ Tc) κ (T ⬎ Tc ; T ⬍ Tc) κ (T ⬎ Tc ; T ⬍ Tc) ρ, Hall coefficient ρ ρ

Table 4 Some References to Transport Properties of Transition Metal Nitrides and Borides: Electrical Resistivity (ρ) and Thermal Conductivity (κ) Compound TiN ZrN HfN VN

NbN TiB 2

ZrB 2

References

Property

Lei et al. (44) Lei et al. (44) Lei et al. (44) Tralshawala et al. (6) Zasadzinski et al. (35) Zhao et al. (37) Ajami and MacCrone (38) Gray et al. (39) Nigro et al. (46) Williams et al (9) Williams (26) McLeod et al. (47) Rahman et al. (48) Choi et al. (49) Rahman et al. (48)

ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ, Kondo effect ρ, κ, Seebeck coefficient ρ ρ ρ ρ

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Grimvall

not complete. In particular, many old references have been left out, often because the data were obtained with poorly characterized specimens. Many of the experiments cited refer to thin films. They usually contain lattice defects that strongly affect the transport properties and hence may not reflect the properties of bulk specimens.

REFERENCES 1. WS Williams. Transition metal carbides, nitrides, and borides for electronic applications. JOM J Miner Met Mater Soc 49:38, 1997. 2. CC Wang, SA Akbar, W Chen, VD Patton. Electrical properties of high-temperature oxides, borides, carbides, and nitrides. J Mater Sci 30:1627, 1995. 3. G Grimvall. Thermophysical Properties of Materials. Amsterdam: North-Holland, 1986. 4. G Grimvall. The Electron-Phonon Interaction in Metals. Amsterdam: North-Holland, 1981. 5. TY Kosolapova, ed. Handbook of High-Temperature Compounds: Properties, Production, Applications. New York: Hemisphere, 1990. 6. N Tralshawala, JF Zasadzinski, L Coffey, W Gai, M Romalis, Q Huang, R Vaglio, KE Gray. Tunneling, α 2 F(ω), and transport in superconductors: Nb, V, VN, Ba 1⫺xKxBiO 3, and Nd 1.85 Ce 0.15 CuO 4 . Phys Rev B51:3812, 1995. 7. FA Modine, MD Foegelle, CB Finch, CY Allison. Electrical properties of transition-metal carbides of group IV. Phys Rev B40:9558, 1989. 8. CY Allison, CB Finch, MD Foegelle, FA Modine. Low-temperature electrical resistivity of transitionmetal carbides. Solid State Commun 68:387, 1988. 9. RK Williams, PF Becher, CB Finch. Study of the Kondo effect and intrinsic electrical conduction in titanium diboride. J Appl Phys 56:2295, 1984. 10. JANAF Thermochemical Tables. 3rd ed. (MW Chase, CA Davies, JR Downey, DJ Frurip, RA McDonald, AN Syverud, eds.) J Phys Chem Ref Data 14 (suppl 1), 1985. 11. J Bass, KH Fisher. Electrical resistivity of pure metals and dilute alloys. In: Landolt-Bo¨rnstein New Series. Vol 15. Berlin: Springer-Verlag, 1982. 12. LW Shacklette, WS Williams. Scattering of electrons by vacancies through an order-disorder transition in vanadium carbide. J Appl Phys 42:4698, 1971. 13. LW Shacklette, WS Williams. Influence of order-disorder transformations on the electrical resistivity of vanadium carbide. Phys Rev B7:5041, 1973. 14. S Otani, T Tanaka, Y Ishizawa. Electrical resistivities in single crystals of TiC x and VC x . J Mater Sci 21:1011, 1986. 15. LC Dy, WS Williams. Resistivity, superconductivity, and order-disorder transformations in transition metal carbides and hydrogen-doped carbides. J Appl Phys 53:8915, 1982. 16. N Lorenzelli, R Caudron, JP Landesman, CH de Novion. Influence of the ordering of carbon vacancies on the electronic properties of TiC 0.625 . Solid State Commun 59:765, 1986. 17. G Santoro, RT Dolloff. Hall coefficient of tantalum carbide as a function of carbon content and temperature. J Appl Phys 39:2293, 1968. 18. H Wiesmann, M Gurvitch, H Lutz, A Gosh, B Schwarz, M Strongin, PB Allen, JW Halley. Simple model for characterizing the electrical resistivity in A-15 superconductors. Phys Rev Lett 38:782, 1977. 19. JH Mooij. Electrical conduction in concentrated disordered transition metal alloys. Phys Status Solidi A17:521, 1973. 20. TK Nath, AK Majumdar. Resistivity saturation in substitutionally disordered γ-Fe 80⫺x Ni x Cr 20 (14 ⱕ x ⱕ 30) alloys. Phys Rev B53:12148, 1996. 21. H Christiansson, G Grimvall. Thermal and electrical conductivity of cementite. Therm Conductivity 22:147, 1994. 22. DT Morelli. Thermal conductivity and thermoelectric power of titanium carbide single crystals. Phys Rev B 44:5453, 1991.

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23. LG Radosevich, WS Williams. Phonon scattering by conduction electrons and by lattice vacancies in carbides of the transition metals. Phys Rev 181:1110, 1969. 24. RK Williams, RS Graves, FJ Weaver. Transport properties of high purity, polycrystalline titanium diboride. J Appl Phys 59:1552, 1986. 25. LG Radosevich, WS Williams. Lattice thermal conductivity of superconducting niobium carbide. Phys Rev 188:770, 1969. 26. WS Williams. Thermal conductivity peaks in old and new ceramic superconductors. Solid State Commun 87:355, 1993. 27. Z Hashin, S Shtrikman. A variational approach to the theory of the effective magnetic permeability of multiphase materials. J Appl Phys 33:3125, 1962. 28. SP Turner, R Taylor, FH Gordon, TW Clyne. Thermal conductivities of Ti-SiC and Ti-TiB 2 particulate composites. J Mater Sci 28:3969, 1993. 29. J Helsing, A Helte. Effective conductivity of aggregates of anisotropic grains. J Appl Phys 69:3583, 1991. 30. KE Kihlstrom, RW Simon, SA Wolf. Tunneling α 2 F(ω) from sputtered thin-film NbN. Phys Rev B32:1843, 1985. 31. WL McMillan. Transition temperature of strong-coupled superconductors. Phys Rev 167:331, 1968. 32. LW Shacklette, LG Radosevich, WS Williams. Gap energy of superconducting niobium carbide. Phys Rev B4:84, 1971. 33. EK Storms, AL Giorgi, EG Szklarz. Atom vacancies and their effects on the properties of NbN containing carbon, oxygen or boron—II. J Phys Chem Solids 36:689, 1975. 34. Z Wokulski, C Sulkowski. Electrical properties and superconductivity of TiN 1⫺x C x films. Phys. Status Solidi (a) 144:K53, 1989. 35. J Zasadzinski, R Vaglio, G Rubino, KE Gray, M Russo. Properties of superconducting vanadium nitride sputtered films. Phys Rev B32:2929, 1985. 36. T Chen, X Yang, P Sourivong, K Kamimura, AJ Viescas, CJY Chen, JD Curley, DJ Phares, HE Hall, PA Dayton, CB Hart, JT Wang. Fabrication, superconducting Tc and charge transfer of VN x , NbN x and TaN x foils. Phys Lett A217:167, 1996. 37. BR Zhao, L Chen, HL Luo, MD Jack, DP Mullin. Superconducting and normal-state properties of vanadium nitride. Phys Rev B29:6198, 1984. 38. FI Ajami, RK MacCrone. Magnetic susceptibility and superconductivity of cubic vanadium nitrides. J Phys Chem Solids 36:7, 1975. 39. KE Gray, RT Kampwirth, DM Capone II, R Vaglio. Microscopic investigation of NbN sputtered films. Physica 135B:164, 1985. 40. H Rietschel, H Winter, W Reichardt. Strong depression of superconductivity in VN by spin fluctuations. Phys Rev B 22:4284, 1980. 41. H Rietschel. Importance of spin fluctuations for the thermodynamic properties of superconducting V and VN. Phys Rev B24:155, 1981. 42. FA Modine, TW Haywood, CY Allison. Optical and electrical properties of single-crystalline zirconium carbide. Phys Rev B32:7743, 1985. 43. LW Shacklette, H Ashworth. Hall coefficient of vanadium carbide as a function of temperature and carbon concentration. J Appl Phys 44:5254, 1973. 44. J-F Lei, H Okimura, JO Brittain. The electrical resistance of the group IV transition metal monocarbides and mononitrides in the temperature range 20–1000° C. Mater Sci Eng A123:129, 1990. 45. JR Cooper, RL Hansler. Variation of electrical resistivity of cubic tantalum carbide with composition. J Chem Phys 39:248, 1963. 46. A Nigro, G Nobile, MG Rubino, R Vaglio. Electrical resistivity of polycrystalline niobium nitride films. Phys Rev B37:3970, 1988. 47. AD McLeod, JS Haggerty, DR Sadoway. Electrical resistivities of monocrystalline and polycrystalline TiB 2 . J Am Ceram Soc 67:705, 1984. 48. M Rahman, CC Wang, W Chen, SA Akbar, C Mroz. Electrical resistivity of titanium diboride and zirconium diboride. J Am Ceram Soc 78:1380, 1995. 49. CS Choi, GC Xing, GA Ruggles, CM Osburn. The effect of annealing on resistivity of low pressure chemical vapor deposited titanium diboride. J Appl Phys 69:7853, 1991.

8 High-Temperature Characteristics Yukinobu Kumashiro Yokohama National University, Hodogaya-ku, Yokohama, Japan

I.

INTRODUCTION

These refractory metalloids are frequently considered for employment whenever extreme environments are to be encountered. The meaning of ‘‘high temperature’’ and the value assigned to it vary among industries and disciplines. Melting point is the most important criterion in the selection of materials for high-temperature applications. Interest in the carbides and diborides as cathodes in Hall-Heroult cells has a long history, which is due to good corrosion resistance in the use environment, high electrical conductivity, and good wettability by molten aluminum. There is some industrial production of crucibles of titanium diboride for vaporization of metals in high vacuum and at high temperature. Highthermal-conductivity TiB2 and ZrB2 are used for thermocouple protection and tubes in steel baths and in aluminum. Diboride would be desirable for application in rocket nozzles, combustion chambers, and jet engine turbines. Titanium carbide and diborides are materials for a possible first-wall fusion reactor because of their low atomic numbers. When designing new materials for high-temperature structural ceramics, constituents with similar thermal expansion coefficients must be chosen, because large differences in the expansion coefficients would create large stress in the materials. For the various high-temperature applications mentioned above it is necessary to clarify high-temperature electrical, thermal, and mechanical properties using well-characterized specimens. Applications for carbides and diborides would include cathodes for advanced thermionic energy conversion, high-current-density field emission cathodes. These require spectral emittance data, which are also related to measuring accurate high temperatures. High-temperature vaporization behaviors that yield high-temperature thermodynamic data such as activity and enthalpy are necessary for uses as nuclear reactor and fusion materials. High-temperature activity measurements make it possible to determine the Gibbs free energy of formation of compounds from the elements. Accurate high-temperature thermodynamic data serve to establish temperature-composition phase diagrams, i.e., limits for the formation of binary phases. Self-diffusion processes play major roles at high temperatures in the relief of residual stresses and plastic deformation, sintering, homogenization, and grain growth. In this chapter emissivity measurement; vaporization behavior; diffusion studies; and electrical, thermal, and mechanical properties at high temperatures will be discussed. 191

192

Kumashiro

II. EMITTANCE The spectral emittance is defined as the ratio of the radiant power per unit area leaving the surface of a body at some given wavelength to that leaving a blackbody at the same temperature. The spectral emittance can be determined practically by comparing the observed or apparent surface temperature of a material with that of a blackbody cavity existing in the same material. The normal spectral emittance is a special case in which the viewing direction is normal to the smooth, opaque surface of the crystalline material. Emissivity is a property of the surface of real specimens. Emittance was calculated from ⑀ 2 (T ) ⫽ exp[C/λ(1/αTBB ⫺ 1/αTsurf )]

(1)

where TBB is the pyrometer temperature in K shown by the blackbody cavity, Tsurf is the pyrometer temperature in K measured on and in a direction normal to the surface of the specimen, C is a constant (C ⫽ hc/k ⫽ 14388 µm-K), and λ is the wavelength of the light detected. The emittance measurements were taken at the commonly used pyrometer wavelength of 0.65 µm. The α is a correction for the brightness lost in transmission through the Pyrex viewpoint. The normal spectral emittance of crystalline carbides by floating-zone arc refinement were measured in vacuum (10 ⫺8 or low 10 ⫺7 torr) in the temperature range 1200 ⬍ T ⬍ 2400 K (1). Reproducible results within the errors were obtained after thermally cleaning these carbides, despite variations in surface roughness or the type of pyrometer used for the temperature measurements. The values for emittance are for samples that were clean as determined by Auger analysis. The emittance of HfC0.86 tends to increase slightly with temperature, whereas those of NbC0.83, TaC0.79 , TiC0.98 and ZrC0.92 decrease ⑀ HfC ⑀ NbC ⑀ TaC ⑀ TiC ⑀ ZrC

⫽ ⫽ ⫽ ⫽ ⫽

0.4322 ⫹ 1.065 ⫻ 10 ⫺6 T 0.4913 ⫺ 6.6 ⫻ 10 ⫺5 T 0.4662 ⫺ 5.084 ⫻ 10 ⫺5 T 0.8192 ⫺ 1.66 ⫻ 10 ⫺4 T 0.715 ⫺ 1.174 ⫻ 10 ⫺4 T

III. VAPORIZATION BEHAVIORS High-temperature activity measurements for carbide as a function of composition and temperature were performed by using knundsen effusion in a mass spectrometer (2–4). A Langmuir measurement at the congruently vaporizing composition (CVC) was made, from which absolute pressures were obtained. These data give heat and entropy of vaporization and total vaporization energy, defined as the heat needed to produce 1 mole of vapor having the composition of the solid. Activities at 2300 and 2500 K for NbC are plotted as a function of composition in Fig. 1. From a smooth curve through these points, the activity of carbon was calculated by a GibbsDuhem integration. Compositions at the low-carbon boundary of NbC were obtained at 2300 and 2500 K from the intersection between the horizontal line that represents the activity in the two-phase region, Nb2 C ⫹ NbC, and the curve through the single-phase points in Fig. 1. The heat formation and the entropy tend to show an increasing deviation from other measurements as the NbC phase becomes more defective. This discrepancy is reduced considerably if only

High-Temperature Characteristics

193

Figure 1 Activities of niobium and carbon at 1700 and 2000 K as a function of composition. (From Ref. 2.)

Figure 2 Activities of vanadium and carbon at 1700 and 2000 K as a function of composition. (From Ref. 3.)

part of the randomization entropy is added to the measured entropy so that the material used for the heat capacity and heat content measurements was partially ordered. The activity of vanadium at 1700 and 2000 K is shown as a function of composition in Fig. 2. The phase boundaries at 1700 and 2000 K for V2 C and VC were obtained from Fig. 2 by noting where the curve through the single-phase regions intersected the horizontal line through the two-phase regions. There is an indication of a break in the 1700 K activity curve near VC0.66, which might be due to the presence of ζ phase. This effect is gone at 2000 K. The activity measurements place the upper V2C boundary at VC0.58 and 1700 K with a slight trend to higher compositions as the temperature is increased. VC exists between VC0.74 and VC0.91 at 1700 K. At the upper composition, the vacancy order at 1403 K give V8C7 and graphite. A stable phase exists between V2C and VC below approximately 1800 K that has a stoichiometry of V3 C 2 . V2 C extends from VC0.45 to VC0.56 at 1700 K. The failure to observe the upper composi-

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tion in quenched material would be attributed to rapid precipitation of VC at the order-disorder transition in V2C. The zirconium activity for each composition (Fig. 3) accounts well for results calculated by Guillermet (5) using phenomenological models for the Gibbs energy function, i.e., the compound energy model (CEM). The lower phase boundary at 2100 K was placed at ZrC0.565 . The behavior of the partial enthalpy indicates that this boundary will move only slightly to higher compositions as the temperature decreases. The upper boundary at 2100 K is at ZiC1.0 and moves to lower compositions as the temperature is increased. ZiC0.975 will contain two phases above 2603 K, so compositions near ZrC0.96 commonly occur because the material is in equilibrium with carbon at some very high temperature, suggesting that the stoichiometry of ZrC may actually exceed unity below 2100 K. The change in zirconium activity with the carbon content of the ZiC phase is most rapid in the high-carbon region. Near ZrC0.8 the rate becomes much lower and remains constant down to the low-carbon boundary. The partial molar heat of vaporization also shows two regions with a transition near ZrC0.8 . The composition of the upper phase boundary at 2100 K is ZrC1.0 , and this changes to lower compositions as the temperature is increased. The lowcarbon boundary moves slightly to higher compositions as the temperature is reduced. ZiC2 has been found over ZrC ⫹ C at 2660 K with a ZrC2 /Zr ratio of 0.06. This compares with 0.04 for NbC2 /Nb, 0.005 for TiC2 /Ti, and 0.003 for VC2 /V at the same temperatures corresponding to the ionic bond in the solid; i.e., the more ionic the bond in the solid, the more stable the MC2 vapor in the gas. During vaporization of carbides (MC) the surface composition changes with time due to

Figure 3 Zirconium and carbon activities at 2100 K for various compositions. (From Ref. 4.)

High-Temperature Characteristics

195

incongruent loss of metal (M) and carbon (C) atoms, eventually approaching a CVC (6), where M and C atoms are removed in a ratio equal to that present on the solid surface. The temperature dependence of a M and a C and the molar vaporization rate of M and C estimated by Langmuir’s model determine CVC. Calculated CVC values in NbC are in excellent agreement with the observed value above 2600 K. The experimental compositions for ZrC are ⬇ 2% smaller than the calculated value, and those for HfC are ⬇ 12% greater than the calculated values. The calculated values for VC are larger than the values for the carbon-rich phase boundary in the VC phase, suggesting that VC vaporizes incongruently to C. TiC also vaporizes incongruently to C below 2700 K. The surface composition determines the equilibrium vapor pressure of metal and carbon atoms and influences the overall loss of carbide, which is determined in large part by solid-state diffusion of C. Figure 4 summarizes the congruent mass vaporization rates for graphite, TiC, ZrC, HfC, NbC, and VC (6). In laser diagnostic methods developed to study the vaporization behavior of ZrC (7), a vapor phase was produced by laser ablation of a ZrC target. The temperatures of the plasmas are estimated to be between 9000 and 12,000 K. Thermodynamic calculations for 9000 K predict that C 3 has the highest partial pressure, followed by C2 and C5. Zirconium has the lowest calculated partial pressure. The dominant neutral gas species of an expanding plasma plume are predicted to be Zr and C followed by, in decreasing order of importance, C2 , C3 , C4 , and C5 . The optical emission spectra of the ablated ZrC from 200 to 500 nm at delay times from 10 µs to 1 ms (Fig. 5) contain lines only for excited Zr. Emission peaks from C, C2 , and C3 were absent from the spectra, apparently because of the inherently low emission intensities of these species compared with that of Zr, which has a very strong spectrum in the ultraviolet frequency range. On the contrary, the experimental partial pressures of N2 , p(N2), as a function of composition over ZrN in the literature show significant scatter, which would be largely due to the wide homogeneity range of the nitride and the preferential loss of nitrogen from the sample surface: Fig. 6 shows the Zr activity a(Zr) and p(N2) in the face-centered cubic (fcc) phase at 2000 K (8). The activity coefficient of Zr decreases with increasing nitrogen constant, indicating that Zr is stabilized with increasing nitrogen content. At the same time p(N2) increases progressively with increasing nitrogen content.

Figure 4 Congruent mass vaporization rate for carbides. (From Ref. 6.)

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Figure 5 ZrC ablation plume emission spectrum at 10 µs delay. (From Ref. 7.)

Figure 6 Component activities at 2000 K as a function of nitrogen content. Calculated (solid curve) and experimental (circles) results are shown. (From Ref. 8.)

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197

IV. DIFFUSION STUDIES The most commonly defined diffusion coefficients are the chemical or interdiffusion, intrinsic diffusion, and tracer or self-diffusion coefficients. The relevant coefficient depends on the driving force. The diffusion coefficient exhibits Arrhenius behavior, according to the relationship D ⫽ D0 exp(⫺Q/RT), where D 0 is the preexponential factor and Q is the activation energy. The activation energy involves the activation enthalpy and entropy value. The entropy values are consistent with Zener’s theories of volume diffusion. A driving force for diffusion includes any influence that increases the jump frequency. Examples of driving forces include chemical potential, thermal, and stress gradients. The use of single-crystal or well-characterized specimens is important for accurate data and interpretation. Diffusion along grain boundaries in polycrystalline specimens tends to lower both D 0 and Q. Because very little is known about diffusion in diboride, this discussion is restricted to carbides and nitrides. The mechanism of diffusion in transition metal carbides and nitrides differs for metal and nonmetal sublattices. The nonmetal diffusion proceeds via a vacancy mechanism in the nonmetal sublattice because the vacancy concentration is a function of composition within the homogeneity range of fcc phases (9,10). The self-diffusivity of the transition metal in carbides is composition independent, and that of carbon is greater than that for the metal atom by several factors of 10. For metal atom diffusion, formation and migration terms are needed in the diffusion equation. In the metal sublattice, vacancies are formed thermally by Schottky disorder, and these concentrations may be assumed to be independent of the composition, as confirmed by the experimental data (10). Sarian (11–14) and Yu and Davis (15,16) studied systematic variation of the composition for carbides to propose a common diffusion mechanism. Table 1 lists D 0 and Q for various transition metal carbides. The experimental temperatures were high enough that any residual order and hence nonrandom vacancy distribution would be assumed to have no influence on matter transport processes. Sarian (14) pointed out that the activation entropy and enthalpy for carbon migration in VC, TiC, and ZrC are proportional to the melting points and concluded that the geometry of the diffusion path, as well as that of the vacancy distribution, is common to all three compounds. The results are in substantive agreement with the Zener model for the diffusion of interstitials. Yu and Davis (15,16) have argued that, at least for NbCx , the exact diffusion path for carbon may change as a function of composition. The notable difference in the D 0 and Q values between the higher C content crystals (NbC0.87 and NbC0.84) and the lower C content crystal (NbC0.766) was caused by the presence of two diffusion mechanisms. In the former two materials, the Table 1 Arrhenius Coefficients for Carbon-14 Self-Diffusion in Transition Metal Carbides Composition TiC 0.97 TiC 0.89 TiC 0.67 TiC 0.67 ZrC 0.97 VC 0.84 NbC 0.87 NbC 0.84 NbC 0.76

D0 (cm2 /s)

Q (kcal/mol)

Temp. range (°C)

Reference

6.98 45.44 1.14 ⫻ 102 2.85 ⫻ 10⫺4 1.32 ⫻ 102 2.65 2.59 7.44 2.22 ⫻ 10⫺2

95.3 106.8 109.9 49.6 113.2 85.0 100.4 105.0 76.0

1475–2720 1450–2280 1745–2080 2080–2720 1350–2150 1700–2200 1630–2040 1630–2040 1630–2040

11 11 12 12 13 14 15 15 15

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dominant mechanism of 14C transport would be the movement of these species from an occupied octahedral site to a similar vacant octahedral site via a neighboring tetrahedal position (O-T-O mechanism) with an effective jump distance a 0 /√2 and shorter ⬍111⬎ jump. Two jumps are involved in going to and from the tetrahedral site. In NbC0.766 , however, 14 C is thought to move to the vacant octahedral site via an Nb vacancy. The latter process necessitates the formation of a transient ‘‘divacancy’’ between the vacant C and Nb sites in which the diffusing 14 C atom only momentarily resides in the Nb vacancy. The presence of a large number of structural C vacancies in all compositions would indicate that the activation energy for the (O-T-O) and transient divacancy mechanisms would consist essentially of the C migration energy in the former and the energy of Nb vacancy formation in the latter transport path. The Nb vacancy formation energy for NbC0.750 is 60.49 kcal/mol according to the vapor pressure data (2), which is in line with the 76.0 kcal/mol Q value found in NbC0.766 . The Nb self-diffusion coefficients for NbC0.868 . NbC0.834 , and NbC0.766 are essentially independent of the C/Nb ratio in the temperature range 2370–2660 K and are expressed as

冢

D *Nb ⫽ 4.54

冣

⫹2.85 exp[⫺(140.0 ⫾ 2.4 kcal/mol)/RT ] cm 2 /s ⫺1.75

(2)

The 95 Nb migration energy depends on the size of the relevant gap in each mechanism through which the Nb atoms must pass to reach the analogous vacancy. Then Nb atoms diffuse by the (O-O) mechanism, just as a pure metal diffuses in an fcc lattice, in which the atom migrates from its lattice position directly to an analogous vacant site. The activation energy, Q, for selfdiffusion in fcc metals is given by Q/Tm ≅36 cal/K. Using Tm ⫽ 3873 K for niobium carbide, the Q is found to be 139.4 kcal/mol, which is in excellent agreement with the experimental value of ≅ 140 kcal/mol. Modeling the diffusion-coupled vaporization process associated with nonstoichiometric carbides requires the use of the chemical diffusion coefficient to calculate the temporal concentration (6,17). The chemical diffusion coefficient has a strong concentration dependence and has been determined mainly by layer growth, where a diffusion couple consisting of C and M is held at a temperature for varying times. The activation energy for chemical diffusion is smaller than that for self-diffusion in a single crystal. However, there is one report on chemical diffusion using a TiC single crystal (18). The diffusion of carbon was allowed to proceed in a chemical gradient to induce the following expression: D ⫽ 220 exp[⫺(97.7 kcal/mol)/RT] cm 2 /s

(3)

Good agreement between self-diffusion and chemical diffusion was obtained. A smaller activation energy in chemical diffusion would be short-circuited by a grain boundary referring to grain boundary diffusion (19) rather than volume diffusion. Then the data on chemical diffusion for various carbides should be revised by using single crystals. In transition metal nitrides, nitrogen diffusivity is studied mainly by phase-band growth as a function of time and temperature under the assumption that nitrogen is the only diffusing species (20). Table 2 summarizes the diffusion data for nitrides obtained from nitridation kinetics at high temperatures. Although the metal diffusivity in transition metal nitrides has not yet been investigated in detail, the activation energy of that process is probably much higher than that of nitrogen diffusivity by two to three times (26). Data referring to chemical diffusion obtained from nitridation kinetics at relatively high temperatures, i.e., values of D 0 and Q obtained at T ⬍ 1200°C

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199

Table 2 Collected Diffusion Data for Nitrides with NaCl-Type Structure Materials

D0 (cm2 /s)

Q (kcal/mol)

Temp. range (°C)

Reference

δ-TiN δ-ZrN

2.3 ⫻ 10⫺3 6.0 ⫻ 10⫺2 1.7 ⫻ 10⫺2 3.12 0.75 0.02 2.60 12.7 3.27

50.2 59.8 53.6 79.0 78.1 62.9 62.3 67.1 76.0

1300–1600 1250–1700 1260–1720 1200–1500 1600–2200 1160–1800 1100–1700 1100–1700 1400–1900

21 22 22 22 22 23 20 24 25

δ-ZrN 0.76 δ-HfN δ-VN1⫺x δ-VN1⫺x δ-NbN1⫺x

on polycrystalline samples, are actually typical of nitrogen transport associated with a shortcircuit diffusion mechanism (22). However, considering the very limited diffusion data, the mechanism of nitrogen diffusion in single crystals is still an open problem.

V.

ELECTRICAL PROPERTIES

The transition metal carbides, nitrides, and diborides show metallic conductivity with a resistivity of 7–250 µΩ ⋅ cm and have a negative Hall coefficient. Also, the higher carrier concentration of 10 22 /cm 3 and lower thermoelectric power of several µV/K indicate that the electron gas in the specimen could be regarded as strongly degenerate (28). These facts are reflected in Fig. 7, i.e., temperature dependences of resistivity (ρ), thermoelectric power (S), Hall coefficient (RH ), and mobility (µ H) of TiC1.0 single crystals (29). Both RH and S are negative in sign over the entire temperature range, indicating that the predominant charge carriers are electrons. The mobility µ H decreases with temperature and up to about 600°C conduction is performed by vacancy scatter-

Figure 7 Temperature dependences of resistivity (ρ), thermoelectric power (S), Hall coefficient (R H ), and Hall mobility (µ H ) of TiC1.0 single crystal. (From Ref. 29.)

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ing; above 650°C, it is due to the scattering of lattice vibrations as in semiconductors, which is confirmed by plotting the relationship between log µ H and 1/T (µ ⬀H T ⫺3/2 ). The metallic nature of TiB 2 (30) also leads to a resistance that increases linearly with temperature (Fig.8). The resistivity of the bicrystal, single crystal (sample 1), is greater than that of the two single crystals (samples 2 and 3). The increase of resistivity of the bicrystal could be due to the presence of the grain boundary. The average coefficient of resistivity, α ⫽ m/ρ298 would represent intrinsic electrical behavior of a metal-like material (30) and the value of α for TiB2 with a similar type and level of impurites is practically constant and independent of the physical state of aggregation, i.e., monocrystalline or polycrystalline. The coefficient α is not influenced by the presence of pores, grain boundaries, and cracks in the materials. The temperature dependence of the electrical resistivity of the TiB2-ZrB2 system as a function of temperature (31) obeys the same behavior as TiB2 . The ρ298 (µΩ ⋅ cm) and m (µΩ ⋅ cm/K) values for ZrB2 were determined to be 7.8 and 10, both of which increase with TiB2 content. These values for TiB2 were determined to be 20.4 and 36, respectively. Electrical conduction in the diborides of intermediate compositions may be primarily via the zirconium-rich

Figure 8 Resistivity of TiB2 polycrystals and single crystals up to high temperatures. (From Ref. 30.)

High-Temperature Characteristics

201

solid-solution phases, indicating that α values for the intermediate compositions are only slightly higher than that of ZrB2 and, essentially, remain constant regardless of an increasing amount of titanium-rich phase in the system. Williams et al. (32) measured resistivity up to 1800 K using high-purity polycrystalline TiB2 to deduce the ideal resistivity from the Debye temperature, Gru¨neisen parameter, and thermal expansion coefficient. They induced the ideal resistivity ρi(µΩ ⋅ cm) at high temperatures as follows: ρi ⫽ 0.03T ⫹ 0.23 ⫻ 10 ⫺5 T 2

(4)

The resistivity of single-crystal ZrC0.93 in the temperature range 1000–3000 K was measured for the first time by Hinrichs et al. (33). All measurements were made in argon at 1 atm pressure to reduce evaporation to a tolerable level over the time required to make the measurements. Temperatures were corrected by emissivity (1). The resistivity data in Fig. 9 fit the following formula well: ρ ⫽ 176.5 ⫹ 0.0552T ⫺ 650 exp(⫺6900/T )

(5)

The observed temperature dependence of the resistivity can be explained by a combination of phonon-induced interband scattering of electrons and a temperature-dependent Fermi energy. Williams et al. (34–36) studied the electrical resistivity of these VC and NbC phases and the influence of defect scattering on the temperature dependence of the resistivity. They found a discontinuity in the electrical resistivity of 5 to 10% at the transformation temperature and a virtual disappearance of the large residual resistivity normally associated with these nonstoichiometric compounds. This result confirmed the interpretation attributing the residual resistivity to strong scattering of electrons by randomly arranged and abundant carbon vacancies. The behavior of the resistivity around the critical point in V6 C5 is presented in Fig. 10. The change in the resistivity of V6 C5 at its critical point was found to be 5.4 ⫾ 0.3 µΩ ⋅ cm or (3.6 ⫾ 0.2)% of the total resistivity of the disordered solid. The order parameter was computed in the BraggWilliams approximation for a hypothetical A 5B alloy having an fcc lattice, where A was identified with carbon atoms and B with vacancies. This calculation predicts that the order-disorder

Figure 9 Resistivity of ZrC single crystal as a function of temperature. (From Ref. 33.)

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Figure 10 Temperature dependences of well-annealed samples of V6 C5 and V8 C7 prepared by annealing V6 C5 in VC0.875 powder. (From Ref. 35.)

transition in V6C5 will be of first order, as evidenced by the discontinuous jump in the order parameter at Tc. The temperature dependence of the resistivity of a well-annealed sample of V8 C7 also shows a discontinuity at the critical point, indicating a first-order transformation (Fig. 10). The region of metastability (TeH ⫺ TeL) in the V8 C7 transformation is more than three times larger than the corresponding region in V6 C5 . The corresponding change found for V8C7 was 20.1 ⫾ 1.4 µΩ cm or (14.7 ⫾ 1.0)%. The critical temperatures for disordering in the two ordered phases were determined to be (1275 ⫾ 8)°C for V6 C5 and (1124 ⫾ 15)°C for V8 C7 . The vanadiumcarbon system (VCx) has a strong preference for one or the other of the ordered phases for nearly all compositions in the range 0.83 ⱕ X ⱕ 0.90. These temperatures are composition dependent and tend to reach maxima at the ideal compositions VC0.833 and VC0.875 . The resistivities of the ordered phases of vanadium carbide, V6 C7 and V8 C7 , indicate that the scattering of electrons by vacancies makes the dominant contribution to the low-temperature resistivity and, therefore, support conclusions regarding the role of vacancies becoming of less importance as the temperature increases. The decline in the vacancy contribution with increasing temperature is most likely produced by a decrease in the Hall coefficient and/or the effective mass, since such behavior is common in the transition metal carbides. Thus the simple form of Matthiessen’s rule, ρtotal ⫽ ρdefect ⫹ ρ(T ) phonon, which takes the defect resistivity to be temperature independent, does not hold here.

High-Temperature Characteristics

203

The temperature dependence of the resistivity of Nb6 C5 (36) shows the peculiar curvature in ρ(T ) characteristic of the superconducting compounds, which is usually fitted with the empirical expression ρ(T ) ⫽ ρideal ⫹ a exp(b/T ) ⫽ 61.6 ⫹ 0.0145T ⫹ 61.6 exp(355/T )

(6)

VI. THERMAL PROPERTIES The vacancies in transition metal carbides and nitrides induce lattice distortions in their neighborhood and the thermal motion of metal atoms adjacent to the vacancies become asymmetric and anharmonic. Temperature-dependent X-ray diffraction experiments yield reliable information about the thermal vibrations under the assumption that the static part of the Debye-Waller (D-W) factor is temperature independent—i.e., the concentrations of vacancies and lattice distortions remain constant within the given temperature range—but it is very sensitive to the local atomic arrangement. The mean value of the Debye temperature averaged over the temperature range 623 to 1273 K is θ M ⫽ 498 ⫾ 9 K (37), so that the thermal vibrations in ZrC0.98 can be described by the quasi-harmonic one-point potential (OPP) mode in the temperature range 295 to 1273 K. The very weak variation with temperature of the Debye temperature indicates that the potential parameters are temperature independent. Anharmonicity due to the presence of the N vacancies was not observed in VN and was found to be independent of the Debye temperature of (412 ⫾ 12) K within experimental error in the temperature range 293 to 500 K (38). For small relative concentrations of carbon vacancies in nonstoichiometric titanium carbide (39) a large contribution of static displacements to the D-W factor indicates that the static displacements of atoms with point defects must be taken into account in determining vibrational characteristics from the D-W factor. The static D-W factor for TiC0.967 is independent of temperature in the range 293 to 700 K but rapidly increases at temperature T ⬎ 700 K (39), which includes static displacements and changes of thermal vibrations due to the presence of vacancies. Using the quasi-harmonic approximation, the experimental data for the temperature range 293 to 700 K indicate temperature dependence of the Debye temperature. The thermal expansion of a crystal is mainly determined by the amplitude of the atomic vibrations about the mean positions. The repulsion energy increases more rapidly with atomic separation than does the attraction energy, resulting in a nonsymmetrical energy minimum. Consequently, as the temperature is raised, the anharmonicity of the atomic vibrations will result in a larger time-averaged distance between the atoms, corresponding to lattice expansion (40). The linear thermal expansion coefficient α is calculated from α⫽

d(ln a) dT

(7)

To a very good approximation α is given by α⫽

1 da a0 dT

(8)

where a is a lattice constant and is a 0 at room temperature. In cubic crystals α is a scalar, independent of direction, and in the diboride hexagonal crystal the principal values of α are those parallel and perpendicular to the c axis, i.e., α c and α a. The measured linear expansion

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coefficient α is the directionally averaged value, which is just one-third of the volume expansion coefficient. Thus, α¯ ⫽

1 (α c ⫹ 2α a ) 3

(9)

The high-temperature thermal expansion data for transition metal nitrides (41) are summarized in Fig. 11. The thermal expansion values of Ti(CxN1⫺x), Zr(Cx N1⫺x ), and Hf(Cx N1⫺x ) with [C ⫹ N]/[Me] ⬃ 1 and TiN1⫺x with [N]/[Ti] ⫽ 1.0 to 0.67 were determined from lattice prameter measurements made with high-temperature X-ray diffraction in the temperature range of 298– 1473 K (42). The variation in the lattice parameters with temperature is given in Table 3. Titanium carbonitrides, zirconium carbonitrides, and hafnium carbonitrides obey Vegard’s rule quite well up to 1473 K. The linear thermal expansion coefficient and the average thermal expansion coefficient are also given in Table 4. For titanium nitride, the thermal expansion decreases with decreasing nitrogen/titanium ratio. The decreases in the thermal expansion coefficients of the nitrides are always greater than those of the carbides. For titanium carbonitride and hafnium carbonitride, the function expansion versus composition is almost linear, whereas the expansion of the zirconium carbonitrides shows a slight maximum. Lattice parameters of carbides and nitrides were estimated up to 2400 K using an empirical approach (43) that was developed for the estimation of high-temperature lattice parameters and relevant structural and bonding parameters. The equation is as follows: a T ⫽ a 298 ⫹ 1.2 ⫻ 10 ⫺4

ra ⫹ rc (T ⫺ 298) za ⫹ zc

(10)

where a T and a 298 are the lattice parameters at high temperature T and 298 K, ra and rc are atomic radii of the constituents, and z a and z c are the anion and cation valences. Good agreement

Figure 11 High-temperature thermal expansion of various transition nitrides. (From Ref. 41.)

High-Temperature Characteristics

205

˚ ) of Carbide, Nitride, and Table 3 Variation of Lattice Parameter a (A Carbonitrides with Temperature T (K) Compound

Equations a(x,T ) ⫽ 4.2313 ⫹ 0.088x ⫹ (2.338 ⫺ 0.122x) ⫻ 10⫺5 T ⫹ (1.0717 ⫺ 0.2258x) ⫻ 10 ⫺8 T 2 ⫾ 0.002 a(x,T ) ⫽ 4.5718 ⫹ 0.1178x ⫹ (2.107 ⫹ 0.0098x) ⫻ 10 ⫺5 T ⫹ (8.253 ⫺ 0.006x) ⫻ 10 ⫺9 T 2 ⫾ 0.002 a(T ) ⫽ 4.69309 ⫺ 1.0170 ⫻ 10 ⫺5 T ⫹ 4.9767 ⫻ 10 ⫺8 T 2 ⫺ 1.376 ⫻ 10 ⫺11 T 3 a(x,T ) ⫽ 4.5173 ⫹ 0.115x ⫹ (1.9916 ⫹ 0.2875x) ⫻ 10 ⫺5 T ⫹ (1.124 ⫺ 0.877x) ⫻ 10 ⫺8 T 2 ⫾ 0.002 a(x,T ) ⫽ 4.1823 ⫹ 0.0530x ⫹ (1.2206 ⫹ 0.8348x) ⫻ 10 ⫺5 T ⫹ (1.3485 ⫺ 0.1128x) ⫻ 10 ⫺8 T 2 ⫾ 0.002

Ti(CxN1⫺x) Zr(CxN1⫺x) ZrC0.98 [37] Hf(Cx N1⫺x) TiNx Source: From Ref. 42.

(⫾0.5%) between the literature and computed lattice parameters has been confirmed. This method could be used to estimate the thermal expansion behavior. The variation in the lattice parameters of the group IV—VII transition metal diborides with temperature is given in Table 5. All the diborides display similar lattice parameter versus temperature dependences. The equations given in Table 6 were calculated by inserting the equations in Table 5 into Eq. (8). A larger expansion coefficient along the axis is obtained for NbB2 than for TaB2 (44). The experimental data agree fairly well with those reported for similar lattice parameter versus temperature dependences. The equations given in the literature (45–47), that is, α¯ a ⫽ 7.25 ⫻ 10 ⫺6 /K and α¯ c ⫽ 10.20 ⫻ 10 ⫺5 /K for TiB2 , and α¯ ⫽ 8.27 ⫻ 10 ⫺6 /K and 8.8 ⫻ 10⫺6 /K (45) for TiB2 sintered specimens. The coefficients are larger in the c direction than in the a direction, which is due to the anisotropy in the bond strength between the two directions. The bonding strength in the basal plane is determined mainly by the strong covalent BB bonds within the boron layer, while the MB bond strength plays the dominant role in determining the cohesion in the c direction. In the diborides of the larger metal atoms, zirconium and hafnium, the a axis is determined by MM contacts. The BB bonds are therefore streched and the BB bond strength is probably slightly lowered. However, the MB and MM bond strengths increase at the same time, compensating for the decrease in BB bond strength, leading to a decrease in α¯ c . The anisotTable 4 Linear Thermal Expansion Coefficient α (K⫺1) and Average Thermal Expansion Coefficient αav (K⫺1) of Nitride and Carbonitrides in the Temperature Range 298–1473 K Compound

Equation α(x, T) (K ⫺1 )

Ti(CxN1⫺x)

α(x,T ) ⫽ [(2.338 ⫺ 0.122x) ⫻ 10⫺6 ⫹ (2.143 ⫹ 0.451x) ⫻ 10⫺9 T ]/a(x,T ) α(x,T ) ⫽ [(2.107 ⫹ 0.0098x) ⫻ 10⫺6 ⫹ (1.650 ⫹ 0.0012x) ⫻ 10⫺9 T ]/a(x,T ) α(x,T ) ⫽ [(1.9916 ⫹ 0.2875x) ⫻ 10⫺6 ⫹ (2.248 ⫺ 1.754x) ⫻ 10⫺9T ]/a(x,T ) α(x,T ) ⫽ [(1.2206 ⫹ 0.8348x) ⫻ 10⫺6 ⫹ (2.697 ⫺ 0.2256x) ⫻ 10⫺9T ]/a(x,T )

Zr(CxN1⫺x) Hf(CxN1⫺x) TiNx

Source: From Ref. 42.

Equation α av (K ⫺1 ) αav(x) ⫽ (9.9 ⫺ 1.4x) ⫻ 10⫺6 αav(x) ⫽ (7.8 ⫹ 0.3x ⫺ 0.6x 2) ⫻ 10⫺6 αav(x) ⫽ (8.5 ⫺ 2.4x) ⫻ 10⫺6 αav(x) ⫽ (7.0 ⫹ 1.9x) ⫻ 10⫺6

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˚ ) with Table 5 Variation of the Lattice Parameters a and c (A Temperature T (K) Compound

Equations a ⫽ 3.0244 ⫹ 1.447 ⫻ 10⫺5T ⫹ 5.853 ⫻ 10⫺9 T 2 c ⫽ 3.2213 ⫹ 2.348 ⫻ 10⫺5T ⫹ 6.628 ⫻ 10⫺9 T 2 a ⫽ 3.1637 ⫹ 1.391 ⫻ 10⫺5T ⫹ 7.109 ⫻ 10⫺9 T 2 c ⫽ 3.5259 ⫹ 1.651 ⫻ 10⫺5T ⫹ 7.386 ⫻ 10⫺9 T 2 a ⫽ 3.1380 ⫹ 1.168 ⫻ 10⫺5T ⫹ 7.876 ⫻ 10⫺9 T 2 c ⫽ 3.4716 ⫹ 1.726 ⫻ 10⫺5T ⫹ 6.208 ⫻ 10⫺9 T 2 a ⫽ 2.9930 ⫹ 9.703 ⫻ 10⫺6T ⫹ 7.497 ⫻ 10⫺9 T 2 c ⫽ 3.0432 ⫹ 3.946 ⫻ 10⫺5T ⫹ 6.389 ⫻ 10⫺9 T 2 a ⫽ 3.1052 ⫹ 1.421 ⫻ 10⫺5T ⫹ 5.759 ⫻ 10⫺9 T 2 c ⫽ 3.2599 ⫹ 2.295 ⫻ 10⫺5T ⫹ 7.842 ⫻ 10⫺9 T 2 a ⫽ 3.0924 ⫹ 1.276 ⫻ 10⫺5T ⫹ 6.991 ⫻ 10⫺9 T 2 c ⫽ 3.2204 ⫹ 1.389 ⫻ 10⫺5T ⫹ 1.111 ⫻ 10⫺8 T 2

TiB2 ZrB2 HfB2 VB2 NbB2 TaB2 Source: From Ref. 40.

ropy in bond strength can also be seen from the variation in the c/a value with metal radius. The lattice is prevented by the boron layer from expanding in the a direction but is allowed to expand more easily in the c direction, giving an increase in the c/a value with increasing metal radius (40). The difference in the magnitude of α¯ c among the various diborides is substantially larger than the corresponding difference in the magnitude of α¯ a , indicating that the anisotropy decreases with increasing radius of the metal atom. The α¯ a is slightly smaller for diborides having large α¯ c values, which might be due to a Poisson contraction; i.e., the very large expansion along the c axis leads to a contraction of the lattice in the perpendicular direction. The thermal expansion coefficient in the a direction changes very little with the metal radius, owing to the fact that the bonding strength in the basal plane is determined by the strong BB bonds within the boron layer. A change in the type of metal atom has a larger influence on the thermal expansion coefficient than does a change in the boron composition of the diboride.

Table 6 Variation in the Linear Thermal Expansion Coefficients α¯ a and α¯ c (K ⫺1) with Temperature T (K) Compound TiB2 ZrB2 HfB2 VB2 NbB2 TaB2

Equations α¯ a α¯ c α¯ a α¯ c α¯ a α¯ c α¯ a α¯ c α¯ a α¯ c α¯ a α¯ c

⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽

Source: From Ref. 40.

5.351 ⫻ 10⫺6 ⫹ 1.933 ⫻ 10⫺9 T 7.884 ⫻ 10⫺6 ⫹ 2.051 ⫻ 10⫺9 T 5.061 ⫻ 10⫺6 ⫹ 2.243 ⫻ 10⫺9 T 5.298 ⫻ 10⫺6 ⫹ 2.091 ⫻ 10⫺9 T 4.465 ⫻ 10⫺6 ⫹ 2.506 ⫻ 10⫺9 T 5.501 ⫻ 10⫺6 ⫹ 1.784 ⫻ 10⫺9 T 3.984 ⫻ 10⫺6 ⫹ 2.502 ⫻ 10⫺9 T 13.267 ⫻ 10⫺6 ⫹ 2.353 ⫻ 10⫺9 T 6.047 ⫻ 10⫺6 ⫹ 1.851 ⫻ 10⫺9 T 7.740 ⫻ 10⫺6 ⫹ 2.400 ⫻ 10⫺9 T 4.793 ⫻ 10⫺6 ⫹ 2.259 ⫻ 10⫺9 T 5.531 ⫻ 10⫺6 ⫹ 3.443 ⫻ 10⫺9 T

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207

Figure 12 Heat capacities of titanium carbides and nitrides as a function of temperature. (From Ref. 48.)

The molar heat capacities (C p) of TiC and TiN are shown in Fig. 12. Generally, with increasing temperature the molar heat approaches the theoretical value of 52 J mol ⫺1 (DulongPetit rule) or even exceeds it. Nitrides have a larger heat capacity than carbides (48). The heat capacities of the corresponding stoichiometric carbonitrides as a function of temperature were found to lie in between the two curves, i.e., with a linear dependence on the [C]/([C] ⫹ [N]) ratio. An interesting C p versus T behavior was observed for the Ti(Cx N1⫺x ) series. A distinct endothermic C p discontinuity could be detected, 1068 K for TiC0.82 and 973 K for TiN0.82, which is also present in the binary compounds TiN and TiC upon heating. Upon cooling, reversible C p behavior was observed but shifted toward slightly lower temperatures, which is evidence of a phase transition. The transition temperature increases with increasing nitrogen content. But X-ray powder diffraction measurements of samples quenched or cooled from temperatures both above and below the C p discontinuity did not reveal any deviations with respect to the line pattern or the lattice parameters. The discontinuity at around 1000 K observed for the substoichiometric titanium carbonitrides in thermal conductivity is an intrinsic property due to a phase transformation. The transition metal carbides and nitrides do not show the expected decrease in heat conductivities with temperature (Fig. 13) but instead show an increase, which was interpreted as resulting from the strong scattering of electrons by vacancies and polar optical phonons from the strong scattering of phonons by vacancies and conduction electrons (49). An ambipolar diffusion to thermal conductivity was suggested for TiC. Replacement of nitrogen by carbon in group IV transition metal nitrides significantly reduces the heat conductivities (41). In the case of diborides (50), the thermal conductivities decrease with temperature, although those for TiB2 and HfB2 show a gradual decrease in conductivity (Fig. 14). VII. MECHANICAL PROPERTIES The internal friction peaks in carbides are sufficiently small up to 1000°C that the dynamic modulus can be taken as equal to the unrelaxed or Hookean modulus. Above room temperature

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Figure 13 Thermal conductivities of carbides, nitrides, and carbonitrides as a function of temperature. (From Ref. 41.)

Figure 14 Thermal conductivity of the diborides as a function of temperature. (From Ref. 50.)

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209

Figure 15 Plots of log H against T/Tm of various carbides measured along the ⬍001⬎ direction in the (100) plane. The loading time was chosen as 10 s. (From Ref. 29.)

Young’s modulus is linearly related to the temperature coefficient of ⫺1 ⫻ 10 ⫺4 K ⫺1 in TiC and VC (51). Departures from linearity occur in the temperature range 850 to 1050°C for these carbides, depending on nonstoichimetry. The empirical equation is E ⫽ E 0 ⫺ BT exp(⫺T0 /T )

(11)

where E 0 is Young’s modulus at 0 K and B and T0 are constants; B has been determined for TiC as 4.3 ⫻ 10 8 dyn/cm 2 ⋅ K, and T0 is given better by T0 ⬃ (θ D /3). High-temperature indentation hardness can be used as a suitable measure of the plastic properties. However, in indentation experiments above 1000°C, it is not considered easy to obtain reliable data (52). A Nikon high-temperature microhardness tester model QM is designed so that both indenter and specimen can be heated and controlled automatically at the same temperature within an accuracy of ⫾10°C at 1500°C in a separate furnace (53). Cracks observed at each corner at room temperature diminish at high temperatures in TiC (53), VC0.88, and NbC0.80 (54), causing slip traces of the {111} ⬍110⬎ system. These are explained in terms of the dislocation mobility corresponding to the neck in a logarithmic plot of hardness versus homologous temperature T/Tm represented in Fig. 15. In the case of VC0.88, an additional neck caused by the order-disorder transition of vacancies exists (54). Data for Cu and Si (55) are shown for comparison. Unlike that of most metals, the hardness of carbides fall rapidly between 0.2 and 0.4 Tm, which is due to the slip system. The mechanical characteristics are closely related to

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Table 7 Values of Constant m and Activation Energy Q Q (kcal/mol) Carbide TiC 1.0

ZrC 0.9

VC 0.88

NbC 0.8 NbC 0.9

TaC 0.83 a

Plane Direction (100) (110) (111) (100) (110) (111) (100) (110) (111) (100) (100) (110) (111) (100)

⬍001⬎ ⬍001⬎ ⬍110⬎ ⬍001⬎ ⬍001⬎ ⬍110⬎ ⬍001⬎ ⬍001⬎ ⬍110⬎ ⬍001⬎ ⬍001⬎ ⬍001⬎ ⬍110⬎ ⬍001⬎

m 3.85 4.05 3.73 3.80 3.77 4.09 4.27 4.07 3.79 3.91 3.23 3.70 4.74 4.26

From indentation hardness 80.4 81.2 77.0 73.4 73.7 79.2 85.6 83.2 79.8 90.4 77.1 87.6 99.9 111.4

(53) (53) (53) (59) (59) (59) (54) (54) (54) (54) (59) (59) (59) (59)

From diffusion data 91.3 (18); 95.3 (18)

90.0 a ; 113.2 (15)

85 (13)

105 (15) 100.4 (15)

124.0 (14)

Short circuit–enhanced diffusion by grain boundaries.

the bonding state. The change from covalent to metallic-like hardness suggests a change in predominant bonding from covalent to metallic cohesion as the temperature is raised (53–59), which produces the change in the slip system from {110} ⬍110⬎ to {110} ⬍110⬎. Plots of log H and T ⫺1 are characterized by two linear regions, suggesting that there are two thermally activated process corresponding to an elastic and a plastic region. Their changes in slope near the ductile-brittle (D-T) transition suggest a corresponding change in the mechanism controlling the dislocation dynamics. The critical homologous temperature of carbides is the same as that of other rock salt–type crystals of NaCl, LiF, and MgO. ZrC is the softest at high temperatures with the highest thermal softening coefficient (59), related to the lattice vibration of carbides. The hardnesses of carbides tend to decrease with increasing lattice constant, reflecting the strength of the chemical bond. The lattice constant for ZrC is the largest among the carbides, and hence atomic bonds would weaken with raised temperature, enhancing the softing of the material. The gradual decrease in hardness of TaC0.83 is characteristic (59), whereas other carbides show about a 10-fold drop in hardness in the same temperature range. In contrast to the other carbides, TaC0.83 has the {111} ⬍110⬎ slip system over the entire temperature range and its temperature dependence is similar to that in other fcc metals (Cu) and covalent semiconductors (Si) with a slip system of {111} ⬍110⬎. The hightemperature hardness of TaC is probably due to the presence of widely dissociated dislocations resulting in extended stacking faults, i.e., Suzuki hardening (60) limited by carbon diffusion. The Suzuki interaction results from the difference in composition in the fault compared with the bulk observed in TaC using qualitative electron energy loss spectroscopy (61). The indentation hardness decreases with increasing loading time (1 to 100 s) at constant temperature (⬎.3Tm) in the plastic region. A series of straight lines were obtained. The activation energy, Q, for creep and the constant, m, expressed by the following equations are calculated for various carbides (see Table 7): H ⫽ A exp(⫺BT )

(12)

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211

and B/t ⫽ H m exp(⫺Q/RT )

(13)

The activation energies of the self-diffusion of carbon from tracer experiments are also indicated. No data are available for the diffusion of TaC single crystals, so the activation energy was estimated by (29 to 33)Tm (14), a good average, for VC, TiC, and ZrC. The lower activation energy for ZrC would be explained by enhanced diffusion along subgrain boundaries and viscous glide. The mechanism of the slip phenomena in carbides will be governed by carbon diffusion and dislocation climb. Next, the high-temperature indentation hardness of diboride will be shown. The hardness in each plane for ZrB2 crystals (62) decreases monotonously through all the testing temperatures (Fig. 16), maintaining the following relationship: H ⬍1010⬎(0001) ⬎ H ⬍1210⬎(0001), H ⬍1210⬎{1010} ⬎ H [0001]{10110} , H ⬍1100⬎{1120} ⬎ H [0001]{1120}, where the two subscripts of H represent the direction of the long axis of the Knoop indenter and the indentation plane, respectively. In the case of HfB2 crystals, similar temperature dependences are observed except at room temperature. Then the main slip system contributing to the hardness anisotropy of ZrB2 and HfB2 single crystals is {1010} ⬍1210⬎ over the entire temperature range, except that of HfB2 near room temperature. However, in the case of TiB2 single crystals (63), the main slip system changes from (0001) ⬍1120⬎ to {1010} ⬍1210⬎ near 250°C. The high-temperature Knoop hardnesses, of NbB2 and TaB2 single crystals up to 1100°C (64) on the (0001) plane in the ⬍1010⬎ and ⬍1120⬎ indentation directions and on the {1010} plane in the ⬍1210⬎ and [0001] directions indicate the inequalities H ⬍1010⬎(0001) ⬎ H ⬍1120⬎(0001) and H ⬍1210⬎{1010} ⬎ H [0001]{1010} for the entire temperature ranges, showing that slip was mainly on the prismatic {1010} ⬍1210⬎ system. This was also confirmed by slip line observations. High-temperature friction and wear of TiC-TiB2 alloys (65) indicate that the crystal distortion (∆a/a) increases with increasing temperature at high temperatures. The plastic deformation of friction layers in the TiC-TiB2 system at high temperature would increase (∆a/a) for the TiC component, so the TiB2 phase would play the main role in forming working layers of the TiCTiB2 alloys for a wide range of structural component concentrations. Uniaxal compression loading induces deformation directly. Haggerty and Lee (66) studied the plastic deformation of ZrB2 single crystals and showed that the oriented lamellar precipitates controlled the deformation. Stress-strain (crosshead displacement) behavior at 2125°C for ZrB2 single crystals containing Widemanstaetten precipitates is shown in Fig. 17. The important characteristic features are (a) ⬇ 37% yield drop, (b) a short easy-glide region, and (c) the beginning of work hardening. The upper yield point occurred at ⬇ 10.6 kg/mm 2 and the easy-glide region at 6.7 kg/mm 2. The crystal deformed ⬇ 1.2% before beginning to work harden. They attributed the material’s resistance to plastic flow to the presence of lamellar or plate-shaped precipitates lying on the basal and prismatic planes of the hexagonal ZrB2 crystal. Ramberg and Williams (67) reported on the resistance to plastic flow of a polycrystalline TiB2 specimen when subjected to an applied stress of 900 MPa at a temperature of some 2000°C. In the temperature regime 1700 to 2000°C, the yield stress of the polycrystalline TiB2 specimen was found to decrease from 100 kg mm ⫺2 (980 MPa) to 28 kg mm ⫺2 (270 MPa). The TiB2 of 23 µm mean grain size proved to be more deformation resistant below 1750°C than samples with grains averaging 12 µm. The decrease in yield stress with increasing temperature was exponential, with an apparent activation energy ranging between 0.7 and 1.3 eV atom ⫺1 as calculated by taking the slope of log yield stress versus 1/T. Figure 18 illustrates the applicability of the Hall-Petch relation [Eq. (14)] to the high-temperature plastic deformation of TiB2. The relation illustrates that grain boundaries act as barriers to glissile dislocations.

Figure 16 Log H versus T for typical examples of diboride single crystals. (From Refs. 62 and 63.)

212 Kumashiro

High-Temperature Characteristics

213

Figure 17 Stress-crosshead displacement behavior of ZrB2 single crystal deformed at 2125°C. (From Ref. 66.)

Figure 18 Hall-Petch form of the yield stress data (open polygons) and the revised Hall-Petch analysis (shaded polygons) based on best fit to lines of constant activation energy. (From Ref. 67.)

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Figure 19 Temperature dependence of the yielding behavior for pure TiC0.95 and (TiMo)C solid solutions compressed at a strain rate of 6 ⫻ 10 ⫺4 s ⫺1. (From Refs. 71 and 72.)

σ y ⫽ σ 0 ⫹ kd ⫺1/2

(14)

Here σ0 represents the single-crystal yield strength and k its dependence on the reciprocal square root of the mean grain size. The importance of the implied dislocation grain-boundary interactions will motivate further study of this system. The mechanical properties of fine-grained polycrystalline TiC from both four-point bending and compression tests showed that the D-B transition temperature in compression was ⬇ 800°C and depended on grain size and test temperature (68). The yield stress as a function of grain size can be described by a Hall-Petch type of relation. High-temperature vacuum treatment of as-hot-pressed TiC significantly reduced the levels of impurities at grain boundaries, which caused a dramatic improvement in high-temperature strength (69). Work softening was not observed in the carbides before 1982. The phenomenon was reported only for arc-melted ZrC0.94 polycrystals (70) and under very limited testing conditions. Yield drops were observed with plastic strain rates greater than 3 ⫻ 10 ⫺3 s ⫺1 but not with lower strain rates. Das et al. (68) observed yield-point behavior in TiC polycrystals deformed at 1000°C, which was followed by a yield-elongation zone where deformation took place at an approximately constant stress. At the end of the yield-elongation zone, work hardening was observed in the stress-strain curve. The development of high rigidity and responsity of the machine produced success in finding a work softening phenomenon in carbide (71). Figure 19 shows stress-strain curves for TiC0.95 single crystals deformed at various temperatures from 1280 to 2273 K at a strain rate of 1.6 ⫻ 10 ⫺3 s ⫺1. A marked yield drop occurs over a wide temperature range. After the softening, work hardening is observed. In the curves for 1280 and 1400 K, the hardening is almost linear after a narrow transient region. The rate of work hardening after the softening decreases as the temperatures increases above 1400 K, indicating that recovery due to dislocation climb occurs during deformation at these high temperatures. From the temperature and strain-rate dependence of the critical resolved shear stress, τ0.2 , corresponding to 0.2% proof stress, the plastic shear-strain rate, γ, is expressed as a function of τ0.2 and absolute temperature T as follows: γ ⫽ A(τ0.2 /G ) m exp(⫺Q/RT )

(15)

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215

where A is a constant, m the stress exponent, Q the activation energy for deformation, G the shear modulus, and R the gas constant. The stress exponent m is obtained as the reciprocal of the slope of the strain-rate dependence. The values of m and Q in low- and high-temperature ranges I and II, respectively, are shown in Table 8. The large m value in TiC would explain the difficulty in observing the work softening phenomenon in the carbide. A mechanical equation of state has been reported for yield stress in sintered tantalum carbide (grain size, 13µm) (73) and for the steady-state creep of sintered titanium carbide (grain size, 7 µm;porosity, 3.3%) (74), ZrC single crystal (75), NbC single crystal (76), and sintered NbC0.74 (density of 99.7%) (77). In Ref. 73, m ⫽ 13.3, Q ⫽ 89.8 kcal/mol in the low-temperature range and m ⫽ 4.5, Q ⫽ 95.7 kcal/mol in high-temperature range; in Ref. 74, m ⫽ 2.7, Q ⫽ 90.7 kcal/mol in the low-temperature range and m ⫽ 3.5, Q ⫽ 155 kcal/mol in the high-temperature range; in Ref. 75, m ⫽ 5, Q ⫽ 110 kcal/mol in the high-temperature range; in Ref. 76, m ⫽ 3.3, Q ⫽ 85 kcal/mol; and in Ref. 77, m ⫽ 2.0–3.2, Q ⫽ 51.1–111.9 kcal/mol. The Q value for TiC single crystals in the low-temperature range is the activation energy required for a dislocation to overcome a high Peierls barrier, and that in the high-temperature range is close to that for carbon diffusion, suggesting that carbon diffusion may control the dislocation motion. The carbon atoms occupying octahedral interstitial sites in the fcc titanium sublattice act as a barrier to dislocation motion, and hence the deformation is controlled by their diffusion. Similar high-temperature experiments on TiC x single crystals (0.6 ⬉ x ⬉ 0.95) in the temperature range 1180 ⬉ T ⬉ 2270 K (78) showed that Q was lower than the self-diffusion data for carbon, except for x ⫽ 0.75. At this concentration a peak in the Q value, 133.3 kcal/mol, about 75% of that for lattice self-diffusion of Ti in TiC, indicated that the diffusion processes of carbon and titanium were coupled in plastic deformation. Figure 19 also shows the curves around the yield points of solid solutions of (Ti, Mo)C at various temperatures (72). The deformation behavior in the solid solutions is different in three temperature ranges. In the low-temperature range (I), a yield drop is observed and the work hardening after the drop is high. In the intermediate-temperature range, no yield drop occurs, and from the beginning work hardening is high. In the high-temperature range (II), a yield drop occurs again and thereafter the deformation proceeds with almost a constant flow stress. (Ti0.743 Mo0.257 )C0.955 fractured in the low-temperature range without any appreciable plastic deformation and the expected work softening could not be observed. The D-B transition temperature of (Ti0.743 Mo0.257)C0.955 solid solution is higher than that of pure TiC. At 2070 K, where it shows good ductility, a yield point phenomenon is observed. Slip bands are fairly coarse in the intermediatetemperature range (1770 K) compared with those in the low-temperature (1370 K) and hightemperature (2270 K) ranges. Solution softening occurs on the lower side of the Mo concentration, but solution hardening occurs on the higher side. The boundary concentration is about 5 mol %. The deformation in the low-temperature range (I) is considered to be controlled by the Peierls mechanism and in the intermediate-temperature range is considered to be controlled by Table 8 Values of m and Q in the Low- and High-Temperature Regions, I and II Region I Composition TiC 0.95 (Ti 0.955 Mo 0.045)C 0.946 (Ti 0.886 Mo 0.114)C 0.936 (Ti 0.743 Mo 0.257)C 0.955 Source: From Refs. 71 and 72.

Region II

m

Q (kcal/mol)

10.1 ⫾ 0.4 14.7 13.2 —

57.1 50.0 47.6 —

m 5.3 5.7 5.2 5.4

⫾ ⫾ ⫾ ⫾

Q(kcal/mol) 0.3 0.3 0.4 0.3

111.9 135.7 142.9 150.0

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so-called dynamic strain aging (Table 8). In the high-temperature range, another kind of yield point phenomenon occurs and the work-hardening rate after the stress drop is very low. The slip bands are very fine. Therefore deformation in (Ti, Mo) C solid solution is considered to be controlled by a solute-atmosphere-drag mechanism. On the other hand, hypo Mo-10TiC has unlimited compressive ductility at and above 1270 K and hyper Mo-40TiC has unlimited compressive ductility at and above 1470 K (79). In Mo10TiC, the stress exponent, m, is 36 at 1870 K and 13 at 2070 K, and Mo-40TiC, m ⫽ 6.5 at 1870 K and m ⫽ 5.6 at 2070 K. The temperature and strain-rate dependences of yield stress at high temperatures are larger than in Mo-40TiC. The difference between the calculated and experimental curves of yield stress versus temperature is much smaller in the hypoeutectic Mo10TiC than in the hypoeutectic Mo-40TiC, which would arise from the difference in the internal stress induced by the plastic strain of 0.2% and the difference in the volume fraction of the eutectic structure region between the two composites. The smaller volume fraction means a smaller interfacial area between the two components per unit volume, and the effects of boundary sliding and recovery become smaller in Mo-10TiC than in Mo-40TiC. Sufficiently pure titanium diboride (grain size ⱕ 4 µm) densified from plasma-process powder (80) does not exhibit intrinsic slow crack growth at temperatures up to 1400°C. Dynamic fatigue strength tests were performed at 1000 to 1400°C in argon to evaluate the intrinsic (environment-independent) tendency for slow crack growth. The resultant bend strengths are presented in Fig. 20, which shows that strengths generated at the lower stress rate are consistently greater than those obtained at a higher rate. Linear regression analysis was used to fit the strengths to the equation ln S f ⫽ ln XHR/(N ⫹ 1) ⫹ K

(16)

where S f is fracture strength, XHR is machine crosshead rate, N is a slow crack growth exponent, and K is a constant. Slow crack growth exponents for the data for 1000, 1250, and 1400°C were found to be ⫺53.2, ⫺61.4, and ⫺62.2, respectively, using Eq. (16). A negative exponent is incompatible with slow crack growth and implies the presence of a low-strain rate–strengthening effect. The stress-strengthening mechanism operates by blunting flaw tips. Furthermore, mechanical properties in an aluminum environment at 960 to 1000°C were studied by strength versus stress rate and K Ic tests (81). According to dynamic fatigue tests on

Figure 20 Three-point bend strength as a function of stressing rate crosshead rates of 8.5 ⫻ 10 ⫺7 and 8.5 ⫻ 10 ⫺5 m/s for powder sintered at 2100°C, n (number of specimens) ⫽ 5, bars ⫽ ⫾1 standard deviation. (From Ref. 80.)

High-Temperature Characteristics

217

high-purity titanium diborides in a liquid-aluminum environment, the two smallest grain size materials (grain size ⱕ 3 µm) exhibited negative slow crack growth exponents that were the result of stress strengthening and inconsistent with slow crack growth, and the two larger grain size materials (grain size ⱕ 10 µm) exhibited positive slow crack growth exponents. The exponents indicated an increasing tendency for slow crack growth with increasing grain size. The dynamic fatigue results are shown in Fig. 21. The inner bars had a mean strength of 327 MPa (XHR ⫽ 4.2 ⫻ 10 ⫺5 m/s; standard deviation ⫽ 75 MPa; n ⫽ 6). The mechanical behavior of the cell-tested material in either an argon or an aluminum environment is changed little from that of similar, unpenetrated material in a corresponding environment. The trend of the exponents versus grain size suggests the presence of two opposing mechanisms that affect crack extension, at least one of which is grain size dependent. One mechanism is predominant in larger grained material weakening; the other predominates in finer grained materials and leads to material strengthening. Material strength reductions resulting from the slow crack growth mechanism are superimposed on other strength losses arising from loss of toughness in the presence of aluminum; K Ic is reduced whether or not slow crack growth occurs. The reduction of K Ic in the presence of aluminum corresponds to a decrease in the effective fracture energy from 31 to 24 J/m 2 (from K Ic ⫽ (2 Eγ) 1/2, E ⫽ 400 GPa). Then the reduction of K Ic appears to be due to the phenomenon of liquid-metal embrittlement characterized by the chemisorption of metal impurity atoms at the crack tip so that the new chemical bond formation reduces the stability of the bonds between atoms of the material being embrittled. The lowered energy of matrix cohesion results in a lower energy for crack propagation. High strain rate superplasticity (HSRS) would be an efficiently near-net shape forming and forging process for ceramic whisker– or particle-reinforced aluminum alloy composites. The HSRS of TiB2 particle-reinforced aluminum alloy composites (82) was reported to show superplastic characteristics (Fig. 22). The TiB2 f/2014 Al composite has an m value of about 0.25 and total elongation of less than 150% in the strain rate region between 0.08 and 1.0 s ⫺1, and TiB2 f/6061 Al composite exhibits an m value of 0.26 and total elongation of 150–200% in the strain rate region from 0.07 to 1.3 s ⫺1. These composites were deformed superplastically above the solidus temperature of 2014 and 6061 Al alloy, so the matrix and the matrix-reinforcement interface were partially liquid during deformation. Then the main superplastic deformation mechanisms are fine grain boundary sliding and interfacial sliding involving a semiliquid phase. Cermets consisting of two mutually penetrating frames of metal and refractory phases are more promising for high-temperature applications than cermets consisting of a metal matrix

Figure 21 Dynamic fatigue data for sintered at 2100°C, tested at 960°C in Al over long periods of time. (From Ref. 81.)

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Figure 22 Superplastic characteristics of (䊊) TiB2f/2014 and (䊉) TiB2f/6061 aluminium alloy composites. (a) (䊊) Rolling temperature 818 K, testing temperature 833 K, m ⫽ 0.25; (䊉) rolling temperature 833 K, testing temperature 873 K, m ⫽ 0.26 and (b) (䊊) rolling temperature 833 K, testing temperature 873 K. (From Ref. 82.)

with a uniform distribution of refractory particles. New possibilities in the design of plastic frames can be achieved by changing the chemical composition and microstructure type of the refractory compound in TiCx-nickel–based superalloy (83). The cermets based on the stoichiometric TiC provided high strength at high temperatures-above 950°C, because the D-B transition temperature was achieved.

VIII.

CONCLUSION

At present we can obtain well-characterized specimens, so it should be possible to clarify characteristics at higher temperatures, above 2000°C. Measurements up to higher temperatures require sophisticated knowledge of instrumentation to provide reliable data. For these purposes accurate measurements of temperature and emissivity should be established. Transition metal diborides are promising electrode materials for magnetohydrodynamic (MHD) generators, so their spectral emittance data would be necessary. The very high melting point of carbides, low diffusion rate of carbon, and good nuclear properties make them attractive for use in high-temperature nuclear reactors, and knowledge of thermodynamic properties is indispensable for understanding the vaporization behavior. The environment in the core of a rocket in the space is extremely harsh, so many common diagnostic instruments cannot easily be used. Laser diagnostic methods (7) provide some unique advantages over other diagnostic techniques, i.e., imaging ability and excellent temporal and spatial resolution. They are also specific to certain corrosion production when probing a rocket’s exhaust and supply information on local gas stream concentrations and temperatures. High-temperature equilibrium experiments have produced thermodynamic value or limits for the formation of the binary phases. Experimental information on thermochemical properties and phase equilibria in the Zr-C system (5) has been analyzed using phenomenological methods for Gibbs energy. The parameters in the models are determined by computerized optimization of selected experimental data. But some significant discrepancies are found between experiments and model calculations. The thermodynamics of the liquid solution phase could solve the problem related to M-B systems. Accurate thermodynamic data are lacking for M-B systems, (84),

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so that the consistency of the thermodynamic data for the binary phases with temperature-composition phase diagrams could not be tested. Experimental partial pressures over nitride show significant scatter (8), which should be clarified using well-characterized specimens. The experimental information on the phase equilibria in the ternary carbonitride systems was restricted mainly to the quasi-binary MC-MN systems, where complete miscibilities were observed, but isothermal sections of the phase equilibria in the systems Ti-C-N, Zr-C-N, and Hf-C-N have been investigated to clarify the formation regions of δ-carbonitride phases in relation to compositions (85). High-temperature thermodynamic data also give information about optimal preparative conditions in multicomponent gas-solid systems by chemical vapor deposition of the product and optimal molar ratios for making stoichiometric compositions by plasma flame synthesis. The diffusion coefficients are necessary for studying the reaction mechanism including selfpropagating high-temperature synthesis. Diffusion studies using single crystals for nitride should be performed to clarify a common diffusion mechanism. Also, chemical diffusion for carbides using single crystals should be clarified. The diffusion coefficients are needed to study the reaction mechanism, including selfpropagation high-temperature synthesis. Hot-pressing sintering mechanisms are correlated with self-diffusion creep theory and deformation mechanisms at high temperatures. High-temperature mechanical properties of composites would be useful for applications as high-temperature engineering components.

ACKNOWLEDGMENTS A number of figures and tables have been taken from the literature. The author would like to thank the authors and publishers of these materials for permission to reproduce them here, especially the American Physical Society (Fig. 10 (Ref. 35)), the American Institute of Physics (Fig. 9 (Ref. 33) and Fig. 14 (Ref. 50)), the American Ceramic Society (Fig. 5 (Ref. 7), Fig. 8 (Ref. 30), Fig. 17 (Ref. 66), Fig. 20 (Ref. 80) and Fig. 21 (Ref. 81)), Elsevier Science Ltd. (Tables 5 and 6 (Ref. 40), Fig. 6 (Ref. 8), Fig. 12 (Ref. 48) and Fig. 16 (Ref. 62)), John Wiley & Sons, Ltd (Figs. 11 and 13 (Ref. 41)), and Kluwer Academic Publishers (Fig. 18 (Ref. 67) and Fig. 22 (Ref. 82)).

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36. LC Dy, WS Williams. Resistivity, superconductivity, and order-disorder transformations in transition metal carbides and hydrogen-doped carbides. J Appl Phys 53:8915, 1982. 37. P Cˇapkova´, M Merisalo, M Laitinen, V Valvoda, L Dobia´sˇoa´. Thermal vibrations and thermal expansion of ZrC0.98 studied by X-ray diffraction. Phys Status Solidi (a) 106:107, 1988. 38. P Cˇapkova´, M Merisalo, P Boukal, M Blomberg, W Lengauer. Thermal vibrations in vanadium nitride studied by x-ray diffraction. Phys Status Solidi (a) 112:K81, 1989. 39. P Cˇapkova´, R Kuzˇel, J Sˇedivy´. Thermal vibrations and static displacements of atoms in nonstoichiometric titanium carbide. Phys Status Solidi (a) 76:383, 1983. 40. B Lo¨nnberg. Thermal expansion studies on the group IV–VII transition metal diborides. J Less Common Met 141:145, 1988. 41. P Ettmayer, W Lengauer. Nitrides: Transition metal solid-state chemistry. In: Encyclopedia of Inorganic Chemistry. New York: Wiley, 1994, p 2498. 42. K Aigner, W Lengauer, D Rafaja, P Ettmayer. Lattice parameters and thermal expansion of Ti(Cx N1⫺x ), Zr(Cx N1⫺x ), Hf(CxN1⫺x) and TiN1⫺x from 298 to 1473 K as investigated by high-temperature x-ray diffraction. J Alloys Compos 215:121, 1994. 43. M Singh, H Wiedemeir. Estimation of thermal expansion behavior of some refractory carbides and nitrides. J Mater Sci 32:5749, 1997. 44. B Lo¨nnberg, T Lundstro¨m. A study of the thermal expansion of samples within the homogeneity ranges of NbB2 and TaB2 . J Less Common Met 139:L7, 1988. 45. MK Ferber, PF Becher, CB Finch. Effect of microstructure on the properties of TiB2 ceramics. J Am Ceram Soc 66:C2, 1983. 46. H Itoh, S Naka, T Matsudaira, H Hamamoto. Preparation of TiB2 sintered compacts by hot pressing. J Mater Sci 25:533, 1990. 47. EC Skaar, WJ Croft. Thermal expansion of TiB2 . J Am Ceram Soc 56:45, 1973. 48. W Lengauer, S Binder, K Aigner, P Ettmayer, A Guillou, J Debuigne, G Groboth. Solid state properties of group IV b carbonitrides. J Alloys Compos 217:137, 1995. 49. J Bethin, WS Williams. Ambipolar diffusion contribution to high-temperature thermal conductivity of titanium carbide. J Am Ceram Soc 60:424, 1977. 50. TM Branscomb, O Hunter Jr. Improved thermal diffusivity method applied to TiB2 , ZrB2 , and HfB2 from 200–1300°C. J Appl Phys 42:2309, 1971. 51. RHJ Hannink, MJ Murray. Elastic moduli measurements of some cubic transition metal carbides and alloyed carbides. J Mater Sci 9:223, 1974. 52. DL Kohlstedt. The temperature dependence of microhardness of the transition-metal carbides. J Mater Sci 8:777, 1973. 53. Y Kumashiro, A Itoh, T Kinoshita, M Sobajima. The micro-Vickers hardness of TiC single crystals up to 1500°C. J Mater Sci 12:595, 1977. 54. Y Kumashiro, E Sakuma. The Vickers micro-hardness of non-stoichiometric niobium carbides and vanadium carbide single crystals up to 1500°C. J Mater Sci 15:1321, 1980. 55. RHJ Hannink, DL Kohlstedt, MJ Murray. Slip system determination in carbides by hardness anisotropy. Proc R Soc A326:409, 1972. 56. H Ihara, Y Kumashiro, A Itoh. X-ray photoelectron spectrum and band structure of TiC. Phys Rev B12:5465, 1975. 57. H Ihara, M Hirabayashi, H Nakagawa. Electronic band structures and x-ray photoelectron spectra of ZrC, HfC, and TaC. Phys Rev B14:1707, 1976. 58. RHJ Hannink, MJ Murray. Comment on slip and microhardness of IV a and VI a refractory materials. J Less Common Met 60:143, 1978. 59. Y Kumashiro, Y Nagai, H Kato. The Vickers micro-hardness of NbC, ZrC, and TaC single crystals up to 1500 °C. J Mater Sci Lett 1:49, 1982. 60. M Hoffman, WS Williams. A simple model for the deformation behavior of tantalum carbide. J Am Ceram Soc 69:612, 1986. 61. C Allison, M Hoffman, WS Williams. Electron energy loss spectroscopy of carbon in dissociated dislocations in tantalum carbides. J Appl Phys 53:6757, 1982. 62. K Nakano, H Matsubara, T Imura. High-temperature hardness of IV a-diboride single crystals. J Less Common Met 47:259, 1976.

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63. K Nakano, H Matsubara, T Imura. High temperature hardness of titanium diboride single crystal. Jpn J Appl Phys 13:1005, 1974. 64. K Nakano, K Nakamura, T Okubo, T Sugimura. High temperature hardness and slip system of NbB2 and TaB2 single crystals. J Less Common Met 84:79C, 1982. 65. YG Tkachenko, SS Ordanyan, VK Yulyugin, DS Yurchenko, VI Unrod. The role of the boride phase in MeC-MeB2 alloys when subjected to wear in a vacuum. J Less Common Met 67:437, 1979. 66. JS Haggerty, DW Lee. Plastic deformation of ZrB2 single crystals. J Am Ceram Soc 51:572, 1971. 67. JR Ramberg, WS Williams. High temperature deformation of titanium diboride. J Mater Sci 22:1815, 1987. 68. G Das, KS Mazdiyasni, HA Lipsitt. Mechanical properties of polycrystalline TiC. J Am Ceram Soc 65:104, 1982. 69. AP Katz, HA Lipsitt, T Mah, MG Mendiratta. Mechanical behavior of polycrystalline TiC. J Mater Sci 18:1983, 1983. 70. R Darolia, TF Archbold. Plastic deformation of polycrystalline zirconium carbide. J Mater Sci 11:283, 1976. 71. H Kurishita, K Nakajima, H Yoshinaga. The high temperature deformation mechanism in titanium carbide single crystals. Mater Sci Eng 54:177, 1982. 72. H Kurishita, R Matsubara, J Shiraishi, H Yoshinaga. Solution hardening of titanium carbide by molybdenum. Trans Jpn Inst Met 27:858, 1986. 73. PF Becher. Mechanical behavior of polycrystalline TaC. J Mater Sci 6:79, 1971. 74. JL Chermant, G Lecherc, BL Mordike. Deformation of titanium carbide at high temperatures. Z Metallkd 71:465, 1980. 75. DW Lee, JS Haggerty. Plasticity and creep in single crystals of zirconium carbide. J Am Ceram Soc 52:641, 1969. 76. LN Denty´ev, PV Zubarev, VN Kruglov, VN Turchin, YD Kharkhadin. High-temperature creep of monocrystalline niobium carbide. Phys Met Metallogr 46:42, 1978. 77. RD Nixon, S Chevacharoenkul, RF Davis. Steady-state creep behavior of hot isostatically pressed niobium carbide. Mater Res Bull 22:1233, 1987. 78. JD Mun˜oz, A Arizmendi, A Mallende, JA Maldrete High temperature activation energy for plastic deformation of titanium carbide single crystals as a function of the C: Ti atom ratio. J Mater Sci 32:3189, 1997. 79. H Kurishita, J Shiraishi, R Matsubara, H Yoshinaga. Measurement and analysis of the strength of Mo-TiC composites in the temperature range 2850–2270K. Trans Jpn Inst Met 28:20, 1987. 80. HR Baumgartner, RA Steiger. Sintering and properties of titanium diboride made from powder synthesized in a plasma-arc heater. J Am Ceram Soc 67:207, 1984. 81. HR Baumgartner. Mechanical properties of densely sintered high-purity titanium diborides in molten aluminum environments. J Am Ceram Soc 67:490, 1984. 82. T Imai, G L’esperance, BD Hong, Y Tozawa. High strain rate superplasticity of TiB2 particulate reinforced aluminium alloy composite. J Mater Sci Lett 14:373, 1995. 83. NG Zaripov, RR Kabirov, VN Bloshenko. Structural peculiarities of cermets design based on titanium carbide. Part 1. Influence of chemical composition on the ductile-brittle transition temperature, microstructure and properties of cermets. J Mater Sci 31:5227, 1996. 84. KE Spear, JH Blanks, MS Wang. Thermodynamic modeling of the V-B system. J Less Common Met 82:237, 1981. 85. S Binder, W Lengauer, P Ettmayer, J Bauer, J Debuigne, M Bohn. Phase equilibria in the systems Ti-C-N, Zr-C-N, and Hf-C-N, J Alloys Compos 217:128, 1995.

9 Surface Electronic Structures and Surface Reactivities Kazuyuki Edamoto Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan

I.

INTRODUCTION

The group IV and V transition metal carbides (TMCs) are of considerable interest because of an interesting combination of physical properties and a number of useful applications. They exhibit ultrahigh hardness, a high melting point, and metallic conductivity, and some of them are superconductors at fairly high temperatures. From a practical point of view, they have been used as very stable field and thermal electron emitters, coating materials, wall materials for nuclear reactors, etc. Because the surface properties play an essential role in all these applications, it has become important to investigate the atomic structures and electronic structures of TMC surfaces. From a chemical point of view, it has been suggested that they are useful as catalytic materials for the hydrogenation of benzene, ethylene, and carbon monoxide, the decomposition of methanol, etc. (1); thus their surface reactivities are also of much interest. However, in contrast to the substantial accumulation of data on elemental metal and semiconductor surfaces, limited information has been available on the physical and chemical properties of the well-defined surfaces of TMCs. This is mainly because the high melting point of the material makes it difficult to prepare a single crystal of good quality. Preparation techniques for TMC single crystals have been developed dramatically, and single crystals of excellent quality have become available by use of the floating-zone method (2). This has made it possible to prepare well-defined surfaces of TMCs, which has stimulated the development of a variety of analyses of the TMC surfaces. In this chapter, I review the developments in studies of the electronic structures and reactivities of well-defined TMC surfaces. First, I briefly discuss the atomic structure of TMC surfaces. The TMCs crystallize in a rock salt structure, and studies of the surface atomic structure have been concentrated on the three typical low-index surfaces, the (100), (110), and (111) faces. The geometries of ideal (100), (110), and (111) surfaces are shown schematically in Fig. 1. The (100) surface of a TMC is a neutral surface composed of equal numbers of metal and carbon atoms (Fig. 1). All the TMC(100) clean surfaces prepared in ultrahigh vacuum conditions show (1 ⫻ 1) low-energy electron diffraction (LEED) patterns, and no lateral reconstruction has been found. However, LEED I–V analysis studies of the TaC(100) (3,4) and HfC(100) (3) surfaces have revealed that rippled reconstructions are brought about on these surfaces. The rippled reconstruction includes displacements of surface atoms vertical to the surface; the metal atoms and carbon atoms are uniformly displaced inward and outward, respec223

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Figure 1 Surface structures (top view) of TMC(100), (110), and (111).

tively, by a few percent of the lattice constants (Fig. 2), which maintains the (1 ⫻ 1) periodicity of the surface. A similar rippled reconstruction has been found for the neutral surfaces of ionic crystals such as alkali halides or metal oxides (5,6). The origin of the rippled reconstruction can be explained by the electrostatic effect characteristic of the ionic crystal surface. At the ionic crystal surface, the electrostatic forces felt by the anion and cation atoms are different from each other; both the anion and cation atoms at the surface feel the electrostatic force directed to the bulk inside because of the lack of countercoordinated ions in the vacuum side; however, the anion and cation atoms usually have different sizes and polarizabilities, which results in a difference in the electrostatic forces working on the surface anion and cation atoms. Thus the rippled reconstruction for the TMC(100) surface can be ascribed to the ionicity of the crystal. It is known that a completely stoichiometric TMC crystal is thermodynamically unstable, and a real crystal should contain some vacancies on the carbon sites forming an MC x (x ⬍ 1) crystal. An impact-collision ion scattering spectroscopy (ICISS) study has shown that the density of the carbon vacancies on the TMC(100) surface depends on the preparation condition of the surface and that a stoichiometric surface with no carbon vacancies can be obtained by flashing the sample to a high temperature (⬎1500°C) (7).

Figure 2 Side view of the rippled TMC(100) surface.

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The (111) surface of TMC is a polar surface; hexagonal carbon layers and metal layers are piled alternately along the ⬍111⬎ direction to form a rock salt type of crystal (Fig. 1), meaning that the first layer of the ideal (111) surface should be a carbon layer or metal layer. Such a polar surface is usually unstable because of its large electrostatic potential, which usually induces surface reconstructions or facetings. However, every TMC(111) surface carefully prepared under ultrahigh vacuum conditions shows a sharp (1 ⫻ 1) LEED pattern and no lateral reconstruction has been found [the exception is found only for VC(111) (8,9)], suggesting that some unique stabilization mechanism should be operative in the TMC(111) surface. As discussed later, the (1 ⫻ 1) structure is stabilized through a charge redistribution around the surface to screen the long-range electric field, and the charge redistribution modifies the electronic structure in the surface region largely to form surface states characteristic of the TMC(111) surface. The atomic structure of the TMC(111) surface has been extensively studied by use of the ICISS technique. Investigations have been made for TiC(111) (10,11), HfC(111) (12), TaC(111) (13), and NbC(111) (14), and it has been established that the first layers should be metal layers on these surfaces. The ICISS studies have also revealed that, although TMC(111) surfaces show no lateral reconstruction, some surface relaxation, which means a change in interlayer spacings in the surface region from that in the bulk (Fig. 3), is brought about (10,12,14). The surface relaxation is caused by the lack of coodinated carbon atoms in the vacuum side of the first metal layer, which results in an attractive force only toward the bulk inside. Thus, the relaxation in this case means shortening of the interlayer spacing between the first and second layers relative to that in the bulk. The contraction of interlayer spacing at the surface is estimated to be 30% of the interlayer spacing in the bulk for TiC(111) (11), 13.4% for HfC(111) (12), and 15.5% for NbC(111) (14). Among the group IV and V TMC(111) surfaces, only the VC(111) surface has been found to be reconstructed. Scanning tunneling microscopy (STM) and LEED studies have shown that the VC(111) surface is composed of a mixture of (8 ⫻ 1) and (√3 ⫻ √3)R30° reconstructed areas (8,9). Structural analyses have shown that the atomic concentration is reduced in these areas compared with ideal (111) surfaces (8,9). Because the cohesive energy of the VC crystal

Figure 3 Side views of the ideal (a) and relaxed (b) TMC(111) surface.

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Figure 4 Side view of the TaC(110) surface.

is relatively small among the group IV and V TMCs, it has been proposed that the surface reconstruction occurs because the reduced atomic concentration is energetically favored on the VC(111) surface (8,9). In contrast to the accumulation of data on the (100) and (111) surfaces of TMCs, limited information is available at this point for the (110) surface. The ideal (110) surface should be composed of equal numbers of carbon and metal atoms that form alternating carbon and metal rows along the ⬍110⬎ direction (Fig. 1). The TMC(110) surface has been studied for TiC(110) (11), TaC(110) (15,16), and NbC(110) (17), and these studies have concluded that the (110) surfaces are reconstructed. The most extensive studies of the surface atomic structure were made on the TaC(110) surface, which was found to consist of alternate (010) and (100) facets periodically propagating along the ⬍011⬎ direction as in a ridge-and-valley grating with an average period of about six lattice spacings (Fig. 4) (15,16). The atomic structure of the TiC(110) surface was also studied, and it was found that the surface is covered with (310) facets that consist of (100) terraces and (010) steps (11). The NbC(110) surface shows a c(2 ⫻ 2) LEED pattern, indicating some surface reconstruction, although the detailed atomic configuration is still unknown (17). These studies suggest that the ideal TMC(110) surface is unstable, and the general tendency of the reconstruction seems to be to make (100) facets. In the following sections, progress in studies of the electronic structure of TMC(100), (110), and (111) surfaces by the application of angle-resolved photoemission spectroscopy (ARPES) will be reviewed. Adsorption of oxygen and alkali metal on the TMC(100) and (111) surfaces will also be reviewed as an example of progress in the surface chemistry of TMCs.

II. SURFACE ELECTRONIC STRUCTURE In the TMC crystals, ionic, covalent, and metallic bonding components all contribute to the atom-atom bonding to form the crystal. Details of the bonding character of TMC crystals are covered in other parts of this monograph. The surface of the TMC is made by breaking such unique bonding. The electronic structure of the TMC surface thus made is of interest from a physical point of view for the following reasons. First, the electronic structure of the TMC surface is expected to be modified from that in the bulk because of the change of the potential felt by electrons in the surface region. The change of the potential is thought to be mainly due to the ionicity of the TMC crystal. In the crystal, each metal (carbon) atom is surrounded by six carbon (metal) atoms. Because the metal and carbon atoms are positively and negatively charged respectively, in the TMC crystal, the electrons are located in a sort of octahedral crystal field at each atom site in the bulk. However, at the surface, the number of coordinated atoms is decreased by one, two, and three for the (100),

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(110), and (111) ideal surfaces, respectively. The decrease of coordinated atoms should induce considerable modification of the potential at each atom site on the surface compared with that in the bulk. Similar potential modification should occur on the surfaces of essentially all the compound crystals where the component atoms should have more or less different electronegativities. However, few systematic studies of the electronic structure of these surfaces have been made. This is because most of the compound crystals having ionicity strong enough to have ionic effects on the surface electronic structure are insulators, which are not suited for electron spectroscopic studies. As for TMC, the crystal is characterized by its metallic conductivity, and the two typical low-index surfaces, (100) and (111), can be prepared as almost ideal surfaces [except for VC(111)], which enables systematic studies of surface electronic structures. In this sense, the TMC surfaces can be viewed as a model of compound crystal surfaces. The second point is that the metallic character of the bond makes it possible to redistribute electronic charge easily around the surface to compensate for the potential change. This effect may induce substantial modification of surface electronic structure compared with that in the bulk, which also makes the electronic structure of TMC surfaces a very interesting field from a physical viewpoint. Before discussing the surface electronic structures, I briefly review the bulk electronic structure of TMC to make the latter discussion clearer. Figure 5 shows an example of an angleintegrated soft X-ray photoemission spectrum taken for the NbC(100) surface. In this experimental condition, the spectrum includes overall features of the bulk density of states (DOS) of the valence band and the inner-valence core levels for the TMCs. The band at 0–7 eV is the emission from the valence band composed of Nb 4d and C 2p orbitals, which are hybridized to form a metal-carbon bond. All of the group IV and V TMC valence bands are formed through hybridization between the metal nd and carbon 2p orbitals. It is noted that the DOS around the Fermi level (E F) is relatively small, which is common to all the DOSs of TMCs. The band at 12 eV is the emission from the C 2s band. It is clear that the C 2s band is split from the above valence band, and thus the C 2s orbital makes little contribution to the metal-carbon bond. The Nb 4p3/2 , 4p1/2 , and 4s states are observed at 32.0, 34.2, and 57.5 eV, respectively (Fig. 5). These binding energies are higher than those for pure Nb metal (30.8, 32.6, and 56.4 eV, respectively).

Figure 5 Angle-integrated soft X-ray photoemission spectrum of NbC(100).

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This reflects the ionicity of the NbC crystal; the charge is transferred from Nb to C, which should result in a smaller relaxation effect on the final state of the core-level photoemission process at the Nb atom in the NbC crystal. A.

(100) Surface

The electronic structure of the TMC(100) surface has been studied most extensively among the low-index TMC surfaces. It is well known that the use of angle-resolved photoemission spectroscopy (ARPES) can give direct information about the valence band structure around the surface (18,19), and extensive ARPES studies have been performed on the valence band structure of TMC(100) surfaces such as TiC(100) (20,21), ZrC(100) (22,23), VC(100) (24–27), NbC(100) (28–31), and TaC(100) (32,33). These studies have shown that most of the features in ARPE spectra can be understood as emissions from the bulk bands, and thus the electronic structures of TMC(100) are well regarded as the cross sections of the bulk electronic states. However, in some systems, surface induced electronic states have been identified as described in the following. An electronic state localized to a surface, called a surface state, has been found on a variety of solid surfaces (18,19). The surface states are considered to play an important role in almost all the physical phenomena on solid surfaces, such as atomic reconstruction, adsorption, and surface magnetism (34), and thus the surface state has become the subject of many experimental (18,19) and theoretical (34,35) investigations. The surface states are categorized on the basis of their origin into two types: the Shockley state and the Tamm state. The former is the state mainly formed through breaking of the three-dimensional periodic boundary condition at the surface; an electronic state whose wave function decays with propagation is forbidden in the bulk, but at the surface, a state having an exponentially decaying wave function in both directions, into the bulk and into the vacuum, can exist. Such a state should exist in a bulk band gap and should be substantially localized to the surface. The latter state is mainly caused by the modification of the potential felt by electrons in the surface region, which may induce a wave function different from that in the bulk. The state is also localized to the surface when the potential modification is large enough. These surface states are essentially two-dimensional electronic states, and thus the wave vector component normal to the surface (k ⊥ ) is not a quantum number for these states. In an ARPES study, we can select the k ⊥ of the initial state by selecting the photon energy (hν), which enables us to map the k ⊥-dependent band dispersion of the bulk state. The surface state should not have k ⊥-dependent band dispersion, which means that the binding energy of the peak emitted from a surface state should be independent of the photon energy. This is one of the criteria used to identify the surface state in ARPES spectra. In addition, surface states are substantially sensitive to surface conditions, particularly to surface contamination, which enables us to identify the surface state in ARPES spectra by gas adsorption studies. Figure 6 shows an example from an ARPES study conducted to identify surface states on the NbC(100) surface. Figure 6 shows the effect of a small amount of oxygen exposure on the NbC(100) surface for the normal emission spectra where the 1 L exposure is defined as 1 ⫻ 10 ⫺6 torr sec. The peaks labeled B1 and B2 are the emissions from the ∆5 and ∆1 bulk bands along the Γ-Χ direction, respectively (31), which are almost unaffected by a small amount of oxygen exposure. However, the peak labeled S is removed sensitively by small amount of oxygen exposure, meaning that the initial state of peak S is very sensitive to surface contamination. It was also confirmed that the binding energy of peak S (1.2 eV) is independent of the photon energy. These results show that peak S can be ascribed to the emission from a surface state. The state can be ascribed to a Tamm surface state pulled from the ∆5 bulk band (B 1 peak) (31). The appearance of the Tamm surface state on the NbC(100) surface can be explained by

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Figure 6 Change in the normal emission spectrum of the NbC(100) surface as a function of oxygen exposure.

the ionicity of the crystal. In the NbC crystal, each Nb(C) atom is surrounded by six C(Nb) atoms, and electrons would feel a sort of octahedral crystal field at each atom site. However, on the (100) surface, each surface atom loses one coordinated atom on the vacuum side, which results in considerable modulation of the electrostatic potential in the surface region. The modulation of the potential may induce energy shifts of levels in the surface region to form new levels localized to the surface. Such a state is a typical Tamm surface state and can be resolved from the bulk bands in photoemission spectra when the energy shift is large enough. An upward shift of the state is expected at the carbon site on the NbC(100) surface because the lack of a coordinated Nb atom that is positively charged should enhance the negative potential at the surface C atom. The ∆5 bulk band observed as peak B1 is mainly composed of C 2px,y orbitals (31); thus the state observed as peak S can be ascribed to a Tamm surface state pulled off from the ∆5 bulk band in the carbon site. Similar modulation of the electrostatic potential is more or less expected for the surface of every compound crystal; thus the surface state labeled S can be regarded as the state characteristic of compound crystal surfaces. As described before, a Tamm surface state is observed in ARPE spectra for the NbC(100) surface. However, the Tamm surface state has not always been observed on compound crystal surfaces because the degree of the modification of the electrostatic potential at the surface is dependent on several factors, such as the degree of charge transfer and surface relaxation. As for the transition metal nitride and carbide (100) surfaces, similar surface states have been found only for TiN(100) (36), ZrC(100) (36,37), and VC(100) (26) in addition to NbC(100) (28–31).

B.

(110) Surface

In contrast to the accumulation of data on (100) and (111) surfaces of TMCs, very limited information is available for the TMC(110) surface. The ideal (100) surface should be composed of equal numbers of metal and carbon rows and each surface atom loses two coordinated atoms

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Figure 7 Change in the normal emission spectrum of the NbC(110) surface as a function of oxygen exposure.

in the vacuum side; however, all the TMC(110) surfaces previously studied have been proved to be reconstructed [TiC (11), TaC (15,16), and NbC (17)]. The electronic structure of TMC(110) has been studied in terms of the NbC(110) surface using ARPES (17). Figure 7 shows an example of an ARPES study to identify a surface state in the valence band region. Figure 7 shows normal emission spectra for an NbC(110) clean surface and for a surface exposed to a small amount of oxygen (⬉1 L). It is seen in Fig. 7 that a peak at 1.7 eV (peak S) is very sensitive to surface contamination; the peak is almost removed by a small amount of oxygen exposure (0.1 L) while the other peaks are almost unaffected. It is also confirmed that the binding energy of peak S is independent of the exciting photon energy; that is the state has no dispersion along the surface normal direction. Thus, the peak at 1.7 eV is well ascribed to emission from a surface state. Further analysis of ARPE spectra has proved that the state is a Tamm surface state pulled off from the ⌺3 bulk band mostly at the surface carbon site where the lack of coodinated Nb atoms in the vacuum side should shift the bulk state toward the lower binding energy side (17). The peaks in the ARPE spectra (Fig. 7) other than that at 1.7 eV are well ascribed to emissions from the Nb 4d–C 2p bulk bands. C.

(111) Surface

The (111) surface of TMCs is a polar surface, and the surface atom loses three coordinated atoms in the vacuum side. As mentioned in Sec. I, all the TMC(111) surfaces [except for VC(111)] are covered with metal layers. The polar surface is usually unstable because of its large electrostatic potential at the surface, which usually induces surface reconstructions or facetings. However, no reconstruction of TMC(111) has been found except for the VC(111) surface (8,9), suggesting

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that some unique stabilization mechanism should be operative in these surfaces. Such a stabilization mechanism should have considerable influence on the surface electronic structure; thus the electronic structure of the TMC(111) surface is of particular interest. The electronic structure of TMC(111) has been studied with ARPES for the TiC(111) (20,21,38,39), ZrC(111) (40), NbC(111) (41,42), and TaC(111) (43) surfaces, and these studies have shown that the electronic structure of the TMC(111) surface is much different from those of the (100) and (110) neutral surfaces; surface states derived from the nd orbitals of the surface metal atoms are formed around the Fermi level. The states give main features in the normal emission ARPE spectra in the case of the TMC(111) surface. An example of ARPE spectra of the TMC(111) surface is given in Fig. 8. Figure 8 shows normal emission spectra for the TaC(111) surface taken at various excitation photon energies (14 ⬉ hν ⬉ 32 eV). A prominent peak is observed just below the Fermi level in the normal emission spectra (Fig. 8). This spectral feature is characteristic of all the observed normal emission spectra of TMC(111) surfaces (20,21,38–43). The binding energy region around the Fermi level is the region where the bulk valence DOS is relatively small (Fig. 5), and the spectra of the (100) and (110) surfaces do not show such a prominent peak around the Fermi level (Figs. 6 and 7). The peak just below the Fermi level is observed at 0.7 eV independently of the exciting photon energy, indicating that the initial state has no dispersion as a function of k ⊥ . Figure 9 shows normal emission spectra for the TaC(111) surface and for the surface exposed to a small amount of oxygen (1.5 L). The gas adsorption study shows that the prominent peak just below the Fermi level is sensitively attenuated by surface contamination. These features are characteristic of the emission from a surface state, and the peak can be well ascribed to the emission from a surface state.

Figure 8 Normal emission spectra of the TaC(111) surface as a function of photon energy.

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Figure 9 Normal emission spectrum for the TaC(111) surface exposed to 1.5 L of oxygen together with that of the clean surface.

Some theoretical studies have been performed on the electronic structures of TMC(111) surfaces such as TiC(111) (44–47), ZrC(111) (47), and NbC(111) (47). These studies have shown that the (1 ⫻ 1) surfaces are stabilized through charge redistribution around the surfaces; the electron density at the first metal layers is increased to screen the long-range electrostatic field at the surface. These studies have also shown that the charge redistribution should be accompanied by the appearance of surface states derived from the metal nd orbitals (3d for TiC and 4d for ZrC, NbC) in the first metal layers. The states are expected to be formed around the Fermi level (44–47) which is in good agreement with ARPES studies (20,38–43). Resonant photoemission spectroscopy can give valuable information about the atomic orbital component of the state in the spectra. Figure 10 shows a plot of area intensities of the surface state induced peak for TaC(111) as a function of the exciting photon energy. In Fig. 10, a cross section of the Ta 5d band observed in the photoemission spectra for poly-Ta (48) is also shown. The photoionization cross section for the surface state on TaC(111) is resonantly enhanced at hν of ⬃40 and ⬃50 eV, as in the case for the Ta 5d band in poly-Ta. These enhancements of the cross section are well explained by the resonance process that proceeds via photon-induced excitation, Ta 5p 6 5d n ⫹ hν → Ta 5p 5 5d n⫹1 followed by the emission of a Ta 5d electron known as a super-Coster-Kronig decay, Ta 5p 5 5d n⫹1 → Ta 5p 6 5d n⫺1 ⫹ e ⫺

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Figure 10 Intensities of the surface state induced peak in the normal emission spectra of TaC(111) as a function of photon energy. Intensities of the Ta 5d band in the photoemission spectra for poly-Ta (48) are also plotted.

Because the Ta 5p orbitals split into two levels due to the spin-orbit coupling (5p 1/2 ⫽ 42.2 eV, 5p 3/2 ⫽ 32.7 eV), there are two maxima separated by ⬃10 eV in the plot. As a conclusion, the cross section of the surface state has the hν dependence characteristic of Ta 5d photoemission, and the state is formed through recombination of the dangling bond–like Ta 5d orbitals, as expected from theoretical studies (44–47). Previous resonant photoemission studies of TiC(111) (39) and NbC(111) (42) have also shown that the surface states have resonances near the 3p3d and 4p-4d photoexcitation thresholds, respectively. According to the theoretical studies, the electron density at the first layer of the (111) surface is increased relative to that at the metal layer in the bulk. In other words, the chemical environment of a metal atom in the first layer is different from that in the bulk. It is known that core-level binding energies in photoemission spectra are very sensitive to the chemical environment of atoms. Figure 11 shows Ta 4f core-level spectra for clean and oxygen-adsorbed TaC(111) surfaces. For the clean surface, two pairs of doublet peaks are observed in the Ta 4f region. One of the pairs at 25.4 and 24.9 eV represents the emission from 4f5/2 orbitals and the other pair at 23.5 and 22.9 eV the emission from 4f7/2 orbitals. In the spectrum for the oxygenadsorbed surface, one of the components of each doublet observed at the lower binding energy side (24.9 and 22.9 eV) is not observed. As the oxygen adsorption should have a significant effect on the surface Ta, this result indicates that the lower binding energy components of pairs are due to the emission from the surface core-level components of Ta 4f5/2 and 4f7/2, respectively. Furthermore, the core-level photoemission spectra show that the kinetic energy of the photoelectrons emitted from the 4f levels of surface Ta atoms is greater than that of electrons emitted from bulk Ta atoms. This result is compatible with a charge redistribution model, because the model predicts an increase of electron density at the first Ta layer that results in more effective screening of the core-hole final state at the surface to increase the kinetic energy of photoelectrons from the core level.

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Figure 11 Ta 4f core-level spectra for a TaC(111) clean surface and a surface exposed to 10 L of oxygen.

As just described, characteristic surface states are formed on the TMC(111) surfaces. The states are derived through charge redistribution around the surface to screen the long-range electric field arising from the polar structure of the surface; thus the state should be characteristic of the ideal (nonreconstructed) polar surface. However, polar surfaces of ionic crystals are generally unstable and stabilized through atomic rearrangements such as reconstruction or facetting rather than electronic redistributions. As for the TMC(111) surface, the ideal (1 ⫻ 1) surface is maintained [except for the VC(111) surface], probably for the following reasons: (a) atomic rearrangement is restrained in the TMC crystal because the metal-carbon bond in the crystal includes considerable contribution of the covalent bond, which has strong directivity and, (b) the TMC crystal has metallic conductivity so the charge can be redistributed with ease. As described before, it can be concluded that the surface state on the (111) surface is characteristic of the polar surface formed by breaking of bonds that contain ionic, covalent, and metallic bond contributions. The two-dimensional band structure in the surface Brillouin zone (SBZ) of surface states can be determined from measurements of the off-normal-emission ARPE spectra. Figure 12 shows off-normal emission spectra for the (111) surface of TaC. The spectra are taken at various detection angles (θ d ) along the ⬍211⬎ direction. The detection angles are given relative to the surface normal direction. The surface parallel component of the wave vector (k 储) of electrons is well approximated as conserved in the photoemission process if the surface is periodic and the exciting photon energy is in the ultraviolet region. Thus, k 储 of the initial state of the peak in ARPE spectra can be evaluated from k 储 ⫽ [(2m/h 2) (hν ⫺ E B ⫺ eφ)] 1/2 sin ␪ d where hν is the excitation photon energy, E B is the binding energy of the peak, and eφ is the work function of the surface. Figure 12 shows that the surface state observed in normal emission spectra (S 1) disperses toward the Fermi level with increasing θ d (i.e., with increasing k 储) and

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Figure 12 Off-normal emission spectra of the TaC(111) surface as a function of detection angle. The detection plane is parallel to the ⬍21 1⬎ direction.

crosses the Fermi level at θ d ⬃ 20°. Another surface state (S 2) appears at θ d ⬎ 10°. The twodimensional band structure in the SBZ can be mapped using the preceding equation. The SBZ of the TMC(111) surface is shown in Fig. 13. The band structure of the surface states on TaC(111) is summarized in Fig. 14. Our systematic studies of the surface electronic structure of TMC(111) have revealed that

Figure 13 Real space atomic geometry and surface Brillouin zone for the TaC(111) surface.

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Figure 14 Measured dispersion of the surface states on the TaC(111) surface.

the band structures of the surface states on group IV and V TMC(111) are rather different from each other; the surface states on group V TMC(111) show substantial dispersion, as shown in Fig. 14 (41–43), whereas those on group IV TMC(111) show little dispersion (39,40). This difference cannot be explained by the simple rigid band model, and a careful theoretical study that treats the effect of surface relaxation, the many-body effect, etc. would be needed to explain fully the band structures of the surface states on TMC(111) surfaces. ARPES studies performed on TMC surfaces are summarized in Table 1.

III. SURFACE REACTIVITY The surface reactivity of TMCs has attracted considerable attention because of their use as catalytic materials for the hydrogenation of benzene, ethylene, and carbon monoxide; the decomposition of methanol; etc. (1). Studies of gas adsorption on well-defined surfaces of TMCs have been performed for some systems, and it has been found that the surface reactivity of TMCs shows considerable face dependence; the surface reactivity toward gas adsorption of (111) is much higher than that of (100). For example, oxygen adsorption studies of TiC(100) and (111) surfaces have shown that the sticking probability of oxygen on (111) is two orders of magnitude

Table 1 Summary of Published ARPES Studies of TMCs Compound TiC ZrC VC NbC TaC

(100)

(110)

(111)

(20,21) (22,23) (24–27) (28–31) (32,33)

(21)

(20,21,38,39) (40)

(17)

(41,42) (43)

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larger than that on (100) (11,49). Adsorption states of CO and CH 3OH have been studied on the NbC(100) and (111) surfaces, and it has been found that at room temperature CO adsorbs on the (111) surface but not on the (100) surface, and CH 3OH adsorbs dissociatively to form CH 3O and H species on the (111) surface but CH 3OH adsorbs molecularly on the (100) surface (50). The face dependence of the reactivity described here is also predicted from theoretical analysis using extended Hu¨ckel tight binding calculations (51). From a scientific point of view, the face dependence of reactivity is of interest because it is considered to be due to a pure surface effect; differences in the surface electronic structure should be responsible for the reactivity difference. As discussed in the previous section, the electronic structure of the (111) surface is characterized by the presence of surface states formed around the Fermi level, which should act as so-called frontier orbitals for gas-surface interaction. The lack of such states may make the (100) surface rather inert. In this section, comparative studies of oxygen adsorption on TiC(100) and (111) surfaces are reviewed. Adsorption of oxygen on TiC surfaces is the most extensively studied system in the field of surface chemistry of TMCs. Several oxygen adsorption studies have been performed on TiC(100) (7,49,52–54) and TiC(111) (11,49,55,56) to elucidate chemisorption sites or electronic bonding levels of chemisorption. Figure 15 shows the change in the normal emission ARPE spectra for the TiC(100) (a) and TiC(111) (b) surfaces as a function of oxygen exposure at room temperature. On both surfaces, oxygen is adsorbed dissociatively, forming (1 ⫻ 1) overlayers at saturation [the (1 ⫻ 1) overlayer means that the adsorbed oxygen atoms form a two-dimensional lattice whose periodicity is the same as that of the substrate surface atoms]. For the (100) surface, chemisorption bonding states are formed at 4.1 and 5.9 eV below the Fermi level (Fig. 15a). Polarization-dependent analysis by the use of symmetry selection rules (18) has proved that the states found at 4.1 and 5.9 eV in the normal emission spectra are oxygen 2p x,y and 2p z

Figure 15 Change in the normal emission spectra of TiC(100) (a) and TiC(111) (b) as a function of oxygen exposure.

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derived chemisorption states, respectively (54). For the (111) surface, chemisorption bonding states are found as a single peak at ⬃6 eV (Fig. 15b); however, the polarization-dependent analysis by the use of symmetry selection rules has proved that the peak has two components: oxygen 2px,y and 2pz derived states, and the former is formed at a slightly higher binding energy side (56). The adsorption is saturated at exposure to 2000 L and 5 L (1 L ⫽ 1 ⫻ 10 ⫺6 torr s) for the TiC(100) and (111) surfaces, respectively. It was confirmed that the (1 ⫻ 1) overlayers are nearly complete on both surfaces at saturation, so that the densities of oxygen atoms can be estimated to be 1.08 ⫻ 10 15 and 1.25 ⫻ 10 15 per cm 2 for the oxygen-saturated TiC(100) and (111) surfaces, respectively. Thus, it is concluded that the sticking probability of oxygen on the (111) surface is about two orders of magnitude larger than that on the (100) surface on average. Nearly the same conclusion was obtained from the O 1s uptake measurements with X-ray photoelectron spectroscopy (XPS) (11,49). It is well known that the study of the photoionization cross section of the adsorbateinduced state can give valuable information about orbital components of chemisorption bonding states. Figure 16 shows a plot of area intensities of O 2p–derived states for the TiC(100)-(1 ⫻ 1)O and TiC(111)-(1 ⫻ 1)O systems as a function of excitation photon energy. Figure 16 shows that the cross section for the TiC(111)-(1 ⫻ 1)O system has a large maximum in the energy range of the Ti 3p-3d photoexcitation threshold (45–50 eV). The cross section of O 2p orbitals does not have a resonance in this energy region, and the resonance is ascribed to the photoninduced Ti 3p → 3d excitation followed by deexcitation through the emission of O 2p electrons mediated by interatomic energy transfer (54). This process is expected to proceed when strong Ti 3d–O 2p hybridization is formed. Thus the existence of the resonance is reasonable, since the first layer of TiC(111) is composed of only Ti atoms, and the adsorbed oxygen atoms should form strong chemisorption bonds with the surface Ti atoms. On the other hand, in the case of the TiC(100)-(1 ⫻ 1)O system, the cross section of the O 2p derived band has a much weaker resonance in the Ti 3p-3d photoexcitation threshold region (Fig. 16). This indicates that the

Figure 16 Intensities of the total O 2p band emission for the TiC(111)-(1 ⫻ 1)O and TiC(100)(1 ⫻ 1)O systems as a function of photon energy.

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hybridization between the Ti 3d and O 2p levels is less important for chemisorption bonding on the TiC(100) surface. The (100) surface is composed of equal numbers of Ti and C atoms (Fig. 1), and the result shown in Fig. 16 is compatible with an adsorption model in which oxygen atoms are adsorbed on the carbon on-top sites on the TiC(100) surface to form chemisorption bonds mostly with carbon atoms. This interesting adsorption model has also been proposed in an ICISS study (52) and a theoretical study using extended Hu¨ckel tight binding calculations (51). Because the adsorbed oxygen atoms form periodic (1 ⫻ 1) overlayers on both TiC(100) and (111) surfaces, it is expected that the O 2p–derived states should have two-dimensional band dispersions due to the lateral interaction between bonding orbitals. The two-dimensional band structure of the chemisorption bonding state can give valuable information about the nature of the chemisorption bond. The two-dimensional band structure is deduced from off-normal emission ARPES measurements, as discussed in the previous section. The results for the O 2p– derived states for the TiC(111)-(1 ⫻ 1)O system are summarized in Fig. 17. In this plot, the coordinate system is chosen such that the z axis is normal to the surface and the x and y axes coincide with the crystallographic ⬍011⬎ and ⬍211⬎ directions, respectively. The 2p z and 2p x,y –derived states are nearly degenerate around the Γ point and cannot be resolved in the spectra in this region. The dispersive features for the O 2p derived states are qualitatively reproduced by the theoretical band structure calculated by a tight binding method for an unsupported two-dimensional hexagonal oxygen layer (57).

Figure 17 Measured dispersion of the O 2p–derived states for the TiC(111)-(1 ⫻ 1)O system. The surface Brillouin zone is shown in the inset.

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The experimental band structure of the O 2p–derived states is characterized by stabilization of the energy levels of 2px and 2py –derived states relative to that of the 2pz derived state. This is not expected from the calculated band structure for an unsupported oxygen layer (57), and thus it should reflect bonding characteristics of oxygen on the TiC(111) surface. The selective stabilization of 2px and 2py –derived states means that the O 2px,y orbitals are more important for chemisorption bonding than the 2pz orbital on the TiC(111) surface, i.e., are stabilized through hybridization with Ti orbitals more effectively. According to the adsorption model proposed in the ICISS investigation (55), the oxygen atom is adsorbed on the threefold hollow site (fcc site) on the TiC(111) surface. In this case, the adsorbed oxygen interacts dominantly with the surrounding three surface Ti atoms; the vertical interaction with the underlying Ti atom just below the O atom is expected to be small because the bulk Ti atom in the TiC crystal should already have completed covalent bonds with surrounding C atoms and is more inert than the surface Ti atoms. Thus the lateral bonding caused by the hybridization of the O 2px,y with surrounding orbitals of surface Ti is considered to be important for chemisorption on this site, which is confirmed by the two-dimensional dispersive feature of chemisorption bonding states shown in Fig. 17. Figure 18 shows a plot of band dispersions of O 2p–derived states for the TiC(100)(1 ⫻ 1)O system, measured along the ⬍100⬎ direction. In contrast to the case of the TiC(111)O system, the bonding state derived from the O 2pz level is observed on the higher binding energy side relative to the 2px,y-derived states. This result indicates that, for the TiC(100)-O system, the oxygen-surface interaction vertical to the surface is more important for the chemisorption bonding; the 2pz orbital is stabilized through hybridization with surface orbitals more effectively. The vertical interaction is expected to be important when the oygen atom is adsorbed

Figure 18 Measured dispersion of the O 2p–derived states for the TiC(100)-(1 ⫻ 1)O system. The surface Brillouin zone is shown in the inset.

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Figure 19 Schematic views of the TiC(100)-(1 ⫻ 1)O and TiC(111)-(1 ⫻ 1)O systems.

just above the surface atom (on-top site). Thus, the two-dimensional band structure shown in Fig. 18 is compatible with the adsorption model; an oxygen atom is adsorbed on the carbon atom on the TiC(100) surface (52). Adsorption models for the TiC(100)-(1 ⫻ 1)O and TiC(111)(1 ⫻ 1)O systems are shown schematically in Fig. 19. Another interesting example of the face dependence of surface reactivity of TMCs has been found for alkali metal adsorption systems. Alkali metal adsorption has been studied on NbC(100) (58) and NbC(111) (59,60), on which the mechanisms of adsorption of alkali metal have been found to be different. For the K/NbC(111) system, the 4s level of the K atom strongly interacts with the surface states characteristic of the (111) surface formed around the Fermi level, which results in strong polarization of adsorbed K in the initial stage of adsorption (59,60). Adsorbed K atoms are dipersive on the surface due to the Coulomb repulsion in the initial stage. With increasing K coverage, adsorbed K atoms are depolarized to form a metallic K overlayer at high coverages (59,60). The adsorption mechanism of K on the NbC(111) surface is characterized by a polarization-depolarization transition that is directly evidenced by ARPES measurements (60). On the other hand, the surface state of high density of state formed around the Fermi level is lacking on the NbC(100) surface, which results in weak interactions between adsorbed K atoms and the surface. On the NbC(100) surface, it has been proposed that adsorbed K atoms form islands from the very initial stage of adsorption and the adsorption proceeds through the growth of islands (58). The island formation is proposed to be possible because the polarization of adsorbed K is relatively weak due to the weak interaction with the (100) surface even in the initial stage of adsorption. Thus the face dependence of the K adsorption process may be ascribed to the difference in surface electronic structures of TMC(100) and (111) surfaces.

IV. SUMMARY In this part, ARPES studies of the electronic structure and reactivity of the three typical lowindex surfaces of TMCs, (100), (110), and (111), are reviewed. For the neutral (100) and (110) surfaces, most of the features in the ARPE spectra can be understood as the emissions from

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bulk bands; thus the surface electronic structures are mostly viewed as the cross sections of bulk bands. However, surface states derived from the potential modification at the surface due to the lack of coordinated atoms in the vacuum side are found on some surfaces. For the polar (111) surface [except for VC(111)], characteristic surface states composed of d orbitals of the surface metal atoms are formed around the Fermi level, where the DOSs of neutral surfaces are rather small. The surface states are formed through charge redistribution around the surface to stabilize the polar structure of the surface. Because of the difference in electronic structure between the neutral and polar surfaces, in particular in the region around the Fermi level, reactivities of these surfaces are quite different from each other; the (111) surface is more active toward gas adsorption than the neutral surfaces. Adsorption processes for an alkali metal (K) are also found to be different; on the NbC(111) surface, the 4s orbital of adsorbed K is strongly hybridized with the surface states to form a highly polarized state in the initial state, but the K-surface interaction is weak and adsorbed K atoms form islands even in the very initial stage on the NbC(100) surface. It is evident from this review that TMC surfaces are interesting subjects of both experimental and theoretical investigations. However, at this point, information on TMC surfaces is limited compared with the substantial accumulation of data on elemental metal and semiconductor surfaces. There remain many unsolved elemental problems for the TMC surfaces. For example, the surface states on the group V TMC(111) have substantial dispersion, whereas those the group IV TMC(111) have little dispersion, which cannot be explained by a simple rigid band model. The TMC crystals inevitably include vacancies on the carbon site, which should have considerable effects on the surface electronic structure, although systematic studies of this point have not yet been performed. Parallel extensive studies, both theoretical and experimental, are needed for further progress in the surface chemistry and physics of TMCs.

ACKNOWLEDGMENTS I am pleased to thank the staff of Photon Factory, National Laboratory for High Energy Physics, particularly Dr. H. Kato, for their excellent support. I am also pleased to thank Dr. S. Otani of the National Institute for Research in Inorganic Materials for providing the single-crystal TMC samples.

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Surface Electronic Structures and Reactivities 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56.

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10 Irradiation Properties of Electric Refractory Materials Naoto Kobayashi Electrotechnical Laboratory, Tsukuba, Ibaraki, Japan

I.

INTRODUCTION

Refractory transition metal carbides and nitrides have been explored extensively in experiment and theory because of their attractive physical and chemical properties. These compounds are characterized by extreme hardness and high melting points due to strong covalent bonding as in nonmetallic materials. They have high electrical conductivity, and some of them are superconductors with superconducting transition temperatures Tc around 10 K. Most of the compounds have a simple B1 (NaCl) structure, but the physical properties including Tc are strongly affected by any deviation from stoichiometric composition (1). A characteristic property of B1-phase compounds is that Tc shows far less susceptibility to disorder than in other high-Tc materials such as A15, cluster compounds, or oxide compounds (2–4). These materials are also used in semiconductor technology for good contact or a diffusion barrier. This suggests many potential applications of these compounds in environments subject to irradiation. NbC, ZrN, and HfN are included in these compounds and have attractive properties not only for superconducting materials but also for electric materials. NbC is a B1-phase compound with a superconducting Tc above 11 K and a stable B1 structure over a wide range of vacancy concentrations. Structural investigations of NbC have been performed in various experiments. Short-range ordering in NbC was detected by electron diffraction experiments (5,6) and elastic diffuse neutron scattering experiments (7). Local atomic displacements around isolated C vacancies were investigated by X-ray diffraction experiments (8) and channeling experiments (9). Theoretical investigations of the Tc depressions in NbC due to deviations from the stoichiometry by existing C vacancies have been performed using cluster calculations (10,11) and with the LCAO-CPA (linear combination of atomic orbitals–coherent potential approximation) approach (12). The Tc depressions due to disorder are, however, governed not only by vacancies but also by other defects (lattice distortion, substitution, etc.), which influence Tc through changes in the electronic and phonon structure, and an exact knowledge of structural disorder is necessary in order to explain the variation of superconducting properties. In addition to the fact that ZrN and HfN are similar in physical and chemical nature to NbC as B1-phase compounds, they are found to have an attractive insulating phase in the higher nitride state. Zr 3 N 4 and Hf 3 N 4 have been found to produce an insulating phase, and applications of these compounds to cryoelectronic devices were suggested (13). This chapter discusses some typical aspects of ion beam irradiation and ion implantation of these materials. 245

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On the other hand, refractory semiconductors can have many uses as wide–bandgap semiconductors. BP is a III-V compound semiconductor with a band gap of 2.1 eV. This compound semiconductor is also characterized by several outstanding properties, such as a high melting point above 3000°C, a high decomposition temperature of about 1130°C under 1 atm, extreme hardness, excellent stability, and high oxidation resistance at high temperatures (14). This material therefore has potential for application for electronic devices in extreme conditions such as high-temperature and high-radiative conditions. This chapter also gives typical results for highenergy ion beam irradiation, ion beam–induced reaction for metal thin films and BP, and ion beam–induced epitaxial crystallization (IBIEC) for preamorphized BP.

II. ION BEAM IRRADIATION EFFECTS ON NbC A.

Lattice Parameter and Static Atomic Displacements

X-ray diffraction experiments on polycrystalline NbC thin films irradiated with energetic ions at room temperature (RT) revealed appreciable changes of the lattice parameter a0 with the preservation of the B1 structure, line broadening, and intensity weakening of the Bragg peaks. Figure 1 shows the variation of the lattice parameter a 0 of NbC thin films as a function of He ⫹ (200 keV) and Ar 2⫹ (600 keV) fluences and the corresponding value of energy deposited into nuclear collisions Q (eV/atom) calculated by the TRIM code (15). The samples were nearstoichiometric NbC thin films with thicknesses of about 200 nm prepared by reactive radio frequency (RF) sputtering using CH 4 gas. The highest Tc was 11.7 K with a transition width of ˚ . The values of the residual resistivity ranged 0.3 K and the lattice parameter a 0 was 4.475 A from 15 to 100 µΩ cm. The energy losses due to nuclear collisions were in the range 2.4 to 4.6 eV/nm for 200-keV He and from 350 to 500 eV/nm for 600-keV Ar, respectively, between

Figure 1 The lattice parameter a 0 of ion-irradiated NbC thin films as a function of the fluences of 200keV He ⫹ and 600-keV Ar 2⫹ and the corresponding deposited energy value. The lattice parameter of the bulk sample is indicated by an arrow.

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the surface and a depth of 200 nm. The fluence necessary to reach a certain value of deposited energy Q is almost two orders of magnitude larger for He irradiation than for Ar irradiation. For both He- and Ar-irradiated samples, a 0 increases and reaches a maximum value that is greater than the initial a 0 value by 0.4% and decreases down to a value 0.5% smaller than the initial a 0 value. Variations of a 0 on irradiation by both ion species agree on a fluence scale corresponding to the same deposited energy. Furthermore, a 0 shows saturation at higher fluences for Ar-irradiated samples. Because the atomic scattering factor of the C atom, fC , is much smaller than that of Nb, fNb , X-ray scattering by Nb atoms contributes dominantly to the line intensities. Information about static atomic displacements can be obtained from the analysis of the DebyeWaller factor (16). In this analysis the natural logarithm of the X-ray intensity ratio ln (I/I0 ) is plotted as a function of sin 2 θ/λ 2 where I denotes the intensity of a line after irradiation, I0 is the intensity of the same line prior to the irradiation, θ is the diffraction angle, and λ is the Xray wavelength (modified Wilson plot). The relation is expressed by ln(I/I0 ) ⫽ ⫺2B(sin 2 θ/λ 2 ) ⫹ ln C

(1)

where B is a irradiation-induced static Debye-Waller factor that is equal to 8π ⬍u ⬎, where ⬍u 2⬎ is the mean square displacement amplitude of the atoms perpendicular to the reflection planes and C is a constant that indicates the ratio of the material volume contributing to the crystalline diffraction after and before irradiation. When ln(I/I0 ) is plotted as a function of sin 2 θ/ λ 2 , the slope of a least-squares-fit line through the data points gives the value B, from which ⬍u 2⬎ values can be calculated, and C is obtained from the axial section value on the ordinate. Under the assumption that the dynamical behavior of the lattice atoms is not much influenced by the irradiation, ⬍u 2⬎ corresponds to a value of average static displacements of the lattice atoms, especially Nb atoms. In Fig. 2, the one-dimensional static atomic displacement amplitudes of the lattice atoms ⬍u 2⬎ 1/2 are plotted as a function of He and Ar fluence and the corresponding deposited energy. 2

2

Figure 2 One-dimensional static atomic displacements ⬍u 2⬎ 1/2 of He- and Ar-irradiated NbC thin films as a function of the ion fluences and the corresponding deposited energy.

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One can see a distinct variation of ⬍u 2⬎ 1/2 on irradiation by both ion species and an overall behavior similar to the variation of a 0 in spite of large uncertainties. The displacements have ˚ at irradiation state Φ 1 , where the maximum a 0 was observed, a maximum value of 0.08 ⫾ 0.02 A and decrease with subsequent irradiation. Saturation was also observed for the Ar-irradiated sample at higher fluences. The material volume contributing to the crystalline diffraction was found to decrease with increasing fluence. This concentration amounts to about 10% at state Φ 1 and to about 20% at state Φ 2 for samples irradiated by both ions. B.

Channeling Experiments

Rutherford backscattering spectrometry (RBS) channeling experiments with 2-MeV He ions backscattered from an NbC single crystal have revealed the structural disorder induced by 200keV He irradiation at state Φ 1 (4 ⫻ 10 16 He/cm 2), where the maximum a 0 in thin films was observed. NbC 0.98 single crystals with ⬍110⬎ crystalline direction prepared by RF zone melting were used because the Nb and C atoms are arranged in separate chains in this direction. The Tc value of the sample obtained by this treatment was 11.2 K (9). The aligned spectrum for the ion-irradiated sample reflects the damage distribution, with a deep large peak that shows typical features found in materials in which covalent bonding prevails. In the transmission region of thin films up to 200 nm, a small increase in the dechanneling yield is observed. Angular tilt measurements performed in the region close to the surface prior to and after the irradiation with the window at a depth region between 20 and 80 nm from the surface have shown the angular scans of the He ion yield backscattered by Nb atoms in the irradiated sample with a narrowing of the critical angle ψ1/2 (half-angular width at half-height between the minimum yield and the yield for the random direction) and a slight increase of χ min (minimum yield normalized to the random yield). After the measurements of angular scans with some typical tilt planes in the present experiments, the increase of the total displacements of Nb atoms ∆u tot induced by irradiation can be obtained by comparison with the calculated values (9). The total displacements after the irradiation are ⬍u 2tot⬎ ⫽ ⬍u 2th⬎ ⫹ ⬍u 2st,0⬎ ⫹ ⬍u 2st,i⬎

(2)

where uth are the thermal displacements, u st,0 are the static displacements of the virgin crystal, and u st,i are the static displacements induced by the irradiation, respectively. If no interaction between these displacements and no change in u th on irradiation are assumed, ∆⬍u 2tot⬎ corre˚ . This value is slightly smaller sponds to ⬍u 2st,i⬎. The value of ⬍u 2st,i⬎ 1/2 thus obtained is 0.05 A than the displacement value obtained in the X-ray experiments, mainly because channeling experiments give information for a shallower region of the sample than the X-ray experiments. The angular tilt curves obtained from the 12 C(d,p) 13C nuclear reaction as well as from elastic scattering of the deuterons by Nb atoms are shown in Fig. 3. The window settings for both the reaction part and the elastic scattering part range from the surface to 200 nm. Although the Nb(d,d )Nb angular scan shows a similar small disorder in Nb sublattice as observed with He ions, the tilt curve of the reaction part (C sublattice) reflects the feature of a highly disordered C-sublattice. The values Ψ1/2 ⫽ 0.38 and 0.33 and χ min ⫽ 0.21 and 0.73 are observed prior to and after the irradiation, respectively. The analysis of defects in NbC by Monte Carlo calculations (17) has revealed quite different contributions of randomly displaced C atoms and stacking faults to the dechanneling yield in the Nb sublattice and has reproduced well the experimental results for C-implanted NbC. On introducing stacking faults, the Nb dechanneling yield revealed a considerable enhancement, whereas randomly displaced C atoms only slightly contributed to the dechanneling yield in the Nb sublattice. Because the present results reflect the latter case, the type of defects is different from stacking faults. Instead, C interstitial clusters could be

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Figure 3 Angular scans of p yield produced by the 12C(d,p) 13C nuclear reaction and d yield by the Nb (d,d )Nb elastic scattering through the ⬍110⬎ direction of an NbC 0.98 single crystal prior to and after 4 ⫻ 10 16 He/cm 2 irradiation.

predominant because isolated C interstitials hardly exist after irradiation at RT. Channeling experiments on the He-irradiated sample were performed after the same annealing processes up to 250°C. The observed values of Ψ1/2 and χ min in the C sublattice are 0.32 and 0.74. The Ψ1/2 value shows a small decrease after 250°C and χ min increases, indicating defect redistribution. A striking feature is the change in the dependence of the dechanneling rate on the analyzing beam energy. The difference in the dechanneling rates after the annealing processes up to 250°C is nearly independent of the energy, which implies the formation of stacking faults, because such a constant dependence on energy on introducing stacking faults with partial dislocations has also been confirmed in the Monte Carlo calculations. The enhancement of χ min is due to the fact that the dechanneling contribution is significantly greater for stacking faults than for isolated interstitials (18). On the other hand, Ψ1/2 and χ min of the C sublattice show almost no change after the annealing processes, which indicates the high stability of defects in the C sublattice.

C.

Properties of Structural Disorder

In the fluence range at the irradiation state Φ 1 where the lattice parameter a 0 of the thin films has a maximum value, the irradiation-induced defects could have the same characteristics in He- and Ar-irradiated samples because a 0 , static displacements, Tc , and resistivities revealed almost the same variations at the same deposited energy values and showed the same annealing behavior, as will be described later. The structural disorder is composed of defects that cause small Nb displacements and highly displaced C defects. The observed average static displace˚ from X-ray diffraction experiments and 0.05 A ˚ ments of the Nb atoms, whose value is 0.08 A from channeling experiments, are correlated with the existence of point defects such as interstitial Nb atoms, including antisite defects or very small Nb clusters as suggested by channeling experiments. In irradiation experiments of TaC0.99 with high-energy electrons (19), all C defects

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(interstitials) have been annealed out below 380 K and part of the Ta defects (30%) remained after annealing at 380 K. The same annealing behavior was also observed in TiC0.97 (20). Judging from these results for other carbides, isolated C interstitials should have been already annealed out and the rest could be stabilized in form of clusters in NbC by the irradiation at RT, whereas part of the isolated Nb interstitials should remain even at RT. Although the large difference in atomic scattering factors of Nb and C atoms makes it difficult to distinguish small amounts of antisite defects in X-ray diffraction experiments, part of the Nb atoms that undergo displacements in this fluence region can occupy the sites of C vacancies produced by the irradiation. The increase of a 0 at state Φ 1 can therefore be attributed to Nb interstitials including antisite defects. These defects will produce a large strain field and will cause a lattice expansion by overcompensating the effects of vacancies that cause the lattice contraction (21). On the other hand, the highly disordered C sublattice observed in the channeling experiments indicates the presence of C interstitial clusters that survive at RT. Partial recovery of a 0 after the annealing process up to 250°C was observed, as shown later, and this correlated with the formation of extended defects such as stacking faults with partial dislocations as inferred from the energydependent dechanneling analysis. Interstitial Nb clustering into faulted loops will make such stacking faults (extrinsic stacking faults). The clustering of Nb interstitials will reduce the strain field and cause the partial a 0 recovery. For the samples after high-fluence irradiation (state Φ 2 ), the nature of the defects is different in He- and Ar-irradiated samples because Tc and resistivities showed different behavior in spite of the close agreement of the a 0 variations. However, the main origin of the a0 decrease is the same in both samples and is thought to be due to vacancies that did not recombine with Nb interstitials because these agglomerate into clusters or precipitates. This is suggested because of the continuous increase of the concentration of off-lattice-site Nb atoms in spite of an a 0 decrease during the irradiation up to this irradiation state. D.

Superconducting Transition Temperatures and Resistivities

Tc decreases continuously with increasing irradiation fluence for both He- and Ar-irradiated thinfilm samples. The Tc values determined by resistive and inductive methods are shown in Fig. 4. The widths of the transition ∆Tc are also indicated by vertical bars for inductively determined values, whereas the widths of the resistively determined values are less than 0.4 K. Agreement of the Tc variations between He- and Ar-irradiated samples is observed except for higher fluences, where Tc shows slight deviations. For He-irradiated samples Tc decreases down to a minimum value of 3.4 K at state Φ 2 , and for Ar-irradiated samples Tc decreases down to 4.1 K at this state and shows saturation in the fluence range where the lattice parameter a 0 has saturated. Irradiation-induced changes of the residual resistivity at 12 K, ∆ρ0 , the thermal part of the resistivity ρth (⫽ρRT ⫺ ρ0, where ρRT and ρ0 are resistivities at RT and 12 K, respectively), and the residual resistivity ratio RRR (⫽ρRT /ρ0 ) of He- and Ar-irradiated samples are observed. In contrast to the variations of a 0 and Tc , which depended only on the total energy deposited into nuclear collisions irrespective of the impinging ion species, the behavior of the resistivities depends on the irradiating ions. In the fluence range above Φ 1 , ρ 0 shows a continuous increase up to 340 µΩcm and a saturation for He-irradiated samples, while it reaches a maximum value of 190 µΩ cm and then decreases down to a value of about 110 µΩ cm for the Ar-irradiated sample. The residual resistivity ratio RRR decreases continuously for irradiations by both ion species but a difference is also found in the variations of ρth. The value of Ar-irradiated samples decreases after a slight constant region and remains positive, whereas ρth of the He-irradiated samples decreases down to negative values. The different dependence of ρ0 and ρth on fluence

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Figure 4 The superconducting transition temperature T c of He- and Ar-irradiated NbC thin films, determined by the resistive and inductive methods, respectively. Transition widths in the inductive measurements are indicated by vertical bars; those in resistive measurements are less than 0.4 K.

in the He- and Ar-irradiated samples is probably due to the difference of the deposited energy density in the displacement cascades and its influence on the structure, size, and distribution of defects. This difference apparently has no significant influence on the a 0 and Tc variations as can be seen in Figs. 1 and 4. The decrease of ∆ρ 0 in Ar-irradiated samples will be associated with defect recombination phenomena in the cascades. Such an effect would be feeble in dilute cascades in the He-irradiated samples. A negative ρth has sometimes been observed in A15 compounds or cluster compounds (22). Nevertheless, up to the critical fluence of state Φ 1 at which the maximum a 0 is observed, the agreements of resistivities are fairly good for irradiations by both ion species and the type of defects induced should be similar in He- and Ar-irradiated samples. E.

Annealing Experiments on Thin Films

Isochronal annealing processes were performed for Ar-irradiated thin-film samples irradiated at state Φ 1 (4 ⫻ 10 14 Ar/cm 2) and at state Φ 2 (10 16 Ar/cm 2 ). The annealing was performed in the temperature range between 50 and 900°C in steps of 50 K with an annealing period of 30 min at each temperature. The results for the Tc and a 0 recoveries in the first case (state Φ 1 ) are shown in Fig. 5, where a 0 and Tc are plotted as a function of the annealing temperature TA. The a 0 and Tc show a few recovery stages. One can see close agreement between the recoveries of a 0 and Tc at temperatures around 250°C and from 650 to 800°C. This means that the defects that cause the lattice parameter increase are also responsible for the Tc depression. However, Tc shows no change at the recovery stage of a 0 around 450°C. By the annealing processes up to 850°C, a0 has recovered to its initial value, whereas Tc has not yet reached its initial value but has begun to decrease again. This decrease could be due to beginning of diffusion of C atoms to grain boundaries. Defects that could be annealed above 700°C are correlated with the displacements

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Figure 5 The superconducting transition temperature T c and the lattice parameter a 0 as a function of the temperature T A in the isochronal annealing process for the NbC thin film with the maximum a 0 after 4 ⫻ 10 14 Ar/cm 2 irradiation. a 0,i, T c,i (R), and T c,i (I) denote the initial values of a 0, resistively determined T c , and inductively determined T c , respectively.

of Nb atoms. This is evident from the fact that the recovery stage of the static displacements of Nb atoms coincided well with the recovery stage of a 0 . The averaged one-dimensional static ˚ above 700°C. This recovery displacements ⬍u 2⬎ 1/2 of Nb atoms decrease down to about 0.03 A of the Nb displacements could be associated with the dissociation of vacancy clusters, which are produced by ion irradiation and partly in the subsequent annealing process. These vacancy clusters could be dissociated at temperatures in the range from 650 to 850°C and then vacancies could be annihilated by recombination with Nb interstitial clusters (stage V). It is commonly assumed that self-diffusion occurs through vacancy formation and migration and that the energies of vacancy formation and migration are comparable; therefore the explanation of vacancy cluster dissociation and migration from 650 to 850°C appears plausible. The release of strain fields due to annihilation of Nb interstitial clusters thus induces lattice relaxation and reduction of Nb displacements. Variations of the resistivities of the same sample (state Φ 1 ) during the annealing processes were investigated as a function of the annealing temperature TA . One can see some recovery stages of the residual resistivity change ∆ρ 0 . However, these stages are at lower temperatures than the recovery stages of a 0 and Tc . The decrease of ∆ρ 0 at 150°C preceding a 0 and Tc recoveries could be due to defect recombination effects and the decrease from 550 to 850°C to defect dissociation effects. RRR increased gradually in the course of the annealing processes. The same annealing behavior of a 0 , Tc , and resistivities has been found for the He-irradiated sample up to 250°C, and this again reflects the existence of the same type of defects in both He- and Arirradiated samples. As for the recoveries of a 0 and Tc of the Ar-irradiated sample at state Φ 2, a 0 shows a gradual increase above 600°C but does not reach the initial value up to 900°C. Also, Tc shows a gradual increase above 500°C, but some inhomogeneous redistribution of defects is induced

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above 600°C as inferred from the increase in the transition width ∆Tc . Complete annealing is also not yet obtained at 900°C. The residual resistivity showed first a small increase and subsequently a gradual decrease during the annealing process. The broad recovery behavior above 500°C is in agreement with that of the sample irradiated at state Φ 1 , which also suggests dissociation of defect clusters. F.

Superconducting Properties

The results of the channeling experiments show that the C sublattice is highly disordered and certain amounts of C vacancies exist in the irradiated sample. The increase of C vacancy concentration in NbC is a reason for Tc depression (21,23). Cluster calculations (11) have demonstrated that the partial local atomic density of states is heavily affected by the C vacancy concentration, and a reduction of the electron-phonon coupling parameter λ is found to be due mainly to its electronic part rather than to the phonon part. Calculations based on the LCAO-PA approach have revealed that the total density of states N(0) at the Fermi energy E F increases with the vacancy concentration (12). They have suggested other reasons for the Tc depression of NbC, such as lifetime effects. However, the Tc depressions are not only due to C vacancies but also have other origins such as Nb vacancies and lattice distortions. Nb vacancies heavily affect Tc as well as C vacancies because the continuous depressions of Tc are correlated with a continuous increase of off-lattice-site Nb atoms. The band structure calculation for NbO will give a good inference. NbO is a compound with B1 structure usually with ordered vacancies on both metal and nonmetal sublattices and is not superconducting above 1.2 K (24). According to the selfconsistent energy band structure calculations (25) for Nb 0.75 O 0.75 , where 25% of Nb and O vacancies are ordered, there arise additional band structures that are related to Nb and O vacancies, and these lead to variations of the density of states at E F. Although the total density of states N(0) at E F shows a small decrease, the partial density of states of the O-p band shows a large decrease in comparison with those of ordered and stoichiometric B1 NbO. By this analogy, the partial density of states of the C-p band in NbC would be heavily changed and would affect Tc through the electronic part of λ in ion-irradiated NbC, where Nb and C vacancies coexist. Furthermore, the phonon anomalies that are crucial for high Tc in NbC (26) could also be fairly affected by a change in the partial density of states of the C-p band, because nonmetal-p and metal-d scattering is important for phonon anomalies (10). It was predicted that lattice distortions have little influence on the results of the Tc calculations in the cluster calculations, and the present results also support this idea because no direct correlation of the variation of Tc with the variations of a 0 and static displacements was observed in the course of the irradiation (11). The agreement between the recovery stages of a 0 and Tc around 250°C (Fig. 5) indicates, however, that a small amount of Tc depression still depends on the lattice distortion, because it is thought that Nb interstitial clustering has occurred at this temperature and the strain field is released by this effect and not by vacancy annihilation. As one can see from Fig. 5, the recovery of Tc at this temperature is much smaller than the recovery in the temperature range from 650 to 850°C, where vacancy annihilation is thought to be predominant. III. ION BEAM IRRADIATION AND ION IMPLANTATION ON REFRACTORY METAL NITRIDES A.

Ion Beam Irradiation Effects on ZrN and HfN

Remarkable changes in the lattice parameters (a 0 ) with preservation of the B1 structure, intensity weakening, and line broadening of the Bragg peaks were also observed in both ZrN and HfN

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films that were ion irradiated at RT. Samples used in these ion beam irradiation experiments are stoichiometric thin films of ZrN with thicknesses of about 170 nm and HfN with thicknesses of about 600 nm deposited on sapphire substrates by RF sputtering using N 2 gas at around ˚ for ZrN and around 4.522 1000°C. These samples have lattice parameters (a 0 ) around 4.573 A ˚ A for HfN and Tc values around 9.2 K for ZrN and around 8.3 K for HfN, respectively. Figure 6 shows the variations of the lattice parameter as a function of ion fluences (200-ke V He ⫹ ions and 600-keV Ar 2⫹ ions for ZrN and 400-keV He ⫹ ions for HfN) and the corresponding values of energy deposited into nuclear collisions Q (eV/atom) for ZrN and HfN films. The fluence necessary to reach a certain value of deposited energy Q is almost 150 times larger for the He irradiation than for the Ar irradiation of ZrN. The agreement between a 0 variations due to He and Ar ion irradiations of ZrN samples on a fluence scale corresponding to the same deposited energy indicates that the residual ions in thin films have little influence and displacements by

Figure 6 The lattice parameter a 0 of ion-irradiated ZrN and HfN thin films as a function of the fluences of 200-keV He, 600-KeV Ar, or 400-keV He and the corresponding value of the deposited energy. Z28 and Z30 denote sample names of ZrN films. H45 and H46 denote sample names of HfN films.

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nuclear collisions are the major origin of the variation in the lattice parameter. The deposited energy Q values that give the maximum a 0 values are shifted to higher values in both nitride films and the relative a 0 increases are smaller than for NbC (∆a 0 /a 0 ⫽ 0.3% in ZrN and ∆a 0 / a 0 ⫽ 0.2% in HfN). The subsequent lattice contractions of ZrN and HfN are smaller than in NbC at the same deposited energy values. In contrast to NbC films, where a large amount of lattice contraction is observed, a 0 values reach to the initial values for both ZrN and HfN samples. For the one-dimensional static atomic displacement amplitudes of the lattice atoms, one can see a variation of static atomic displacements similar to that of the lattice parameter for ZrN as for NbC, whereas the displacements in HfN increase continuously during the irradiations. The increases of the lattice parameter in both ZrN and HfN thin films at the first stage of the irradiations could be attributed to the same origin as in the case of NbC. Isolated nonmetal interstitials should already have been annealed out and the rest could be stabilized in the form of clusters by the irradiation at RT, whereas isolated metal interstitials, some of which can occupy the vacancy sites of nonmetal atoms (antisite defects), should remain even at RT. These metal defects can produce a large strain field and also cause a lattice expansion in these nitrides. The subsequent decrease in the lattice parameter could be due to precipitation of metal atoms, which results in release of the strain in the regular lattice sites. Agreement between the variation of the lattice parameter and that of the static atomic displacements in ZrN supports this idea, because static displacements would become small after the strain release by precipitation. Nevertheless, the continuous increase in the static displacements observed in HfN indicates another mechanism such as stacking fault formation, because a strain field still remains during the decrease of the lattice parameter. The variations of the lattice parameter with composition in ZrN and HfN show unusual behaviors. They have stable phases on both the metal atom–rich side and the nonmetal atom–rich side (1) In both ZrN and HfN, the lattice parameters show slight increases when the nonmetal atom sublattices are defective, whereas they show decreases when the metal atom sublattices are defective (27). This unusual variation is very different from the case of NbC, where no stable B1 phase exists on the nonmetal atom–rich side and nonmetal atom vacancies lead to lattice contraction (21). In the present nitride compounds, the small decrease in the lattice parameter at high irradiation fluence could be attributed to the coexistence of vacancies in both sublattices, because the vacancies in both sublattices have opposite influences on the lattice parameter. The Tc values of the Ar-irradiated ZrN film and the He-irradiated HfN film are shown as a function of the irradiation fluence and the deposited energy in Fig. 7. They decrease continuously with increasing irradiation fluence from 9.2 K down to 3.8 K for ZrN and from 8.3 K down to 3.0 K for HfN. The widths of the transition temperature (temperature difference between 10% and 90% drops in the resistivity) were maintained within 0.4 K during the irradiations. The residual resistivities at 11 K (ρ 0) and the residual resistivity ratios (RRR ⫽ ρ RT /ρ 0) were measured before and after the irradiation procedures. The residual resistivities increase continuously from the initial value of ρ 0 ⫽ 30 µΩ cm to 200 µΩ cm in ZrN and from the initial value of ρ 0 ⫽ 230 µΩ cm to 490 µΩ cm in HfN. The residual resistivity ratios decrease continuously from the initial value of RRR ⫽ 3.0 to 1.15 in ZrN and from the initial value of RRR ⫽ 1.15 to 1.05 in HfN. The continuous decreases in Tc during the irradiations in ZrN and HfN should be relevant to the vacancies, because no direct correlation between the variations of Tc and those of the lattice parameter suggests little influence by the lattice distortion. Because in substoichiometric phases of HfN, Tc remains constant on the metal atom–rich side and shows a decrease with the content of nonmetal atoms on the nonmetal atom–rich side (27), metal vacancies might be mainly responsible for the Tc depression in HfN.

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Figure 7 The superconducting transition temperature T c of Ar-irradiated ZrN thin film and He-irradiated HfN thin film as a function of the ion fluences and the deposited energy. Transition widths are less than 0.4 K.

B.

Ion Implantation into ZrN

1. Structural Properties ZrN and HfN have attracted interest because of the insulating property of the metastable higher nitride state. Johansson et al. (28) have investigated the structural and electrical properties of the phase Z r3 N 4 synthesized with dual ion beam deposition. Schwarz et al. (13) have calculated the electron energy band structure of this new phase and have proposed this material as an ideal material for building Josephson junction devices. Experiments on N ion implantation in ZrN thin films were performed in order to investigate the process of N atom incorporation in this material and its influence on the structure, electrical resistivity, and superconductivity. Polycrystalline stoichiometric thin films of ZrN with thicknesses of about 250 nm deposited on single-crystal sapphire substrates by RF sputtering using Ar and N 2 gas were used for the implantation samples. The partial pressure was 2 ⫻ 10 ⫺2 torr for Ar gas and in the range 1.7 to 8 ⫻ 10 ⫺3 torr for N 2 gas, and the substrate temperature was maintained at 1000°C during the deposition. Samples had a well-developed polycrystalline ˚ , Tc around 9.5 K, and structure and had values of the lattice parameter (a 0 ) around 4.572 A residual resistivity (at 11 K) around 30 µΩ cm. Nitrogen ions were implanted at RT and at 380°C (high temperature, HT) up to the fluence corresponding to the composition with Zr 3 N 4 (x ⫽ 0.33 in ZrN 1⫹x). Multiple-energy implantation with a suitable fluence ratio was employed in order to achieve homogeneous doping of the films throughout the depth. In a typical case of a sample of thickness 250 nm, N implantation was performed at energies of 40, 90, and 200 keV with a fluence ratio of 1:2.1:6. In this case, doping of 1% of the existing N concentration (x ⫽ 0.01 in ZrN 1⫹x) requires a total fluence of 1.49 ⫻ 10 16 N/cm 2 . Throughout the whole implantation process at both RT and HT, the B1 structure was

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preserved and no other phase was observed. An initial increase followed by a decrease in the lattice parameter was observed for the low-dose implantation such as in Ar (600 keV)–irradiated samples. In the Ar irradiation experiments, the range of the Ar ions was beyond the film thickness. The agreement of the lattice parameter variations between the N-implanted and the Arirradiated samples in the low-fluence region could imply a major influence of defects (displaced atoms, vacancies, and their clusters) induced by the implantation and a minor influence of implanted N atoms on the lattice expansion and contraction, because of the much smaller concentration of the residual irradiated atoms throughout the film thickness in the Ar-irradiated samples. However, the observed reincrease in the lattice parameters in N-implanted samples at RT in the high-fluence region reflects the influence of the implanted N atoms on the lattice expansion. In Fig. 8, lattice parameters in the ZrN films implanted with N ions to higher fluences at RT and at HT are shown as a function of the implanted N atom concentration x. Here the lattice parameter decreases monotonically at HT and increases monotonically at RT. The color of the samples implanted at both RT and HT changed from shiny gold to dark brown during the implantation processes below x ⫽ 0.25 and showed an obscure transparency with a dark green color at the composition with x ⫽ 0.33. Values of atomic displacements for both RT implantation and HT implantation increased with the concentration of implanted N atoms. Nevertheless, displacement values for RT implantation exceed those for HT implantation by 50 to 100% reflecting the nature of the highly distorted structure. As stated, the lattice parameter in ZrN shows an unusual dependence on the composition. It shows a decrease in the N-rich side and remains constant in the Zr-rich side (1). The augmented ˚ spherical wave (ASW) calculations of Schwarz et al. show the lattice parameter around 4.52 A in Zr 3 N4 , where 25% of Zr sites are left vacant (13). The progressive decrease of the lattice ˚ in the N-implanted ZrN films at HT, therefore, suggests incorporaparameter down to 4.556 A tion of most of the implanted N atoms in the substitutional sites, leaving vacancies at Zr sites, whereas the increase of the lattice parameter in the samples implanted at RT could be due to

Figure 8 The lattice parameter a 0 of N-implanted ZrN films for RT implantation and HT (at 380°C) implantation as a function of the implanted N atom concentration x in the high-fluence region.

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an increase of the strain field in the host lattice with incorporated extra N atoms mainly in the interstitial sites. The larger static atomic displacements in the host lattice in the samples implanted at RT than in the samples implanted at HT also suggest high lattice distortion in the implanted samples at RT. 2. Electrical Resistivity and Superconducting Transition Temperature Increases in the electrical resistivities at RT (ρ RT ) and 11 K (ρ 0 ) in N-implanted ZrN films at both RT and HT are shown in Fig. 9 as a function of the implanted N atom concentration. Although we can see higher resistivities with an increasing N atom concentration, full insulating properties were not reached even up to the final implantation concentration of x ⫽ 0.33 with both RT and HT implantations. Resistivities in the samples implanted at HT exceed considerably those in the samples for RT implantation in the initial implantation processes. They showed, however, rather constant values at x ⫽ 0.22 and smaller values than those for RT implantation at the final implantation step with x ⫽ 0.33. Semiconducting behavior in resistivities where the ρ 0 is in excess of ρ RT was observed beyond x ⫽ 0.25 for RT implantation and beyond x ⫽ 0.15 for HT implantation. The Tc in the samples implanted at RT first shows a prominent decrease down to 3.5 K at x ⫽ 0.02 followed by a constant region and degradation below 1.3 K. In the range between x ⫽ 0 and x ⫽ 0.02 for RT implantation, Tc decreases exponentially as a function of the total implanted fluence. The Tc for HT implantation showed a decrease down to 5 K at x ⫽ 0.05 followed by a gradual decrease to 3.1 K at x ⫽ 0.33. The superconducting transition width was maintained within 0.2 K for HT implantation but increased gradually for RT implantation. The increase in the electrical resistivities with implanted N atom concentration could have two origins. One is the localization effects (Anderson localization) due to implantation-induced disorder (29). The other is the change in the electronic band structure due to the occurrence of

Figure 9 Resistivities at RT and at 11 K in N-implanted ZrN thin films for RT implantation and for HT (at 380°C) implantation as a function of the implanted N atom concentration x.

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another phase. Electron energy band calculations based on a simple defect structure indicate that Zr 3 N 4 with 25% Zr vacancies on the B1 lattice has a low density of states at the Fermi energy and suggest that Zr 3 N 4 is almost an insulator (13). The influence of the localization effects could be smaller in the samples implanted at HT rather than RT, because less disorder has been introduced at HT than at RT. Therefore, the larger resistivities in the samples at HT are thought to be due mainly to the change in the electronic band structure as a result of the higher nitride state formation. On the other hand, the change in the increasing behavior of resistivity in the high N concentration region (x ⱖ 0.28) in the samples implanted at HT may imply a change in the mechanism of the direct incorporation of N atoms into the substitutional N sites. The metastable phase of Zr 3 N 4 with 25% vacancies in Zr lattice sites is not known from the equilibrium phase diagram and is based on the model proposed by Johansson et al. (28). They showed experimental results with incorporation of large amounts of noble gas atoms (Ne, Ar, or Xe) into Zr 3 N 4 . This can support the picture of the structure with vacant Zr sites, because all these noble gas atoms are considerably larger than the N atoms and it is impossible for the gas atoms to occupy the N lattice sites. Higher nitride states could be produced especially with the HT implantation, as discussed earlier.

IV. ION BEAM IRRADIATION EFFECTS ON BP A.

Ion Beam Irradiation Effects on BP

In contrast to that of Si or GaAs, the study of ion beam irradiation effects on BP is very limited. There has been little knowledge of the nature of defects induced by irradiation or implantation for BP (30). It is of interest to investigate the basic properties of defects in ion-implanted BP and the potential of BP in radiation environments, which can extend its applications in a new field. For these purposes, knowledge of the structural disorder induced by irradiations with MeV ions in this material is important. Figure 10 shows RBS-channeling spectra (P yield) for a singlecrystalline BP sample observed with 2-MeV He ions at 135° to the beam incidence direction

Figure 10 RBS-channeling spectra (P yield) for a CVD-grown BP sample observed with 2-MeV He ions at 135° to the beam incidence direction. Spectra are shown for the random and the aligned incidences before and after 1-MeV Ar irradiations with fluences up to 3.0 ⫻ 10 14 Ar/cm 2.

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(31). The BP samples were prepared by thermal decomposition of B 2 H 6 and PH 3 on Si(100) (14). Spectra are shown for the random and the aligned incidences before and after 1-MeV Ar irradiations with fluences up to 3.0 ⫻ 10 14 He/cm 2 at RT. The calculated range of 1-MeV Ar in BP is nearly 790 nm with straggling of 105 nm. After the irradiation with 3.0 ⫻ 10 14 Ar/ cm 2 , the maximum aligned yield reached the random yield and a broad peak of dechanneling yield in the depth direction was observed. The structure that exhibits the broad disordered region in depth is similar to that in GaAs and a feature of compound semiconductors. Full amorphization was observed after 1.4 ⫻ 10 15 Ar/cm 2 irradiation. For the Ar-irradiated sample, Fig. 11 shows angular scans of the He ion yield backscattered by P atoms and α yield by the 11B( p,α) 8 Be nuclear reaction of a BP sample before and after 1-MeV Ar irradiations. The interferences between sublattices should be taken into account in the dechanneling by the individual sublattices because displacements of atoms in the heavier sublattice could have a large influence on the dechanneling yield in the lighter sublattice. Atomic displacements in the P sublattice could affect the dechanneling by steering the incident ions that make close collisions with atoms in the B sublattice for BP. Even when this effect is taken into account, the increase of the dechanneling yield for the B sublattice is still larger than when the same amounts of displacement are assumed (32). Therefore, the B sublattice shows a large susceptibility to irradiation, and this might be due to the difference between values of the displacement energy (E d ) for B atoms and P atoms. With the investigation of the dependence of the dechanneling rate dχ/dz (the variation of dechanneling yield χ as a function of depth z) on the analyzing ion beam energy and the relation that expresses the product of the dechanneling cross section σ D and the defect concentration N s as σ D Ns ⫽ ∆(dχ/dz) (1 ⫺ χ min) ⫺1, where χ min is the minimum dechanneling yield, one can extract some features of defects in ion-irradiated BP (33,34). This analysis revealed that a stacking fault seems predominant in Ar-irradiated BP. On the other hand, for light ion irradiation (2MeV He) where the defect region is very broad in depth and does not show any defect peak, the dependence of the value of σ D N s has revealed that sparse amorphous clusters or lattice distortions with small static displacements mainly induced by antisite defects are the major

Figure 11 Angular scans of the He ion yield backscattered by P atoms and α yield by the 11B( p,α) 8Be nuclear reaction of a BP sample before and after 1-MeV Ar irradiations. The angle φ indicates the orientation of the tilt plane relative to the {110} crystal plane.

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defect features for He-irradiated BP samples that have the same level of increase of the dechanneling yield. In this case, however, similar large susceptibilities for the B sublattice have also been observed. The difference in the defect structure between light and heavy ion irradiations can be attributed to the difference in the deposited energy density in the collision cascades. B.

Ion Beam–Induced Reactions of Metal Thin Films and BP

The reactions of metal films with BP substrate are useful from the viewpoint of device application of this compound. For Ni on BP(100), the thermal reaction processes were observed to start between 350 and 400°C. Transient metastable phases were formed at a temperature between 400 and 450°C. Formation of the crystalline phase corresponding to a mixed binary phase (NiB ⫹ Ni 3 P) was observed at 450°C. A second phase with less Ni content was observed to be formed beyond 600°C (35,36). On the other hand, the solid-phase reactions of Ni thin films with BP(100) by the ion bombardment process have also been investigated from the viewpoints of advantage in ion process for local process capability and low-temperature process possibility. Figure 12 shows RBS spectra of the reacted layer of Ni on BP with ion bombardments at various temperatures. BP samples with a 50-nm-thick Ni thin film were bombarded with 600-keV Xe 2⫹ ions at liquid nitrogen (LN 2 ) temperature, RT, and 200°C. The feature of inhomogeneous reaction was observed for the samples bombarded at LN 2 . The reaction induced at RT shows partly reacted

Figure 12 RBS spectra of Ni thin film (50 nm) on BP(100) bombarded with 600-keV Xe 2⫹ at various substrate temperatures to a constant fluence of 5 ⫻ 10 15 Xe/cm 2.

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behavior of the Ni layer and the reacted layer has the same composition as that induced at 200°C. The fully reacted layer with ion beam bombardments at 200°C has revealed a crystalline phase that is the same as that of the thermally induced first phase, whereas the reacted layer induced at LN 2 and RT shows an amorphous phase. The progress of the reacted layer thickness as a function of the fluence of 600-keV Xe 2⫹ ions was observed in the fluence range from 1 ⫻ 10 14 to 8 ⫻ 10 15 Xe/cm 2 at various substrate temperatures. The full reaction (50 nm) was observed with bombardments to 7 ⫻ 10 14 Xe/cm 2 at 200°C. The results reflect the progress of the reaction depending linearly on the ion fluence. The dependence of the reaction progress in the thermal process examined at temperatures between 350 and 475°C has shown approximately linear dependence of the reaction on the duration of the annealing time. In the ion beam–induced process, an overall linear dependence of the reacted layer on the ion fluence in the temperature range between RT and 300°C was observed, and the reaction had a small temperature dependence below RT and a strong temperature dependence above RT. Although the activation energy for the reaction in the thermal reaction process was observed to be 1.3 ⫾ 0.3 eV, an activation energy of 0.31 ⫾ 0.06 eV was obtained for the ion beam–induced process at elevated temperatures above 100°C. The strong temperature dependence of the ion beam–induced reaction process above 100°C could reflect the feature of radiation-enhanced reaction. Intracascade effects that lead to the collapse of point defects into dislocation loops could be responsible for the reaction, and these intracascade effects should also be taken into account in the present Ni-BP system, where the activation energy is relatively low. The reaction at temperatures lower than RT could be attributed to the cascade mixing mechanism, which dominates at lower temperatures and is relatively insensitive to temperature. Linear dependence of the reaction on bombarding ion fluence is a feature of the reaction of the system of Ni on BP. In silicide formation in some metal-Si systems linear dependence of the reaction progress on the ion fluence was observed in the ion beam–induced reaction (37). This is thought to be due not to a simple diffusion process but mainly to the nonequilibrium nature of the reaction process. In the Ni-BP system, amorphous phase formation at RT and metastable phase formation in the thermal process suggest a complex mechanism of nonequilibrium reaction. As an example of the reaction of metal films on a refractory compound semiconductor, a thermal reaction process (38,39) and ion beam– and laser-induced processes were reported for Ni on SiC (40). In these cases, the first reacted phase was induced around 500°C and was found to be a binary phase (Ni 31 Si 12 or Ni 2 Si); no reaction of Ni with C atoms was observed. In contrast to the case of SiC, the reaction in the Ni-BP system was induced at lower temperatures and the mixed binary phase of NiB ⫹ Ni 3P was the first phase of the Ni thin film on BP. The preceding metastable phase below 450°C in the thermal reaction process before formation of the first stable phase could be due to competing Ni-B and Ni-P reactions. The dominant moving species in the reaction of Ni on BP is thought to be Ni from the results for oxygen accumulation between the reacted layer and the nonreacted layer (35,36). C.

Ion Beam–Induced Crystallization for Preamorphized BP

Ion beam–induced epitaxial crystallization (IBIEC) has attractive features from the viewpoint of beam-solid interactions especially in semiconductors. Specific properties and phenomenological understandings of IBIEC in Si have been hitherto obtained on the basis of extensive investigations (41–45). The features of the process have provided not only a new field of investigation of beam-solid interactions but also a possibility of process application of Si because of its advantages, such as processing at low temperatures, local process capability, and metastable phase formation by impurity atom incorporation at a nonthermal equilibrium concentration. Crystalline growth properties of IBIEC in III-V compound semiconductors are, however,

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less well known than in Si (46). In the refractory material BP, IBIEC was observed at extremely lower temperatures than those expected from the high melting point (47,48). For the IBIEC experiments, a 90-nm-thick amorphous surface layer on CVD-grown BP(100) was formed by 100-keV As implantation to a dose of 6 ⫻ 10 14 As/cm 2 at RT. The samples were preannealed at 450°C for 15 min to provide an abrupt crystalline-amorphous (c/a) interface. The amorphized samples were then bombarded with 400-keV Ar and Kr ions at 350°C. The current density was changed from 0.06 to 4 µA/cm 2. Calculated values of nuclear energy deposition ν n (E ) at the initial c/a interface are 0.45 and 1.9 keV/nm per ion for 400-keV Ar and 400-keV Kr, respectively. The beam incidence direction for implantation and IBIEC was set to 7° with respect to the sample surface normal. Analyses of the crystalline growth and structural properties of the grown layers were performed by the RBS-channeling technique using 2-MeV He ⫹ ions. The scattering angle used was 105° to the beam incidence direction. RBS-channeling spectra (P yield) representing IBIEC in the P sublattice of BP by 400KeV Ar bombardments at 350°C are shown in Fig. 13, where planar growth up to the surface is demonstrated. Nevertheless, a deviation from the stoichiometric composition (decrease of P concentration) was observed in the last stage of crystalline growth. Recovery in the B sublattice could also be observed in the lower energy region in RBS spectra, but the large dechanneling yield near the end of the range of bombarding ions affects precise analyses of the growth in the B sublattice. It is noted that IBIEC for BP was induced at such a low temperature in spite of the high critical temperature for Solid Phase Epitaxial Growth (SPEG) (above 800°C), which was confirmed in the separate experiments. Overall linear dependences on the ion dose in the initial bombardment stages (⬍1.5 ⫻ 10 15 Ar/cm 2) could be seen at 250–400°C, whereas growth thicknesses show deviations from linear growth at higher doses. As shown in Fig. 13, fairly high doses of Ar ions were required to attain the final crystallization up to the surface. This

Figure 13 Random and ⬍100⬎-aligned RBS spectra representing crystalline growth of a-BP by IBIEC with 400-keV Ar at 350°C (P yield). The initial amorphous layer was obtained by 100-keV As implantation to a dose of 6 ⫻ 10 14 As/cm 2 at RT.

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feature is different from the IBIEC in GaAs. A weak dependence of the crystalline growth rate on the ion species used for preamorphization (Ar, As, and P) was also observed in BP (47). Figure 14 shows crystalline growth rate versus nuclear energy deposition density at 350°C in a-BP (amorphous-BP) as a function of nuclear energy deposition density rate and corresponding ion current density (dose rate) for 400-keV Ar and Kr bombardments. The results also reflect the large dependence of growth rate on ion dose rate in BP, although the growth rate with Kr is larger than with Ar at the lowest dose rate. The large dependence of the growth rate on the dose rate implies that the dynamic behavior of the defect motion is also responsible for the IBIEC process in BP. In the same nuclear energy deposition regime, heavy ions produce a low density of collision cascades with a large cascade volume, whereas light ions produce a high density of collision cascades with a small cascade volume. The interaction among collision cascades becomes prominent in the higher dose rate region for heavy ion bombardments because of the large volume of the collision cascade and this can prohibit effective migration of defects to the c/a interface or rearrangements of atoms at the interface, resulting in the decrease in growth rate in IBIEC. On the other hand, in the lower dose rate region, where interactions between collision cascades are small, the interaction between defects in a cascade that forms some type of defect complex

Figure 14 Crystalline growth rate per nuclear energy deposition density at 350°C for BP preamorphized by 100-keV As implantation as a function of ion current density of 400-keV Ar and 400-keV Kr and corresponding nuclear energy deposition density rate.

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could have a crucial role. Characterization for amorphous silicon (a-Si) by positron annihilation experiments has revealed that small vacancies (trivacancies and/or quadrivacancies) exist in the IBIEC-grown Si layer (49) and some of the dangling bonds are located at small vacancy-type defects in a-Si (50). If the dangling bond is responsible for IBIEC, the small vacancies formed by ion bombardments in the amorphous layer could have a crucial role. The reason that Krinduced IBIEC has shown a higher growth rate per nuclear energy deposition density (nuclearly normalized growth rate, NNGR) than Ar-induced IBIEC in BP in the lowest dose region (Fig. 14) might be that highly efficient small vacancy cluster formation is caused by high-density defect formation in a collision cascade by heavier ion bombardments. Therefore the dependence of NNGR on ion species is thought to be a result of the competitive process between the interaction of collision cascades and the interaction of defects in a cascade.

V.

CONCLUSIONS

Ion beam irradiation–induced changes in structure and superconducting properties were investigated for refractory metal carbides and nitrides. Structural disorder in He- and Ar-irradiated thin films of NbC, ZrN, and HfN and single crystals of NbC has been investigated by X-ray diffraction and channeling experiments, respectively. An appreciable change of the lattice parameter with the preservation of B1 structure and a continuous Tc depression down to around 3–4 K during the irradiation have been observed. The influences of He and Ar irradiations on both the lattice parameter and Tc are nearly the same at a given deposited energy value. The increase of the lattice parameter in the low-fluence range is attributed to interstitial metal defects including antisite defects, and the subsequent decrease of the lattice parameter is attributed to the clustering or precipitation of metal atoms. The Tc depression would be due mainly to both metal and nonmetal vacancies. Examples of incorporation of implanted N atoms in ZrN thin films are presented with RT implantation and with HT implantation. X-ray diffraction experiments showed the B1 structure to be stable throughout the implantation. The N atoms are thought to be incorporated mainly in interstitial sites with RT implantation and in substitutional sites with HT implantation. The increase in the resistivity in the samples implanted at RT should be due mainly to localization effects, and that in the samples implanted at HT should be due to the change in the electronic band structure. Although full insulating properties due to Zr 3 N 4 phase formation could not be obtained and Tc remained at 3.1 K in the HT implantation experiments, fairly large amounts of implanted N atoms are thought to be incorporated in the substitutional sites with HT implantation. This emphasizes the usefulness of the ion implantation technique in the modification of B1 phase compounds. Reactions were induced by energetic heavy ion bombardments from LN 2 temperature to 300°C. A metal-rich mixed binary phase was also formed in the ion beam–induced reactions at 200°C, whereas an amorphous layer with the same composition was formed by the bombardments at RT. The crystalline phase has the same compositions and X-ray diffraction patterns for thermal and ion beam–induced reactions. The reaction progress in the thermal process depends approximately linearly on the duration of the annealing time with an activation energy E a ⫽ 1.3 ⫾ 0.3 eV. A linear dependence of the reacted thickness on the ion fluence was observed between RT and 300°C. An activation energy of E a ⫽ 0.31 ⫾ 0.06 eV was observed in the ion beam–induced process above 100°C. In addition to the high-energy ion irradiation properties where large susceptibility of the B-sublattice was observed, IBIEC in BP has revealed crystallization up to the sample surface. A large dependence of the growth rate especially with heavy ions on the ion dose rate was

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observed for BP. This is thought to reflect a crucial role of interactions between collision cascades and between defects in a collision cascade. The IBIEC experiments performed for BP have shown a novel feature of the epitaxial growth at lower temperatures for compound semiconductors.

REFERENCES 1. LE Toth. Transition Metal Carbides and Nitrides, Academic Press, London, 1971. 2. D Dew-Hughes, R Jones. Appl Phys Lett 36:856, 1980. 3. B Enger, J Geerk, HC Li, G Linker, O Meyer, B Strehlau. Proceedings of 18th International Conference on Low Temperature Physics, Kyoto, 1987, p 2141. 4. N Kobayashi, G Linker, O Meyer. J Phys F Metal Phys 17:1491, 1987. 5. J Billingham, PS Bell, MH Lewis. Acta Crystallogr A28:602, 1972. 6. M Sauvage, E Parthe. Acta Crystallogr A28:607, 1972. 7. V Moisy-Maurice, CH de Novion, AN Christensen, W Just. Solid State Commun 39:661, 1981. 8. TH Metzger, J Peisl, R Kaufmann. J Phys F Metal Phys 13:1103, 1983. 9. R Kaufmann, O Meyer. Phys Rev B28:6216, 1983. 10. M Schwarz, N Ro¨sch. J Phys C Solid State Phys 9:L433, 1976. 11. G Ries, H Winter. J Phys F Metal Phys 10:1, 1980 12. BM Klein, DA Papaconstantopoulos, LL Boyer. Phys Rev B22:1946, 1980. 13. K Schwarz, AR Williams JJ Cuomo, JHE Harper, HTG Hentzell. Phys Rev B32:8312, 1985. 14. Y Kumashiro, Y Okada, S Gonda. J Cryst Growth 70:7, 1984. 15. JP Biersack, LG Haggmark. Nucl Instrum. Methods 174:257, 1980. 16. G Linker. Nucl Instrum Methods 182/183:501, 1981. 17. R Kaufmann, O Meyer. Radiat Effects 52:53, 1979. 18. LC Feldman, JW Mayer, ST Picraux. Materials Analysis by Ion Channeling. New York: Academic Press, 1982. 19. D Gosset, C Allison, J Morillo. Ann Chim Fr 9:99, 1984. 20. J Morrilo, CH de Novion, J Dural. Radiat Effects 55:67, 1981. 21. LE Toth, M Ishikawa, YA Chang. Acta Metall 16:1183, 1968. 22. RC Dynes, JM Rowell, PH Schmidt. In: (GK Shenoy, BD Dunlop, FY Fradion, eds.) Ternary Superconductors. Amsterdam: North-Holland, 1971, p 169. 23. AL Giorgi, EG Szklarz, EK Storms, AL Bowman, BT Matthias. Phys Rev 125:837, 1962. 24. HR Khan, CJ Raub, WE Gardner, WA Ferti, DC Johnson, MB Maple. Mater Res Bull 9:1129, 1974. 25. E Wimmer, K Schwarz, R Podloucky, P Herzig, E Neckel. J Phys Chem Solids 5:439, 1982. 26. W Weber. Phys Rev B8:5093, 1973. 27. AL Giorgi, EG Szklarz, TC Wallace. Proc Br Ceram Soc 10:183, 1968. 28. BO Johansson HTG Hentzell, JME Harper, JJ Cuomo. J Mater Res 1: 442, 1986. 29. PW Anderson. Phys Rev 109:1492, 1958. 30. K Gamo, H Yagita, M Takai, S Namba, M Takigawa. Radiat Effects 47:64, 1980. 31. N Kobayashi, Y Kumashiro, I Nashiyama, T Nishijima. In: T Sebe, I Yamamoto, eds. Application of Ion Beams Tokyo: Hosei University, Press, 1988, p 481. 32. DS Gemmel, RL Mikkelson. Radiat Effects 12:21, 1972. 33. KL Merkle, PP Pronko, DS Gemmel, CR Mikkelson, JR Wrobel. Phys Rev B8:1002, 1975. 34. Y Que´re´. Radiat Effects 28:353, 1976. 35. N Kobayashi, Y Kumashiro, P Revesz, Jian Li, JW Mayer. Appl Phys Lett 54:1914, 1989. 36. N Kobayashi, Y Kumashiro, P Revesz, Jian Li, JW Mayer. Mater Res Soc Symp Proc 162:595, 1990. 37. JW Mayer, BY Tsaur, SS Lau, LS Hung. Nucl Instrum Methods 182/183:1, 1981. 38. CS Pai, CM Hanson, SS Lau. J Appl Phys 57:618, 1985. 39. I Ohdomari, S Sha, H Aochi, T Chikyow, S Suzuki. J Appl Phys 62:3747, 1987.

Irradiation Properties 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

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J Narayan, D Fath Y, OW Holland, BR Appleton, RF Davis, PF Becher. J Appl Phys 56:1577, 1984. J Linnros, G Holmen, B Svensson. Phys Rev B32:2770, 1985. J Linnros, G Holmen. J Appl Phys 62:4737, 1987. RG Elliman, JS Williams, WL Brown, A Lieberich, DM Maher, RV Knoell. Nucl Instrum Methods B19/20:435, 1987. KA Jackson. J Mater Res 3:1218, 1988. J Nakata. Phys Rev B43:14643, 1991. N Kobayashi, M Hasegawa, H Kobayashi, N Hayashi, M Shinohara, F Ohtani, M Asari. Nucl Instrum Methods B59/60:449, 1991. N Kobayashi, H Kobayashi, H Tanoue, N Hayashi, Y Kumashiro. Mater Res Soc Symp Proc 157: 119, 1990. N Kobayashi. Thin Solid Films 270:307, 1995. N Hayashi, R Suzuki, M Hasegawa, N Kobayashi, S Tanigawa, T Mikado. Phys Rev Lett 70:45, 1993. RA Hakvoort, A van Veen, H Shcut, MJ van den Boogaard, AJM Bernstein, S Roodra, PA Stolk, AH Reader. In: E Ottewitte, AH Weiss, eds. Slow Position Beam Technique for Solids and Surfaces. New York: American Institute of Physics, 1994, p 48.

11 Transition Metal Carbide Field Emitters Yoshio Ishizawa Iwaki Meisei University, Iwaki, Fukushima, Japan

I.

INTRODUCTION

The phenomenon that electrons are emitted from a metal surface or a semiconductor surface in the presence of a strong electric field is called field emission (FE). The emission mechanism has been well understood as electron tunneling through the surface potential barrier (1). Features of field emission are high brightness and coherence and its small source size. Cold field emission sources that operate at room temperature have attracted much attention in the fields of highbrightness cathodes and vacuum microelectronics (2). Investigations (3–8) of field emission characteristics from atomic sources constitute a new field in cold field emission. Among conventional cathode materials, the present field emission source is a tungsten single crystal. However, the field emission current from a tungsten source is not very stable and a more stable field emission source is expected to be developed for wide use. The transition metal carbide emitters are promising field emission sources that produces highly stable emission currents (9,10). The transition metal carbides (TMCs) with an NaCl-type structure such as TiC and NbC have strong advantages as field electron emitters. These carbides have high melting temperatures of around 3000–4000°C and form some of the most stable materials (11,12). Important features of TMCs are high mechanical strength, low ion-sputtering rate, low electrical resistivity, high chemical inertness, and low work function. The main bonding is strong covalency between metal d and carbon p states. The group IV carbides are semimetals, and the group V carbides are typically metals from standard band theory. Wide nonstoichiometry is another feature of carbides, indicating that there are carbon-deficient carbides without metal deficiencies. Many properties depend largely on the carbon vacancy concentration. Therefore the exact chemical composition is quite important for carbides. In the case of TiC x, the NaCl structure exists in the composition range of x from 0.55 to 0.97. In Table 1, several properties of TMCs with the NaCl-type structure are collected and compared with each other. In this chapter, we focus on FE characteristics of TMC emitters using ⬍110⬎-oriented tips that show highly stable emission at room temperature because of the appropriate surface processing (9,10). That is, emission currents from the graphite-covered surface on carbides are highly stable because of the surface processing. In the case of the TiC FE source. FE properties of clean surface tips were studied by several investigators (13–17). Emission current instabilities such as step- and spikelike fluctuations were found as a feature of the TiC FE source. In some cases, stable emission currents were observed 269

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Table 1 Features of Transition Metal Carbides with the NaCl-Type Structure a,b Property Melting Point b(K) Microhardness (kg/mm 2) Electrical resistivity (µΩ cm) Work function c (eV) Nonstoichiometry (C/M)

TiC

ZrC

HfC

NbC

TaC

3340 2900 130 3.8 0.55–0.97

3693 2700 40 4.0 0.60–0.99

4201 2300 34 4.5 0.60–0.98

3873 2400 32 4.2 0.72–0.98

4256 1600 18 4.3 0.75–0.99

a

Properties of the TMC with nearly stoichiometric composition at room temperature. Highest melting point temperatures at the relevant composition. c The value for the (100) clean surface (44,46). b

with appropriate flashing temperatures. However, it is difficult to obtain stable emission currents with good reproducibility. The surface-processed tip overcame obstacles of emission instability (18,19). It was also found that emission currents from graphite-covered surfaces of NbC tips are highly stable (20). These excellent FE properties are common features among the group IV and group V carbides.

II. FIELD EMISSION PROPERTIES OF TRANSITION METAL CARBIDE EMITTERS A.

Field Emission Patterns and Emission Characteristics of Transition Metal Carbide Emitters

1. Single-Crystal Tips There have been several investigations of the FE properties of the TMCs. The FE properties of TiC were first reported by Senzaki and Kumashiro (13) in 1974. Since then, many papers have been published on TiC (14–17,21–27), ZrC (17,24), HfC (17), NbC (20), and TaC (23,28,29). Of these TMCs, we focus on TiC as a typical case of the group IV carbides and NbC as a typical case of the group V carbides and compare TiC with NbC. TiC x and NbC x single crystals with nearly stoichiometric (x ⫽ 0.96) and highly uniform composition were grown by the zone leveling–floating zone technique (30,31). Single-crystal rods with approximate dimensions of 0.2 ⫻ 0.2 ⫻ 3 mm were cut from a single crystal with a spark-erosion machine. The rod axis was selected along the ⬍100⬎, ⬍111⬎, or ⬍110⬎ direction. Then the rod was spot welded at a tantalum hairpin wire and electrolytically sharpened to a tip with a radius of about 0.1 µm. An expanded view of the carbide single-crystal tip is shown in Fig. 1. The single-crystal tip was then set in the ultrahigh vacuum system. In this experiment, the carbide tips were operated at room temperature, and the FE patterns and emission currents were studied to clarify emission characteristics of TMC emitters. 2. Field Emission Patterns In order to get the FE pattern from a clean surface, the single-crystal tips of TiC⬍100⬎ and ⬍110⬎ emitters were flash heated up to 1500–1600°C in a high-vacuum system. Figure 2a and c show typical FE patterns from clean surfaces of these tips (9). The FE patterns changed from asymmetrical patterns to symmetrical patterns through several flash-heating procedures. The ⬍100⬎ tip shows a fourfold symmetrical pattern, and the ⬍110⬎ tip shows a twofold symmetrical pattern. The ⬍111⬎ tip also shows a threefold symmetrical pattern, which is not shown in

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Figure 1 Expanded view of carbide ⬍110⬎ field emitter tip. (From Ref. 18.)

Fig. 2. It was clarified experimentally that these emission patterns do not change even on exposure to a gas such as oxygen up to 2000 L (Langumuir; 1 L ⫽ 1.33 ⫻ 10 ⫺4 Pa s). This property of the FE pattern is much different from that of a tungsten tip. The FE patterns can be interpreted as follows. In TiC, the lowest work function of about 3.7 eV appears in the (100), (110), (210), and (310) planes and the highest value of 4.7 eV is in the (111) plane (32). It is easily predicted from this knowledge that a ⬍100⬎-oriented tip should show an FE electron beam at the center if the electrons are emitted from a plane with a low work function. The experiment does not show the predicted pattern. There is no electron beam at the center as shown in Fig. 2a. The FE patterns are related to the tip shape change. The tip shape becomes a polyhedron composed of the (100) and (111) planes after flash heating above 1500° C, because the surface energy of the (100) and (111) planes in TiC is relatively low compared with those of other crystal planes (32). The polyhedral shape of the tip was directly confirmed by field ion microscopy (FIM) studies of a TiC single crystal (14). The tip has several sharp points on the top, which are indicated by letters A and B in Fig. 2b and d. Points A and B correspond to bright spots of emission patterns. Therefore, observed emission patterns can be interpreted in terms of emissions from strong electric field portions of the tip. This interpretation is consistent with the insensitivity of the FE patterns to exposures such as oxygen as explained earlier. The TiC⬍110⬎ tip has an electron beam on the center as shown in Fig. 2c. Therefore, the TiC⬍110⬎ tip is important from an application point of view. There are no differences in current stability between the ⬍100⬎ tip, the ⬍111⬎ tip, and the ⬍110⬎ tip as shown later, so most data are taken for the carbide ⬍110⬎ tip. In the case of NbC tips, the same FE patterns as for TiC tips have been observed (10). In order to get the FE pattern for a clean surface, NbC⬍110⬎ tips were flash heated at 1600°C at a pressure of 10 ⫺8 Pa. As in the case of the TiC⬍110⬎ tip, emitted electrons hit the central part of the fluorescent screen as shown in Fig. 2c. This means that electrons are emitted parallel to the tip axis. Therefore, the NbC⬍110⬎ tip is important for applications. Other NbC tips such as the ⬍100⬎ and ⬍111⬎ tips show a fourfold or threefold symmetrical patterns, respectively, the same as for TiC tips.

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Figure 2 Field emission patterns and tip shape models of TiC⬍100⬎ and ⬍110⬎ tips. (From Ref. 9.)

3. Emission Currents The following data on emission currents from carbide tips were obtained at room temperature immediately after flash heating a tip. As it has been found that the stability of the total field emission currents is almost equivalent to that of the local emission currents, measured emission currents are usually the total field emission if there is no indication in the text. The most important thing in evaluating cathode materials is to do the emission experiment under no degassing environment from the anode surface. In order to achieve such a condition, it is necessary to use small currents for the evaluation. Figure 3 shows the applied voltage versus flashing temperature relation for a TiC⬍100⬎ tip while the total emission current is kept constant at 25 nA (16). The TiC tip was first flashed at 1850°C to obtain a clean surface, then exposed to air. The applied voltage was measured at room temperature at a pressure of 1 ⫻ 10 ⫺8 Pa after each flashing temperature. Emission properties of the TiC⬍100⬎ tip are characterized by three temperature regions as shown in Fig. 3. Emission currents are stable in low-temperature region 1 (1300°C ⱕ T ⱕ 1450°C) and high-temperature region 3 (T ⱖ 1700°C) and unstable in temperature region 2 (1450°C ⱕ T ⱕ 1700°C). The total field emission currents with time in temperature regions 1

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Figure 3 Applied voltage versus flashing temperature relation of TiC⬍100⬎ tip at P ⫽ 7.5 ⫻ 10 ⫺9 Pa. (From Ref. 16.)

and 3 are shown in Fig. 4 (17). The current fluctuation is below 0.2%, and the current drift is quite small, below ⫺0.5%/h. However, it was also confirmed that higher currents result in larger fluctuation and drift than in Fig. 4. The current fluctuations are composed of steplike and spikelike fluctuations which are characteristic properties of emission currents from a TiC tip. Figure 5 shows emission currents in temperature region 2 (17). Typical steplike and spikelike fluctuations

Figure 4 Field emission currents with time of TiC⬍100⬎ tip in flashing-temperature regions 1 and 3. P ⫽ 7.5 ⫻ 10 ⫺9 Pa. (From Ref. 17.)

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Figure 5 Field emission currents with time of TiC⬍100⬎ tip in flashing-temperature region 2. P ⫽ 7.5 ⫻ 10 ⫺9 Pa. (From Ref. 17.)

instead of 1/f noise as usually seen in W and metal emitters are seen in the figure. This current fluctuation in TiC is very similar to that in a glassy carbon emitter (33,34). It has also been established that the current stability of TiC tips is independent of the tip axis. Emission currents of the TiC⬍110⬎ tip (18–20) at 1600°C (temperature region 2), which are very important for applications are shown in Fig. 6 (18). The steplike and spikelike fluctuations peculiar to carbide tips are seen. As emission currents are relatively large, the stable temperature regions 1 and 3 cannot be defined in this experiment. Also, the TiC⬍111⬎ tip (24) has the same current feature as ⬍100⬎ and ⬍110⬎ tips. As for the mechanism for noise generation, it is useful to note the noise frequencies. It has been found that the number of steps and spikes of the TiC⬍100⬎ tip is nearly proportional to the product of the current and residual pressure (15). In this case, the number of steps and spikes per 20 min was plotted against the product of total emission currents and the vacuum pressure as shown in Fig. 7 (15). This type of fluctuation is considered to be caused by ionic collision of the residual gas at the tip surface (35). As seen in the figure, the generation frequencies of the steps and spikes are large at 1600°C (region 2) but on heating the tip at 1950°C (region 3) decrease to about 1/40 of that. Here, some speculation is presented to explain the existence of the three temperature regions of current stability. The boundary temperature of 1450°C between regions 1 and 2 is clearly that for making the clean surface. The tip in region 1 is composed of the adsorbed surfaces. Therefore the tip in regions 2 and 3 corresponds to the clean surface and produces almost the same symmetrical FE pattern. The boundary temperature of regions 2 and 3 is relevant to the surface composition. The carbon vacancy at the TiC(100) surface was investigated by impact collision ion scattering spectroscopy (36). This experiment suggests that the observed carbon vacancies al-

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Figure 6 Field emission currents with time of TiC⬍110⬎ tip in flashing-temperature region 2. P ⫽ 3.2 ⫻ 10 ⫺8 Pa. (From Ref. 18.)

Figure 7 Number of steps and spikes per 20 minutes observed in the emission currents from a TiC⬍100⬎ tip with the product of total emission currents (I ) and the background pressure (P). The upper line corresponds to a flashing temperature of 1600°C and the lower line to 1950°C. P ⫽ 1.5 ⫻ 10 ⫺8 Pa. (From Ref. 15.)

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Figure 8 Field emission currents with time of NbC⬍110⬎ tip at a flashing temperature of 1900°C. P ⫽ 1.5 ⫻ 10 ⫺8 Pa. (From Ref. 10.)

most disappear on heating the tip in temperature region 3. That is, the surface composition in region 3 is nearly stoichiometric, whereas the surface in region 2 includes some carbon vacancies produced by the ion sputtering and desorption processes of adsorbed oxygen in addition to the intrinsic vacancies. At the surface with carbon vacancies, the activation energy of atom migration around the vacancies decreases and the atoms near the vacancies are easy to move by thermal excitation and ion bombardment. Moreover, reactivity with residual gases increases more on a surface without vacancies. This difference in the surface properties produces the different emission stability. Emission characteristics of the TiC tip with flash heating in region 3 are quite good, but a higher current produces higher fluctuations, and the tip shape changes after many flashings, which causes a drastic change in the FE pattern. Moreover, it is quite difficult to get to the stable state in region 3. An easier way to get more stable emission was investigated starting with the emission from the adsorbed surfaces, and finally a graphite-covered TiC⬍110⬎ tip was found to be a highly stable field emitter (9,10,18–20). As an important TMC emitter, the NbC⬍110⬎ tip among the group V carbides was selected and investigated. Emission currents from the clean surface of an NbC⬍110⬎ tip (10) are shown in Fig. 8. Step- and spikelike fluctuations superposed on current decrease with time are observed under the ultrahigh vacuum condition. Higher evacuation does not reduce the current fluctuations. The graphite-covered NbC⬍110⬎ tip has been found to be a highly stable emitter (10,20). The next section discusses how they were developed and their highly stable emission.

III. FIELD EMISSION PROPERTIES OF MONOLAYER GRAPHITE/TMC EMITTERS A.

Forming and Evaluating a Monolayer Graphite on TMC

It has been established that TiC⬍110⬎ and NbC⬍110⬎ tips produce highly stable emission currents after optimal surface processing (9,10). Investigations of HfC indicate similar FE properties (37,38). The present surface processing of the tips is carried out in the following two

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Table 2 Forming Conditions and Lattice Constants of Monolayer Graphite on Transition Metal Carbide Surfaces Substrate

Forming condition (°C, L)

TiC(001) W/TiC(001) TiC(111) ZrC(001) ZrC(111) HfC(001) HfC(111) NbC(001) NbC(111) TaC(001) TaC(111)

1250, 1100, 1100, 1100, 1050, 1500, 1050, 1250, 1100, 1500, 1100,

7 ⫻ 10 5 30,000 200 1 ⫻ 10 6 300 1 ⫻ 10 6 200 50,000 300 50,000 200

Lattice constant (nm) 0.247 0.245 0.250 0.247 0.250 0.249 0.247 0.252 0.246 0.253

Source: Refs. 40–46.

steps. First, the clean surface tips are heated at 1000–1100°C with the voltage off in a gas such as ethylene (C 2 H 4 ) for a suitable exposure time. Ethylene is a typical reaction gas in hydrocarbon systems. Second, the total field emission of 10–20 µA is extracted at room temperature after evacuation into the ultrahigh vacuum and maintained at least for 30 min. After this procedure, the effects of the surface processing appear. The first effect is a change in the FE pattern, the second is an increase in the emission currents under the constantvoltage condition, and the third is stabilization of the emission currents. These effects are always reproduced by the same procedure. This is a general phenomenon among transition metal carbides. It has to be noted that monolayer graphite (MLG) can be synthesized on the tip surface due to the surface processing using ethylene. This was confirmed by forming monolayer graphite on the surfaces of carbide single-crystal disks under the same condition as the surface processing of the tip (39–41). Monolayer graphite can be formed on the flat surfaces by heating the single-crystal carbide disks in an ethylene atmosphere. It has been found that the (111) surface is much more reactive than the (001) surface. The forming conditions on carbide surfaces (40–46) are summarized in Table 2. In the case of the TiC(111) surface, minimal ethylene exposure is 100–200 L at 1100°C. It is very difficult to form MLG on a TiC(001) surface, indicating that exposures over 1 million L using ethylene gas are needed (45). In the case of the NbC(111) surface, minimal ethylene exposure is 100 L at 1000–1100°C, and more than about 25,000 L exposure at 1100–1250°C is needed to form graphite on an NbC(100) substrate. Forming graphite on carbide surfaces can be characterized and confirmed by low-energy electron diffraction (LEED), Auger electron spectroscopy (AES), high-resolution electron energy loss spectroscopy, and ultraviolet photoelectron spectroscopy. Figure 9a shows a LEED pattern of a graphite overlayer on NbC(111) (41) after 300 L exposure at 1100°C: six fundamental spots of the graphite overlayer in addition to fundamental substrate spots with satellite spots. The satellite spots are attributable to multiple diffraction. The lattice constant of the graphite overlayer is estimated to be 0.252 ⫾ 0.002 nm. This is about 2% larger than that of pristine graphite. A LEED pattern of the graphite overlayer on NbC(100) after 50,000 L exposure at 1250°C shows a ring pattern with 12 spots on it and fundamental substrate spots as shown in

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Figure 9 LEED pattern of monolayer graphite on NbC single-crystal surfaces. (a) Monolayer graphite on the NbC(111) surface, E ⫽ 117.3 eV. (b) Monolayer graphite on the NbC(100) surface, E ⫽ 170.1 eV. (From Ref. 41.)

Fig. 9b. The former shows a randomly oriented graphite layer and two-domain epitaxial parts. The estimated lattice constant is 0.247 ⫾ 0.001 nm, which is the same as that for pristine graphite. A more powerful technique for identifying the graphite overlayer is high-resolution electron energy loss spectroscopy. Figure 10a and b are phonon dispersion relations of the graphite overlayer on NbC(100) and NbC(111) surfaces, respectively (10,41). The phonon wave number parallel to the surface is obtained from the electron energy and the scattering geometry according to the momentum conservation law (40). The phonon dispersion relation also indicates that the

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Figure 10 Phonon dispersion relations of monolayer graphite on NbC single-crystal surfaces. (a) Monolayer graphite on the NbC(100) surface. (b) Monolayer graphite on the NbC(111) surface. (From Ref. 10 and 41.)

overlayer is graphite and the six branches of the phonon indicate that the graphite overlayer consists of a single layer. This is monolayer graphite, which is also confirmed by other data such as LEED intensity, AES intensity, and the π band dispersion relation (42,44,45,47–49). It is evident from Fig. 10 that there are six distinct phonon modes in the monolayer graphite. The LO branch is a longitudinal optical mode. The LA branch is a longitudinal acousticlike mode. The ZO branch is a vertically vibrating transverse optical mode. The ZA branch is a vertically vibrating acoustic-like mode. The SHO branch is a shear horizontal optical mode. The SHA is a shear horizontal acoustic-like mode. The last two SH modes appear because of the lack of mirror symmetry in these experiments (39). The phonon dispersion relation of the monolayer graphite on the NbC(001) surface is almost same as that of pristine graphite, whereas that of monolayer graphite on NbC(111) shows large softening as shown in Fig. 10. This tendency is observed in other TMCs, indicating that

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the monolayer graphite is softened on the ‘‘metallic’’ (111) surfaces but not on the ‘‘carbidic’’ (001) surfaces (44). This behavior has been discussed in detail based on the covalent bond formation between the π orbitals of the graphite and the d orbitals of the substrate (44,45,48). B.

Field Emission Characteristics of Monolayer Graphite/TMC Emitters

1. Field Emission Patterns The first effect of the surface processing is a change in the FE pattern. Figure 11a shows the FE pattern of the ethylene-processed TiC⬍110⬎ tip (9). The central beam is strongly enhanced compared with the clean FE pattern. Finally, only a central beam remains in the FE pattern. A similar FE change occurs at the NbC⬍110⬎ tip (10) as shown in Fig. 11b. These pattern changes are interpreted by sharpening the central portion of the tip whose model is shown in Fig. 11c. The tip shape change is considered to be caused by transfer of carbon atoms due to the strong field. 2. Increase in the Emission Currents The second effect of the surface processing for TMC⬍110⬎ tips is that the emission currents increase under constant-voltage conditions. A typical ethylene exposure dependence (10) of the

Figure 11 Field emission patterns and tip shapes of surface-processed TMC⬍110⬎ tips. (a) Surfaceprocessed TiC ⬍110⬎ tip; (b) surface-processed NbC⬍110⬎ tip; (c) the tip shape. (From Ref. 9 and 10.)

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Figure 12 Ethylene exposure dependence of the applied voltage of the NbC⬍110⬎ tip under constantcurrent condition (10 hA). (a) Applied voltages just after the first step of the surface processing. (b) Applied voltages after continuous emission of 20 µA for 30 min. (From Ref. 10.)

applied voltage for the NbC⬍110⬎ tip is shown in Fig. 12. These data were obtained under a constant-current condition (10 nA). The open circles represent the applied voltages just after the first step of the surface processing. In this step, a pattern change does not occur yet. The applied voltages increase a little with the exposure owing to an increase in the work function. The solid circles represent the applied voltages after continuous emissions of 20 µA for 30 min, which is the second step of the processing. The applied voltages decrease rapidly over 100 L exposure. The FE pattern also changes according to the rapid decreases of the applied voltages over 100 L exposure. Therefore the emission current increase under constant-voltage conditions is due to the tip sharpening. Fowler-Nordheim plots of the TMC⬍110⬎ tip also support the tip sharpening. FowlerNordheim plots of the TiC⬍110⬎ tip (9) are shown in Fig. 13. In this case, the surface processing was done with 500 L ethylene exposure at 1000°C. Open circles (a) are the FowlerNordheim plot of the clean surface tip flashing at 1600°C. Open and solid squares (b) and (c) are data for the surface-processed tip flashing at 950 and 1150°C, respectively. The slope for the surface-processed tip is clearly smaller than that for the clean surface tip. The ratio of the slope for the surface-processed tip to that for the clean surface tip is about 0.4 in this case. When we flashed the surface-processed tip at 1200°C, experimental points, solid circles (d), returned to the state of the clean surface tip. The FE pattern also returned to that of the clean surface tip. This indicates that the surface state of the surface-processed tip changes back to that of the clean surface tip on flashing above 1200°C. This is due to the diffusion into the bulk

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Figure 13 Fowler-Nordheim plots of the TiC⬍110⬎ tip. The surface processing was done with 500 L ethylene exposure at 1000°C. (a) Flashing temperature (Tf ) ⫽ 1600°C (the clean surface tip); (b) Tf ⫽ 950°C; (c) Tf ⫽ 1150°C; (d) Tf ⫽ 1200°C. (From Ref. 9.)

from the graphite overlayer that is formed by the surface processing. The NbC⬍110⬎ tip also shows the same behavior, and the ratio of the slopes of the surface-processed tip to clean surface tip is about 0.3 in this case (10). The slope of the Fowler-Nordheim plot is approximately proportional to rφ 3/2 , where r and φ are the tip radius and the work function, respectively (1). After the surface processing, the value of the r s φ s3/2 /rc φ c 3/2 ratio in the Fowler-Nordheim plots becomes about 1/3, where the suffixes s and c corresponding to the surface-processed tip and the clean surface tip, respectively. Because the work function does not change much after the surface processing, as shown in Table 3, the rs /rc ratio becomes almost the same as the slope ratio of about 1/3. Therefore, the change in the slope indicates the smaller tip radius. That is, sharpening of the tip happens at the surface-processed tip. This is probably due to mass transfer caused by the high electric field effect.

Table 3 Work Function of the Clean Surfaces and Graphite-Covered Surfaces of Transition Metal Carbides Work function (eV) Substrate

Clean surface

Graphite-covered surface

TiC(111) TiC(001) ZrC(111) ZrC(001) HfC(111) HfC(001) NbC(111) NbC(001) TaC(111) TaC(001)

4.7 3.8 4.7 4.0 4.9 4.5 5.0 4.2 4.7 4.3

4.4 4.5 4.3 4.2 3.7 4.3 3.8 4.2 3.5 3.9

Source: Refs. 42, 44–46, 48.

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Figure 14 Field emission currents with time after flashing the surface-processed TMC⬍110⬎ tips. (a) NbC⬍110⬎ tip; P ⫽ 2.1 ⫻ 10 ⫺8 Pa. The surface processing was done with 25,000 L ethylene exposure at 1000°C. (b) TiC⬍110⬎ tip; P ⫽ 2.0 ⫻ 10 ⫺8 Pa. The surface processing was done with 100 L ethylene exposure at 1100°C. (From Ref. 9 and 10.)

3. Emission Current Stabilization The most striking effect of the surface processing is stabilization of the emission currents. It has been found that the surface processing forms monolayer graphite on the surfaces of transition metal carbides and the existence of the monolayer graphite is deeply related to current stabilization. Figure 14 shows emission currents with time for the TiC⬍110⬎ and NbC⬍110⬎ tips after the surface processing (9,10,18). The step- and spikelike fluctuations of the emission currents from the clean surfaces of TiC⬍110⬎ and NbC⬍110⬎ tips can be greatly reduced by surface processing. In the most stable emission, the step- and spikelike fluctuations are less than 0.2% and the current decrease with time is less than 0.1% per hour. The surface-processed tip shows highly stable emission compared with a W tip. Therefore the usual evaluation of current fluctuations is not adequate. Here we define a new term, ‘‘stable emission current’’ (9). This is the maximum current whose fluctuation amplitude is less than 1% in the initial 20 min after applying the voltage. In contrast to the surface-processed TiC⬍110⬎ tip, the emission stability of the NbC⬍110⬎ tip depends on the ethylene exposure (10). These experimental data are shown in Fig. 15. The ordinate is stable emission current (I ) times the environmental pressure (P), which means the degree of the stability. The stability of

Figure 15 Ethylene exposure dependence of the emission stability of the surface-processed NbC⬍110⬎ tip. The surface processing was done at 1000°C. (From Ref. 10.)

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the 25,000 L tip is better than that of 100–500 L tips. This difference can be explained by the existence of monolayer graphite on the carbide surfaces of the emission area. Monolayer graphite is formed on the NbC(111) surface at an exposure over 100 L, and at least 25,000 L exposure is needed to form on the NbC(100) surface. The different conditions for forming monolayer graphite on the (111) and (100) surfaces are deeply related to the degree of emission stability of the NbC⬍110⬎ tip. Figure 16 shows the stable emission current versus pressure relation for the surface-processed TiC⬍110⬎ and NbC⬍110⬎ tips (10). Data represented by open circles (a) are for the TiC⬍110⬎ tip and data shown by full circles (b) and a solid line (c) are for the NbC⬍110⬎ tips. The data of (a) and (b) show that log I is proportional to ⫺log P. The current fluctuations are proportional to the product of I and P. The solid line in Fig. 16c is a calculated stable emission current for the 25,000 L ethylene-processed NbC⬍110⬎ tip using data for the stable emission current of 24 µA at 2.1 ⫻ 10 ⫺8 Pa. The stable emission current of the 25,000 L ethyleneprocessed NbC⬍110⬎ tip is about 50 µA at 1 ⫻ 10 ⫺8 Pa. Figure 16 indicates that the stable emission current for the ethylene-processed NbC⬍110⬎ tip is larger than that for the ethyleneprocessed TiC⬍110⬎ tip. That is, the NbC tip is more stable than the TiC tip. This difference in emission stability is attributable to lack or existence of monolayer graphite on the (100) surface. Monolayer graphite can be formed on the NbC(100) surface over 25,000 L ethylene exposure, but it is quite difficult to form monolayer graphite on the TiC(100) surface. It is quite important to identify the built-up region of the surface-processed carbide tip. It is mainly composed of graphite because the same phenomenon was not observed for the clean carbide tip, but experimental identification remains for future work. Moreover, it is noted that the monolayer graphite on the carbide surfaces is chemically inert. Oxygen and hydrogen atoms could not be detected on monolayer graphite at room temperature even on oxygen and hydrogen

Figure 16 ‘‘Stable emission currents’’ versus pressure relation of the surface-processed TiC⬍110⬎ and NbC⬍110⬎ tips. (a) TiC⬍110⬎ tip; the surface processing was done with 100 L ethylene exposure at 1100°C. (b) NbC⬍110⬎ tip; the surface processing was done with 100 L ethylene exposure at 1000°C. (c) NbC⬍110⬎ tip; the surface processing was done with 25,000 L ethylene exposure at 1100°C. (From Ref. 10.)

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gas exposure (46). This inertness of the monolayer graphite is greatly related to stabilization of the emission currents.

IV. SUMMARY Surface-processed TMC⬍110⬎ tips have been developed as cold field emission sources. The surface processing consists of heating the tip at about 1000°C in an ethylene atmosphere and subsequent continuous emission of 10–20 µA for more than 30 min. Emission current instability is less than 0.2% with optimal surface processing. Monolayer graphite has been found on TMC(111) and (100) surfaces using ethylene exposure conditions similar to those for surface processing. It is concluded that the monolayer graphite formed on the tip after surface processing is greatly related to stabilization of the emission currents.

ACKNOWLEDGMENTS The author would like to thank Dr. Takashi Aizawa for numerous helpful discussions and for supplying phonon dispersion figures for monolayer graphite and photographs of their LEED patterns.

REFERENCES 1. LW Swanson, AE Bell. Recent advances in field electron microscopy of metals. Adv Electron Phys 32:193, 1973. 2. PR Schwoebel, I Brodie. Surface-science aspects of vacuum microelectronics. J Vac Sci Technol B 13:1391, 1995. 3. Vu Thien Binh, ST Purcell, N Garcia, J Doglioni. Field-emission electron spectroscopy of singleatom tips. Phys Rev Lett 69:2527, 1992. 4. ST Purcell, Vu Thien Binh, N Garcia. 64 meV measured energy dispersion from cold field emission nanotips. Appl Phys Lett 67:436, 1995. 5. Vu Thien Binh, N Garcia, ST Purcell. Electron field emission from atom-sources: Fabrication, properties, and applications of nanotips. Adv Imaging Electron Phys 95:63, 1996. 6. H-W Fink. Point source for ions and electrons. Phys Scr 38:260, 1988. 7. H-W Fink, W Stocker, H Schmid. Holography with low-energy electrons. Phys Rev Lett 65:1204, 1990. 8. R Morin, H-W Fink. Highly monochromatic electron point-source beams. Appl Phys Lett 65:2362, 1994. 9. Y Ishizawa, S Aoki, C Oshima, S Otani. Field emission properties of surface-processed TiC tips. J Phys D Appl Phys 22:1763, 1989. 10. Y Ishizawa, T Aizawa, S Otani. Stable field emission and surface evaluation of surface-processed NbC⬍110⬎ tips. Appl Surf Sci 67:36, 1993. 11. LE Toth. Transition Metal Carbides and Nitrides. New York: Academic Press, 1971. 12. ST Oyama, ed. The Chemistry of Transition Metal Carbides and Nitrides. London: Chapman & Hall, 1996. 13. K Senzaki, Y Kumashiro. Field emission studies of TiC single crystal. Jpn J Appl Phys Suppl 2 Pt 1:289, 1974. 14. M Futamoto, I Yuito, U Kawabe, O Nishikawa, Y Tsunashima, Y Hara. Study on titanium carbide

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Ishizawa field emitters by field-ion microscopy, field-electron emission microscopy, Auger electron spectroscopy, and atom-probe field ion microscopy. Surf Sci 120:90, 1982. H Adachi, K Fujii, S Zaima, Y Shibata, C Oshima, S Otani, Y Ishizawa. Stable carbide field emitter. Appl Phys Lett 43:702, 1983. C Oshima, R Souda, S Otani, Y Ishizawa. Stable TiC field emitter. Oyo Buturi 53:206, 1984. Y Ishizawa, C Oshima, S Otani. Field emission properties of transition metal carbides. NIRIM Report No. 40, 1984, p 80 (in Japanese). Y Ishizawa, S Aoki, C Oshima, S Otani. Field emission properties of surface-processed TiC⬍110⬎ field emitter. J Vac Soc Jpn 29:578, 1986 (in Japanese). Y Ishizawa, S Aoki, C Oshima, S Otani. Carbide field emission source. Proceeding XIth International Congress on Electron Microscopy, Kyoto Japan, 1986, p 223. Y Ishizawa, M Koizumi, C Oshima, S Otani. Field emission properties of ⬍110⬎-oriented carbide tips. J Phys (Paris) 48:C6–9, 1987. Y Kumashiro, H Shimizu, A Itoh. Electron emission characteristics and surface states of carbide emitters—TiC single crystal and other transition metal carbides. Oyo Buturi 45:607, 1976 (in Japanese). K Kawasaki, K Senzaki, Y Kumashiro, A Okada. Energy distribution of field-emitted electrons from TiC single crystal. Surf Sci 62:313, 1977. M Futamoto, I Yuito, U Kawabe. Field-ion and field emission microscopy of titanium carbide. Proceedings 27th International Field Emission Symposium, (Tokyo), 1980, p 363. K Fujii, S Zaima, H Adachi, S Otani, C Oshima, Y Ishizawa, Y Shibata. Basic field emission properties of TiC and ZrC single crystals. J Vac Soc Jpn 26:251, 1983 (in Japanese). H Adachi, K Fujii, S Zaima, Y Shibata, S Otani. Flashing temperature dependence of field electron emission from TiC single crystals. J Vac Soc Jpn 27:658, 1984 (in Japanese). K Fujii, S Zaima, Y Shibata, H Adachi, S Otani. Field electron emission properties of TiC single crystals. J Appl Phys 57:1723, 1985. H Adachi. Carbide field emitters. Scanning Microsc 1:919, 1987. S Zaima, K Saito, H Adachi, Y Shibata, H Hojo M Ono. Field emission from TaC, Proceedings 27th International Field Emission Symposium, Tokyo, 1980, p 348. M Ono, H Hojo, H Shimizu, H Murakami. Tantalum carbide cathode for field emission guns. Proceedings 27th International Field Emission Symposium, Tokyo, 1980, p 353. S Otani, T Tanaka, Y Ishizawa. Preparation of NbC x single crystals by a floating zone technique. J Cryst Growth 62:211, 1983. S Otani, Y Ishizawa. Single crystals of carbides and borides as electron emitters. Prog Crystal Growth Charact 23:153, 1991. S Zaima, Y Shibata, H Adachi, C Oshima, S Otani, M Aono, Y Ishizawa. Atomic chemical composition and reactivity of the TiC(111) surface. Surf Sci 157:380, 1985. S Hosoki, S Yamamoto, M Futamoto, S Fukuhara. Field emission characteristics of carbon tips. Surf Sci 86:723, 1979. S Yamamoto, H Hosoki, S Fukuhara, M Futamoto. Stability of carbon field emission current. Surf Sci 86:734, 1979. T Todokoro, N Saitou, S Yamamoto. Role of ion bombardment in field emission current instability. Jpn J Appl Phys 21:1513, 1982. M Aono, Y Hou, R Souda, C Oshima, S Otani, Y Ishizawa. Direct analysis of the structure, concentration, and chemical activity of surface atomic vacancies by specialized low-energy ion scattering spectroscopy: TiC(001). Phys Rev Lett 50:1293, 1983. ML Yu, BW Hussey, E Kratschmer, THP Chang, W Mackey. Improved emission stability of carburized HfC⬍100⬎ and ultrasharp tungusten field emitters. J Vac Sci Technol B 13:2436, 1995. ML Yu, ND Lang, BW Hussey, THP Chang, W Mackey. New evidence for localized electronic states on atomically sharp field emitters. Phys Rev Lett 77:1636, 1996. T Aizawa, R Souda, S Otani, Y Ishizawa, C Oshima. Anomalous bond of monolayer graphite on transition-metal carbide surfaces. Phys Rev Lett 64:768, 1990.

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40. T Aizawa, R Souda, S Otani, Y Ishizawa, C Oshima. Bond softening in monolayer graphite formed on transition-metal carbide surfaces. Phys Rev B42:11469, 1990. 41. T Aizawa, Y Hwang, W Hayami, R Souda, S Otani, Y Ishizawa. Phonon dispersion of monolayer graphite on Pt(111) and NbC surfaces: Bond softening and interface structure. Surf Sci 260:311, 1992. 42. Y Hwang, T Aizawa, W Hayami, S Otani, Y Ishizawa, SJ Park. Surface phonon and electronic structure of a graphite monolayer formed on ZrC(111) and (001) surfaces. Surf Sci 271:299, 1992. 43. B Tilley, T Aizawa, R Souda, W Hayami, S Otani, Y Ishizawa. Monolayer graphite on a tungstensegregated TiC(100) surface. Solid State Commun 94:685, 1995. 44. T Aizawa. PhD Thesis, University of Tokyo, 1994. 45. A Nagashima, K Nuka, K Satoh, H Itoh, T Ichinokawa, C Oshima, S Otani. Electronic structure of monolayer graphite on some transition metal carbide surfaces. Surf Sci 287/288:609, 1993. 46. T Aizawa, Y Ishizawa. Monolayer graphite on transition-metal carbides and application to field emitter. TANSO [No 155]:335, 1992 (in Japanese). 47. Y Hwang, T Aizawa, W Hayami, S Otani, Y Ishizawa, SJ Park. Charge transfer between monolayer graphite and NbC single crystal substrates. Solid State Commun 81:397, 1992. 48. A Nagashima, K Nuka, H Itoh, T Ichinokawa, C Oshima, S Otani. Electronic states of monolayer graphite formed on TiC(111) surface. Surf Sci 291:93, 1993. 49. A Nagashima, H Itoh, T Ichinokawa, C Oshima, S Otani. Change in the electronic states of graphite overlayer depending on thickness. Phys Rev B50:4756, 1994.

12 NbN Superconducting Devices Masahiro Aoyagi Electrotechnical Laboratory, Tsukuba, Ibaraki, Japan

I.

INTRODUCTION: HISTORY OF NbN SUPERCONDUCTING DEVICES

A superconductor shows specific characteristics such as no resistance, gap voltages, a Josephson effect, and a Meissner effect. These characteristics are utilized for to realize an electron device. An ultralow loss transmission line can be realized by using a superconducting electrode. A highspeed switching device and memory device, high-frequency mixing device, and voltage standard device can be realized by using a Josephson tunnel junction. The initial research on superconducting devices was done using soft and fragile metals such as Pb and Sn. The superconducting devices made with soft metals deteriorated easily with a thermal cycle between room temperature and liquid He temperature. The introduction of hard and refractory materials such as Nb and NbN into Josephson junctions improved the durability in thermal cycles. This improvement has promoted rapid development of superconducting devices. Nb/oxide/Nb, Nb/a-Si/Nb, and NbN/oxide/NbN junction processes were proposed by IBM (1), Sperry (2), and ETL (3), respectively. Some preliminary work on an integrated device succeeded with these processes. After that, an Nb/AlO x /Nb junction process was proposed by AT&T (4). This process is widely used in the field of superconducting electronics. Many researchers have obtained fine results in application work on a superconducting device. In some application fields of superconducting devices, the Nb junction is not sufficient. Nb compounds such as NbN, Nb 3 Al, Nb 3Sn, and Nb 3Ge were studied for this purpose. Only NbN has been continuously studied for superconducting devices. Concerning the other materials, no one has succeeded in developing a method of making a high-quality superconducting device. Today, oxide superconducting materials are widely studied but have problems of reliability and reproducibility. Niobium nitride (NbN) of B1 crystal structure has attractive characteristics, such as a higher superconducting transition temperature of ⬃15 K, a larger superconducting gap energy of ⬃2.5 eV, and higher chemical and thermal stability, compared with Nb. The high transition temperature of NbN makes it possible to realize a higher temperature operation than with Nb devices and improves the durability against temperature variation. The large gap energy of NbN produces a higher frequency response. This property is very important for mixing devices and microwave devices. NbN can be stored for a long time in the air at room temperature. Moreover, NbN is stable even in the vacuum annealing process at 800°C. Nb is oxidized even in air at room temperature. 289

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II. NbN THIN FILMS A.

Fabrication

1. Chemical Vapor Deposition In the chemical vapor deposition (CVD) method, NbN films are fabricated by decomposing NbCl 5 gas in NH 3 and H 2 gases at a high temperature, about 1000°C. When MgO single crystal is used as a substrate, single-crystal NbN film can be grown (5). 2. RF Sputtering In the radio frequency (RF) sputtering method, NbN films are fabricated by reactive sputtering in an RF glow discharge with an Nb target in Ar and N 2 gases (6–16). A typical sputtering system is shown in Fig. 1. To obtain highly uniform properties of NbN films, rotation of the substrate is necessary. High-Tc NbN films, which have a Tc of over 15 K, are normally obtained by heating a substrate at over 500°C. To make a Josephson junction, decreasing the substrate temperature is required. We can obtain a high-Tc NbN film by adding a carbon source such as CH 4 or C 2 H 2 gas without substrate heating (9,14). When an MgO or SiC single crystal is used as a substrate, single-crystal NbN film can be grown by heating the substrate at over 300°C (15,16). 3. DC Sputtering In the DC sputtering method, NbN films are fabricated by reactive sputtering in the DC glow discharge with an Nb target in a mixture of Ar gas and N 2 gas (17–20). For making a Josephson junction, RF sputtering is more suitable than DC sputtering. The grain sizes of the fabricated films are smaller than that of the films fabricated in DC sputtering. The film surface is smoother than that of the films fabricated in DC sputtering. 4. Ion Beam Sputtering NbN film fabrication has been reported (21). Low deposition rate is a serious problem. Junction fabrication has never been reported.

Figure 1 Schematic diagram of RF sputtering system for NbN films.

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5. Pulsed Laser Deposition This method has been developed recently. We can make a film of a material with a high melting point by this method. NbN film fabrication has been reported. A high deposition rate is easily realized in this method (22,23). Junction fabrication has never been reported.

B.

Properties of NbN Films

1. Superconducting Transition Temperature The superconducting transition temperature Tc of an NbN film fabricated by the RF sputtering method is as shown in Fig. 2. The Tc of the fabricated NbN film is varied with the nitrogen content and methane content of the sputtering gas. After annealing in a vacuum at about 800°C, the Tc of the NbN film does not change. The NbN film is very stable against high-temperature treatment (24). 2. Magnetic Penetration Depth In a superconductor, magnetic field penetrates to penetration depth λ, called the magnetic penetration depth. Generally speaking, λ of NbN is thought to be larger than that of other superconducting materials. This is a problem for integrated circuit applications. Large λ requires a thick film for a wiring layer in an integrated circuit. A film thickness of 1.5λ is needed to avoid adding extra inductance. Measured values of λ in NbN films have been reported (14,25). For a polycrystalline film fabricated by RF sputtering, the value of λ is from 300 to 400 nm. When the value increases, the film thickness decreases. The reason is thought to be that the grain size of the film decreases with decreasing film thickness. For a single-crystal film fabricated by RF sputtering, the value of λ is about 200 nm. The value is independent of the film thickness. This is thought to be acceptable for integrated circuit applications.

Figure 2 (a) Superconducting transition temperature Tc of the NbN film with changing ratio of N 2 gas partial pressure. (b) Superconducting transition temperature Tc of the NbN film with changing ratio of CH 4 gas pertial pressure (N 2 gas, 6.7 %).

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3. Grain Size and Morphology In an NbN polycrystalline film fabricated by RF sputtering, a columnar structure has grown perpendicular to the substrate. The columnar grain diameter in a 200-nm-thick film was measured in the range from 20 to 50 nm (26).

III. NbN JOSEPHSON JUNCTIONS Josephson junctions using NbN as electrodes have been developed in several institutes. Amorphous silicon (α-Si), niobium oxide (NbO x ), magnesium oxide (MgO), aluminum oxide (AlO x), and aluminum nitride (AlN) have been investigated as tunnel barriers for all NbN junctions. NbN base junctions were studied in the beginning stage of junction development (27,28). Today, these are not investigated because of poor reliability. A.

␣-Si Tunnel Barrier

α-Si was first investigated as a tunnel barrier in NbN junction development (29–33). It has the attractive characteristic of a low dielectric constant (⑀ r ⬃ 10), which produces a low junction capacitance. The α-Si tunnel barrier is made by glow discharge (29–31). This method has a problem with the controllability of the thickness. The α-Si barrier is also made by RF sputtering (32). The controllability of the thickness is improved by this method. Hydrogenation of the barrier improves the subgap leakage current (33). B.

NbO x Tunnel Barrier

NbO x was also investigated as a tunnel barrier in NbN junction development (3,26,34,35). The NbO x tunnel barrier is easy to make from NbN by plasma oxidation. The plasma oxidation can be controlled precisely. After the oxidation, Ar sputter etching with a low bias voltage of about 30 V improves the subgap leakage current. Thus, both reproducibility and uniformity have reached an acceptable level for an integrated circuit. Some integrated circuits using such a junction were developed successfully. The junction is stable even in the vacuum annealing process at about 300°C. But the junction has a high dielectric constant (⑀ r ⬃ 30), which produces a high junction capacitance. This is a disadvantage for high-speed operation. C.

AlO x Tunnel Barrier

AlO x was also investigated as a tunnel barrier in NbN junction development (36–39). It has the attractive characteristic of a low dielectric constant (⑀ r ⬃ 8), which produces a low junction capacitance. The AlO x tunnel barrier is the most successful one in Nb junction development, but a high-quality NbN junction with an AlO x tunnel barrier has not yet been obtained. D.

MgO Tunnel Barrier

Moreover, MgO was investigated as a tunnel barrier in NbN junction development (40–53). The MgO tunnel barrier is normally made by RF sputtering in Ar gas with an MgO target (40). The use of an Mg target does not produce a better subgap characteristic than that of an MgO target. Sputtering with an MgO target is the best way to make an MgO tunnel barrier. The thickness of the MgO barrier is controlled precisely. Thus, both reproducibility and uniformity

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have reached an acceptable level for an integrated circuit (50). Figure 3 shows typical I–V characteristics of NbN/MgO/NbN junctions. Figure 4 shows the dependence of the Josephson critical current density on the thickness of the MgO tunnel barrier. The junction has attractive characteristics for integrated circuits, because it has a larger gap voltage (about 5 mV) than the other junctions. The junction is stable even in the annealing process at about 350°C. MgO is

Figure 3 Typical I-V characteristics of NbN/MgO/NbN junctions. (a) J c , 200 A/cm 2. (b) J c , 30 kA/cm 2.

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Figure 4 Dependence of Josephson critical current density J c on the thickness of the MgO tunnel barrier.

the most promising material as a tunnel barrier for NbN electrode junctions. It has, however, a relatively high dielectric constant (⑀ r ⬃ 10), which produces a high junction capacitance. This is a disadvantage for high-speed operation. E.

AlN Tunnel Barrier

AlN was also investigated in NbN junction development (54–57). The AlN tunnel barrier is normally made by sputtering with an Al target in an Ar ⫹ N2 gas mixture (54) or N 2 gas (55). It has the attractive characteristic of a relatively low dielectric constant (⑀ r ⬃ 8.5), which produces a low junction capacitance. AlN is one of the promising materials as a tunnel barrier for NbN electrode junctions.

IV. APPLICATIONS OF NbN JUNCTIONS A.

Digital Circuits

Fabrication processes for integrated circuits using NbN junctions have been reported (58–76). A fabrication process for an integrated circuit using NbN junctions (66,69,72,74) is described as follows. Figure 5 shows the process flow. Table 1 shows a list of layers in the NbN integrated circuit. (1) An Nb film is deposited by DC sputtering. A resist pattern for the ground plane is formed by ultraviolet (UV) lithography. Part of the Nb film is etched by reactive ion etching (RIE). Then an SiO film is deposited by evaporation and lifted off. (2) A resist pattern for the ground plane contact hole is formed by UV lithography. The surface of the Nb ground plane is anodized. Then an SiO film and an MgO film are deposited and lifted off. (3) The surface of the Nb ground plane contact is cleaned by Ar plasma etching. An Nb film and an NbN/ MgO/NbN trilayer film are deposited by RF sputtering. (4) A resist pattern for the base electrode is formed by UV lithography. Part of the trilayer film is etched by RIE. (5) A resist pattern for the small Josephson junctions is formed by UV or electron beam (EB) lithography. The upper NbN layer is etched by RIE. Then an SiO film is deposited by evaporation and lifted off. (6)

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Figure 5 Process flow of integrated circuits using NbN/MgO/NbN junctions (figure continues).

A resist pattern of the base contact hole is formed by UV lithography. Part of the SiO layer is etched by RIE. (7) A resist pattern of the resistor is formed by UV lithography. A Pd film is deposited by EB evaporation and lifted off. (8) A resist pattern of the wiring is formed by UV lithography. A Pb-In film is deposited by evaporation and lifted off. In the other processes, an Mo film deposited by sputtering is used as a resistor layer (61,68,73). An SiO 2 film deposited by sputtering (67,73) or CVD (63,68) is used as an insulation layer. An Si film deposited by evaporation is also used as an insulation layer. An Nb film deposited by sputtering is used as a wiring layer (61). An NbN film deposited by sputtering is used as a wiring layer (67,68,73) for high-temperature operation at about 10 K. Active areas of Josephson junctions must be controlled with very high precision. A highresolution lithography system is required to get a wide operating margin for a circuit with a small spread of the junction critical current. Some logic gates such as four-junction logic (4JL) (59,60) and modified variable threshold logic (MVTL) (73,75,76) have been fabricated using NbN junctions. The smallest logic delay

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Figure 5 Continued.

of 3.0 ps/gate has been demonstrated using 4JL gates (74). This value is still larger than that of the gates using Nb junctions because of the large capacitance of NbN junctions. Many integrated circuits have been demonstrated using NbN junctions. Details are shown in Table 2. NbN/NbO x /NbN junctions were mainly used in the integrated circuits until the end of the 1980s. After that, only NbN/MgO/NbN junctions were used. In the United States, hightemperature (9–10 K) operation of integrated circuits has been investigated (67,75). The largest circuit, fabricated and tested experimentally, was a 1280-bit ROM unit using NbN/MgO/

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Table 1 Layers in NbN Integrated Circuits Layer Ground plane Planarization insulation Ground plane insulation Base electrode Tunnel barrier Counter electrode Junction insulation Resistor Wiring

Material

Thickness (nm)

Nb SiO Nb 2O 5 /SiO/MgO Nb/NbN MgO NbN SiO Pd Pb/In

400 250 40/200/20 100/100 0.7 150 320 40 900/100

NbN junctions. Figure 6 shows a chip photograph of the NbN ROM unit. The size is 5 mm ⫻ 3.45 mm. B.

SIS Mixing Devices

For 10 years, heterodyne receivers using superconductor-insulator-superconductor (SIS) tunnel junctions as mixer elements have been used in radiotelescopes in the frequency range from 100 to about 350 GHz. A few receivers working at even higher frequencies have been developed, and there is much interest in SIS receivers that can be operated up to 1 THz. The upper frequency limit of the SIS quasi-particle mixer is related to the energy gap ∆ of the superconductors in the mixer circuit. It is predicted theoretically that the tunnel junction itself should work at up to twice the gap frequency, that is, 4∆/h. It has, however, been suggested that RF losses in the junction electrodes and in the superconducting embedding circuit of the mixer can conflict with optimal performance when the operating frequency approaches or exceeds the gap frequency 2∆/h. NbN is an interesting material for the development of submillimeter SIS mixers that can be operated even above 1 THz. It has a higher gap frequency of about 1.2 THz. The upper frequency limit of Nb SIS devices, about 700 GHz, is set by the increase in the loss above the Nb gap frequency. Further progress in the frequency of SIS devices has been related to NbN junctions with a highest gap frequency of about 1200 GHz. An experimental study was performed in the millimeter band with a full NbN SIS mixer (71–76). The lowest double sideband (DSB) receiver noise temperature is about 65 K at 160 GHz and approaches the Nb SIS mixer performance in the millimeter band. The NbN SIS junctions can be operated at temperature of 5.4 K, which is unacceptable with the Nb devices. This means that the introduction of low-noise NbN mixers may simplify closed-cycle refrigerators. C.

Josephson Mixing Devices

Josephson tunnel junctions have harmonic generating and mixing properties due to their highly nonlinear current-voltage (I–V ) characteristic (83–85). Josephson junctions are able to generate high harmonics of an externally applied frequency. Constant-voltage (Shapiro) steps on the junction I–V characteristic are observed when the junction is irradiated with microwaves. The steps, occurring at voltages corresponding to harmonics of the incident frequency, are at integer multiples of hf/(2e), where f is the frequency of the incident microwaves. This feature can be used in the direct measurement of the frequency of far infrared laser lines. A mixing experiment at 4.25 THz has been done using Nb point-contact devices. A mixing

ETL Hypres

NbN/NbOx /NbN NbN/MgO/NbN NbN/MgO/NbN NbN/MgO/NbN NbN/MgO/NbN NbN/MgO/NbN NbN/MgO/NbN

Address control unit for 4-bit microcomputer Time domain reflectrometer

1280-bit ROM unit

8-bit SFQ counter Logic gate chain Logic gate chain Shift register

Hughes ETL ETL TRW

ETL

ETL ETL ETL ETL ETL Hitachi

Institutes

NbN/NbOx /NbN NbN/a-Si/NbN NbN/NbOx /NbN NbN/NbOx /NbN NbN/NbOx /NbN NbN/NbOx /Pb-In-Au

Junctions

Logic gate chain Logic gate chain 8-bit ripple carry adder 4⫻4-bit parallel multiplier 1K-bit SFQ memory 3K gate array

Integrated circuits

Table 2 List of Fabricated Integrated Circuits

16 junctions and 2 DC-SQUID 789 gates and 1280 cells 16 gates 53 gates 53 gates 384 gates

14 gates 14 gates 364 gates 652 gates Decoder, driver 419 gates 348 gates 593 gates

Tested parts

Functions and 60-Ghz operation 3.6 ps/gate (logic delay) 3.0 ps/gate (logic delay) Functions at 10 K

Functions and 710 ps (access time)

Functions at 9 K

18 ps/gate (logic delay) 9 ps/gate (logic delay) Functions and 0.8 ns (critical path) Functions and 1.0 ns (critical path) Functions 21 ps/gate (logic delay) 37 ps/gate (logic delay) Functions and 345 ps (critical path)

Performances

1991 1992 1993 1993

1991

1989

1983 1984 1985 1985 1985 1987 1987 1989

Year

70 72 74 75

69

67

59 60 61 61 62 64 64 65

Reference

298 Aoyagi

NbN Superconducting Devices

299

Figure 6 Chip photograph of a 1280-bit ROM unit containing NbN/MgO/NbN junctions.

experiment at 10 THz should be possible with NbN devices because they have about double the energy gap of Nb. The maximum operating frequency of a Josephson mixer is proportional to the energy gap of the superconductor used. Mixing experiment using NbN/MgO/NbN junctions have already been achieved up to 3.1 THz (84).

D.

X-Ray Detector

Superconducting tunnel junctions have become promising devices for X-ray detection with high energy resolution, as an energy resolution of 37 eV at 6 keV was achieved using an Sn junction (86). However, the Sn junction did not thermally cycle well, so there was a shift to fabricating Nb junctions. The current record for energy resolution for Nb junctions is 36 eV at 6 keV (87). There are two reasons for investigating NbN junctions for X-ray detection (88–90). The first is the possibility of operating at higher temperatures than with Nb-based devices (88,89). The second is making junctions with ‘‘trapping layers.’’ In order to suppress the thermal quasi-particle current to levels that allow high energy resolution, it is necessary to operate the junction at a temperature 0.1 Tc. NbN has a Tc of 15 K, which would require an operating temperature of 1.5 K. This temperature is very convenient compared with the 0.9 K of Nb junctions. In particular, in a space application the NbN junctions are suitable for a space qualified cryostat. For the NbN junctions, we expect that they have fewer losses and therefore higher energy resolution. On the other hand, a thick NbN overlayer was used as a wiring and radiation absorber for Nb/AlOx /Nb Josephson junctions (90). The NbN/Nb bilayer is also an interesting candidate for quasi-particle trapping, because it has the best scattering rate, which enhances the trapping process. The scattering time is strongly dependent on the quasi-particle energy and on the material characteristic time τ 0 . We can reduce loss of excitations and obtain enhancement of the quantum efficiency of the detector, employing quasi-particle trapping. The Nb layer in an Nb/AlOx /Nb junction can

300

Aoyagi

act as an effective trapping layer when an NbN overlayer with a higher energy gap than Nb is used. E.

Bolometer Mixing Devices

Nb SIS junctions are very sensitive mixer devices, but only for frequencies below the gap energy of Nb(⬃700 GHz). Superconducting hot electron bolometers (HEBs) use the electron temperature-dependent resistance in superconducting narrow film strips. The mixer performance of the Nb HEB mixer is promising but the bandwidth, determined by the electron-phonon interaction time, is very narrow (⬃90 MHz). NbN has a short electron-phonon interaction time, so it is possible to obtain a larger bandwidth of 1 GHz. NbN has a larger gap energy than Nb, so the NbN HEB mixer can be operated over 1 THz. In some studies, preliminary experimental results were achieved (91–94). F.

SQUID

Integrated DC superconducting quantum interference device (DC-SQUID) magnetometers were fabricated using NbN/NbO x /NbN or NbN/MgO/NbN junctions (95–97). By using NbN/MgO/ NbN junctions, 10 K operation was achieved (96). G.

Microwave Devices

Some microwave devices have been reported (96–102). A tunable superconducting phase shifter has been demonstrated using NbN microstrips (99). The tuning mechanism is based on inductance modulation by injecting excess quasi-particles into the NbN microstrips. Flux-flow oscillators have been demonstrated using NbCN/MgO/NbCN junctions (101). Radiation in a frequency range from 580 to 710 GHz was confirmed experimentally. H.

Others

Large series arrays for Josephson voltage standards were demonstrated using NbN/MgO/NbN junctions (103). In the voltage standards, we use constant voltage steps which appear in the I– V characteristic of the junction at Vn ⫽ n(h/2e)fc (n ⫽ 0,1,2, . . .) under microwave irradiation. In the large series arrays, the voltage steps are multiplied by the number of junctions. A 1-V step has been demonstrated under microwave irradiation at 69 GHz. A study of using an NbN gate electrode in a semiconductor MOS device has been reported (24). NbN is suitable for high-temperature (800–900°C) annealing in the self-aligned MOS gate process. Superconducting wiring should be realized in a low-temperature (4.2–10 K) operation.

V.

SUMMARY

Fabrication processes for NbN Josephson tunnel junctions have been developed successfully. Many application works are in progress. In particular, high-frequency devices such as an SIS mixer and a Josephson mixer have been fabricated and tested with practical performance. NbN integrated circuits have also been fabricated and tested. Reproducibility and uniformity of the NbN integrated circuit process are still worse than those of the Nb integrated circuit process. The integration level is still less than the large-scale integration (LSI) level. The performance

NbN Superconducting Devices

301

has not yet reached GHz clock operation. Further investigations will be required. High-temperature (9–10 K) operation is promising for satellite and mobile applications.

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48. A Shoji. Fabrication of all NbN Josephson tunnel junctions using single crystal NbN films for the base electrodes. IEEE Trans Magn 27:3184, 1991. 49. HG LeDuc, A Judas, SR Cypher, B Bumble, BD Hunt, JA Stern. Submicron area NbN/MgO/NbN tunnel junctions for SIS mixer applications. IEEE Trans Magn 27:3192, 1991. 50. M Aoyagi, H Nakagawa, I Kurosawa, S Takada. NbN/MgO/NbN Josephson junctions for integrated circuits. Jpn J Appl Phys 31:1778, 1992. 51. JM Murduck, J DiMond, C Dang, H Chan. Niobium nitride Josephson junction process development. IEEE Trans Appl Supercond 3:2211, 1993. 52. W Rothmund, H Downar, P Meisterjahn, W Scherber, M Wu¨lker. NbN-MgO-NbN Josephson junctions prepared by window isolation process. IEEE Trans Appl Supercond 3:2208, 1993. 53. ZH Barber, MG Blamire, NJ Dawes. Postfabrication resistance trimming of a superconducting tunnel junction using a focused ion beam. J Vac Sci Technol B13:318, 1995. 54. SL Thomasson, JM Murduck, and H Chan, NbCN Josephson junctions with AlN barriers, IEEE Trans Magn 27:3188, 1991. 55. Z Wang, A Kawakami, Y Uzawa, B Komiyama. High critical current density NbN/AlN/NbN tunnel junctions fabricated on ambient temperature MgO substrates. Appl Phys Lett 64:2034, 1994. 56. ZH Barber, DM Tricker, MG Blamire. The fabrication and characterization of NbCN/AlN heterostructures. IEEE Trans Appl Supercond 5:2314, 1995. 57. Z Wang, A Kawakami, Y Uzawa, B Komiyama. NbN/AlN/NbN tunnel junctions fabricated at ambient substrate temperature. IEEE Trans Appl Supercond 5:2322, 1995. 58. S Kosaka, F Shinoki, S Takada, H Hayakawa. Fabrication of NbN/Pb Josephson tunnel junctions with a novel integration method. IEEE Trans Magn 17:314, 1981. 59. S Kosaka, A Shoji, M Aoyagi, F Shinoki, H Nakagawa, S Takada, H Hayakawa. High speed logic operations of all refractory Josephson integrated circuit. Appl Phys Lett 43:213, 1983. 60. M Aoyagi, A Shoji, S Kosaka, F Shinoki, H Nakagawa, S Takada, H Hayakawa. All niobium nitride Josephson junction with hydrogenated amorphous silicon barrier and its application to the logic circuit. Jpn J Appl Phys 23:L916, 1984. 61. S Kosaka, A Shoji, M Aoyagi, F Shinoki, S Tahara, H Ohigashi, H Nakagawa, S Takada, H Hayakawa. An integration of all refractory logic LSI circuit. IEEE Trans Magn 21:102, 1985. 62. S Tahara, S Kosaka, A Shoji, M Aoyagi, F Shinoki, H Hayakawa. Fabrication and performance of all refractory Josephson logic circuits for 1 kbit SFQ memory. IEEE Trans Magn 21:733, 1985. 63. S Kosaka, A Shoji, M Aoyagi, Y Sakamoto, F Shinoki, H Hayakawa. PECVD-SiO 2 film as a junction isolation for all refractory Josephson IC. IEEE Trans Magn 23:1389, 1987. 64. S Yano, Y Tarutani, H Mori, H Yamada, M Hirano, U Kawabe. Fabrication and characteristics of NbN-based Josephson junctions for logic LSI circuits. IEEE Trans Magn 23:1472, 1987. 65. S Kosaka, H Nakagawa, H Kawamura, Y Okada, Y Hamazaki, M Aoyagi, I Kurosawa, A Shoji, S Takada. Josephson address control unit IC for a 4-bit microcomputer prototype. IEEE Trans Magn 25:789, 1989. 66. M Aoyagi, A Shoji, S Kosaka, H Nakagawa, S Takada. Submicron NbN Josephson tunnel junctions for digital applications. IEEE Trans Magn 25:1223, 1989. 67. SR Whiteley, F Kuo, M Radparvar, SM Faris. An all-NbN time domain reflectometer chip functional above 8K. IEEE Trans Magn 25:770, 1989. 68. GL Kerber, IE Cooper, HW Fry, GR King, RS Morris, JW Spargo, AG Toth. An all refractory NbN Josephson junction medium scale integrated circuit process. J Appl Phys 68:4853, 1990. 69. M Aoyagi, H Nakagawa, I Kurosawa, S Takada. Josephson LSI fabrication technology using NbN/ MgO/NbN tunnel junctions. IEEE Trans Magn 27:3180, 1991. 70. JW Spargo, JE Cooper, GL Kerber, GR King, RS Morris, AG Toth. A 60-GHz NbN single-flux quantum counnter circuit. IEEE J Solid State Circuits 26:884, 1991. 71. M Aoyagi, H Nakagawa, I Kurosawa, S Takada. NbN Josephson junction with high critical current density for integrated cirouits. Supercond Sci Technol 4:626, 1992. 72. M Aoyagi, H Nakagawa, I Kurosawa, S Takada. Submicron NbN/MgO/NbN Josephson tunnel junctions and their application to the logic circuit. IEEE Trans Appl Supercond 2:183, 1992. 73. SL Thomasson, AW Moopenn, R Elmadjian, JM Murduck, JW Spargo, LA Abelson, HW Chan. All refractory NbN integrated circuit process. IEEE Trans Appl Supercond 3:2058, 1993.

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74. M Aoyagi, H Nakagawa, I Kurosawa, S Takada. A speedup method of a high-speed direct-coupled Josephson logic gate. IEEE Trans Appl Supercond 3:2679, 1993. 75. DJ Durand, LA Abelson, LR Eaton, M Leung, A Moopenn, JM Murduck, J Spargo. Ten Kelvin NbN integrated digital circuits. Extended Abstracts of 4th International Superconducting Electronics Conference, Boulder, CO, 1993, pp 209–210. 76. M Leung, DJ Durand, LA Abelson, LR Eaton, J Spargo. Optimization of NbN MVTL logic gates for 10 K operation. IEEE Trans Appl Supercond 5:3179, 1995. 77. WR McGrath, JA Stern, HHS Javadi, SR Cypher, BD Hunt, HG LeDuc. Performance of NbN superconductive tunnel junctions as SIS mixers at 205 GHz. IEEE Trans Magn 27:2650, 1991. 78. MG Blamire, ZH Barber, H van de Stadt, JJ Wezelman, S Withington. High quality NbN-based junctions for 500 GHz waveguide mixers. Proc SPIE 2104:265, 1993. 79. B Plathner, KH Gundlach, H Rothermel, M Aoyagi, S Takada. Niobium nitride tunnel junctions as frequency mixer. Proceedings of the European Conference on Applied Superconductors (EUCAS), Go¨ttingen, Germany, 1993, pp 1477–1480. 80. H Rothermel, B Plathner, KH Gundlach, M Aoyagi, S Takada. Antenna-coupled superconducting contacts in submillimeter and FIR astronomy. Infrared Phys Technol 35:463, 1994. 81. Y Uzawa, Z Wang, A Kawakami, B Komiyama. Submillimeter wave responses in NbN/AlN/NbN tunnel junctions. Appl Phys Lett 66:1992, 1995. 82. A Karpov, B Plathner, KH Gundlach, M Aoyagi, S Takada. Noise properties of a mixer with SIS NbN quasiparticle tunnel junctions. Proceedings of the 6th International Symposium on Space Terahertz Technology, Pasadena, CA, 1995. 83. MG Wicks, PR Haycocks, T Hori. AC Josephson effect in superconducting niobium nitride tunnel junctions at up to 2.5 THz. Electron Lett 26:610, 1990. 84. MC Wicks, PR Haycocks, JR Birch. Frequency metrology to 3 THz using thin film niomium nitride Josephson tunnel junctions. Dig CEPM 1992, pp 26–27. 85. CH Bryant, MC Wicks, Y Liu, JR Birch, PB Davies. Frequency determination of far infrared opticaly pumped laser lines of vinyl fluoride using a niobium nitride Josephson mixer. J Phys D 28: 19, 1995. 86. W, Rothmund, A Zehnder. In: A Barone, ed. Superconductive Particle Detectors. Singapore: World Scientific, 1988, pp 52–65. 87. CA Mears, SE Labov, LH Hiller, M Frank, H Netel, F Azgui. High-resolution superconducting Xray spectometers with aluminum trapping layers of different thicknesses. IEEE Appl Supercond 5: 3069, 1995. 88. GG Saulnief, RA Zacher, GG Fritz, B Hunt, HG LeDuc, A Judas. NbN/MgO/NbN superconducting tunnel junctions as X-ray detectors. J Low Temp Phys 93:653, 1993. 89. RA Zacher, GG Saulnier, GG Fritz, B Hunt, HG LeDuc, A Judas. X-ray detection with NbN/MgO/ NbN SIS tunnel junctions, Extended Abstracts of 4th International Superconducting Electronics Conference, Boulder CO, 1993, pp 394–395. 90. R Cristiano, E Esposito, L Frunzio, S Pagano, L Parlato, G Peluso, GP Pepe, U Scotti di Uccio, H Akoh, M Aoyagi, H Nakagawa, S Takada. Influence of a NbN thick overlayer on Nb/AlOx/Nb high quality Josephson tunnel junctions for X-ray detection. Appl Phys Lett 67:3340, 1995. 91. GN Gol’tsman, AD Semenov, YP Gousev, MA Zorin, IG Gogidze, EM Gershenzon, PT Lang, WJ Knott, KF Renk. Sensitive picosecond NbN detector for radiation from millimetre wavelengths to visible light. Supercond Sci Technol 4:453, 1991. 92. H Ekstro¨m, B Karasik, E Kollberg, G Gol’tsman, E Gershenzon. 350 GHz NbN hot electron bolometer mixer. Proceedings of the 6th International Symposium on Space Terahertz Technology Pasadena, CA, 1995, pp 269–283. 93. BS Karasik, GN Gol’tsman, BM Voronov, SI Svechnikov, EM Gershenzon, H Ekstro¨m, S Jacobsson, E Kollberg, KS Yngvesson. Hot electron quesioptical NbN superconducting mixer. IEEE Trans Appl Supercond 5:2232, 1995. 94. H Ekstro¨m, B Karasik. Electron temperature fluctuation noise in hot-electron superconduting mixers. Appl Phys Lett 66:3212, 1995. 95. M Nakanishi, M Koyanagi, S Kosaka, A Shoji, M Aoyagi, F Shinoki. Integrated DC-SQUID magnetometer. J J Appl Phys 26:1050, 1987.

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13 Solar Absorbers—Selective Surfaces Robert Blickensderfer Research Metallurgist, Consultant, Albany, Oregon

I.

INTRODUCTION

Thin films of the carbides and nitrides of Ti and Zr have shown promise as solar absorbers. Such films can absorb a high percentage of the incident solar radiation while reradiating only a small percentage of the thermal energy. The net thermal energy can thus be withdrawn for use. A surface that has the ability to absorb solar energy effectively while limiting the energy it reradiates, or emits, is spectrally selective. For applications such as solar-thermal power plants, high operating temperatures are desirable to provide high thermal efficiency of the heat cycle, but the convection, conduction, and radiation losses must be minimized. Conduction and convection can be nearly eliminated by operating in vacuum, and radiation losses can be reduced by utilizing a spectrally selective surface. Because radiation losses increase with the fourth power of temperature, the need for spectral selectivity becomes imperative for solar-thermal collectors operating at elevated temperatures in vacuum.

II. BACKGROUND A.

The Idealized Spectrally Selective Solar Absorber

Most of the solar radiation falling on the earth is in the wavelength range below 2 µm. For surfaces at any temperature up to about 1000 K, most of the emitted energy is at a wavelength greater than 2 µm. Therefore, spectral selectivity of a surface will occur in a desirable way for solar-thermal conversion when the absorptance at wavelengths below 2 µm is greater than the emittance at wavelengths above 2 µm. The solar radiation leaving the sun is mainly within the wavelength range 0.3 to 2.5 µm. The distribution of solar energy is close to the Planck blackbody distribution corresponding to a temperature of 5500 K and with a maximum flux at a wavelength of 0.55 µm. The earth’s atmosphere absorbs some of the solar energy but not uniformly over wavelength. Absorption is strongly dependent on interactions with the molecules of water, carbon dioxide, ozone, and to a lesser degree nitrogen oxides and hydrocarbons. Several strong absorption bands occur in the solar infrared region of the spectrum between 0.7 and 2 µm. Figure 1 shows the spectral flux (energy distribution) for solar energy arriving at the surface of the earth after passing through an average atmosphere. This is based on average atmospheric pressure, temperature, and relative humidity and is for air mass 2. Air mass 1 corresponds to absorption at sea level of the sun’s 307

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Blickensderfer

Figure 1 Spectral flux distribution of sunlight and blackbodies.

rays arriving from the zenith. Air mass 2 (AM2) allows double the absorptance and is close to the average energy distribution received from 1 h after sunrise to 1 h before sunset in the midlatitudes. The total solar flux for AM2 is approximately 800 W/m 2. Thermal emittance from the surface of most solids approximates some fraction of the theoretical Planck blackbody distribution. The maximum of the distribution is temperature dependent according to Wien’s law, shifting to shorter wavelengths and increasing in magnitude as the temperature increases. The blackbody emittance distributions for two temperatures are included in Fig. 1. For a temperature a little above the boiling point of water, such as 400 K, the maximum flux is at about 7 µm wavelength, with almost no flux below 3 µm; but at 600 K the maximum flux is at about 5 µm with a small amount emitted below 2 µm. An ideal solar-thermal surface would absorb all solar radiation up to a certain cutoff wavelength, λc . At all wavelengths greater than λ c , the emittance would be zero. The ideal cutoff wavelength varies slightly depending on the temperature and, thus, the shape of the emittance curve. However, a value usually taken for the cutoff is 2 µm. The spectral absorptance of the ideal solar-thermal surface with a 2-µm cutoff would look like that of Fig. 2, where absorptance (α) is 1 for λ ⬍ 2 µm and emittance (ε) is 0 for λ ⬎ 2 µm. Unfortunately, surfaces with more than slight spectral selectivity do not exist in nature. But because of the vast differences in electro-optic properties among materials, opportunities exist for combining materials into a system that approaches the ideal spectrally selectivity absorber.

B.

Definitions and Equations

At a given wavelength λ, absorptance equals emittance: α(λ) ⫽ ε(λ)

(1)

Absorptance plus reflectance plus transmittance equals unity. Therefore, for an opaque solid with no transmittance, the relation between reflectance, r, and absorptance, at wavelength λ, is given by α(λ) ⫽ 1 ⫺ r(λ)

(2)

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309

Figure 2 Spectral absorptance of an ideal solar absorber. Transition from total to zero absorptance is at 2 µm wavelength.

The solar absorptance a(s) is the fraction of the incident solar energy absorbed by the surface: ∫ φ(λ)α(λ)dλ ∫ φ(λ) dλ

a(s) ⫽

(3)

where λ ⫽ wavelength φ(λ) ⫽ solar flux as a function of λ, left curve of Fig. 1 α(λ) ⫽ spectral absorptance of the surface as function of λ The thermal emittance (e T) at temperature T is calculated from eT ⫽

∫ b T (λ)ε T (λ) dλ ∫ε T (λ)dλ

(4)

where b T (λ) ⫽ flux of blackbody radiation at temperature T, as given by a curve similar to those on the right of Fig. 1 ε T (λ) ⫽ spectral hemispherical emittance at temperature T. Because the functions φ(λ), α(λ), and ε T (λ) are not simple, the integration is made numerically. The stagnation temperature (T s) is the maximum temperature reached by a surface exposed to sunlight. It is reached when the losses from thermal radiation, convection, and conduction equal the solar input. Under vacuum conditions, convection losses are eliminated, conduction losses can be negligible, and the stagnation temperature is given by Ts ⫽

冤

冥

a(s)φ ⫹ T 04 KεTs

1/4

(5)

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Blickensderfer

where φ T0 K εTs

⫽ ⫽ ⫽ ⫽

solar flux, taken as 800 W/m 2 ambient temperature, taken as 273 K Stefan-Boltzmann constant, 5.673 ⫻ 10⫺8 W/m 2 K4 total hemispherical emittance at temperature T s

The conversion efficiency, CE, is a good criterion for evaluating a solar surface for both selectivity and absorbing effectiveness. It indicates the amount of heat that can be withdrawn at the operating temperature: CE ⫽

Q a ⫺ Q e ∫ φ(λ)α(λ) dλ ⫺ ∫ b T (λ)e T (λ)dλ ⫽ Qs ∫ φ(λ) dλ

(6)

where Q a is the absorbed solar flux, Q e the emitted flux, and Q s the incoming solar flux. If the solar flux is concentrated by some means, the concentration factor must be multiplied into the Q a and Q s terms, and the equation then gives the Nettogutezahl number (N). Concentration of the solar flux will increase Q a and Q s and hence will increase the CE. C.

Criteria for Evaluating Solar-Thermal Spectral Selectivity

1. Absorptance and Emittance The spectral selectivity of a solar absorber can be judged by comparing its solar absorptance and thermal emittance with the ideal values. Because of the overlap of the solar and thermal spectra, as seen in Fig. 1, the solar absorptance of the ideal surface is limited to a maximum of about 0.99 and the total emittance (600 K) is limited to a minimum of about 0.01. 2. Ratio of a/e The ratio of a(s) to e T is useful for comparing the degree of spectral selectivity among various surfaces. For a surface with no spectral selectivity, such as black paint, a/e ⫽ 1. For the idealized surface of Fig. 2 at 600 K, the a/e ratio is approximately 0.99/0.01 or 99. The maximum a/e ratio will decrease with increasing temperature as the radiation distribution shifts to shorter wavelengths. In practice, it is difficult to achieve an a/e ratio greater than 10. 3.

Stagnation Temperature

A high stagnation temperature is desirable because it defines the upper limit at which heat may be extracted from a solar absorber. The stagnation temperature increases with increasing solar absorptance and decreasing thermal emittance; therefore it is closely related to the a/e ratio. 4. Conversion Efficiency The conversion efficiency is probably the best single indicator of the potential usefulness of a selective solar absorber. The conversion efficiency is dependent on both the solar absorptance and the thermal emittance. For the ideal surface mentioned before, operating at 600 K, CE ⫽ 0.98. Only a few absorbers have been developed that give a CE(600 K) greater than 0.3 without resorting to solar concentration. Many of the known selective surfaces are unable to give a CE(600 K) greater than 0.

Solar Absorbers—Selective Surfaces

D.

311

Measurements of Solar Absorptance and Thermal Emittance

Several methods are used to determine solar absorptance and thermal emittance. Measurement of spectral reflectance is the easiest and most commonly used. This indirect method and three direct methods of measurement (1) are briefly discussed. 1. Spectral Reflectance Normal spectral reflectance data are obtained by scanning the surface with spectrophotometers over the wavelength range 0.3 to 40 µm. Using Eqs. (1) and (2), the reflectance data are converted numerically to absorptance and emittance data. The integrations of Eqs. (3) and (4) are then carried out by numerical methods using φ(λ) for AM2 and e T (λ) for the desired temperature. Such calculated values have agreed well with the direct measurement methods mentioned in the following. 2. Normal Emittance A detector that absorbs the total radiation within the range 1 to 40 µm is used to determine the normal total emittance of a heated specimen. A typical detector uses a thin-film thermopile that accepts a known solid angle of radiation from the specimen. 3. Heating and Cooling Rates A laboratory light source that approximates the solar energy spectral distribution at the earth’s surface is used to irradiate a specimen in vacuum. Knowing the specific heat of the specimen, the initial rate of temperature rise is used to determine the solar absorptance. After reaching T s , where the temperature stabilizes because the thermal emittance of energy equals the solar absorptance, the light source is turned off and the initial cooling rate determines the total hemispherical emittance at T s . The stagnation temperature, in addition, gives a direct measurement of the a/e ratio at T s . 4. Microcalorimetry A specimen is heated by electrical self-resistance in vacuum. Total hemispherical emittance is determined from the Stefan-Boltzmann law of radiation, knowing the power input, the total surface area, and the temperature. By using a solar simulator, as in method 3, the difference in electric power required to maintain a given temperature with the solar simulator on and off determines the solar absorptance. 5.

Comparisons

For the Zr and Ti type of absorbers the calculated values of solar absorptance and emittance based on reflectance data agree within a half percent of the direct measurements made with a solar simulator at a temperature of 400 K. At 600 K, the direct measurements gave a solar absorptance 1% greater than the calculated values and gave a total hemispherical emittance ranging from 0 to 20% lower than the calculated values. The lower measured emittance is a result of the angular dependence of emittance—it decreases with increasing angle from the normal; thus actual emittance is lower than calculated values, which are based on normal reflectance data. In summary, under experimental conditions at elevated temperature, the solar absorptance is desirably increased and the thermal emittance is desirably decreased compared with calculations based on room temperature reflectance data. Therefore, use of room temperature reflectance data is conservative.

312

E.

Blickensderfer

Types of Spectrally Selective Surfaces

The basic approach to design of selective surfaces has been to provide a thin surface layer of particles or films that absorb the solar radiation but are transparent to the longer wavelength thermal radiation. The layer is placed on a highly reflective base, which then limits the emission of thermal radiation. A number of mechanisms operate simultaneously to produce spectral selectivity, namely texture effects, resonant scattering, interband transitions, free electron interactions, and interference effects. Types of spectrally selective surfaces, as reviewed in Ref. 2, are categorized into four general types:

1.

Microrough Surfaces

A metallic surface with a dendritic structure or covered with small particles or whiskers or otherwise roughened at a size of about 1 µm will exhibit spectral selectivity. The solar radiation becomes absorbed while making multiple reflections among the particles, because each reflection results in partial absorption. The longer thermal wavelengths are relatively unaffected by the small particles, and therefore emission is only slightly higher than that of the bulk metal. Examples of a microrough surface include dendritic tungsten prepared by chemical vapor deposition (3) and surfaces of copper, nickel, and stainless steel made by sputter etching (4). Such surfaces typically have high solar absorptance, a ⫽ 0.9, and moderately low emittance, e ⫽ 0.2.

2. Metal Particles in a Dielectric Film Coatings consisting of small metallic particles within a dielectric film, or layers of metal particles between dielectric layers that are deposited on a reflective surface, have proved very selective. The small particles absorb short waves preferentially, while the dielectric is transparent (nonemitting) to long waves. The system offers many choices regarding particle size, shape, orientation, spacing, film thickness, and composition. Two of the best known surfaces are black chrome (5,6) and black nickel (6,7). These surfaces are produced by electroplating and consist of small metal particles in an oxide phase. Typical solar absorptance ranges from 0.90 to 0.95, and thermal emittance (400 K) is typically in the range of 0.07 to 0.20. Chemical vapor deposition has been used to make black molybdenum films consisting of small MoO 2 particles with small Mo inclusions (8). Metals and dielectrics have been codeposited by evaporation and sputtering. For example, a system of cobalt particles in an alumina film was optimized to give a solar absorptance of about 0.9 and thermal emittance of 0.08 (400 K) (9). Alternate thin films of MoSi 2 and alumina and multiple layers of Pt and alumina deposited by sputtering produced good spectral selectivity (10). Ion implantation of surfaces of vanadium and zirconium has produced moderate spectral selectivity by formation of nitrides and surface roughness (11).

3. Semiconductor Films Semiconductor films on metal can absorb solar radiation if the band gap energy is about 0.6 eV. Most photons in the solar spectrum have more than 0.6 eV energy and therefore are captured in the semiconductor. The semiconductor does not emit the longer wavelength thermal radiation. Silicon films produced by chemical vapor deposition on silver have proved the most promising (12,13). Solar absorptance is not particularly high because of the high reflective losses of incident waves at the silicon outer surface. Application of an antireflection coating raises the absorptance to 0.76.

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313

Figure 3 Model of surface of TiN xO y proposed by Lazarov et al. (16).

4. Interference-Absorbing Films Absorbers of this type depend primarily on photon interference within the film to produce a sharp transition at 2 µm wavelength. The film must be relatively transparent at wavelengths greater than about 1 µm in order to provide the necessary interference between the surface and the reflective base metal. If a transparent film is the appropriate thickness to give the first interference minimum at about 1 µm wavelength, no interference occurs at longer wavelengths and the reflectance is high. However, in the shortwave region, the first interference maximum will occur near 0.5 µm, which results in poor solar absorptance. It is necessary, therefore, for the film to absorb radiation in the shortwave region, from about 0.3 to 0.8 µm. Zirconium and titanium nitrides, carbides, and suboxide films have the ability to absorb a large part of this shortwave radiation while being highly transparent to longer waves (1,14,15). A partial explanation for the short-wavelength absorptance is found in the structure proposed by Lazarov et al. (18) for TiN xO y coatings. As shown in Fig. 3, the structure consists of columnar TiN and TiO covered by a thin TiO 2 film. The voids between the columns tend to entrap the shortwave radiation. It is believed that interband transitions and resonant scattering in the film also contribute to the solar absorptance.

III. TITANIUM AND ZIRCONIUM INTERFERENCE ABSORBERS A.

Procedures for Making the Absorbers

The reflective substrate on which the absorber films are subsequently deposited is usually silver or aluminum. Either one is easily deposited by radio frequency (RF) sputtering methods. Silver is preferred because of its greater stability when the absorber is used at elevated temperatures. After depositing the silver, titanium or zirconium is sputter deposited in the presence of a partial pressure of nitrogen and an inert gas such as argon. During sputtering, the metal atoms react

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Blickensderfer

Figure 4 Spectral reflectance of the ideal solar absorber and of silver.

with the nitrogen to form a film of TiN or ZrN. To produce a titanium or zirconium carbide, a TiC or ZrC source is used for sputtering. By introducing nitrogen at a low partial pressure during sputtering, a TiC xN y or ZrC xN y film can be deposited. The subscripts x and y are not known, but their sum is probably about 1 because the two compounds are isomorphic. Similarly, by introducing various partial pressures of nitrogen and oxygen into the sputtering chamber, films of TiC xN yO z or ZrC xN yO z can be synthesized. Absorber films are also prepared simply by heating Zr-Ag sputter-deposited films in air. As both nitrogen and oxygen diffuse into the zirconium, the spectral selectivity increases. Ihara et al. (15) produced ZrC x films by sputtering Zr in a mixture of methane and argon. In this case, x ranged from 0.8 to 8. The optimal film was ZrC 6 and consisted of ZrC and graphite. B.

Spectral Reflectance

The spectral reflectance curve of a surface can readily be compared with the ideal curve to give a visual indication of spectral selectivity. Figure 4 shows the the reflectance of the ideal solar photothermal absorber with the transition at 2 µm. The reflectance curve for silver is also included. Silver reaches a maximum reflectance of about 0.985 in the long-wavelength region, thus placing a practical limit on longwave reflectance of a solar absorber. The spectral reflectance of two titanium and zirconium nitride films of 0.16 µm thickness on a silver substrate are shown in Fig. 5. Both films show relatively low reflectance in the solar spectrum with interference minima around 1 µm. The transition from low to high reflectance is fairly sharp near the ideal wavelength of 2 µm. At increasing wavelengths, the reflectance rapidly approaches that of silver, indicating that the absorptive film is highly transparent to long waves. Zirconium carbide and zirconium carbide-nitride films on silver (ZrC–Ag and

Figure 5 Normal spectral reflectance of TiN x-Ag and ZrN x-Ag coatings.

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315

Figure 6 Normal spectral reflectance of ZrC-Ag and ZrC xN y-Ag coatings.

ZrC xN y Ag), Fig. 6, provide spectral characteristics similar to those of the TiN and ZrN films. The ZrC 6 film of Ihara et al. (15) has the lowest shortwave reflectance, but the transition from low to high reflectance is not as sharp as the others. The longwave reflectance of the ZrC films, especially the ZrC 6 film, is not as high as that of the nitride-type films. The transition wavelength between low and high reflectance depends on the film thickness, as shown in Fig. 7 for ZrN films on silver. Film thickness is easily controlled, being proportional to sputtering time. The thinnest film results in a transition wavelength at about 1.4 µm, which is too short, and insufficient solar absorption is indicated by the relatively high interference maxima near 0.4 µm. The thickest film has a transition wavelength too far into the long wavelengths. The intermediate film, 0.16 µm thick, appears to be near the optimum. The transition is near the desired 2 µm wavelength, and fairly good solar absorptance and low thermal emittance are indicated.

Figure 7 Effect of absorber film thickness on reflectance of ZrN x-Ag coatings. Zr sputtered in nitrogen at pressure of 0.16 Pa.

Absorbers made by air oxidation on zirconium films also showed good spectral selectivity. The normal spectral reflectances of two such films are shown in Fig. 8. Unoxidized ‘‘pure’’ zirconium, shown for comparison, possesses a slight intrinsic spectral selectivity as seen in the upper curve. This may be attributed in part to the existence of the thin film of stable ZrO 2 that forms on zirconium at room temperature. The 4-h oxidation time greatly decreases the shortwave reflectance while also increasing the longwave reflectance. After further heating (20 h total), the reflectance curve is less desirable. Increased reaction with air makes the film more transparent to both short and long waves, as indicated by the development of the interference pattern below 2 µm and the increased reflectance beyond 4 µm. The transition from low to high reflectance of the best air-oxidized specimen is not as sharp as in the reactively sputtered specimens. This is probably due to the composition gradient resulting from the diffusion gradient of oxygen and nitrogen into the zirconium film. The surface composition approaches that of ZrO 2 , which is quite transparent.

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Blickensderfer

Figure 8 Spectral selectivity produced by air oxidation of a Zr film on Ag. The Zr film was 2.4 µm thick, heated in air at 473 K for the times shown.

For specimens prepared by sputtering in a partial pressure of oxygen, reflectance curves are similar to the preceding ones. At low levels of oxygen the reflectance curves display the spectral selectivity typical of those in Figs. 5 and 6. As the oxygen content increases, the surfaces become increasingly transparent to short wavelengths, as indicated by increasing reflectance and interference effects, with a net increase in shortwave reflectance, similar to that of the airoxidized specimens. C.

Performance and Comparison of Solar Absorbers

Performances of six typical Ti- and Zr-type selective absorbers are compared in Table 1. Six other representative types of absorbers are included for comparison. Most of the absorptance and emittance data were calculated from normal spectral reflectance. Emittance calculations were based on a temperature of 600 K for all specimens. Table 1 Performance of Several Solar Absorbersa

Absorber

Source

TiN x Ag ZrN x Ag ZrCAg ZrC 6 SS ZrC x N y Ag ZrO x N y Ag SiliconAg PtAl 2O 3 Pt Black nickel Black chromium Dendritic tungsten Black Paint

Fig. 5 Fig. 5 Fig. 6 Fig. 6 Fig. 6 Ref. 14 Ref. 11 Ref. 9

Ref. 2

Solar absorp. a(s)

Thermal emitt. e(600 K)

Ratio a(s)/ e(600 K)

Stagnation

Conversion efficiency, CE, at 600 K

e Tsb

T s (K)

1 ⫻ conc.

3 ⫻ conc.

0.88 0.86 0.81 0.87c 0.88 0.88 0.76 0.92d 0.94e 0.96e 0.96 0.98

0.065 0.039 0.075 0.123c 0.052 0.084 0.05 0.126d 0.09e 0.15e 0.26 0.98

14 22 11 7 17 10 15 7 10 6 4 1

0.073 0.041 0.080 0.116 0.055 0.088 0.050 0.122 0.095 0.136 0.26 0.98

650 740 620 580 690 620 680 580 620 570 490 374

0.31 0.52 0.15 0 0.42 0.14 0.32 0 0.15 0 0 0

0.69 0.75 0.59 0.51 0.73 0.63 0.61 0.55 0.68 0.52 0.20 0

Most a(s) and e(600 K) values were calculated from normal spectral reflectance data. Solar flux, φ(λ), is for AM2. Total solar flux of 800 W/m 2 used for calculating stagnation temperature and conversion efficiency. b Approximate emittance values; interpolated or extrapolated at stagnation temperature, T s . c Calculated by Blickensderfer from Ihara’s reflectance data. d Calculated by Blickensderfer from Schon’s reflectance data. e Typical of best values in the literature. a

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317

1. Solar Absorptance All of the TiN x , ZrC xN y , and ZrO xN y films provide solar absorptance of 0.86 to 0.88 except the ZrC, which has an absorptance of 0.81. Direct measurements of solar absorptance give values about 1% higher. Other absorbers in Table 1 show absorptance above 0.92, except silicon, whose absorptance is 0.76. 2. Thermal Emittance The thermal emittance (600 K) of the ZrN x film is a very low 0.039. The TiN x and ZrC xN y films show an emittance of about 0.05, which is similar to that of the best silicon film. The other Tiand Zr-type films all have an emittance less than 0.1, except ZrC 6 , which has 0.123. It is believed that the emittance of the ZrC 6 film could be reduced by deposition of a silver film between it and the stainless steel substrate, as used for the other Zr absorbers. The other types of absorbers shown in Table 1 have emittances of 0.09 or higher. 3. Ratio of a(s)/e (600 K) All but one of the Ti- and Zr-type films show a/e ratios greater than 10. The ZrN x film provides the highest a/e ratio, namely 22, which is considered very high. The ZrC xN y film is also very good, with an a/e of 17. The lower a/e ratio of 7 for the ZrC 6 film is again attributed to its higher emittance than the others. The silicon film has an a/e ratio of 15 even though its absorptance is rather low. The other selective absorbers listed show a/e ratios of 10 for black nickel down to 4 for dendritic tungsten. 4.

Stagnation Temperature

The ZrN x film has the highest stagnation temperature, namely 740 K. The other Ti- and Zr-type films have a stagnation temperature above 600 K except for ZrC 6 , which stagnates at 580 K. The other surfaces stagnate at temperatures from 680 K for silicon down to 374 K for nonselective black paint. 5. Conversion Efficiency The conversion efficiencies of the absorbers operating at a temperature of 600 K and with a solar input of 800 W/m 2 are listed in Table 1. Without concentration (1⫻), the ZrN x-Ag absorber with a CE of 0.52, or 52%, is the highest. The CEs of the other absorbers range from 0.14 to 0.42 except for the five surfaces with zero conversion, because their stagnation temperature is below 600 K. By concentrating the solar input three times (3⫻), the conversion efficiency of the surfaces increases, with the Ti and Zr type ranging from 0.51 to 0.75. The silicon and black nickel have values of 0.61 and 0.68, respectively. Only black paint still has a stagnation temperature below 600 K and therefore, has no conversion. D.

Thermal Stability

Good stability of a solar absorber over an economical lifetime at operating temperatures is important. The Ti- and Zr-type films show no change in their optical properties after several years in an industrially polluted atmosphere at ambient temperatures. At elevated temperatures, changes in optical properties result from two causes; oxidation of the absorptive film and deterioration of the silver film (17). Oxidation of the absorptive film causes it to approach the composition of the stable oxide TiO 2 or ZrO 2 . Because these oxides are relatively transparent to solar

318

Blickensderfer

radiation, oxidation of the absorptive film decreases the solar absorptance. Exposure to air at 400 K for 300 h reduces the solar absorptance 10 to 50%. The resistance to oxidation is greatly increased by coating the TiN and ZrN films with a very thin film of a stable oxide. Such films show no change in optical properties after heating in air at 450 K for 300 h and almost no change after an additional 300 h at 500 K. Under vacuum, absorptive films are stable when heated for 500 h at 1000 K. The second cause of changes in optical properties, deterioration of the silver film, occurs above 600 to 650 K. The deterioration occurs in air or vacuum as a result of agglomeration of the silver film or diffusion of the silver into the substrate. The problem has been partially resolved on silicon-silver absorbers (12,13) by applying a thin film of a stabilizing chromium oxide between the silver and substrate. Oxidized films of Cr, Ti, and Zr of 0.02 µm thickness on the substrate can stabilize the silver film to temperatures of 773 K in vacuum (17). Another method for stabilizing the silver film is by oxidizing a stainless steel substrate for 10 min in air at 773 K to form an FeO film (17). A specimen prepared in this manner with a ZrC xN y film showed only small changes in optical properties after 500-h exposures at 773 and 873 K in vacuum.

IV. SUMMARY Thin films of titanium and zirconium subnitrides, carbides, and oxides deposited on a thin film of silver provide some of the greatest spectral selectivity for solar energy absorbers of any known. Solar absorptance ranges from 0.81 to 0.88 and thermal emittance at 600 K is below 0.1 and as low as 0.039. The a(s)/e T ratios at 600 K range from 7 to 22. This high degree of spectral selectivity allows a significant amount of heat energy to be extracted from the absorber while operating at relatively high temperature. For example, the ZrN x Ag absorber operating at 600 K in vacuum will allow 52% of the incoming solar energy to be extracted as heat without requiring concentration of the sunlight. Black chromium and other less selective surfaces, on the other hand, cannot reach 600 K because the radiant heat losses equal the solar input at a temperature below 600 K, whence it stagnates. The Ti- and Zr-type films are stable in vacuum to temperatures above 600 K and possibly to 1000 K. The silver film, which tends to agglomerate at temperatures above 600 K, can be stabilized to a temperature of 773 K or higher by application of a very thin film of a stable oxide between it and the substrate. The Ti- and Zr-type solar absorbers show promise in applications for large-scale photothermal power plants operating at temperatures up to 600 K without requiring optical concentration of sunlight. Higher operating temperatures or higher conversion efficiencies may be expected with concentration of the sunlight.

REFERENCES 1. R Blickensderfer, RL Lincoln, DK Deardorff. Reflectance and emittance of spectrally selective titanium and zirconium nitrides. Bureau of Mines RI8167, U.S. Department of Interior, 1976. 2. DG Granqvist. Spectrally selective surfaces for heating and cooling applications. J Phys Tech Solar Energy 2:191, 1987. 3. JJ Cuomo, JF Ziegler, JM Woodall. New concept for solar-thermal energy conversion. Appl Phys Lett 26:557, 1975. 4. GL Harding, MR Lake. Sputter etched metal solar selective absorbing surfaces for high temperature thermal collectors. Solar Energy Mater 5:445, 1981.

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5. PM Driver. An electrochemical approach to the characterisation of black chrome selective surfaces. Solar Energy Mater 4:179, 1981. 6. HYB Mar, RE Peterson, PB Zimmer. Low cost coatings for flat plate solar collectors. Thin Solid Films 39:95, 1976. 7. PK Gogna, KL Chopra. Structure-dependent thermal and optical properties of black nickel coatings. Thin Solid Films 57:299, 1979. 8. EE Chain, K Seshan, BO Seraphin. Optical and structural properties of black molybdenum photothermal converter layers deposited by the pyrolysis of Mo (CO) 6 . J Appl Phys 52:1536, 1981. 9. GA Niklasson, CG Granqvist. Ultrta fine chromium particles for photothermal conversion of solar energy. J Appl Phys 55:3382, 1984. 10. JH Schon, G Binder, E Bucher. Performance and stability of some new high-temperature selective absorber systems based on metal/dielectric multilayers, Solar Energy Mater Solar Cells 33:403, 1994. 11. JS Liu, A Ignatiev. Optical tailoring of solar absorbers by ion implantation. Solar Energy Mater 13: 399, 1986. 12. M Janai, DD Allred, DC Booth, BO Seraphin. Optical properties and structure of amorphous silicon films prepared by CVD. Solar Energy Mater 1:11, 1979. 13. DC Booth, DD Allred, BO Seraphin. Stabilized CVD amorphous silicon for high temperature photothermal solar energy conversion. Solar Energy Mater 2:107, 1979. 14. R Blickensderfer, DK Deardorff, RL Lincoln. Spectral reflectance of TiN x and ZrN x films as solar absorbers. Solar Energy 19:429, 1977. 15. H Ihara, S Ebisawa, A Itch. Solar-selective surface of zirconium carbide film. Proceedings of International Vacuum Congress and 3rd International Conference on Solid Surfaces, Vienna, 1977, pp 1813– 1816. 16. M Lazarov, P Raths, H Metzger, W Spirkl. Optical constants and film density of TiN xO y solar selective absorbers. J Appl Phys 77:2133, 1995. 17. FW Wood, R Blickensderfer. Stabilization of absorber stacks containing Zr or Ti compounds on Ag. Thin Solid Films 39:133, 1976.

14 Metalloids for Plasma-Facing Materials Tatsuhiko Tanabe and Masakazu Fujitsuka National Research Institute for Metals, Tsukuba-shi, Ibaraki, Japan

I.

INTRODUCTION

The constituent elements of the plasma-facing components of fusion reactors often intrude into plasma as impurities due to sputtering, erosion, sublimation, and so on. Plasma impurities result in plasma cooling by line radiation, prevent neutral beam penetration into the plasma core, initiate runaway electrons, and possibly affect sputtering arcing erosion rates (1). As the radiative losses due to impurity ions increases abruptly with increasing atomic number of the impurities, the plasma-facing materials of fusion reactors, at least their surface, should be composed of low-atomic-weight materials (low-Z materials). Further, the materials should be resistant to thermal shock and should have good properties in their interaction with plasma. The substantial property needed for the plasma-facing materials is a high melting point. Many high-melting-point materials such as W and Mo have high Z. Therefore, low-Z bulk materials as well as low-Z materials coated onto the high-melting-point materials are candidates for the first wall of fusion reactors (1,2). The merits of using coated materials are as follows: 1. Alteration of the surface films can be performed easily and cheaply. This enables us to provide for the evaluation tests of various coated films in the experimental equipment. 2. Substrates can be selected from the standpoint of structural materials and the surface films can be selected from the standpoint of surface functional materials, with the result that a broad choice of the materials is possible. 3. The thermal and mechanical properties of the coated materials can be assumed in the structural design to be the same as those of the substrates when the films are thin. With this, safety and reliability of the structures can easily be achieved. 4. The microstructures of the films can be so easily controlled that the freedom of the material design increases. In addition, they have some demerits: 1. Surface films exfoliate easily. 2. Thick films would be needed because of the increasing wastage of surface films when the particle load against the first wall of the reactors increase with the enlargement of fusion reactors. This leads to easy fracture and exfoliation of the films. 3. The chemical interactions between coated films and substrates at high temperatures often cause deterioration of the films. 321

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4. Degradation of the substrates occurs because of the existence of surface films. In developing low-Z coated materials, these demerits should be surmounted. It is natural to select low-Z, high-melting-point materials as the coating materials. The selected low-Z, high-melting-point materials are TiC (m.p. 3340 K), TiB 2 (m.p. 3190 K), and graphite (m.p. 4020 K). Among the low-Z coatings, TiC is considered one of the most promising materials because of its low chemical sputtering yield and high melting point (3). On the other hand, TiB 2 coating has a distinct advantage over TiC coating; i.e., hydrogen isotope retention in TiB 2 is less than that in TiC, especially at elevated temperatures (4,5). Therefore, it would be possible to get better characteristics by fabricating the bulk mixtures of TiC and TiB 2 rather than the individual compound. From these standpoints, the formation of TiC and TiB 2 coatings onto the high-meltingpoint materials and of mixtures of TiC and TiB 2, the thermal stability of the coated materials, and thermal shock test results for both materials are mentioned in this chapter. All the data shown here were derived at the National Research Institute for Metals (NRIM), Japan.

II. THE RESEARCH AND DEVELOPMENT ON LOW-Z COATING MATERIALS There are many low-Z coating methods, such as the chemical vapor deposition (CVD), radio frequency (RF)–reactive ion plating, the magnetron sputtering, solid reaction bonding, and vacuum arc deposition methods. As the properties of the coated materials depend on the coating methods and fabricating conditions, it is important to control the conditions for each method to get heat-resistant coated materials. Here, the RF–reactive ion plating method and magnetron sputtering method are mentioned. A.

TiC Formation by the Ion Plating Method

Figure 1 shows a schematic representation of ion plating equipment. With this equipment, the films could be deposited both by modified Activated Reactive Evaporation (ARE) (DC discharge method) and by ion plating using RF electrodes (RF discharge method). The raw materials are evaporated by the electron beam and ionized with the reactive gases in the plasma through DC or RF glow discharge. The films are formed when the ions are accelerated by the bias voltage and impinge on the substrate with high energy. The formation of TiC films on Mo plate was performed by the ion plating method, whereby the temperature of the substrate was controlled according to a program. Figure 2 shows the principle. As the deposition rate of carbon is rate controlled through the pyrolitic reaction of acetylene, the rate increases with increasing substrate temperature. When the deposition of the films is done according to the heating and cooling program shown in the figure, a continuous concentration gradient of carbon is formed at the interface. This leads to relaxation of thermal stress, with the result that their adherence is improved. The properties of the films are dependent on the activation rate of the plasma in the ion plating methods. Here, two activation methods were compared. One is the RF discharge method and the other is the ARE method. As shown in Fig. 1, RF coil was used in the former case, and a direct current of about 20 A with 50–60 V between the Mo probe and evaporation substances was supplied in the latter case. Measurement of the specimen current revealed that the ionization efficiency in the latter case is several times larger than in the former. The relation between the composition ratio of Ti and C and the ratio of impinging acetylene

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323

Figure 1 Schematic representation of an ion plating apparatus.

molecules and titanium atoms on the substrate is shown in Fig. 3. In the DC method, the C / Ti compositional ratio becomes 1 when the acetylene/titanium ratio is larger than 40, whereas in the RF method, the compositional ratio varies widely depending on the acetylene/titanium ratio. This is reduced to easy decomposition and ionization of acetylene gas during the RF discharge. In this case, the released carbons are accommodated easily in the films. (6,7)

B.

TiC Formation by Magnetron Sputtering Method

Among the various coating methods, the magnetron sputtering process has the characteristics that coating of large substrate materials is easy and coating at low temperature is possible. The equipment for the magnetron sputtering method is shown in Fig. 4. This is a conventional RFtype planar magnetron sputter coating device. Sintered TiC 6 inches in diameter and 1/4 inch thick was used as a target and the supplied RF power was 3 kW with a frequency of 13.56 MHz. The substrate can be heated up to 973 K by the heater. A quadrupole mass spectrometer was used for the analysis of the composition of the working gas during the sputtering. TiC films were deposited on an Mo substrate with an area of 5 ⫻ 10 mm 2 at 870 K in a discharged Ar environment by the magnetron sputtering method. The relations between the film properties and the sputtering conditions are shown in Table 1. When titanium flakes lie on the TiC target during sputtering, the Ti/C ratio increases accompanying a decrease in the lattice parameter. The degree of crystallization becomes worse with decreasing substrate temperatures if evaluated from the half-width of the X-ray diffraction line. If the substrate is highly RF biased, the concentration of Ar accommodated in the film and the lattice parameter increase. This means

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Figure 2 Improvement of adhesion between TiC film and the Mo substrate through control of the substrate temperature (pressure of C 2H 2 , 1.5 ⫻ 10 ⫺2 torr).

a decrease in the degree of crystallization. Lower working gas pressure during sputtering leads to the same result. The Ti/C compositional ratio can easily be changed with the magnetron sputtering method by placing Ti flakes or graphite flakes on the TiC target. TiC films were deposited on Mo substrates with an area of 10 ⫻ 10 mm 2 heated to 870 K in a 5 ⫻ 10 ⫺1 Pa Ar environment by applying 1 kW of RF power to the TiC target. The result is shown in Fig. 5. X-ray diffraction revealed that the preferred plane is (111) for C-rich TiC films and (200) for Ti- rich TiC films. No preferred texture was observed in the films that had a concentration near stoichiometry. Figure 5 also shows the relation between the Ti/C ratio and the lattice parameter. The lattice parameter increases with increasing C content. The internal stress in the films, estimated by using the curvature radius of the substrate, and the Ar content in the films increased with increasing C content. From these results, the cause of internal stress would be that in the C-rich films the vacancy concentration of Ti becomes large and Ar gas can be accommodated in the vacancies. Figure 6 shows the relation between the density and the compositional ratio of the films. The figure indicates that about one-half of the extra C atoms become interstitial and one-half of the deficient Ti atoms become vacancies. (8–11) C.

TiB 2 Formation by the Magnetron Sputtering Method

The same equipment was used to obtain TiB 2 films on an Mo substrate. The sputter working gas was 5 ⫻ 10 ⫺1 Pa Ar. A 99.98 wt % Ti disk with a diameter of 150 mm was used as a

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Figure 3 Relation between compositional ratio in TiC and the ratio of injected acetylene (C 2H 2) to Ti.

Figure 4 Schematic representation of magnetron sputtering apparatus.

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Table 1 Relation Between Characteristics of TiC Films and Sputtering Conditions a

Condition

Ti/C ratio

Ar content

Lattice parameter

Half-width of X-ray diffraction peak

Existence of Ti on the target Substrate temperature Substrate bias voltage Gas pressure at sputtering

⫹⫹ ⫹⫺ ⫺ ⫺

⫺ ⫺ ⫹⫹ ⫺⫺

⫺⫺ ⫹ ⫹⫹ ⫺⫺

⫺ ⫺⫺ ⫹⫹ ⫹⫺

a

⫹⫹, strong positive relation; ⫹, positive relation; ⫹⫺, no relation; ⫺, negative relation; ⫺⫺, strong negative relation.

sputter target. The RF power applied to the target was 1 kW. A suitable amount of single-crystal 99.9 wt % B particles about 5 mm in size was placed on the target. In order to control the chemical composition of the deposited film, the amount of B particles was changed. The distance between the target and the Mo substrate was 80 mm. The deposition temperature was 870 K. Figure 7 shows the deposition rate of Ti 1⫺xBx measured by gravimetry as a function of the amount of B placed on the titanium target. The deposition rate was independent of an amount of B less than 15 g and was estimated to be about 15 µg min ⫺1 cm ⫺2 . For an amount of B in the range 15–20 g, the deposition rate decreased with increasing amount of B to 7–8 µg min ⫺1 cm ⫺2 . The deposition rate seems to be independent of the amount of B with an increase in the amount of boron of more than 20 g. Figure 8 represents the relation between the chemical composition of the deposited films and the amount of B placed on the Ti target. Electron probe microanalysis (EPMA) did not reveal any evidence of Ar atoms in the deposited Ti 1⫺xB x films. This is in contrast to the case of Ti xC 1⫺x deposition just mentioned. The B content in the films increased with increasing amount of B. In the range of 15–20 g of B, the B content in the deposited films increased abruptly. In this region, a nearly stoichiometric composition of TiB 2 can be obtained. The phe-

Figure 5 Relation between lattice parameter of TiC and the compositional ratio (Ti/C).

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Figure 6 Relation between density of Ti xC 1⫺x coating on Mo substrate and chemical composition. Curve a, excess C atoms exist as interstitials; curve b, deficient Ti atoms exist as vacancies; curve c, half of the excess C atoms and half of the deficient Ti atoms exist as interstitials and vacancies, respectively; curve d, excess C atoms exist as graphite.

Figure 7 Deposition rate of Ti 1⫺xB x as a function of the amount of boron on 150 mmφ Ti target.

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Figure 8 Chemical composition of deposited films as a function of the amount of boron on 150 mmφ Ti target.

nomena (drop in deposition rate, abrupt change in chemical composition of deposited films, and formation of stoichiometric products) are similar to those observed with the reactive sputtering technique (14). Figure 9 shows the results of microhardness measurements on the deposited Ti 1⫺xB x films with a 25 gf load. Among the films, stoichiometric TiB 2 had the highest microhardness of about 3000 kgf cm ⫺2 , which is nearly equal to that of sintered TiB 2 . In spite of this, the intensities of the TiB 2 diffraction peaks from the stoichiometric films were very weak when the films were deposited without a bias voltage applied to the molybdenum substrate. Strong intensities of the hexagonal TiB 2 diffraction peaks were obtained when the stoichiometric films were deposited with a negative bias voltage. These results are shown in Fig. 10. The application of a negative bias voltage does not affect the results of the microhardness measurements. The results of X-ray diffractometry suggest that crystallization is imperfect in the stoichiometric TiB 2 films deposited without a negative bias voltage and that the application of a bias voltage to the substrate enhances the crystallization of TiB 2 . In the X-ray diffraction analysis, the 00n diffraction peaks of the hexagonal TiB 2 had the strongest intensity, while the intensities of 101 and 102 were weak. These results indicate that the deposited TiB 2 films have a strong preferred (001) orientation. Figure 11 represents the lattice parameters c and a of the deposited hexagonal TiB 2 as a function of the applied bias voltage. Increasing the applied bias voltage slightly changed the ˚ , although the reported value is 3.22 A ˚ (15). lattice parameter c of TiB 2 from 3.18 to 3.25 A ˚ which is slightly larger than the reported The lattice parameter a is estimated to be about 3.05 A ˚ . It can be said that the two estimated lattice parameters coincide well with the value of 3.02 A reported values. (12,13)

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Figure 9 Change in microhardness of Ti 1⫺xB x as a function of chemical composition x.

Figure 10 Diffraction patterns of TiB 2: (a) TiB 2 deposited without a negative bias voltage. (b) TiB 2 deposited with a ⫺50 V bias voltage.

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Figure 11 Lattice parameters, a and c, of TiB 2 as a function of applied bias voltage.

III. THERMAL STABILITY OF THE COATED METALLOID FILMS It is important to examine the thermal stability of the formed metalloid films, because when the operating temperature is high, the formed metalloid may decompose and diffuse into the substrate or the substrate elements intrude into the metalloid films, both of which cause deterioration of the metalloid films.

A.

Thermal Stability of TiC Films Coated by Ion Plating Method

A comparison was made of the thermal stabilities of the TiC films on Mo substrates formed by the ion plating method with and without controlling the substrate temperature. The specimens with TiC films were heated at 2073 K in a vacuum of 5 ⫻ 10 ⫺6 torr for 40 min. Figure 12 gives the compositional analysis by EPMA from the film surface to the substrate. The specimen, whose substrate temperature was controlled, had a layer in which the carbon contents changed continuously. In this specimen, there was a thick diffusion layer at the interface between the film and the substrate. Scanning electron microscopy showed that TiC precipitated like a wedge in the Mo substrate near the interface. The films did not exfoliate because of the thick diffusion layer and the anchoring effect of the precipitates. The effect of compositional ratio of TiC x on the evaporation rate of the films on the Mo substrate was examined by heating for 40 min in the temperature range 1873–2273 K in a vacuum of 5 ⫻ 10 ⫺6 torr. The compositional ratio, x ⫽ C/Ti, was determined from the EPMA measurement. The results are shown in Fig. 13, where TiC films on graphites formed by the CVD process were taken as a reference. The weight loss of the films became larger with deviation of the compositional ratio from stoichiometry. From X-ray photoelectron spectroscopy (XPS), the existence of free Ti was recognized in the films whose composition deviated from stoichiometry.

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Figure 12 Compositional changes of TiC films on Mo substrates after heat treatment. (a) Coated material with continuously varying content of C formed by the substrate temperature controlling method; (b) coated material produced by normal method (substrate temperature was kept constant).

This is assumed to be the main cause of weight loss due to evaporation. The effect of temperature on the evaporation rate of TiC films is shown in Fig. 14. The evaporation rate of TiC on Mo increased gradually with increasing temperature from 2073 K, whereas that of TiC on graphite was almost null. After heating to 2273 K, the surface of TiC on Mo became spongelike; however, that on graphite did not change. X-ray diffraction revealed that after the heating, Mo 2C was recognized on the surface of TiC on Mo. This means that free Ti appears because of the formation of Mo 2C. The formation of Mo 2C is energetically preferred to that of TiC at temperatures higher than 1973 K from the standard free energy of formation. (3,7) B.

Thermal Stability of TiC Films Coated by the Magnetron Sputtering Method

The effect of the amount of Ar atoms incorporated in the TiC films on the thermal stability of the films was examined. TiC films were deposited onto Mo substrates at 870 K in a 5 ⫻ 10 ⫺1 Pa discharged Ar environment by RF planar magnetron sputter coating with a deposition rate of about 2.5 mg/m 2 s and a deposition duration of 6 h. Some of the deposited TiC films were heat treated at 1100–2300 K in a vacuum of about 1 ⫻ 10 ⫺4 Pa for 5 h in order to examine

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Figure 13 Relation between the compositional ratio X(C/Ti) of TiC x film and the evaporation rate for heating tests under vacuum.

their thermal stability. The deposited films had the chemical composition Ti 0.6C 0.4 (in atomic ratio) with an NaCl-type structure, regardless of the applied voltage Va . The deposition rate, thickness of the deposited films, Ar content, and lattice constant as a function of V a are shown in Table 2. The deposition rate decreased with decreasing V a . The amount of Ar atoms incorporated increased appreciably with decreasing V a as indicated in Table 2. The lattice constant of matrix TiC increased with an increase of incorporated Ar. This suggests that the incorporated Ar exists as a solute in the TiC matrix in the as-deposited condition. When the deposited TiC films containing Ar atoms were heat treated, the lattice constant

Figure 14 Temperature dependence of evaporation rate of TiC coatings on Mo and POCO graphite substrates. Solid line, IP-TiC/Mo and CVD-TiC/Mo; dotted line, IP-TiC/POCO G and CVD-TiC/ POCO G.

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Table 2 Characteristics of Deposited TiC Films Produced by the Magnetron Sputtering Method Bias voltage (V) Characteristic Deposition rate (mg/m 2 s) Thickness (µm) a Ar content (wt%) Half-width of (200) X-ray diffraction peak ˚) Lattice constant (A ∑(hkl) (au) b a b

⫹30

⫺70

⫺170

⫺220

2.785 12.26 0 ⬃ 0.3 ⬃0.4

2.622 11.31 3⬃8 ⬃0.6

2.267 9.98 8 ⬃ 15 ⬃1.0

2.080 9.15 9 ⬃ 15 ⬃1.1

4.31 ⬃70

4.35 ⬃80

4.38 ⬃80

4.40 ⬃50

Density is assumed to be 4.91 g/cm 3. au, arbitrary unit.

began to decrease at about 1100 K as shown in Fig. 15, indicating that the solutes (Ar atoms) become mobile and begin to segregate at this temperature. Observation of the surface morphology of as-deposited and heat-treated TiC films revealed that faceting occurred at temperatures higher than 1500 K, indicating that the evaporation was appreciable from this temperature. The faceting temperature rose with decreasing V a . This means that films deposited with a higher negative bias voltage V a are more stable and resistant to thermal evaporation. At higher temperatures, blisters formed on films containing more than a few wt % Ar. Depending on the Ar content, the temperature at which blisters started to form during 5 h of heat treatment varied, from 2100 K with 3 wt % Ar to about 1300 K with 12 w % Ar. The measured blister density was independent of the heat treatment temperatures and was proportional to the Ar content. From 100 to 150 µm was a typical diameter of a blister with a density of about 20 mm ⫺2 at 1800 K, with 12 wt % Ar. The measured thickness of the erupted blister skin was about 7–10 µm, nearly equal to the film thickness. This means that blisters could be

Figure 15 Relation between lattice parameter of TiC films and heat treatment temperature.

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formed within the film if the films were thicker than, say, 20 µm. The blister morphology changed from flat-shaped to high-roof and dome shaped as the negative bias voltage V a increased. The film began to exfoliate after blisters grew and erupted with increasing heat treatment temperature. The growth of the blisters was as follows. The flat blisters grew by increasing their diameter without appreciable increase in their roof height, and the high-roof and dome-shaped blisters grew by increasing their roof height without appreciable increase in their diameter. These morphological differences in the blisters could be attributed to the difference in the adhesive strength of the deposited film. Because the film deposited with low bias voltage, V a , was considered to have weak adhesive strength, the blisters formed at the interface between the film and its substrate could accommodate the rising internal pressure through expanding the volume by debonding the film interface; that is, the blisters grew along the film interface without appreciable increase of their heights. Meanwhile, the film deposited with higher negative bias voltage, V a , would have higher adhesive strength, with the result that the increasing internal pressure could not debond the adhesive interface but would exceed the fracture strength of blister skin and would finally cause the skin to erupt. After the blisters erupted, the film commenced to exfoliate. The TiC films with more than 15 wt % incorporated Ar did not form blisters. Instead, many small pits were formed at temperatures above 1300 K. In this case, exfoliation of the films occurred substantially at above 1500 K. Figure 16 shows a schematic representation of the behavior of deposited TiC films at elevated temperatures as a function of the bias voltage, V a , or as a function of their Ar content. (10)

C.

Thermal Stability of TiB 2 Films Coated by the Magnetron Sputtering Method

TiB 2 films with a thickness of 6 µm were deposited on an Mo substrate at 870 K by the cosputter coating method using a conventional RF-type planar magnetron sputtering coating device. The sputter working gas was 5 ⫻ 10 ⫺1 Pa Ar and the sputter target was a Ti disk with a diameter of 150 mm. To control the ratio of Ti and B in the films, a suitable amount of boron particles was placed on the Ti disk. In order to examine the thermal stability of TiB 2 films, the coated specimens were heated in a vacuum of 1 ⫻ 10 ⫺4 Pa for 5 h in the temperature range 1270– 1670 K and for 0.33 h at 2273 K. Table 3 shows the results of thermal stability tests of deposited TiB 2 . Evaporation in Tirich films (Ti 1⫺xB x; x ⬍ 0.67) occurred easily at relatively low temperatures. Ar gas incorporation was not observed in the films. In spite of this fact, some blister formation was observed on the Ti-rich specimens. The stoichiometric and B-rich films possessed good resistance to evaporation. However, they showed weak adherence to Mo substrates when they were deposited without the application of a negative bias voltage to the Mo substrates. The adherence of TiB 2 films to their Mo substrate was improved by application of a negative bias voltage. The TiB 2 films deposited with a negative bias voltage larger than ⫺50 V exhibited excellent thermal stability even at the highest temperature, 2273 K. (12)

D.

Improvement of TiC Films Coated on Molybdenum Substrate

In the foregoing section, it was shown that the thermal stability of TiC coated on an Mo substrate degraded in vacuum at temperatures higher than 2073 K because of the formation of (Ti,Mo) xC 1⫺x and Mo 2C layers at the interface of the TiC film and Mo substrate. To prevent the reaction, it is supposed to be effective to ensure an intermediate layer between TiC and the substrate. From the standpoint of the high-temperature chemical reactions between Mo and

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Figure 16 Stability diagram of TiC films containing Ar gas as a function of bias voltage.

Table 3 Appearance of Ti 1⫺xB x Films After Heat Treatment a Specimen Ti 0.5B 0.5 Ti 0.4B 0.6 Ti 0.33B 0.67 Ti 0.23B 0.77 Ti 0.33B 0.67(bias, ⫺50 V) a

1273 K, 5h

1473 K, 5h

1673 K, 5 h

2273 K, 20 min

G G G Ex G

B (Ev) B B (Ex) Ex G

B (Ev) B (Ev) B (Ex) (Ev) Ex G

Ev Ev Ev

G, good; B, blistering; Ev, evaporation; Ex, exfoliation.

Ev

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Figure 17 Effect of an intermediate W layer on the thermal stability of TiC coatings on Mo substrates.

materials with a high melting point and from a comparison of the standard free energies of formation in several carbides, tungsten (W) was selected as an intermediate layer. As an intermediate layer, W films with a thickness of 5 µm were coated on an Mo substrate by the magnetron sputtering method under the following conditions: substrate temperature, 873 K; pressure of Ar, 6.7 Pa; RF power, 500 W. It is well known that Ar incorporation occurs during the formation of W by sputtering. In order to lower the Ar content to a level at which blisters do not form on heating in vacuum at high temperature, an additional heat treatment in a vacuum lower than 10 ⫺3 Pa was needed. The TiC films were formed on W layers on an Mo substrate by the RF–reactive ion plating method mentioned in the previous section. The thermal stability of TiC films was examined by heating in vacuum at temperatures ranging from 1873 to 2273 K for 15–30 min. Figure 17 shows the effect of the W intermediate layer on the film thickness. Little charge in the film thickness of the TiC-coated materials with a W intermediate layer occurred after heat treatment at 2273 K. Characteristic X-ray images of elements along the cross section of the specimen after heating at 2273 K reveal that an Mo 2C phase was not formed and only a small amount of W existed in the TiC films coated on a W intermediate layer. (16,17)

IV. FORMATION OF BULK CARBON MATERIALS CONTAINING TiC AND TiB 2 Carbon materials such as graphite and C/C composites have high melting points and high thermal conductivities. Furthermore, carbon is a typical low-atomic-number element. Because of these characteristics, the materials are used for components subjected to a high heat load and high particle fluxes of the plasma in nuclear fusion reactors. However, they also have distinct disadvantages as plasma-facing materials, namely radiation-enhanced sublimation (21), high retention of hydrogen isotopes, high sublimation at elevated temperatures, and radiation-induced degradation of thermal conductivity (22). As these disadvantages will be key issues in the next-

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Table 4 Results of X-Ray Diffraction Analysis in C-B-Ti Compounds Composition of raw material (at %) C 50 45 42.5 40 37.5 35 35 35.4 33.5 31.3 30 25.9 24 12

Relative X-ray intensity ratio (TiB 2 (101) as standard)

B

Ti

TiB 2(101)

TiC(200)

Graphite(002)

30 35 42.5 40 37.5 45 35 13.1 37.2 34.7 50 28.8 26 38

20 20 15 20 25 20 30 51.5 29.3 34 20 45.3 50 50

1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.13 0.10 0.04 0.09 0.06 0.11 0.29 5.6 0.36 1.63 1.07 0.89 3.03 1.43

0.15 0.19 0.26 0.13 0.08 0.16 0.08 0 0.87 0 0.26 0 0 0

generation fusion devices, many attempts are being made to improve graphites. One such example is boronized carbon. In this material, radiation-enhanced sublimation is suppressed (23), and the plasma performance will be highly improved because of the reduction of oxygen impurity levels in the plasma with the addition of boron (24). It is clear from the phase diagram that the melting point of the carbon-boron system is much lower than that of graphite, and this is the disadvantage of the system. But if we could add titanium to the system, the material obtained would contain TiC, TiB 2 , and carbon. As both of the former compounds have relatively higher melting points (higher than 3173 K) than boron carbides, the drop in the melting point due to boronizing would be avoided. Furthermore, the radiation-induced sublimation of TiC is smaller than that of graphite (25), and also the retention of hydrogen isotopes of TiB 2 is lower than that of graphite (4). These will make the mixed compounds superior to graphite as plasma-facing materials. For the preceding reasons, carbon-boron-titanium compounds were fabricated by the following methods. Powders of graphite (10 µm), boron (0.15 µm), and titanium (30 µm) were dry blended and hot pressed to disk-shaped compacts at 1073 K for 5 min under a uniaxial stress of 30 MPa in a vacuum of 1 ⫻ 10 ⫺3 Pa. The diameter of the compacts was about 30 mm and their thicknesses were 3–10 mm. The compacts were then sintered gradually from 1473 to 1773 K and finally at 2273 K for 30 min. Some of the compacts were Hot Isostatic Pressing (HIP) treated at 2273 K under a pressure of 2000 atm for 30 min after the hot pressing. Table 4 shows the atomic compositions of carbon, boron and titanium in raw materials and the relative existence ratios of TiC, TiB 2 , and graphite obtained after sintering in terms of X-ray diffraction intensity ratios using TiB2 (101) as a standard. As can be seen in the table, TiC, TiB 2 , and graphite are formed by the production method mentioned before. (18–20)

V.

THERMAL SHOCK RESISTANCE OF METALLOIDS

In fusion reactors, heat load on their first wall often reaches 5–10 kW/cm 2 for several reasons, such as the existence of abnormally accelerated runaway electrons, arcing between plasma and

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the first wall, and plasma disruption due to sudden break of a stable plasma discharge. The firstwall materials are damaged by such high heat loads. At NRIM, a convenient electron beam high-heat-flux test apparatus with a hot hollow cathode discharge gun (HCD gun) was designed to modify high heat loads attacking the first walls of fusion reactors (26,27). Figure 18 shows a schematic representation of the apparatus. This type of electron gun provides a low-energy (40–50 eV) and high-current (100–200 A) electron beam; thus the surface heating is similar to that which occurs by plasma ion bombardment. The beam was focused by a solenoid and passed through an Mo aperture (22 mm diameter). The center of a specimen that was mounted on a cooled copper holder was irradiated. The beam diameter was 13 mm and the average heat flux was estimated from the following relation: Φ ⫽ I a xV c where I s is the electron beam current to the specimen and V c is the voltage between the electron beam gun and the specimen. In order to analyze the phenomena, including erosion and vaporization, the specimen current was continuously monitored during the test. Typical current changes during the thermal shock tests are shown in Fig. 19. At the onset of erosion, the current abruptly rose and was almost constant until the end of the test. Therefore, the incubation time for erosion could easily be determined from the specimen current-time relation chart. A.

Thermal Shock Resistance of TiC-Coated Molybdenum

Three kinds of TiC-coated Mo specimens were tested using the thermal shock test apparatus just mentioned, namely TiC directly coated Mo (TiC/Mo), TiC-coated Mo precoated with a thin W layer (TiC/W/Mo), and TiC-coated vacuum-heat-treated Mo with a W intermediate layer (TiC/HT-W/Mo). High heat flux was 5.3 kW/cm 2 and the heat duration was 1.5 s. The surface morphology was observed after the tests. In the case of TiC/Mo, there was

Figure 18 Schematic representation of pulsed electron beam heating apparatus.

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Figure 19 Typical examples of change in specimen current with exposure time during pulsed electron beam heating tests: (a) in the case of specimen fracturing; (b) in the case of specimen melting.

a melted area corresponding to the beam spot and bare Mo substrate was observed. In the case of TiC/W/Mo, a color change of TiC was observed in the beam-heated area and there was a melted area in its center with a diameter of 1 mm Φ. In the case of TiC/HT-W/Mo, a small change of the color in the heated region was recognized. Therefore TiC/HT-W/Mo has adequate thermal shock resistance. Figure 20 shows times to surface melt of bare Mo, of TiC/Mo, and of TiC/HT-W/Mo at a heat flux of 5.3 kW/cm 2 . It should be noted that TiC/Mo has a much shorter time to melt than bare Mo. This indicates that compounds with low melting points would be formed at the interface between TiC and Mo. Here also the superiority of TiC/HT-W/Mo is recognized. (17) B.

Thermal Shock Resistance of Graphite and Carbon Materials Containing TiC and TiB 2

Fracture and/or erosion appears in specimens heated by the electron beam from the thermal shock testing apparatus. When the specimen is thin (⬉1 mm), fracture often occurs within 1 s of heating. When the specimen is thick (⬃10 mm), erosion occurs. The extent of erosion and the thickness of the specimen at which fracture occurs, say just after 1 s of heating, depend on the heat flux and the material properties. 1. Fracture of Graphite Various kinds of isotropic and anisotropic graphites were exposed to the electron beam, whose diameter was 13 mm. Table 5 shows the experimental results. All the specimens fractured within 1 s of the heat load. In this table, W denotes the heat flux when the specimen fractures with 1 s of heat load duration. These values were evaluated from the experimental results using an empirical relation that the time to fracture is inversely proportional to the third power of the incident flux. The relation was confirmed by both experiments and computer simulation. From

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Figure 20 Time to surface melting in electron beam heating tests as a function of number of heating. The heat flux was 5.3 kW/cm 2 . (a) Bare Mo substrate; (b) TiC/Mo; (c) TiC/HT-W/Mo.

Table 5 Properties of Graphite Samples and Results of High-Heat-Flux Tests

Specimen ISO-880U IG-110U ETP-10 G1950S (储 ) (⊥) AX650K YPD-K ( 储 ) (⊥)

Thermal Thermal Elastic Tensile Pore conductivity expansion modulus strength size Heat flux Fracture W (kcal/mhK) (10 ⫺6 /K) (kg/mm 2) (kg/mm 2) (µm) (kW/cm 2) time (S) (kW/cm 2) 73 100 90 90 50 90 220 60

6.5 4.6 3.8 4.5 5.6 4.8 1-2 12–13

1300 1000 1100 1225 850 1180 1450 470

7.0 2.5 3.5 3.0

0.4 3 2 ⬍0.5

1.31 1.31 1.42 1.49

0.6 1.0 0.65 0.75

1.0 1.1 1.3 1.5

3.1

2 0.7

1.24 2.10

1.0 1.0

1.4 2.0

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the W values, one can see that YPD-K endures the high heat flux about twice as long as the other samples without fracture. Also, anisotropic G1950S has the second best W value. These two anisotropic samples have higher thermal conductivity, lower thermal expansion, and higher elastic modulus in the direction parallel to the specimen surface than in the thickness direction. The well-known thermal shock parameter of the material is defined as R ⫽ σ t(1 ⫺ ν)K/(Eα) where σ t is the fracture strength, K the thermal expansion coefficient, E Young’s modulus, and α thermal conductivity. The lower the value of R, the lower the thermal shock to the material becomes. If fracture stress and Poisson’s ratio do not change greatly in the present graphite materials, the graphites with higher thermal conductivity, lower thermal expansion coefficient, and higher Young’s modulus suffer lower thermal shock, as in the case of anisotropic graphites. (27) 2. Erosion of Graphites and C/C Composite Heat load tests were performed on isotropic graphites, pyrolytic coated graphites with a coating thickness of 5–30 µm, and a C/C composite (felt type). The sample sizes were 25 ⫻ 25 ⫻ 3– 10 mm, the beam diameter was 12.7 mm, and the heat load duration was 5 s. The results are shown in Table 6. Severe erosion was observed on the surface of most specimens. The erosion mechanism may be vaporization and ejection of small carbon particles from the surface due to thermal stress. The incubation time to erosion increased in all cases with sample thickness. This means that the erosion process is controlled by the surface temperature, because increasing rate of the surface temperature decreases with increasing of thickness. In the case of pyrolytic coated graphites, the incubation time to erosion decreased with increasing coating thickness. Also, the damaged region of pyrolytic coated graphites increased with increasing coating thickness. This increase may be attributed to the difference in thermal and mechanical properties between the coating and the substrate. The damaged region of the C/C composite was larger than those of isotropic graphites

Table 6 Erosion Data of Carbon Materials

Material ATX-20U

ATX-30U

PyC-coated IG110-U

PyC-coated ETP-10

C/C composite (felt type)

Sample Coating Heat flux thickness thickness density (mm) (µm) (kW/cm 2) 3 5 10 3 5 10 3 3 3 3 3 3 3 5

5 10 30 5 10 30

2.27 2.5 2.61 2.39 2.39 3.3 2.3 2.17 2.22 2.74 2.76 2.88 2.65 2.55

Incubation time of erosion (s) 1.8 (fracture) 2.85 No erosion 2.3 4.6 4.5 1.65 1.65 1.1 1.3 1.2 0.95 1.1 3.9

Diameter Area of of eroded eroded Erosion region region depth (mm) (cm 2) (µm) 5.6

0.25

135

6.2 4.2 3.6 6.4 6.8 6.8 6.4 4.9 6.8 6.8 5

0.30 0.14 0.10 0.32 0.36 0.36 0.32 0.188 0.36 0.36 0.196

195 20 20 225 235 240 230 60 265 310 75

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under nearly the same conditions. Nevertheless, the C/C composite is superior as a plasmafacing materials to graphites in the sense that the former did not fracture in this experiment. SEM observation after the test revealed that erosion of the matrix was faster than that of carbon fibers. (19,28) 3. Fracture of Graphite Containing TiC and TiB 2 Table 7 shows the results of the thermal shock test of carbon-boron-titanium materials. Resistance to thermal shock fracture decreased with increasing titanium content. As shown in Table 4, the relative X-ray intensity of graphite decreased with increasing titanium content. This suggests that the resistance to thermal shock fracture increases with increasing relative amount of graphite. During the thermal shock tests, samples with a high titanium content fractured into many pieces. The cracks originated at the center of the sample surface and propagated radially. These cracks were probably caused by shear stresses at the central surface region, where strong compressive stresses were induced by thermal expansion. Samples with a high graphite content did not fracture; however, central regions of the sample surfaces were severely eroded. Microcracks were observed around the eroded regions From these results, it seems that there exists an appropriate content range of graphite, titanium, and boron for which the sample does not fracture and suffers only slight erosion. It is difficult, however, to clarify the role of TiC and/or TiB 2 in the thermal shock resistance from these results. (18,20,29) 4. Thermal Shock Resistance of Mixtures of TiC and TiB 2 The fabrication method mentioned in Sec. IV also provides a TiC and TiB 2 mixture from mixed powders of titanium, boron, and graphite. The mixtures obtained are shown in Table 8. Thermal shock resistance of the mixtures is also shown as the heat load of crack initiation. Here, the heat load of crack initiation is defined as the heat flux that causes catastrophic fracture of a specimen 30 mm in diameter and 3 mm thick. It is clear that mixture No. 4, whose molar ratio TiB 2 /TiC equals nearly 1, showed the best thermal shock property. This may be attributed to the superiority of thermal diffusivity in No. 3 compared with the others, as shown in Table 8.

Table 7 Thermal Shock Test Data of C-B-Ti Materials Composition of raw material (at %) C

B

Ti

95 90 85 50 50 35 34 26 26 12

5 10 15 50 40 13 37 29 29 38

0 0 0 0 10 52 29 45 45 50

a

Heat flux (kW/cm 2)

Duration (s)

Thermal shock fracture

Surface erosion

2.3 3.0 2.8

5 3 5

a

a

a

a

1.4 4.0 2.3 1.4 3.8

1 1 1 1 1

Not fractured Not fractured Fractured Not fractured Not fractured Fractured Not fractured Fractured Fractured Fractured

Severe Severe Severe Severe Severe Little Severe Little Little Little

Heat flux could not be estimated because specimen current was unstable.

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Table 8 Chemical Composition, Molar Fraction of TiB 2, Heat Load of Crack Initiation, Thermal Diffusivity of the Compounds Composition (at %) Specimen

C

B

Ti

Molar fraction of TiB 2, TiB 2 / (TiC ⫹ TiB 2)

1 2 3 4 5

35 24 26 12 35

13 26 29 38 35

52 50 45 50 30

0.15 0.30 0.36 0.45 0.55 a

a

Heat load of crack initiation (kW/cm 2)

Thermal diffusivity at room temperature (10⫺6 m 2 /s)

⬍1.7 ⬍1.4 ⬍2.3 ⬍3.8 ⬍3.0

4.4 5.6 8.7 15.0 8.7

A slight graphite phase coexisted (see Table 4).

As the maximum heat power density obtained, 3.8 kW/cm 2, is much lower than that in the case of TiC/HT-W/Mo, further improvement of these materials is needed. (20,29,30)

VI. CONCLUSION As possible candidates for the plasma-facing materials of fusion reactors, TiC and TiB 2 coatings on high-melting-point materials and bulk mixtures of TiC and TiB 2 were manufactured by various methods and their stabilities at elevated temperatures or their thermal shock resistances were examined. The results obtained were as follows: 1. An appreciable improvement in the adhesion of TiC coatings on Mo prepared by controlling the substrate temperature during the ion plating process was achieved. 2. Efficient ionization of the vapor species was achieved in the DC discharge method during the ion plating process; however, careful optimization of the deposition conditions was needed in the RF discharge method during the process. Stoichiometric TiC deposits could easily be obtained by the former method, but the formation of carbon-excess TiC films was characteristic of the latter method. 3. TiC films containing large amount of Ar were deposited on an Mo substrate by RF magnetron sputtering when the substrate RF bias was high or the working gas pressure was low. These films had large compressive internal stresses. Without Ti addition, the deposited films were excessively rich in carbon. 4. Carbon-excess Ti xC 1⫺x deposits showed a strongly preferred orientation and a much higher hardness than nearly stoichiometric deposits. 5. Stoichiometric TiB 2 films on Mo substrates can be deposited by cosputtering Ti and B without applying a negative bias voltage to the substrates; however, they had a poorly crystallized structure. The application of a small negative bias voltage enhanced the crystallization of the films. 6. Thermal stability of the TiC films deposited by the ion plating method depended strongly on the stoichiometry. The TiC coatings on Mo showed a large degree of vaporization above 2073 K. Interactions between the coating and the Mo substrate at elevated temperatures became another cause of degradation of the film. 7. The study of the behavior of TiC films deposited on Mo substrates by magnetron sputtering in a discharged Ar environment revealed that the film deposited with a lower bias voltage contained fewer Ar atoms but was easy to evaporate and had

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8.

9.

10.

11.

weaker adhesive strength. The Tic films deposited with a higher negative bias voltage resisted thermal evaporation and had better adhesive strength but contained more Ar atoms and formed many blisters at elevated temperatures. The blister formation caused film exfoliation. The TiB 2 films deposited on an Mo substrate by magnetron cosputtering without a negative bias voltage showed good thermal stability but exfoliated easily at elevated temperatures. The most prominent effect of the application of a negative bias voltage is improvement of the adherence of the deposited films. TiC coatings prepared on vacuum heat-treated Mo with a W intermediate layer showed good high-temperature stability and survived 2.0 pulses of heating at a power density as high as 5.3 kW/cm 2 . Among the commercial-grade graphites, the most anisotropic sample had the highest thermal shock resistance. Although the damaged regions of C/C composites observed after the thermal shock test were larger than those of graphites, C/C composites are superior to graphites as plasma-facing materials because they did not fracture in the experiments. Bulk mixtures of TiC, TiB 2 , and graphite can be manufactured from powders of Ti, B, and graphite by powder metallurgy. In bulk mixtures of TiC, TiB 2 , and graphite, the mixture with the molar ratio TiC/TiB 2 ⫽ 1 exhibited the best thermal shock resistance, but it fractured at a power density of 3.8 kW/cm 2 , which is lower than that in the case of TiC/HT-W/Mo. Further improvement of these materials is needed.

REFERENCES 1. DM Mattox, AW Mullendore, HO Pierson, DJ Sharp. J Nucl Mater 85–86:1127, 1979. 2. M Urlickson. J Nucl Mater 85–86:231, 1979. 3. M Fukutomi, M Fujitsuka, H Shinno, M Kitajima, T Shikama, M Okada. Proceedings 7th ICVM, Tokyo, 1982, p 711. 4. BL Doyle, WR Wampler, DK Brice, ST Picraux. J Nucl Mater 93–94:551, 1980. 5. T Shikama, T Noda, M Fukutomi, M Okada. J Nucl Mater 141–143:156, 1986. 6. M Fukutomi, M Fujitsuka, M Okada. Thin Solid Films 120:283, 1984. 7. M Fukutomi, M Fujitsuka, M Kitajima, T Shikama, M Okada. Thin Solid Films 80:271, 1981. 8. H Shinno, M Fukutomi, M Fujitsuka, T Shikama, M Kitajima, M Okada. Proceeding 7th ICVM, Tokyo, 1982, p 618. 9. T Shikama, H Shinno, M Fukutomi, M Fujitsuka, M Kitajima, M Okada. Thin Solid Films 101:233, 1983. 10. T Shikama, M Fukutomi, M Fujitsuka, M Okada. J Nucl Mater 122–123:1281, 1984. 11. T Shikama, H Araki, M Fujitsuka, H Shinno, M Okada. Thin Solid Films 106:185, 1983. 12. T Shikama, Y Sakai, M Fujitsuka, Y Yamauchi, H Shinno, M Okada. Thin Solid Films 164:95, 1988. 13. T Shikama, Y Sakai, M Fukutomi, M Okada. Thin Solid Films 156:287, 1988. 14. JL Vossen, W Kern, eds. Thin Film Process. New York: Academic Press, 1978, p 48. 15. Joint Committee on Powder Diffraction Standard, Powder Diffraction File, Sets 6–10, p 310, Card 8–121. Philadelphia: Joint Committee on Powder Diffraction Standard, 1967. 16. M Fukutomi, M Fujitsuka, T Shikama, M Okada. J Vac Sci Technol A3:2650, 1985. 17. M Fujitsuka, M Fukutomi, M Okada. J Jpn Inst Met 52:954, 1988. 18. H Shinno, M Fujitsuka, T Tanabe. International Symposium on Carbon, Tsukuba, Japan, Extended Abstract, II, 1990, p 916.

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19. T Tanabe, M Fujitsuka, H Shinno. Proceedings International Symposium on Material Chemistry in Nuclear Environment, Tsukuba Japan, 1992, p 565. 20. T Tanabe, T Baba, A Ono, M Fujitsuka, T Shikama, H Shinno. J Nucl Mater 191–194:382, 1992. 21. V Philipps, E Vietzke, H Trinkaus. J Nucl Mater 179–181:25, 1991. 22. A Miyahara, JB Whitley. J Nucl Mater 179–181:19, 1991. 23. Y Hirooka, R Conn, R Causey, D Croessmann, R Doerner, D Holland, M Khandagle, T Matsuda, G Smolik, T Sogabe, J Whitley, K Wilson. J Nucl Mater 176–177:473, 1990. 24. J Winter, HG Esser, L Ko¨nen, V Philipps, H Reimer, JV Seggern, J Schlu¨ter, E Vietzke, F Waelbroeck, P Wienhold, T Banno, D Ringer, S Veprˇek. J Nucl Mater 162–164:713, 1989. 25. J Ross. J Nucl Mater 176–177:132, 1990. 26. M Fujitsuka, T Shikama, Y Yamauchi, H Shinno, M Okada. J Nucl Mater 152:163, 1988. 27. Y Yamauchi, M Fujitsuka, H Shinno, T Tanabe, T Shikama, M Okada. Nucl Eng Des Fusion 9:265, 1989. 28. M Fujitsuka, H Shinno, T Tanabe, H Shiraishi. J Nucl Mater 179–181:189, 1991. 29. M Fujitsuka, I Mutoh, H Nagai, T Tanabe. Proceedings 3rd Japan International SAMPE Symposium, Makuhari, Japan, I, 1993, p. 641. 30. M Fujitsuka, I Mutoh, T Tanabe. Proceedings 21st Japan-Korea Seminar on Ceramics, Tsukuba, Japan, 1995, p. 311.

15 Synthesis of Diamond from the Gas Phase Andrzej Badzian Materials Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania

I.

INTRODUCTION

This chapter reviews the status of chemical vapor deposition (CVD) of diamonds as electronic materials. The CVD process was confirmed in 1952 (1). In the same year a discovery was made that some rare bluish, boron-doped natural diamond crystals, known as type IIb, behave as semiconductors (2). High pressure/high temperature (HP/HT) synthesis, which appeared just after these events, allowed doping of diamonds with boron. The small size of HP/HT crystals and limited control over doping level posed difficulties in electronic applications. In contrast, CVD techniques introduced thin-film deposition, suitable for fabrication of devices and large substrates for packaging. It was CVD that opened the way to diamond electronics. In the past decade great progress has been made; however, many setbacks accompanied this success. Diamond is considered a new electronic material because of its applications, which are currently in the developmental stage. Semiconductor devices such as transistors, diodes, and sensors Single-crystal films, for device fabrication, have an advantage over polycrystalline films because, among others, they have low levels of carrier scattering, facilitate uniformity of doping, and control contact characteristics. Heat sinks (heat spreaders) as substrates for packaging of electronic devices Diamond has superior thermal conductivity, five times higher than that of pure copper at room temperature. Heat sinks are currently available on the market. The other products are infrared (IR) windows, cutting tools, and surface acoustic wave filters. Electron field emitters This is a new anticipated area of diamond application. A variety of diamond materials are being studied, including highly disordered diamonds.

II. CHEMICAL VAPOR DEPOSITION OF DIAMOND A.

Pyrolysis of Hydrocarbons

Pyrolysis of CH 4 over a diamond surface was the first extensively studied process in which synthesis of diamond was documented in the laboratory (3,4). Molecules of CH 4 at low pressure (⬃0.1 torr) undergo decomposition on the hot (e.g., 1000°C) diamond surface. Carbon atoms are bonded to the surface and hydrogen atoms return to the gas phase after an abstraction process. 347

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This method, because of surface forces, allows diamond to start growing epitaxially; that is, its atomic structure is replicated. Unfortunately, graphite nucleates simultaneously, making the process of pyrolysis unpractical. Progress in the gas-phase approach to diamond synthesis was achieved when graphite conucleation was stopped by increased concentrations of atomic hydrogen (H°) in the gas phase. This was achieved when a plasma was introduced into the CVD reactor to enhance the process. Because of the higher excitation of the plasma, more H° was involved in abstraction of hydrogen atoms from hydrocarbon radicals chemisorbed on the diamond surface. Higher growth rates followed an increase of plasma excitation. B.

Plasma-Enhanced CVD

There are two main groups of CVD methods. One group has its origin in thermal CVD as mentioned earlier. Different means have been taken to enhance the CVD process: hot filament (5), microwave plasma (6) (Fig. 1), electrical discharges developed as plasma jets, radio frequency plasma, and oxyacetylene flame (7). The basic gas composition is C and H, but ternary gas systems such as CHO (8), CHN, CHAr, and CH-metal have also been studied. Process parameters are as follows: Power. Gas activation depends on the power consumed to excite the plasma. At a power density of 30 W/cm3, 50% of hydrogen was detected as H°. High concentrations of H° are essential to reach high growth rates of diamond. The CH 4 concentration in H 2 is preferentially 1% but depends on the plasma temperature and pressure. Diamond is grown in wide concentration ranges of CH 4, 0.2–100%. The temperature of the substrate is usually in the range 700–1000°C, but diamonds can be grown in the range 300–1800°C. It is difficult to establish the low-temperature limit because of problematic surface temperature measurements. Pressure is usually in the 20–80 torr range but the growth process runs in the 0.1 torr– 1 atm range. C.

Chemical Transport Reactions

The second group of methods evolved from a solid source of hydrocarbon species formed during etching of graphite by hydrogen; see Fig. 2. Using this method, homoepitaxial, doped films have been obtained to demonstrate that semiconductor diamond films can be grown from the

Figure 1 Schematic of tubular reactor inside resonant microwave cavity (3). The substrate is heated by plasma; 3000°C can be reached on graphite.

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Figure 2 Chemical transport reaction apparatus. The distance between graphite and diamond substrate is in the range 0.1–1 mm.

gas phase (9). The etching-deposition process can also be performed in different ways, as shown in Fig. 3. In a short distance between the etched graphite and the growing diamond, growth rates of 10 µm/h were observed. A microscale version of this experiment, which involves a mixture of graphite powder and diamond or metal powders, has been studied (10).

III. PHASE STABILITY VERSUS GROWTH MECHANISMS A.

Phase Diagram of Carbon

New developments in diamond synthesis demonstrate the diversity of pressures, temperatures, and chemical compositions under which diamond can be grown. For a long time, common opinion cast doubt on the feasibility of diamond growth outside its stability region in the p, T phase diagram of carbon. It has been known since the beginning of high pressure/high temperature synthesis that crystallization of graphite takes place simultaneously with the crystallization of diamond in some metals or alloys (11). This means that graphite was grown in the region

Figure 3 Etching-deposition experiment in a microwave plasma conducted in the system shown in Fig. 1.

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of its thermodynamic metastability. It was widely held true that the solvent-catalyst process cannot be extended below the borderline of diamond-graphite stability regions. This assumption was abolished, and it is an important contribution to clarification of the understanding of diamond synthesis. This new finding states that when glassy carbon was used as a source of carbon, crystallization of diamond was possible below the borderline (12). At a temperature of 1700°C, the pressure was 3.8 GPa, whereas the pressure is 6.1 GPa on the borderline. Glassy carbon is fabricated by thermal treatment of phenol formaldehyde resins and contains some H and O. These experiments were reproduced, and a further decrease of pressure was possible down to 3.1 GPa at 1200°C (13) (Fig. 4). Justification for these spectacular results is rather simple. The growth process of diamond is not directly related to the p, T phase stability diagram of carbon because diamond-graphite growth takes place in particular chemical environments: metal solvents, hydrogen, oxygen, etc. Diamond crystallization under HP/HT conditions is related to growth mechanisms that depend in part on the particular metal solvent. These growth mechanisms and p, T conditions will be different in different chemical environments, such as with the addition of H and/or O. In a similar way, CVD techniques allow growth of diamond and graphite simultaneously. Let us consider two substrates placed close to one another and immersed in a microwave plasma as in Fig. 1. On the Si substrate, diamond was nucleated and grew. However, on the Fe substrate, graphite fibers were nucleated and grew at the same atomic hydrogen (H°) concentration. This means that the concentration of H°, which preserved diamond growth, was not enough to stop

Figure 4 A part of carbon phase diagram: 1, a triple point; 2, melting of graphite; 3, diamond → graphite transformation; 4, Liepunski’s prediction for indirect conversion (FeC); 5, Bundy’s minimum for diamond formation from FeC; 6, synthesis of diamond from glassy carbon (12); 7, the same according to Ref. 13.

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graphite formation. Graphite growth proceeds by a mechanism involving Fe participation in the building of carbon fibers. In another type of experiment, at a particular CH 4 concentration in H 2, it was possible to grow oriented inclusions of graphite in a diamond crystal matrix. Heteroepitaxial relationships between (111) diamond planes and (0001) graphite planes were observed (14). CVD diamonds were synthesized using gas mixtures of different compositions, e.g., hydrocarbons-H 2, COH 2, CH 3OHAr(He), and flame of C 2H 2 O 2. It is reasonable to assume that growth mechanisms are different in these cases.

B.

Active Surface Process

This discussion formulates what we understand about the diamond growth mechanism. The growth mechanism is related to surface processes that are difficult to describe on the atomic scale because of their complexity and the lack of adequate tools for in situ observation and measurements. In this case, modeling of the growth process is required to fill the gap in experimental data. We refer to the diamond growth process as an active surface CVD because of the importance of surface processes. This requires consideration of the following issues: Activation of gas phase, e.g., formation of CH 3, C 2H 2. Transport of carbon from gas phase to the growing surface of diamond by means of surface reactions under bombardment of the surface by H°. In the case of microwave plasma, there is an additional interaction of the microwave field with the species on the surface. Thermodynamics and chemical kinetics of possible chemical surface reactions. Atomic structure of growing surface. Eventual modification of crystal structure due to surface reactions. In the case of diamond, stacking faults and/or twinning can be introduced. Growth mechanisms link together activated gas phase, surface processes, and the resulting crystal.

C.

Novel Approaches

There are no obstacles in searching for novel approaches to diamond synthesis by studying new growth processes: electrolysis, hydrothermal (15) and laser assisted. Graphite has been transformed to diamond by laser process (16,17) and some laser assisted CVD processes were successful (18). A new discovery exploits a set of multiplexed pulsed lasers applied for the first time to solids in general, and specifically to film deposition. The process utilizes excimer, YAG :Nd and CO 2 lasers focused on WC/Co substrate in ambient with CO 2 and N 2 as shrouding gases (19,20). Hydrogen-driven CVD processes are not necessarily the only type. In a nitrogen environment, diamonds are also formed (21). Supposition that diamond can be synthesized only under conditions of its thermodynamic stability is an old concept that has passed away. The diamondgraphite borderline, known as Berman-Simon extrapolation, is not an exclusion to growth of diamond at lower pressures.

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IV. NEARLY PERFECT CRYSTALS OF DIAMOND A.

Growth Sectors

After nucleation, diamond crystals start to grow. The growth proceeds in different crystallographic directions. Most frequently, separate diamond crystals develop cubooctahedral morphology (Fig. 5). Such crystals are built from two types of growth sectors. One growth sector is related to the 〈001〉 growth direction and the other to the 〈111〉 direction. The 〈110〉 growth sectors disappear because of the particular ratio of growth rates in the 〈111〉 and 〈001〉 directions. The change in morphology of diamond crystals from cube to octahedron involves intermediary forms such as a cubooctahedron. The growth rates depend on growth mechanisms, which are different for different crystallographic directions. One can change morphology by the addition of small amounts of nitrogen or by a change of temperature. Transmission electron microscopy, electron diffraction, and Raman spectroscopy indicated that the 〈001〉 growth sector has less defects, whereas the 〈111〉 sector shows many stacking faults and twins. Epitaxy on the (001) surface of diamond was the first choice in searching for electronic quality films. Growth in the 〈110〉 direction is the fastest. Single crystals of 0.25 carat have been grown using a microwave plasma at Raytheon Company (Fig. 6a and b). A single crystal prism of 1.2 mm height and 0.17 carat also grown by microwave plasma CVD on the (110) substrate was assessed as gem quality diamond (22). Growth in the 〈110〉 direction has a useful feature: it allows preparation of epitaxial films at 1300°C with no secondary nucleation and with a smooth surface probably due to surface diffusion. CVD single crystals are small in comparison with HP/HT ones. Record size crystals were grown at Sumitomo Electric, De Beers, and General Electric Companies. Sumitomo single crystals reach 12 mm in linear dimension. The largest De Beers crystal weights 34 carats and is approximately 15 mm in linear dimension. Also at De Beers, a regular octahedron with an edge length of about 1 cm was grown. Narrow [110] corrugated faces appeared at the octahedron edges. Experiments on thermal conductivity of synthetic diamond crystals were conducted at General Electric. Record high thermal conductivities, 50% higher than that of the best natural crystals, have been measured for isotopically pure crystals grown by the HP/HT method. These

Figure 5 Growth sectors of a diamond crystal. Normalized growth rates ν are indicated.

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Figure 6 Single crystals grown by microwave plasma–assisted CVD. (a) Crystal grown on a (110) seed that was 1 mm in diameter ⫻ 200 µm thick. (b) Crystal grown on a (001) seed. The center is water clear. The crystals were grown in a 5-kW reactor. Both crystals are about 2 mm thick. (Courtesy of Thomas Hartnett, Raytheon Co.) (c) Cross-Polarized transmission photographs along the 〈001〉 direction of waterclear 60-µm-thick film on 250-µm-thick type IIa natural crystal. The longer edge is 2 mm long. The crystal was grown in the system shown in Fig. 1 at 875°C and 1% CH 4 in H 2. Stresses at the growth sectors boundaries are visible.

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crystals were synthesized using 12C polycrystalline CVD diamond material as the carbon source (23). Also, 12C and 13C crystals and their solid solutions were successfully prepared.

B.

Characterization of Single Crystal

A semiconductor material, in an ideal situation, should be a single crystal with a strictly periodic lattice. Electrons or holes travel easily in such a crystal, suffering only from phonon scattering. In a periodic potential field, electron-hole propagation takes place as nearly loss-free transport. In a similar way, heat transport in diamond is conducted by thermal waves. The waves are least scattered when the crystal lattice is periodic. Vibrating atoms in a crystal have potential wells prescribed to them and the minima of these wells form a three-dimensional crystal lattice. Lattice periodicity of CVD diamond single crystals can be evaluated by X-ray diffraction methods and by measurements of thermal conductivity. When the lattice is strictly periodic, diffraction patterns are composed only of Bragg peaks at the reciprocal lattice points. If lattice periodicity is disturbed by a ‘‘defect,’’ the sharp Bragg peaks can be broadened and additional scattering between reciprocal lattice points appears. This is so-called diffuse scattering. When atoms are shifted from their equilibrium positions by thermal vibrations, diffuse scattering arises, but Bragg peaks do not broaden. In the case of diamond, thermal diffuse scattering is weak. Static defects in CVD diamonds such as stacking faults, dislocations, twinning, hydrogen, and other impurity atoms introduce displacement disorder of the carbon atoms. They cause shifts of atoms from the equilibrium positions. Static disturbances of lattice periodicity are the cause of X-ray or electron diffuse scattering. The intensity of diffuse scattering is a direct measure of the departure from the periodic network. The diffuse scattering around the 111 reciprocal lattice point is a very sensitive test for lattice periodicity of a CVD single crystal. Natural and HP/HT crystals also show diffuse scattering associated with the 111 Bragg reflection. Despite the fact that CVD crystals and films produce diffuse scattering, we can consider some of them as nearly perfect crystals. The following data support this statement: X-ray diffraction patterns consist of sharp Bragg peaks and some diffuse scattering. Rocking curves, measured for the 004 Bragg reflection, from homoepitaxial films grown on HP/HT Sumitomo crystals are only slightly broader when compared with the substrate curves. Some of the type Ib Sumitomo crystals have a rocking curve full width at half-maximum (FWHM) as small as 5–6 arc sec. The best homoepitaxial films have FWHM equal to 8 arc sec and are comparable to the best type Ia natural crystals (24). Such rocking curves demonstrate perfect long-range order of CVD homoepitaxial films. The narrowest Raman 1332 cm⫺1 peak for a CVD crystal is sharp as the narrowest peak measured for type IIa natural diamond. The FWHM is 1.6 cm⫺1. The narrow peak is an indication of perfect long-range order. A sharp Raman peak and low background scattering are necessary but not sufficient proof of high-quality films. Type IIa diamond crystals have a mosaic structure with mosaic block spreads of arc minutes or even higher. This orientation effect is not directly measured by Raman spectroscopy. If some parts of the crystal are not Raman active, they will not contribute to the Raman spectrum, and information about these regions will be lost. For this reason it is necessary to correlate the Raman spectrum with diffraction studies. Thermal conductivity measured for isotopically pure, 12C homoepitaxial films was higher than for perfect natural diamonds. The hole mobility of the (001) homoepitaxial films doped with boron reached 1580 cm2 /V⋅s

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at carrier concentrations of 1017 cm⫺3. High mobility of carriers indicates perfect lattice periodicity (25). The preceding measurements allow cautious optimism for the development of single-crystal films for electronic applications. C.

Homoepitaxy

Perfect epitaxy is difficult to achieve. The first obstacle is seen in diamond substrate crystals. Micrometer-size defects on the diamond surface initiated by inclusions and other bulk defects of natural crystals and enhanced by cutting and polishing contribute to nucleation of diamond grains with crystallographic orientations different from those of epitaxial films. Hillocks frequently originate at such spots and many microtwins, with 〈111〉 growth sectors, are developed in the craters. Sometimes these craters represent such disordered diamond that even the 1332 cm⫺1 signature disappears from Raman spectrum. During boron doping these 〈111〉 microsectors accommodate more B atoms than a (001) homoepitaxial film. Hence, they are much more conductive than a homoepitaxial film. When a transistor is fabricated, a micro short circuit, at hillock spots, disturbs the transistor’s performance by contributing to leakage current. Elimination of hillocks is the issue of primary importance. Perfect substrates should be used, such as Sumitomo HP/HT crystals or selected type IIa natural crystals. Growth processes should be conducted in chemically clean environments. There should be no interaction of the plasma with any element of the reactor, because the plasma can etch materials and transport them to the growing substrate. In general, any etching should be eliminated, and only diamond growth should occur. Hot filaments are not advised for homoepitaxial growth, due to contamination of the diamond by materials from the filament. Dust particles originating inside the system should be eliminated because they can provide secondary nucleation sites. Stable growth conditions are also an important factor in growth of nearly perfect crystals. Substrate temperature, pressure, and gas flow should be kept constant during the process. How can we improve the growth of nearly perfect crystals of diamond? Two approaches are anticipated. One is to use C-H gas systems with no additives and impose step flow growth on a misoriented (001) surface to avoid hillock formation. There are data supporting this approach. The second possibility is the addition to the gas phase of gases such as O 2 and N 2 and molecules such as Ni x C yH z. These gases and their derivatives participate in growth process by influencing step formation and elimination of twinning. Smooth surfaces have been obtained in such processes. It is not clear, at this moment, which process parameters and gas concentrations these observations validate. Parametric study of the growth of homoepitaxial films is not complete. It is possible to grow smooth diamond surfaces for certain sets of process parameters, but this does not mean that bulk diamond will be crystallographically perfect. 1. Step Flow Growth We have mentioned that hillocks, originating from the interface, disturb epitaxial growth. Hillocks are also developed when the top surface is almost parallel to the (001) plane. There are large (extensive) terraces on such surfaces and island growth proceeds on them. These islands

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have square shapes with 〈110〉 edges. When hillocks are developed, their side surfaces have vicinal planes, (11ᏸ), where ᏸ is a number larger than 10, according to atomic force microscopy measurements. Hillocks can interact during the growth and some twins may be formed. Step flow growth is a new concept for diamond growth that has been adopted from Si and SiC epitaxy (26–29). This type of growth takes place on misoriented surfaces, preferably when the top surface is inclined along the 〈110〉 direction (Fig. 7). Step flow means that growth proceeds through the addition of atoms to the edges of the steps. When angle γ is 3–4°, flat surfaces free from hillocks have been grown (30). Why this value of angle γ awaits explanation. Probably it is related to compatibility between diffusion length, step width, and CH 4 concentration. For 11° the surface morphology consists of macrosteps and the surface is rough. What is the microstep height in the case of flat surfaces? When we look into a diamond structure in the 〈110〉 direction, we see rows of tetrahedra. They form an orthogonal pattern of ˚ , half of the unit cell edge of diamond. Inside rows. The height of the tetrahedron row is 1.78 A ˚ . The atoms on this height are involved the tetrahedron there are carbon atoms of height 0.89 A in single-layer growth. We call this a single atomic step. In the case of a tetrahedron we call it a double atomic step. This is a crude simplification based on the bulk atomic structure. In reality, the surface is reconstructed and hydrogen atoms are chemisorbed. Hydrogen atoms form a monohydride structure, which means that one hydrogen atom is bonded to a carbon atom. Carbon atoms are shifted from their face-centered cubic (fcc) lattice positions in such a way ˚ width and has 2 ⫻ 1 surface lattice symmetry that dimers are formed. The dimer row has 5 A (31). The dimer rows reflect the positions of the rows of tetrahedra beneath them. This is stable structure, but it has atoms at positions different from those in the bulk ˚ , comdiamond lattice. For example, the distance between carbon atoms in the dimer is 1.63 A ˚ pared with 2.5 A in the bulk diamond. The bulk structure is thermodynamically metastable according to the phase diagram (Fig. 4), but near-surface structure is stable and growth of diamond proceeds with the stable structure at the surface. Determination of how the dimer rows are oriented on terraces with respect to the terrace edge was facilitated by scanning tunneling microscopy (STM) (32). Dimer rows run in two orthogonal directions. They form 2 ⫻ 1 and 1 ⫻ 2 domains. The ratio of these domains can be determined by reflection high-energy electron diffraction (RHEED) and low-energy electron diffraction (LEED). These methods are used to search for a 2 ⫻ 1 single domain surface. Analysis of different step structures suggests that the single domain step structure known in Si terminology as a D B – double atomic step should have the lowest formation energy (33). According to Figs. 8 and 9,

Figure 7 Schematic of step flow growth on a misoriented surface.

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Figure 8 Double atomic layer step flow growth. Dimers and dimer rows conversion on consecutive terraces are shown.

growth proceeds along dimer rows. It is anticipated that step flow should prevent defect formation under special growth conditions. This issue is presently under study to reveal the crystallographic perfection of 3° misoriented films. The morphology of the top surface does not change during growth of thicker films; the films stay smooth. 2.

Antiphase Domains

By analogy with Si (001) epitaxy we can expect formation of antiphase domains. A diamond structure reconstructed to a 2 ⫻ 1 dimer structure allows two positions for new dimer nucleation (34). If, after nucleation, two islands grow and interact, there is a 50% probability that they will have opposite phases. At the intersection, two kinds of antiphase boundaries exist (34). Such boundaries have been revealed on hydrogen-etched CVD diamond surfaces by STM. In Fig. 10 ˚ . In addition we see an orthogonal network of dimer rows. The distance between rows is 5 A to antiphase boundaries, there are narrower rows that correspond to 3 ⫻ 1 reconstruction. In such reconstruction we have one dihydride row (35).

Figure 9 Model of double atomic layer step D B. Open and closed circles denote carbon and H atoms, respectively. Larger circles are used for upper-terrace atoms. The dimerization direction of surface carbon atoms is along 〈110〉.

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Figure 10 An STM image of a hydrogen plasma annealed (001) CVD diamond surface. Two types of antiphase boundaries are labeled AP1 and AP2. The 3 ⫻ 1 configurations are marked L. The distance ˚ . The compression of images is caused by instrumental calibration. (From between dimer rows is 5 A Ref. 35.)

3. Modeling An in-depth understanding of diamond growth includes knowledge of atomistic surface reaction mechanisms. The first task is to establish surface morphology. Determination of step width, height, and dimer orientation is an important start for the modeling of chemical reactions at the step edges, to show how dimer rows propagate. Such modeling should include the complicated situations of single and double atomic steps. Attempts to model growth mechanisms have already started. Modeling has filled the gap created by nonaccessibility of processes by in situ measurements. Understanding how diamond structures propagate during crystal growth is a basic scientific task. The reader is referred to refs. 36–40 for a more complete account of modeling. Diamond synthesis was developed with limited scientific understanding of the growth processes. Despite this, scientists had the courage to put forth risky hypotheses and work with them. In this way, enormous progress has been made in controlling diamond growth processes as well as developing a comprehensive picture of associated phenomena.

V.

DEFECTS

Graphite codeposition was the main concern at the beginning of the CVD method because of an insufficient concentration of H° in deposition reactors. The sp2 component is of negligible importance for crystals grown in an H°-rich environment when compared with stacking faults and twinning. These planar defects disturb the diamond lattice predominantly in the 〈111〉 growth sectors (41–43). Planar defects cause deformation of regular tetrahedra. Deformation of tetrahedra takes place when the stacking sequence departs from a cubic ABCABC type of stacking. Hexagonal

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diamond, obtained under static high pressure, is composed of deformed tetrahedra because c/ a ⫽ 1.66, instead of 1.63 for a regular tetrahedron. It implicates elongation of the tetrahedron ˚ . The departure from the cubic diamond structure in some CVD films was established by 0.025 A by X-ray diffraction. X-ray measurements indicate the existence of displacement disorder of atoms from the lattice positions in CVD films with defects. Stacking faults and microtwinning imply breaking of the symmetry of the cubic diamond lattice and have the general implication for semiconductor crystals of introducing extra electronic levels in the band gap. In the case of diamond, it is a subject of speculation how complicated and nontypical luminescence spectra can be explained on the basis of new electronic states in the band gap and how new vibrational states result from breaking of the symmetry. Neutral vacancies formed during the growth are rarely observed in CVD crystals. Instead, vacancies appear as silicon (or silicon pair)–vacancy complexes. This defect is frequently observed in diamond crystals grown on Si. Growth sector 〈111〉 can be doped with Si to levels above 1 at%. This doping level introduces displacement disorder of atoms in the diamond lattice to such an extent that the 1332 cm⫺1 Raman peak almost disappears. This means that the vibration mode related to the optical phonon becomes weak in such a distorted lattice.

VI. DOPING Doping of diamond is approached in several ways: doping during the growth, implantation, forced diffusion, and neutron transmutation. Doping during the growth was successful with boron, as it is in nature. High-temperature Schottky diodes and transistors were fabricated on boron-doped films. Doping with N and P has not been fully evaluated. Experiments with Li and Na doping during the growth were not successful. The electrical behavior of diamond with Si and other metal dopants is not known. Inconvenient complications connected with doping during the growth are related to the creation of defects in doped diamond. Experimenting with P doping showed that when high concentrations of PH 3 were introduced in the CH 4 /H 2 plasma the diamond structure was distorted. The X-ray diffraction pattern of this material is composed of broad lines and is interpreted as disordered tetrahedral carbon. Raman peaks disappeared, as in the case of doping with P. When doping levels are as low as 1017 cm⫺3, the resistivity of diamond is too high for device fabrication. This can be caused by lattice defects. Are these defects electrically active? The answer is not yet known. Nevertheless, n-type doping by P was confirmed by Hall measurement (44).

VII. POLYCRYSTALLINE PLATES When the first diamond polycrystalline films, a few µm thick, were grown on silicon wafers, it was easy to etch off the Si from the back side and obtain translucent freestanding diamond windows. Large windows fabricated in this way were considered for high-resolution X-ray lithography. Enormous progress has been made in several companies since this time. Now large, water-clear windows are available. Transparencies vary, but plates as thick as 2 mm and linear sizes of 10 cm and larger are being fabricated. Scaling up the growth process required, at first, increasing the growth rate above 10 µm/ h. This was achieved by careful parametric studies and by creating high-temperature plasmas. Record power for a microwave system is 75 kW and for a DC plasma torch is 100 kW. Large area depositions are relatively easy to achieve with tungsten filament systems; however, it was difficult to reach growth rates higher than 4 µm/h even with biasing. Other tech-

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Figure 11 Photograph of multichip module substrates (MCMs) 7.5 ⫻ 7.5 cm cut from 15-cm plates grown in a 915-MHz, 50-kW reactor. Plates 2 mm thick were grown. (Courtesy of Thomas Hartnett, Raytheon Co.)

niques have problems with uniformity of plate thickness. In the case of microwave, the process depends on the size of plasma ball suspended over the substrate. The size can be increased by increasing the power or by decreasing the microwave frequency. Large plates are manufactured by DC jets. The uniformity in thickness reduces the cost of polishing. New inventions in diamond polishing are necessary to bring the cost of diamond plates down. Ideally, $1 per carat would contribute to CVD diamond commercialization, and even $5 per carat is acceptable. Currently, a 1-carat CVD diamond with a 1-mm-thick plate can cost hundreds of dollars. Despite cost problems, characteristics of diamond substrates are impressive. Figure 11 shows substrates for electronic packaging. Transmission in the visible and IR spectrum is almost identical to that of type IIa natural diamond; the only problem is light scattering at grain boundaries. Microstucture improvement is essential to reduce internal stresses and produce atomic bonding between grains.

VIII.

HETEROEPITAXY

A common opinion is that diamond heteroepitaxy is a necessary step in developing active diamond electronics. This has not materialized yet, and we are waiting for innovative ideas to revolutionize the agenda. The definition of heteroepitaxy is based on the practice of semiconductor technology. Heteroepitaxial growth means that on the surface of a single crystal A (over a macroscopic area) another crystal B starts to nucleate and grows with a specific crystallographic orientation relationship between A and B, which corresponds to some kind of lattice matching. Lack of

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perfect matching at the interface introduces strain between these semicrystals. The strain is released in specific ways, for example, by misfit dislocations. This formulation of heteroepitaxy does not consider any transition interlayer between A and B; instead, direct chemical bonds are formed between atoms of crystals A and B (45). This definition can be applied to heteroepitaxy of diamond on cubic BN. A sharp interface was found by cross-sectional TEM (46). Diamond crystals stick to cubic BN with no interlayer. The two lattices fit together almost perfectly with the exception of misfit dislocations. The growth on the (111) boron-terminated face of a single crystal of cBN (250 µm linear dimension) provided the most perfect heteroepitaxy. Macrosteps on the surface of cBN were replicated during diamond growth when B 2 H 6 was added for doping. Addition of B 2 H 6 seems to be beneficial for the two-dimensional nucleation of diamond. Usually, diamond nucleation has a threedimensional character and separate microcrystals coalesce during the growth. This is an example of perfectly oriented growth (47). A very interesting phenomenon takes place on the nitrogen-terminated (111) face. The nucleation density is very low, a few orders of magnitude lower than on the boron-terminated (111) face. Oriented diamond crystals nucleate along ledges on the surface. The difficulty in nucleation has a connection with the formation of CN bonds. The CN bonds are formed with great difficulty on the diamond surface. Probably for this reason the sp 3 analog of a CN compound was not synthesized. Both CN and BN bonds should be formed simultaneously at the cBN-diamond interface to ensure charge neutrality. Such neutrality exists in the lattice of cBN-diamond solid solutions where CC atom pairs are substituted by BN pairs. The BP a AIIIBV compound shows a 〈111〉 polar axis just as cBN does. One would expect epitaxy to appear on the B-terminated surface and low nucleation density to be observed on the P-terminated (111) surface. Heteroepitaxy on cBN had a limited impact because substrate crystals are not easily available. The cBN and BP single crystals were synthesized by HP/HT processes. The largest cBN crystal has a linear dimension of 3 mm. The BP crystals grown from B solution in liquid P at 1.5 GPa have a dimension of about 1 mm. Ni and Cu single crystals were considered as substrates because of their fcc structure and good lattice matching to diamond. However, heteroepitaxy was not achieved on these substrates; only isolated oriented diamond particles were grown on Ni (48). Some improvement was reported for Ni (49) and Pt (50) oriented growth. Similar efforts were undertaken on the Si (001) ˚ , which fits well the surface. The distance between Si atoms along the 〈110〉 direction is 3.6 A ˚ 〈001〉 direction in diamond structure with a distance of 3.56 A. Diamond growth on Si did not follow this matching. These examples indicate a limitation of the geometrical aspect of heteroepitaxy definition. The chemical interaction between two different crystal phases and the surface energy at the interface should be taken into account. Diamond has an interface energy higher than other materials. Diamond nucleates on small spots on the foreign substrate’s surface. Figure 12 illustrates nucleation on a scratched Si surface and shows 0.2-µm spots. More precise insight into such ˚ (51). It is unknown why diamond nucleates on spots by TEM gives a spot size of about 200 A such a small area. During initiation of diamond nucleation, the substrate surface interacts chemically with the hydrocarbon-hydrogen plasma. Both carbon and hydrogen atoms penetrate the substrate. Metals form carbohydrides before diamond nucleation starts. Nucleation is initiated on such chemically modified surfaces. Heteroepitaxy can be disturbed by the formation of disordered carbon on the surface, creating nucleation sites for diamond. Diamond grains nucleated on carbon have a random orientation. In summary, similarity to semiconductor heteroepitaxy has a limited application to dia-

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Figure 12 Secondary electron image of the back side of a diamond film nucleated on a scratched Si wafer. Bar corresponds to 5 µm.

mond because of its high interface energy. The solution to a task as challenging as making diamond heteroepitaxy a practical process requires a nontraditional approach. Such innovative thinking was involved in oriented growth on Si. However the films grown in this manner are not heteroepitaxial in on the macroscale; nevertheless, their characteristics are in between those of polycrystalline films and homoepitaxial ones.

IX. ORIENTED GROWTH The most popular procedure enhancing nucleation on Si is scratching the wafer surface, preferably with diamond powder. From a practical point of view, let us distinguish between nucleation and growth. Nucleation requires different process parameters than growth. For example, nucleation requires a higher CH 4 concentration and lower temperature than growth. Systematic parametric studies showed how much morphology depends on process conditions. Figure 13 is an illustration of columnar growth. The columns are perpendicular (with some axial tilt distribution) to the wafer surface, but they have a random azimuthal orientation as shown in Fig. 14. Columnar texture is a general rule for film growth. Films develop this microstructure

Figure 13 Columnar growth of diamond at 4% CH 4 in H 2, 850°C and 40 torr (5.2 kPa). Bar corresponds to 3.27 µm. (Courtesy of Yoichiro Sato, NIRIM.)

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Figure 14 Top view of film shown in Fig. 13.

because of growth competition between grains (52). Textured diamond films with 〈001〉, 〈110〉, and 〈111〉 have been grown with specific growth conditions. The next step in controlling nucleation on the surface was to find means that allow all nuclei to have the same crystallographic orientation. According to one trial, nucleation was organized with the help of lithography to get a patterning of the substrate and passivate some areas with Ar ion bombardment. Diamond crystals formed a square network but they had a random orientation (53). The second trial was based on crystallographically selective etching of a (001) Si wafer. Diamond-type structure materials behave anisotropically when they are processed by etching; for example, (001) faces disappear but (111) faces stay, resulting in the formation of specially shaped holes. In this case the holes have a half octahedron, pyramid shape. Whole surfaces of Si wafers can be covered by a regular square array of holes when a lithographic technique is used. In the next step, synthetic diamond octahedral crystals, 100 µm in size, are placed in these holes. Diamond growth was conducted on these arrays of seeds. Continuous films were obtained in this way. They have a mosaic structure, but secondary nucleation disturbs the local orientation of the film. The difficulty with this approach is related to growth sectors. The growth starts on mostly octahedral crystals with cubic face truncation. With this type of seed the process parameters should be changed during the growth to enhance growth in the 〈111〉 directions in such a way that only 〈001〉 growth sectors survive (54). A new era started with the concept of biasing the substrate during the nucleation procedure (55). This procedure revolutionized the nucleation of diamond, giving more control over the process. Negative biasing has been applied to mirror-polished Si substrates and the concentration of CH 4 in the plasma was substantially increased. Nucleation densities reached ⬎10 10cm⫺2. This process leaves flexibility in the choice of energy of bombarding ions, time, CH 4 concentration, and substrate temperature. Careful parametric studies were very successful in finding the right conditions for azimuthal orientation of diamond grains on the (001) nontreated surface of Si (Fig. 15). Such organized nucleation was achieved first on epitaxial β-SiC films grown on Si. Let us compare the morphology of a random azimutal orientation shown in Fig. 14 with the image shown in Fig. 15. The last figure shows impressive improvement in the azimuthal orientation, but we still have some small-angle boundaries in this material. This process was reproduced in many laboratories around the world. We will call these films highly oriented films. Highly oriented films presumably have a columnar structure as shown in Fig. 13; however, such cross-sectional etching images were not published for the bias nucleated films. The 〈001〉

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Figure 15 Top view of highly oriented diamond film grown on (001) Si. This photograph was presented in 1992 by X. Jiang and C.P. Klages, Fraunhofer Institut, Hamburg, Germany. Bar corresponds to 1 µm.

columns are randomly tilted with respect to the (001) Si substrate. The angular distribution of tilts has been measured by X-ray diffraction pole figures, giving a Gaussian function with an FWHM around 10°. This is a substantial disturbance of the columns’ orientation. The angular distributions of tilts are also anisotropic. Usually 80–90% of grains have the 〈001〉 orientation and the rest have a random orientation. Bias-enhanced nucleation has been studied from different points of view, but research has not reached a stage of comprehension. Possible explanations are subplantation of ions, chemical reactions at the surface with impinging ions, and surface diffusion. When nucleation is complete (for example, after 20 min), the bias of the substrate is turned off and process parameters are adjusted to the growth. The choice of new conditions is very important; they should increase the growth of the 〈001〉 columns. For this purpose, temperature– CH 4 concentration diagrams were established to identify conditions for the 〈001〉 and 〈110〉 textures. A series of experiments with continuously changing parameters imposed changes in the ratio of growth rates in the 〈111〉 and 〈001〉 directions. Modeling of columnar morphology was conducted, including (111) twin formation. This simulation allowed the prediction of when (111) twins would disappear (56). Following the proper choice of process parameters, films were grown with column tilts having an FWHM of ⬃10° and a few degree azimuthal grain boundaries. The films contain misoriented crystal grains. The top surface is rough and grooves appear at the grain boundaries. The next stage of oriented film development will consider growth of a smooth top surface. Smooth films over an area of 3 ⫻ 2 mm have already been grown on (001) β-SiC substrates (57). Enhancement of the 〈001〉 and 〈111〉 growth rates was controlled by the gas-phase composition. Three gases were mixed: CH 4, CO, and H 2. The surfaces of these films were studied by RHEED. A single-crystal type of pattern was obtained from a selected crystal grain on the oriented film before the smoothing procedure. After the smooth growth is complete, the surface is no longer crystallographically perfect. The Bragg reflections are very broad. A similar approach to controlling growth rates in the 〈001〉 and 〈111〉 directions and introducing etching in the 〈110〉 steps was also successful in smoothing the surface (57). The oriented diamond films achieved spectacular progress. Boron-doped oriented films demonstrated much higher mobility with a record 280 cm2 /V⋅s and good transistor performance (25). During the study of oriented growth, several problems have been addressed: Nonuniformity of the interface. There is structural and compositional nonuniformity at the

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interface. X-ray photoelectron spectroscopy (XPS) indicated the formation of β-SiC, HRTEM demonstrated direct contact between Si and diamond lattices as well as formation of an amorphous layer. Ellipsometry and Raman spectroscopy found the formation of sp2-type carbon. Direct contact between diamond and Si lattices appears only in a limited area. The ratio of lattice parameters for Si and diamond approaches 3:2. The 3:2 registry has been observed with HRTEM images showing rows corresponding to the (111) Si and diamond planes almost parallel in one case and with a tilt in others. Does this mean that diamond nucleates by different means? All of these data should be analyzed together, seeking a comprehensive picture of the interface and nucleation. It seems that nucleation on scratched surfaces takes place on ˚ 2, whereas bias-enhanced nucleation expands over 1000 A ˚. an area of about 200 A How much of this microheteroepitaxy can be extended? Orientation of columns. Strain energy of the interface is relaxed by the formation of dislocations and the tilt of lattice planes of diamond grains at the contact with the Si lattice. As a result, the columns are randomly tilted. Does any remedy exist to improve the situation? Misoriented grains. Misoriented grains usually disappear during the growth of thicker films, but twinning can still disturb oriented films. Structure of the top surface. The top surface of the oriented films, as in Fig. 15, is rough due to the misorientation of columns. The (001) top facets follow this misorientation. When the smoothing procedure is applied to such a rough surface, a question arises about how to describe the surface crystallographically. Is the surface composed of microvicinal planes? Vicinal planes in this case can have Miller indices of (11ᏸ), where ᏸ is a number larger than 10. Smooth surface films are not necessarily crystallographically perfect films.

X.

CONCLUSIONS

If one calls how much disbelief and discouragement was associated with the CVD process at the beginning of its development, because of a common opinion that diamond cannot grow under the condition of its ‘‘metastability,’’ we can now say that enormous progress has been made in the confirmation of CVD diamond as an electronic material. When CVD diamond was accepted, feelings of euphoria were followed by exorbitant promises that soon a new technology would be created having an impact on everyday life. The dreams and promises have not materialized and have turned into disappointment. The current high cost per carat has prevented diamond from being chosen over inexpensive materials. Diamond possesses the strongest covalent bonding, in some sense this seems to be a luxury property, which implies there is a high cost of bringing carbon atoms together. Someone needs to pay the price for the consumption of energy during diamond synthesis and for control over crystallization. Nevertheless, scaling up of CVD plasma processes has been successful with the fabrication of 27 cm diameter plates and almost water–clear diamond windows of 10 cm in diameter. Passive electronic applications in packaging are now in the marketplace. Active diamond electronics has not successfully developed. After the demonstration of rudimentary high temperature Schottky diodes and transistors, problems with the deposition of semiconductor quality thin diamond films has limited further development. Imposing step flow growth on homoepitaxial growth requires very expensive synthetic HP/HT diamond crystals cut under a specific angle.

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Very limited success with oriented growth on Si can be attributed to a combination of nucleation and growth difficulties. Nucleation leads to a Gaussian distribution of crystal columns orientation. Growth on the top surface, which is the crystallographic plane (001), reveals unexpected defects and undesirable doping with Si. It took 10 years to develop high frequency surface acoustic filters on polycrystalline diamond bases at Sumitomo Electric in Japan. It is an exeptional achievement for CVD diamonds. Diamond possesses such exceptional physical properties that it deserves support for research on its synthesis to allow diamond growth development to reach its maturity. Hydrogendriven CVD processes are at an advanced stage of development; however, novel processes are at an incubation phase, opening new expectations for the future.

ACKNOWLEDGMENTS This work was supported by the National Science Foundation under grant DMR9522566 and by the Office of Naval Research under grant N00014-91-J-4023. The author extends thanks to T Badzian, B Weiss, and N Lee for their help in preparation of the manuscript.

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16 The Electrical and Optical Properties of Diamond Alan T. Collins King’s College London, London, England

I.

INTRODUCTION

Diamond is a wide-band gap semiconductor. At room temperature the electron and hole mobilities can both be as high as 1800 cm 2 V⫺1 s⫺1 in high-quality specimens, and the thermal conductivity is about five times higher than that of copper. The breakdown field and the saturated electron velocity are higher than for any other semiconductor. The material is very hard and abrasion resistant, is relatively inert in a range of corrosive atmospheres, and will withstand temperatures up to 500°C. When excited with a beam of electrons, many diamonds can exhibit blue, green, or red cathodoluminescence, depending on the optical centers that are present. In the late 1980s there was therefore considerable speculation (1–5) that diamond produced by chemical vapor deposition (CVD) exhibits considerable potential for high-power, high-temperature active electronic devices and for optoelectronic applications. Natural semiconducting diamond (type IIb diamond) was discovered in 1952 (6), and the first diamond electronic device was a point contact diode made a few years later by Dyer and Wedepohl (7). This worked not only at room temperature but also at 300°C. Natural type IIb diamond was subsequently used to make a number of prototype devices. Rodgers and Raal (8) made a sensitive high-temperature thermistor. Vermeulen and Harris (9) developed a light-sensitive switch and an optical radiation detector (10). Young et al. (11) used type IIb diamond to produce an ultrafast infrared detector, and Ho and Lee (12) also demonstrated the capability of using semiconducting diamond as an optoelectronic switch. Prins (13) first demonstrated transistor action in diamond using natural crystals, and Tzeng et al. (14) have reported using this material to produce diodes and transistors. General Electric (GE) announced the first manufacture of semiconducting diamond abrasive grit in 1962 (15), and later they demonstrated the ability to make large semiconducting diamonds by the temperature-gradient method (16). Using GE diamonds of this type, Glover (17) fabricated Schottky diodes and Geis et al. (18) constructed a Schottky diode rectifier that operated at 700°C and a point-contact transistor that exhibited power gain at 510°C. Encouraged by the results on prototype devices summarized in the previous paragraphs, research groups around the world have been attempting, during the past 8 years or so, to exploit the apparent potential that diamond possesses for these applications. However, the present author has maintained on a number of occasions (19–22) that the predictions of what may be achieved with diamond are overoptimistic and are based on an incomplete understanding of the electrical 369

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and optical properties of this unique material. In this chapter we will review the electronic properties of diamond that have been established experimentally for natural, high-pressure synthetic, and CVD semiconducting diamond. A full treatment of the optical properties of diamond would require a complete book, and here we will concentrate on some of the optical properties of semiconducting diamond. Having reviewed these electronic and optical properties, the implications for diamond-based semiconducting devices will be briefly reiterated. II. ELECTRICAL PROPERTIES Electrical transport measurements have established that semiconducting diamond, whether of natural origin or made by high-pressure synthesis, is a partially compensated p-type semiconductor (for a review see Ref. 23). With certain exceptions, the electronic properties of CVD diamond can be understood using data established for bulk diamond. The major differences occur with polycrystalline CVD diamond, in which scattering at the grain boundaries drastically reduces the carrier mobilities and, at low doping levels, electronic surface states at the grain boundaries act as donors that compensate p-type acceptors. We will begin by reviewing work carried out on bulk diamond to see how this relates to CVD diamond. A.

Acceptors and Donors in Diamond

Nitrogen and boron are the only elements that significantly affect the bulk electrical conductivity of diamond; in addition, a hydrogen-terminated surface gives rise to p-type conduction (24,25). Nitrogen is the dominant impurity in the majority of diamonds. Most diamonds produced commercially by high-pressure synthesis (referred to hereafter as ‘‘synthetic diamond’’) and a small fraction (about 0.1%) of natural diamonds are type Ib, meaning that the nitrogen is present in isolated substitutional form; typical concentrations are 40 ppm for natural type Ib diamonds and a few hundred ppm for standard synthetic diamonds. Almost all natural diamonds are predominantly type IaA, meaning that the nitrogen is present as nearest neighbor pairs; here the nitrogen concentration can be as high as 3000 ppm. For the rare type IIa natural diamonds the nitrogen concentration is less than about 10 ppm. Isolated substitutional nitrogen is generally present as a trace impurity in CVD diamond, although in the highest quality undoped material the concentration may be no more than 0.01 ppm. The isolated nitrogen and the A form of nitrogen both behave as donors; however, the ionization energies are high—around 1.7 eV and 4.0 eV, respectively. Nitrogen-containing diamonds are therefore good electrical insulators at room temperature. At higher temperatures (⬎ 200°C) conductivity associated with the 1.7-eV donor leads to a deterioration of the insulating properties of diamond compared, for example, with sapphire (26). Among natural diamonds significant electrical conductivity at room temperature occurs only for the very rare type IIb diamonds, in which boron is the major impurity. These diamonds are p-type semiconductors with typical boron concentrations rather less than 1 ppm and an acceptor ionization energy of 0.37 eV. Synthetic diamond containing up to 1000 ppm of uncompensated boron can be produced by removing nitrogen from the growth capsule and adding boron. Boron-doped CVD diamond, again with boron concentrations much higher than those found in natural type IIb diamonds, is readily grown by adding a gaseous compound of boron to the plasma. B.

p-Type Conductivity

For a partially compensated p-type semiconductor, with an acceptor concentration sufficiently small that there is no degeneracy, the hole concentration at temperature T may be written as (27)

Electrical and Optical Properties of Diamond

p(p ⫹ N D)/(N A ⫺ N D ⫺ p) ⫽ (2/g a )(2πm*kT/h 2 )3/2 exp(⫺E A /kT )

371

(1)

where N A and N D are the acceptor and donor concentrations, g a is the ground state degeneracy factor for the acceptor, m* is the density of states effective mass for the holes, and E A is the acceptor ionization energy. At high temperatures p approaches the saturation value N A ⫺ N D; at low temperatures p ⬍⬍ N A or N D and, provided the acceptor concentration is sufficiently low to avoid impurity band conduction, Eq. (1) approximates to p ⬀ (N A /N D ⫺ 1)T 3/2 exp (⫺E A /kT )

(2)

The concentration of free holes can be determined from the Hall coefficient R using p ⫽ r/Re

(3)

where r is the ratio of the Hall mobility µ H to the conductivity mobility µ c and e is the electronic charge. The value of r depends on the scattering processes; in the case of a nondegenerate semiconductor a number of simplifying assumptions lead to r ⫽ 3π/8 for acoustic phonon scattering and r ⫽ 315π/512 for ionized impurity scattering (28). Phonon scattering is the dominant mechanism at high temperatures, and standard analysis (28) suggests the mobility will vary as T 3/2. In practice, the high-temperature mobility µ(T ) of natural type IIb diamond varies approximately as (22) µ(T) ⫽ µ(290) ⫻ (T/290)⫺S

(4)

with S around 2.8. Most workers have analyzed their Hall effect data using Eq. (1) with g a ⫽ 2 and Eq. (3) with r ⫽ 3π/8. Elsewhere (29) I have argued that g a ⫽ 4 may be more appropriate, and perhaps even g a ⫽ 6 at high temperatures. This makes relatively little difference to the analysis, since effectively (m*) 3/2 /g a in Eq. (1) is an adjustable parameter used to obtain the best fit to the experimental data. Figure 1 shows a plot of hole concentration versus reciprocal temperature obtained by Williams (30) for a natural type IIb diamond. We note that this approaches saturation at high temperatures, as expected from Eq. (1), and varies almost linearly at lower temperatures as expected from Eq. (2). Williams found that when the values for N A, N D, and E A that gave the best fits were substituted into Eq. (1), m* was approximately constant at around 0.75m e below room temperature and decreased in a nonmonotonic way at higher temperatures. (m e is the rest mass of the electron.) From measurements on five diamonds Collins and Williams (31) cite an average value of E A ⫽ 368.5 ⫾ 1.5 meV, determined using Eq. (2) in the temperature interval 160 to 330 K. Impurity concentrations for these diamonds were determined (23) as N A between 48 and 83 ⫻ 1015 cm⫺3 and N D between 0.9 and 15 ⫻ 10 15 cm⫺3. The highest value of N A /N D was 56. Substitution of these data in Eq. (2) shows that this approximation becomes inaccurate at temperatures above 330 K. At and below this temperature the approximation also requires N D ⬎⬎ 4 ⫻ 10 13 cm⫺3, and this condition is well satisfied. The hole mobilities at 290 K for the diamonds used by Collins and Williams (31) lay in the range 700 to 2010 cm 2 V⫺1 s⫺1, and similar data had been obtained by many previous workers. More recently, measurements on natural type IIb diamonds have yielded (32,33) rather lower values between 130 and 518 cm 2 V⫺1 s⫺1. At temperatures above room temperature the mobilities of all specimens decrease rapidly, in accordance with Eq. (4).

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Figure 1 Hole concentration as a function of reciprocal temperature for a natural semiconducting diamond containing 8.3 ⫻ 10 16 cm⫺3 acceptors and 4.2 ⫻ 10 15 cm⫺3 donors. (From Ref. 29.)

C.

Impurity Conduction and Hopping Conduction

Figure 2 shows the resistivity as a function of reciprocal temperature for a natural semiconducting diamond and two boron-doped synthetic diamonds. For the natural diamond we see that there is a shallow minimum in the resistivity curve; this is because the carrier concentration has almost reached saturation, Eq. (1), but the mobility is still decreasing at higher temperature, Eq. (4). Between about 400 and 120 K the log(resistivity) increases linearly with an activation energy of 0.37 eV, and at 120 K there is a sharp knee beyond which the resistivity increases very gradually at lower temperature. Curve (b) for the first synthetic diamond has a substantial linear section with a change of slope to a lower value at about 160 K, and curve (c) for the second synthetic diamond has a short section, parallel to that for the other two diamonds, and a change of slope to a lower value at about 280 K. The neutral acceptor concentrations for (b) and (c) were estimated optically to be 3 ⫻ 10 17 and 1 ⫻ 10 18 cm⫺3, respectively (34). The behavior shown in Fig. 2 can be understood if the conductivity σ is expressed as a sum of three terms (35): σ ⫽ σ 1 exp(⫺E 1 /kT ) ⫹ σ 2 exp(⫺E 2 /kT) ⫹ σ 3 exp(⫺E 3 /kT )

(5)

The activation energy E 1 is the normal acceptor ionization energy, associated with transitions from the acceptor ground state to the valence band, and is observed in all samples provided the acceptor concentration is not too high. The activation energy E 2 can be observed only in the intermediate concentration range and is associated with conduction in an impurity band. When the acceptor concentration is small E 2 is close to E 1, but when the acceptor concentration is increased, so that there is an appreciable overlap between the wave functions of neighboring

Electrical and Optical Properties of Diamond

373

Figure 2 Resistivity as a function of reciprocal temperature for (a) a natural semiconducting diamond containing ⬃8 ⫻ 10 16 cm⫺3 neutral acceptors, (b) a synthetic diamond containing ⬃3 ⫻ 10 17 cm⫺3 neutral acceptors, and (c) a synthetic diamond containing ⬃1 ⫻ 10 18 cm⫺3 neutral acceptors. (From Ref. 29.)

centers, E 2 is reduced. Finally, at the acceptor concentration for which the metal-insulator transition occurs, E 2 → 0. For boron in diamond this transition occurs (34) at a concentration around 2 ⫻ 10 20 cm⫺3. The activation energy E 3 is most prominent for specimens with a relatively low impurity concentration and is interpreted in terms of the energy associated with the tunneling transition (‘‘hopping’’) of a hole from an unoccupied to an occupied acceptor site. In Fig. 2a the change of slope in the resistivity curve for the natural diamond is interpreted (31) as hopping conductivity associated with activation energy E 3, whereas all three conductivity mechanisms are believed (34) to be operative for the synthetic diamonds in Fig. 2b and c. For the diamond used to obtain Fig. 2c the data may also be fitted, in the temperature range 80 to 250 K, to Mott’s formula (36) for variable range hopping. In this case log σ ⫽ A ⫺ BT ⫺1/4

(6)

where A and B are constants. In this process carriers prefer to hop to a distant site that has similar energy, rather than to nearest neighbors that have significantly different energy. Massarani et al. (37) have also extensively investigated conductivity mechanisms in boron-doped synthetic diamond and found that for heavily doped samples the behavior at low temperatures is dominated by variable range hopping. They confirmed that the activation energy exhibited a T 3/4 dependence, as expected for variable range hopping.

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Polycrystalline CVD Films

Diamond films grown on nondiamond substrates are invariably polycrystalline, and doping with boron produces semiconducting material. Von Windheim et al. (33) report that the carrier concentration shows a very sharp drop with decreasing dopant density. They note that similar data are observed in B-doped polycrystalline silicon and attributed to surface states at grain boundaries acting as trapping centers. The grain boundaries also cause severe scattering of the carriers, so that mobilities in polycrystalline CVD diamond are typically (38) in the range 1 to 30 cm 2 V⫺1 s⫺1. At high doping levels impurity conduction is observed, as in synthetic type IIb specimens, and for doping levels around 10 21 cm⫺3 metallic conduction is obtained. In that case the conductivity of the material decreases as the temperature is increased (39). When a lightly boron-doped layer is grown on top of an oriented textured film with {100} faces, mobility values up to 165 cm 2 V⫺1 s⫺1 may be obtained (38) and the acceptor ionization energies for such films are around 0.35 eV, close to the value for natural type IIb diamond. E.

Homoepitaxial CVD Diamond Layers

In this section we will consider two representative studies—that by Fujimori et al. (40) using a microwave plasma with doping by B 2H 6 and that by Visser et al. (41) using the hot filament technique and boron doping by out-diffusion of the BN substrate holder. Both groups find that growth onto a {100}-oriented diamond substrate produces a higher quality layer than on a {110}oriented substrate, that boron incorporation is lower in the {100} layer, and that the hole mobility is very much lower in the {110} layers. The quality of homoepitaxial layers on {111} substrates is also poor. It is found that {110} and {111} layers contain a high density of stacking faults where the tetrahedral diamond packing sequence is disrupted by the hexagonal (Lonsdalite) sequence (42). Figure 3 shows the mobilities of the CVD layers grown by Fujimori et al. plotted as a function of the carrier concentration measured at room temperature. We see that as the carrier concentration increases from 7 ⫻ 10 13 to 7 ⫻ 10 16 cm⫺3 the mobility of the {100} layers falls from 600 to less than 8 cm 2 V⫺1 s⫺1. The mobilities of all the {110} layers are less than 6 cm 2 V⫺1 s⫺1. Gildenblat et al. (42) have gathered together the {100} data in Fig. 3 with data inferred from measurements on natural and synthetic type IIb diamonds and shown that there is a general

Figure 3 Mobility as a function of the carrier concentration at room temperature for boron-doped homoepitaxial films grown on substrates with {100} and {110} orientations. (From Ref. 68.)

Electrical and Optical Properties of Diamond

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decreasing downward trend in mobility values with increasing carrier concentration. Fujimori et al. have also shown that the temperature dependence of the mobility for boron-doped CVD diamond is similar to that observed for natural type IIb diamond [Eq. (4)] with S around 3.0 for the lightly doped material, decreasing to 2.2 for more heavily doped layers. Visser et al. (41) show conductivity data from 110 to 500 K for four pairs of diamonds with different impurity concentrations. Each pair had a {100} and a {110} layer produced in the same growth run. The conductivity curves are very similar to those obtained for borondoped synthetic diamonds (Sec. II.C), showing a change in activation energy at 225 K for the lowest doping and around 310 K for the highest doping. They show that their data can be fitted using just two activation energies—E 1 and E 3 of Eq. (5). Their low-temperature data also fitted the Mott T 1 /4 law [Eq. (6)] very closely, and they conclude that the dominant process at low temperatures may be variable range hopping. Visser et al. (41) also carried out Hall effect measurements as a function of temperature. They found that they could not fit the data using Eq. (1) with the effective mass value m* ⫽ 0.75m e used for natural type IIb diamond (Sec. II.B). For their most lightly doped {100} sample they found m* ⫽ 0.35m e and N D /N A ⫽ 0.008. The room-temperature carrier concentration and Hall mobility for this specimen were 1.3 ⫻ 10 14 cm⫺3 and 590 cm 2 V⫺1 s⫺1, respectively. These values are similar to those for the most lightly doped sample studied by Fujimori et al. (40). F.

Hydrogen in CVD Diamond

Virtually all CVD diamond is grown in the presence of large quantities of hydrogen; if the shutdown sequence of the growth system leaves the CVD film exposed to a hydrogen plasma, then undoped films have a conductivity similar to that of doped films (42). Gildenblat et al. (42) showed that the conductivity of the undoped films can be removed by chemical cleaning and is due simply to a surface conducting layer. They showed that such a conducting layer could also be produced on a natural type IIa diamond exposed to the hydrogen plasma. More recently, it has been shown that hydrogenation of the surface leads to a p-type conducting layer and that it is possible to fabricate a field effect transistor using this layer (25). G.

n-Type Conductivity

No technique has been found to produce a useful level of n-type conductivity in either synthetic or CVD diamond. At high temperatures natural type IIa diamond and many samples of CVD diamond exhibit a small amount of n-type conduction with an activation energy of about 1.6 to 2.0 eV (26). This is probably associated with the small concentrations of isolated substitutional nitrogen (43).

III. OPTICAL PROPERTIES OF SEMICONDUCTING DIAMOND In this section we will consider the absorption and luminescence transitions that occur at the band gap of diamond and also the absorption associated with the boron acceptor. A.

Edge Absorption and Edge Emission

Diamond is an indirect-gap semiconductor with an energy gap of 5.49 eV at 77 K (44). Excitation from the valence band to the lowest conduction band can therefore occur only with the participa-

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Figure 4 Absorption edge of a high-purity synthetic diamond at room temperature and at 77 K. (From Ref. 61.)

tion of phonons (45). Figure 4 illustrates the edge absorption of diamond in detail at room temperature and at 77 K. In the room-temperature absorption three thresholds are visible. Thresholds (i) and (ii) correspond to the creation of an exciton with the absorption of a transverse optic (TO) or a transverse acoustic (TA) phonon, respectively, and (iii) corresponds to the creation of an exciton with the emission of a TA phonon (44). At the lower temperature the phonon absorption component is ‘‘frozen out’’ and only threshold (iii) is visible. The figure also shows that the energy gap is about 10 meV higher at 77 K than at room temperature. Although the edge absorption is an intrinsic property of diamond, it is most easily studied in type IIa or type IIb specimens in which there is no nitrogen-related absorption in this ultraviolet spectral region. B.

Free- and Bound-Exciton Luminescence

The only intrinsic luminescence observed in diamond is that associated with the recombination of free excitons, following the generation of electron-hole pairs by, for example, the absorption of ultraviolet radiation at wavelengths less than 225 nm or by using energetic electrons (of typical energy 10 to 50 keV) to produce cathodoluminescence. Typical edge emission spectra obtained from a high-purity synthetic diamond at 77 K and at ⬃4.2 K are shown in Fig. 5a and b, respectively. The interpretation of the features in these spectra was first discussed by Dean et al. (46). The valence band maxima in diamond are at k ⫽ 0 and the conduction band minima are at k ⫽ k min ⫽ 0.76 of the 〈001〉 zone boundary (44,47). The peaks labeled A, B, and C are due to the recombination of a free exciton with the emission of momentum-conserving phonons of wave vector ⫾ k min, having energies of 87 ⫾ 2 meV (transverse acoustic), 141 ⫾ 1 meV (transverse optic), and 163 ⫾ 1 meV (longitudinal optic), respectively. The low-energy threshold of each peak occurs at an energy given by hν ⫽ E g ⫺ E x ⫺ –hω

(7)

Electrical and Optical Properties of Diamond

377

Figure 5 Edge emission spectra from high-purity synthetic diamond at (a) 77 K and (b) 4.2 K. (From Ref. 61.)

where E g is the energy gap, E x is the exciton binding energy, and –hω is the energy of the corresponding phonon. Features B 2 and B 3 are phonon replicas of the major peak B, involving one or two k ⫽ 0 optic phonons, respectively. The shapes of the free-exciton peaks are accurately described by a Maxwell-Boltzmann distribution (46,48) and the peaks are therefore very much sharper at 4.2 K (Fig. 5b) than at 77 K. Measurements at higher resolution (48) have shown that at 4.2 K there is additional fine structure to the low-energy sides of peaks A and B, the origin of which is not currently understood. The spectrum of Fig. 5a is compared in Fig. 6 with the edge emission from a natural type IIb diamond. Here, in addition to the free exciton peaks, we see features D 1 and D′1, which are associated with the recombination of excitons bound to the boron acceptor. The very weak zerophonon lines D 0 and D′0 (not visible in Fig. 6b) occur at energies E(D 0 ) ⫽ E gx ⫺ E 4x and E(D′0 ) ⫽ E′gx ⫺ E′4x where E gx and E′gx are the energies of the excitons associated with the upper and lower valence bands, and E 4x and E′4x are the binding energies of the upper and lower valence band excitons to the neutral acceptors. The peaks D 1 and D′1 are TO phonon replicas of D 0 and D′0, and a further replica D 2 is clearly visible. The intensity of the bound-exciton peaks, relative to that of the free-exciton features, gives an indication of the uncompensated boron concentration in the region of the diamond examined. For the diamond shown in Fig. 6b this is about 5 ⫻ 10 16 cm⫺3, as determined from Hall effect measurements (31). A very weak peak D, due to the accidental presence of a small concentration of boron (estimated as 3 ⫻ 10 14 cm⫺3 ), is also evident in the low-temperature spectrum in Fig. 5. Edge emission can be detected only from diamonds that are relatively free from defects. The first observation of free-exciton luminescence from CVD diamond was made by Collins et al. (49), who examined individual particles grown by the microwave process. Kawarada et al. (50,51) subsequently observed intrinsic edge emission from single particles of their CVD material and also bound-exciton recombination from boron-doped polycrystalline diamond films. Weak intrinsic free-exciton luminescence has also been observed from polycrystalline

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Figure 6 Edge emission spectra at 77 K for (a) a high-purity synthetic diamond and (b) a natural semiconducting diamond. (From Ref. 60.)

films by Partlow et al. (52) and from single particles by Robins et al. (53). The emission is observed only from the {100} growth sectors of the CVD particles (50,51,53), indicating that these regions have the lowest defect density. The growth sector distribution of impurities is considered further in the next section. The free-exciton emission is strongest in diamonds with low concentrations of defects (46), but even in the best natural diamonds this luminescence is weak compared with the luminescence observed in the visible spectral region (discussed briefly in Sec. III.D). By contrast, measurements in the author’s laboratory in 1995 have shown that in very high purity synthetic diamonds the free-exciton emission is strong, compared with the visible luminescence. Some polycrystalline CVD specimens examined also exhibit relatively strong edge emission, and in a few homoepitaxial layers of CVD diamond the free-exciton luminescence is dominant. This indicates that diamond can now be manufactured with a considerably lower defect density than that found in the best natural diamonds. C.

The Absorption Associated with the Boron Acceptor

Transitions from the boron acceptor to the valence band give rise to a series of excited state transitions that start at 0.304 eV and merge with the photoionization continuum at about 0.37 eV. Figure 7 shows this additional absorption produced in a natural type IIb diamond (54) superimposed on the two- and three-phonon combination bands that are present in all diamonds. The photoionization continuum extends into the red part of the visible spectrum and gives type IIb diamonds their characteristic blue color. Absorption due to the higher energy excited states is shown in more detail in Fig. 8. Six of the peaks in this spectrum disappear when the sample is cooled to 4.2 K, and Crowther et al. (55) have associated this effect with a 2.1-meV splitting of the acceptor ground state. The latter authors carried out uniaxial stress measurements on the

Electrical and Optical Properties of Diamond

379

Figure 7 Absorption spectrum at 77 K in the near-infrared spectral region associated with transitions from the boron acceptor to the valence band (full curve). The dotted curve shows the two- and threephonon absorption that is present in all diamonds. (From Ref. 29.)

acceptor absorption spectrum and were able to propose a plausible classification scheme for the peaks at energies below 0.348 eV, but the full complexity of the spectrum is still not understood. Absorption spectra of boron-doped synthetic diamond obtained by Collins et al. (56) resembled the spectrum shown in Fig. 7, but even at low neutral acceptor concentrations the peaks were much broader and the fine structure shown in Fig. 8 could not be detected. As the acceptor concentration increased (assessed semiquantitatively from the depth of blue coloration associated with the photoionization continuum), the peaks became progressively smeared out and

Figure 8 Absorption spectrum at 77 K produced by the higher energy excited states of the boron acceptor. (From Ref. 29.)

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merged with the photoionization continuum. Type IIb diamonds with much better quality than those used by Collins et al. may now be grown by the temperature gradient method (16), but in most cases the absorption peaks are still very much broader than those observed in natural type IIb diamond; furthermore, the broadening of the spectrum is far more severe in some growth sectors than others (57). To understand this latter phenomenon we need to consider the way different impurities are incorporated into different growth sectors of synthetic diamond. This can be summarized on a diagram of the type originally proposed by Kanda et al. (58) and extended by Burns et al. (57), shown in Fig. 9. This diagram also has considerable implications for the boron doping of CVD diamond and goes some way to explaining the results reported in Sec. II.E. The four horizontal lines in Fig. 9 indicate the relative concentrations of isolated substitutional nitrogen in the major growth sectors of a standard nitrogen-containing synthetic diamond.

Figure 9 Behavior of the relative uncompensated boron acceptor concentrations (N A –N D ) in the various growth sectors on moving from low (B L ) to high (B H ) levels of boron doping. Horizontal lines represent the relative concentrations of nitrogen donors, N D, and sloping lines the total concentrations of boron atoms, N A, in the various sectors, as a function of the doping level of boron. Semiconducting behavior begins in each sector as N A exceeds N D for that sector. (From Ref. 29.)

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The {111} sectors contain the most nitrogen and the {011} sectors least. Optical transitions from the nitrogen donor to the conduction band give the synthetic diamonds a characteristic yellow color, and in a polished section of diamond the different nitrogen concentrations in the different growth sectors are evident from the depth of yellow coloration. The gradients of the diagonal lines in Fig. 9 show the rates at which boron is incorporated in the different growth sectors. A given growth sector becomes semiconducting when the boron concentration exceeds the nitrogen concentration. The horizontal lines are effectively the origins of the uncompensated acceptor concentrations (N A ⫺ N D ) in the corresponding growth sectors, as indicated on the right of the diagram. We see that the {011} sector is the first to acquire semiconducting properties and that at relatively low boron concentrations, B L, (N A ⫺ N D ) is highest in this growth sector. Again this effect is visible by eye, because at boron concentrations between 0 and B L some growth sectors are blue while others are still yellow. At higher boron concentrations, B H, the neutral acceptor concentration is highest in the {111} sectors. If there is a significant source of nitrogen in the growth capsule and a sufficient quantity of boron is added to produce semiconducting diamond, then, although the electrically active boron concentration may be small, the total impurity concentration can be quite large. The relatively high concentration of defects, compared with less than 1 ppm in natural type IIb diamond, almost certainly accounts for the much greater line widths observed in the acceptor spectrum (59). This effect is expected to be most pronounced in the {111} growth sectors (see Fig. 9), as observed experimentally (57,59). If the nitrogen in the growth capsule is very efficiently ‘‘gettered’’ by adding materials such as Ti and Zr, the resulting crystals are sometimes semiconducting by virtue of the accidental boron present. In these diamonds the line widths are very much sharper than in the specimens examined by Burns et al. (57). For CVD diamond grown in a low-pressure plasma the nitrogen content is normally very low but can, nevertheless, be detected using luminescence spectroscopy (60). Semiconducting CVD diamond may readily be produced in one of the ways described in Sec. II.E. The optical absorption data for synthetic diamond suggest that the boron concentration in polycrystalline CVD diamond (which certainly contains both {111} and {001} growth sectors) will be inhomogeneous and that the rate of incorporation of boron in homoepitaxial material will be greatly influenced by the orientation of the substrate. This is exactly what is observed. D.

Visible Luminescence from Semiconducting Diamond

It is well known that, following electron-hole pair generation by electron beam excitation or absorption of above-gap radiation, blue luminescence is observed in natural type IIb diamond. In synthetic boron-doped diamond and boron-doped CVD diamond the luminescence may be either blue or green (61). Interpretations of the mechanisms producing these emission bands are controversial. The green luminescence shows some of the properties of donor-acceptor pair recombination (62) but the picture is not fully consistent. Emission is expected at photon energies given by hν ≅ Eg ⫺ (E A ⫹ E D ) ⫹ e/(4π⑀r) (in eV)

(8)

Here E D is the ionization energy of the donor associated with the boron acceptor, ⑀ is the absolute permittivity, and r is the separation of the donor and acceptor. It is argued that the discrete lines produced at different values of r overlap to form a broad band (62). The green emission, characteristic of boron doping in synthetic and CVD diamond, requires a donor ionization energy of around 4 eV, but it is puzzling, if this model is correct, that no recombination is observed in the ultraviolet region from boron-acceptor, single-nitrogen-donor pairs (23). In natural semiconducting diamond it has been demonstrated that the blue cathodolumines-

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cence originates from dislocations (63), although it is not known whether these are ‘‘decorated’’ with some other defect responsible for the luminescence. Experiments with pure CVD diamond have shown that the intensity of the blue cathodoluminescence is greatly increased in regions of the material that have been subjected to plastic deformation—again confirming that the emission originates from dislocations (64). Similar experiments have been carried out with nitrogencontaining synthetic diamonds (65), and here too the intensity of the blue luminescence was increased, although the predominant effect was the production of nitrogen–vacancy centers that produce intense orange emission at 2.156 eV (575 nm). Schottky diodes can be manufactured using boron-doped material, and some of these emit a feeble blue luminescence when forward or reverse biased (66). However, the intensity of the luminescence is much lower than that obtainable with SiC blue light–emitting diodes and many orders of magnitude weaker than the recently developed LEDs based on GaN (67). Unlike diamond or SiC, GaN is a direct-gap semiconductor, and the conversion of electrical power to light is very much more efficient. It may be possible to obtain green injection luminescence from a boron-doped diode structure, but this will not compete, in performance or price, with the commercial LEDs based on GaP.

IV. SUMMARY The electrical and optical properties of semiconducting diamond have been described in detail and it has been shown that the electrical behavior of boron-doped CVD diamond can be understood in terms of models used to interpret results obtained from bulk (natural and synthetic) semiconducting diamond, once allowances have been made for the effects associated with grain boundaries. High-quality synthetic and CVD diamond exhibit the free- and bound-exciton emission first studied in natural semiconducting diamond. The origins of the green and blue cathodoluminescence from boron-doped synthetic and CVD diamond appear to be similar, although the mechanisms are still not fully understood. Although this material has been extensively studied, there are many reasons why it is not suitable for the device applications proposed (1–5) in the late 1980s. We have seen that there is no known method of producing n-type material with a useful electrical conductivity. The ionization energy of the boron acceptor is large (⬃0.37 eV) so that only around 0.2% of the acceptors are ionized at room temperature; consequently, most device structures exhibit a large series resistance. At higher temperatures the device conductivity improves, but there is a rapid decrease in the hole mobility, which limits applications at high frequency. Both synthetic and CVD diamond particles exhibit more than one growth sector (certainly {100} and {111} sectors are present) and it is therefore impossible to obtain uniform doping with boron. In polycrystalline CVD diamond there are additional problems arising from carrier scattering and carrier depletion effects at the grain boundaries. Visible luminescence can be generated from suitable diamond device structures, but the intensity of the luminescence compares unfavorably with that of the existing and (particularly) newly emerging LED technologies. The present author has pointed out on a number of occasions (19–22) that the early enthusiasm for the production of active electronic devices and optoelectronic devices based on diamond was misplaced. At the time of writing the present chapter many laboratories set up to exploit this ‘‘multibillion dollar market’’ are closing down or turning their attention to other materials. The past decade of intense activity on diamond has revealed many interesting characteristics of this unique material, some of which are recorded in this chapter, but sadly all the

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research has confirmed the author’s long-held opinion that diamond is not a suitable material for electronic device applications.

REFERENCES 1. RF Davis, Z Sitar, BE Williams, HS Kong, HJ Kim, JW Palmour, JA Edmund, J Ryu, JT Glass, CH Carter Jr. Mater Sci Eng 1:77, 1988. 2. K Shenai, RS Scott, BJ Baliga. IEEE Trans Electron Devices 36:1811, 1989. 3. AS Brown. Aerosp Am 25(11):12, 1987. 4. MN Yoder. Nav Res Rev 39(2):27, 1987. 5. M Simpson. New Sci 117(1603):50, 1988. 6. JFH Custers. Physica 18:489, 1952. 7. HB Dyer, PT Wedepohl. Proc Phys Soc B 59:410, 1956. 8. GB Rodgers, FA Raal. Rev Sci Instrum 31:663, 1960. 9. LA Vermeulen, AJ Harris. Diamond Res 1977:25, 1977. 10. LA Vermeulen, AJ Harris. J Appl Phys 49:913, 1978. 11. JF Young, LA Vermeulen, HM van Driel. Proceedings International Conference on Lasers, 1981, p 110. 12. P-T Ho, CH Lee. Opt Commun 46:202, 1983. 13. JF Prins. Appl Phys Lett 41:950, 1982. 14. Y Tzeng, TS Lin, JL Davidson, LS Lan. Proceeding 7th Biennial University-Government-Industry Microelectronics Symposium, Rochester, NY. New York: IEEE, 1987. 15. CM Huggins, P Cannon. Nature 194:829, 1962. 16. HM Strong, RM Chrenko. J Phys Chem 75:1835, 1970. 17. GH Glover. Solid State Electron 16:973, 1973. 18. MW Geis, DD Rathman, DJ Ehrlich, RA Murphy, WT Lindley. IEEE Electron Device Lett 8:341, 1987. 19. AT Collins. Semicond Sci Technol 4:605, 1989. 20. AT Collins. In: JT Glass, R Messier, N Fujimori, eds. Diamond, Silicon Carbide and Related Wide Bandgap Semiconductors. Materials Research Society Symposium Proceedings 162, 1990, p 3. 21. AT Collins. Proceedings 2nd International Conference on Electronic Materials. Materials Research Society, 1990, p 565. 22. AT Collins. Materi Sci Eng B 11:257, 1992. 23. AT Collins, EC Lightowlers. In: JE Field, ed. The Properties of Diamond. London: Academic Press, 1979, p 79. 24. GS Gildenblat, SA Grot, CW Hatfield, CR Wronski, AR Badzian, T Badzian, R Messier. In: JT Glass, R Messier, N Fujimori, eds. Diamond, Silicon Carbide and Related Wide Bandgap Semiconductors, Materials Research Society Symposium Proceedings 162, 1990, p 297. 25. H Kawarada. In: M Kamo, H Kanda, Y Matsui, T Sekine, eds. Advanced Materials ’94. Proceedings NIRIM International Symposium. International Communications Specialists, Tokyo, 1994, p 163. 26. JW Vandersande, LD Zoltan. Surf Coatings Technol 47:392, 1991. 27. JS Blakemore. Semiconductor Statistics. Oxford: Pergamon Press, 1962. 28. SM Sze. Physics of Semiconductor Devices. New York: Wiley, 1981. 29. AT Collins. Philos Trans R Soc A 234:233, 1993. 30. AWS Williams. PhD thesis, University of London, 1970. 31. AT Collins, AWS Williams. J Phys C 4:1789, 1971. 32. PR de la Houssaye, CM Penchina, CA Hewett, GR Wilson, J M Zeidler. J Appl Phys 71:3220, 1992. 33. JA von Windheim, V Venkatesan, DM Malta, K Das. Diamond Relat Mater 2:841, 1993. 34. AWS Williams, EC Lightowlers, AT Collins. J Phys C 3:1789, 1970. 35. EA Davis, WD Compton. Phys Rev 140:A2183, 1965.

384 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48.

49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68.

Collins NF Mott. Philos Mag 19:835, 1969. B Massarani, JC Bourgoin, RM Chrenko. Phys Rev B 17:1758, 1978. BR Stoner, C Kao, DM Malta. Appl Phys Lett 62:2347, 1993. M Werner, O Dorsch, HU Baerwind, E Obermeier, L Haase, W Seifert, A Ringhandt, C Johnson, S Romani, H Bishop, PR Chalker. Appl Phys Lett 64:595, 1994. N Fujimori, H Nakahata, T Imai. Jpn J Appl Phys 29:824, 1990. EP Visser, GJ Bauhuis, G Janssen, W Vollenberg, WJP van Enckevort, LJ Giling. J Phys Condens Matter 4:7365, 1992. GS Gildenblat, SA Grot, A Badzian. Proc IEEE 79:647, 1991. AT Collins. In: G Davies, ed. The Properties and Growth of Diamond. Data-Reviews Series. London: IEE, 1994, p 284. CD Clark, PJ Dean, PV Harris. Proc R Soc A 277:312, 1964. See, for example, RA Smith. In: Semiconductors. Cambridge: Cambridge University Press, 1961, pp 201–210. PJ Dean, EC Lightowlers, DR Wight. Phys Rev 140:A352, 1965. PJ Dean, JC Male. J Phys Chem Solids 25:1369, 1964. AT Collins, EC Lightowlers, V Higgs, L Allers, SJ Sharp. In: S Saito, N Fujimori, O Fukunaga, M Kamo, K Kobashi, M Yoshikawa, eds. Advances in New Diamond Science and Technology. Proceedings Fourth International Conference on New Diamond Science and Technology. Tokyo: MYU, 1994, p 307. AT Collins, M Kamo, Y Sato. J Phys Condens Matter 1:4029, 1989. H Kawarada, Y Yokota, A Hiraki. Appl Phys Lett 57:1889, 1990. H Kawarada, Y Yokota, T Sogi, H Matsuyama, A Hiraki. Diamond Opt III SPIE 1325:152, 1990. WD Partlow, J Ruan, WJ Choyke, DS Knight. J Appl Phys 67:7019, 1990. LH Robins, EN Farabaugh, A Feldman. Phys Rev B 48:14167, 1993. SD Smith, W Taylor. Proc Phys Soc 79:1142, 1962. PA Crowther, PJ Dean, WF Sherman. Phys Rev 154:772, 1967. AT Collins, PJ Dean, EC Lightowlers, WF Sherman. Phys Rev 140:A1272, 1965. RC Burns, V Cvetkovic, CN Dodge, DJF Evans, M-LT Rooney, PM Spear, CM Welbourn. J Cryst Growth 104:257, 1990. H Kanda, T Ohsawa, O Fukunaga. In: Abstracts of the Second Meeting of ‘Diamond,’ Tokyo, Japan, 1987, p 23 (in Japanese). M-LT Rooney. J Cryst Growth 116:15, 1992. AT Collins. Diamond Relat Mater 1:457, 1992. AT Collins. Physica B 185:284, 1993. PB Klein, MD Crossfield, JA Freitas, AT Collins. Phys Rev B 51:9634, 1995. N Yamamoto, JCH Spence, D Fathy. Philos Mag B 49:609, 1984. PM Spear. Personal communication, 1994. EJ Brookes, AT Collins, GS Woods. J Hard Mater 4:97, 1993. H Kawarada, Y Yokota, Y Mori, K Nishimura, A Hiraki. J Appl Phys 67:983, 1990. MA Khan, Q Chen, RA Skogman, JN Kuznia. Appl Phys Lett 66:2046, 1995. AT Collins. Ceramics International 22:321, 1996.

17 Semiconducting Diamond and Diamond Devices Shinichi Shikata and Naoji Fujimori Itami Research Laboratories, Sumitomo Electric Industries, Ltd., Itami, Hyogo, Japan

I.

INTRODUCTION

The significant characteristics of diamond as a semiconductor have been expected to allow its use in high-temperature and high-power operation devices and have generated numerous research activities on diamond devices. Based on the electrical characteristics of diamond, which were discussed in the preceding chapter, an overview of diamond device–related technologies as well as recently developed devices will be given in this chapter. First, the feature and possibilities of diamond as a semiconductor are briefly discussed. The band structure of diamond, including exchange and correlation effects, is shown in Fig. 1 (1). Diamond is a material of indirect transition with a large energy gap of 5.47 eV from the top of Γ25′ to the bottom of ∆ 1. As shown in Fig. 2, the lattice constant is too small compared with other semiconductors; thus, unfortunately, it is unlikely to be possible to carry out ‘‘band gap engineering’’ to generate structures such as high electron mobility transistor (HEMT), heterojunction bipolar transistor (HBT), and quantum well (QW) devices. The only exception is cubic BN (cBN), which has 1.3% lattice mismatch with diamond, which will be discussed later. However, this largest energy gap among conventional semiconductors is expected to be a prime characteristic of high-temperature and high-power operation devices associated with high thermal conductivity up to 20 W/cmK. One of the largest problems of semiconductor devices is thermal management, and various types of technologies have been developed to overcome this problem. But for diamond devices, it is likely that the problem can be avoided owing to its ultimate thermal conductivity. The semiconductor properties of diamond are summarized in Table 1 and Fig. 3 (2) compared with typical semiconductors such as Si, GaAs, and SiC. Utilizing these characteristics, several theoretical analyses have been performed. These are well known as figure of merit (FOM) with the author’s name, such as Johnson’s figure of merit (JFOM) (3), Keyes’ FOM (KFOM) (4), Baliga’s FOM (BFOM) (5), and Baliga’s high-frequency FOM (BHFFOM) (6). This is also given in Table 1. 1. JFOM defines the power-frequency product for a low-voltage transistor. JFOM ⫽ E c v s /2π. 2. KFOM defines a thermal limitation of the switching behavior of transistor. KFOM ⫽ λ (CV s /2πε) 1/2 385

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Figure 1 Band structure of diamond including exchange and correlation effects. (From Ref. 1.)

Figure 2 Lattice constant versus band gap of semiconductors.

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Table 1 Typical Semiconductor Properties Property

Si

GaAs

3C-SiC

Diamond

Band gap (eV) Dielectric constant Thermal conductivity (W/cm K) Melting point (°C) Resistivity (Ωcm) Mobility (electron) (cm 2 /V s) (hole) (cm 2 /V s) Breakdown (10 5 V/cm) Typical donor and level (meV) Typical acceptor and level (meV) Effective mass (electron) (hole) Band JFOM KFOM BFOM

1.12 11.8 1.5 1415 E3 1500 450 3 P 45 B 45 0.98 0.16 Indirect 1 1 1

1.42 12.5 0.46 1238 E8 8500 400 60 Si 5.8 Be28 0.067 0.082 Direct 6.9 0.46 13.3

3.0 9.7 5 2540 E2 400 50 40 Al 167 a B 254 a 0.60 1.00 Indirect 1138 6.54 106.3

5.47 5.7 15–20 4000 E13 1800 1200 100

BHFFOM

1

9.5

13.1

a

B 370 0.2 0.25 Indirect 8206 32.2 8574.1 n 6751.3 p 453.7 n 357.2 p

Data for 4H-SiC.

3. BFOM defines the material parameters for minimizing the conduction losses in a power transistor and applies to devices operating at low frequency. BFOM ⫽ εµE 3g. 4. BHFFOM defines the BFOM in a power transistor operating at high frequency. BHFFOM ⫽ 1/(R on , sp C in, sp ) Here, R on,sp ⫽ 4V 2B /(εµE 30 ) and

C in,sp ⫽ (εqN 3B /2V G ) 1/2

and E c is the breakdown field, V s the saturation velocity, µ the mobility, V B the breakdown voltage, and N B ⫽ εE 3c /(2q V B ) As can be seen from the figure of merit in Table 1, diamond fulfills the expectations for power devices from various points of view, unless the technologies are not mature at present. One of the problems with diamond at this stage is that only p-type doping is possible with boron. For varieties of devices and integrated circuits, n-type diamond is preferable, but this is not inevitable because in most cases unipolar devices are possible. For a heterojunction bipolar transistor (HBT), a theoretical study was also reported for SiC/Si/diamond (emitter/base/collector, respectively) (7), and the HBT FOM is 22.21 times larger than for an AlGaAs/GaAs/GaAs HBT. Here, the HBT FOM is defined as the product of operating frequency and output power of the HBT with 3 dB gain. This is also possible

Figure 3

Carrier velocity versus electric field for typical semiconductors. (a) Electron; (b) hole.

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without n-type doping; that is, a pnp HBT is possible with a p diamond collector by using a collector up-configuration device structure. Hereafter, we focus on some of the technologies related to device structures, processing, and characteristics.

II. DOPING As described in the preceding chapter, p-type doping with B is the only successful technique for the formation of channels in diamond at this stage. B atoms in substitutional sites of carbon in diamond have a deep acceptor level of 370 meV. As is well known for various kinds of semiconductors, there are three ways to dope impurities: vapor-phase doping, ion implantation, and diffusion. Following are short reviews of doping technologies for B in diamond.

A.

Vapor-Phase Doping

Vapor-phase doping of B in diamond has been realized by several methods. The first doping was by ‘‘unidentified gaseous B compounds’’ by Spitsyn et al. (8). Currently, the major technique involves introducing B 2H 6 (diborane) diluted in H 2 into the chemical vapor deposition (CVD) chamber during deposition. The results are described in detail in the previous chapter. Most of the diamond devices utilize p-channels formed by this method, and the results will be given in Sec. V. As diborane is a toxic gas, the doping should be carried out in a leaktight deposition chamber with a safety gas feed system. For this reason, some people use only B powder in the CVD chamber for doping (9). Using B 2O 3 (boron trioxide) powder mixed in a liquid is another way to perform B doping in safety conditions (10).

B.

Ion Implantation

Ion implantation represents advances in reproducibility and throughput in device fabrication and is used in most semiconductor device manufacturing processes. But for diamond, a region damaged by ion implantation is graphitized during the subsequent annealing process. With doses of B low enough to prevent graphitization, it is hard to obtain an appropriate carrier concentration for device performance. To overcome this difficulty, Prinz (11) clarified the important role of implantation temperature and spatial distribution of defects. According to this study, successful results were obtained with ion implantation at a low temperature of 77 K by Zeisse et al. (12). The advantage of this technique is low diffusivity of defects created during the implantation process, which enhances the probability of B ions occupying vacant lattice sites. As is well known in ion implantation, coimplantation techniques are also effective for diamond (13). Carbon coimplantation with B injects vacancies that overlap the B profile. The details of ion implantation technologies for diamond and related materials can be found in the book by Dresselhaus and Kalish (14). Despite these investigations, most of the high-performance transistors have been accomplished with channels obtained by vapor-phase doping and ion implantation is not recognized as an indispensable technology for p-channel formation in diamond.

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Diffusion

The B doping by thermal diffusion associated with subsequent rapid thermal annealing (RTA) was employed for the fabrication of a MESFET by Tsai et al. (15). They made a very shallow channel of 50 nm by this method. This is the only successful result obtained with diffusion doping.

III. SURFACE PROPERTIES AND CONTACTS A.

Schottky Contact and MOS Interface

Surface-related characteristics such as the insulator-semiconductor interface and metal-semiconductor interface are among the most important factors in device structure and characteristics. The influence of surface-related phenomena on device characteristics is briefly reviewed. For the metal-insulator (oxide)-semiconductor (MIS or MOS) structure field effect transistor (FET), the state density of the semiconductor-insulator interface is extremely important for the inversion behavior of MOSFETs. For instance, the surface state density of the SiO 2 /GaAs system (16) was expected to be over 10 13 cm ⫺2 eV ⫺1, two to three orders larger than that of the SiO 2 /Si interface, and thus an inversion layer could not be observed. The influence of surface state density is also found in metal-semiconductor (MES) FETs, that is, leakage of the Schottky barrier, a low barrier height of the Schottky gate contact, and an increase in series resistance from source to drain. It is well known that the the current density of the Schottky barrier is related to the barrier height (Φ B ) of the Schottky contact, which is given by J ⫽ J 0 exp(qV/nkT){1 ⫺ exp(⫺qV/kT )}

(1)

Here, J 0 is given by J 0 ⫽ A*T 2 exp{⫺ Φ B /kT }

(2)

where A* is the effective Richardson constant. The interface constant S defined by the following equation is conventionally used to express these phenomena. S ⫽ d Φ B /dX m

(3)

Here, X m is the electronegativity of the metal. As can be seen from Eq. (1), it is necessary to have a higher barrier height to reduce the reverse direction leakage current J 0. It is thought that the Schottky barrier height in metal-semiconductor systems depends on the metal work function (Φ m ). However, when the Fermi level is pinned and the Schottky barrier height does not depend on the metal work function, it is quite constant and sometimes only a low barrier height is available despite using various kinds of metals. This not only affects the leakage current but also leads to a small logic swing in some digital circuits, resulting in malfunction of the logic circuit due to undistinguishability between high and low voltage levels. Also, in MESFETs the surface depletion layer originating from the semiconductor-insulator interface affects MESFET pinch-off characteristics and the series resistance from source to drain, which results in low transconductance and nonuniformity of the transistor characteristics. As described before, the surface state is one of the most important characteristics of a semiconductor when device applications are considered. For diamond, research activities on surfaces by means of Schottky diodes have been carried out at several institutes. From the late 1980s to early 1990s, Schottky diodes with p-channels were investigated for diamond (17–22). Fine rectification rafios of forward and reverse were obtained and were from 5 to 6. For the metal dependence of the Schottky characteristics, Fermi

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level ‘‘pinned’’ results have been reported by several researchers for Schottky contacts fabricated on KNO 3- or CrO 3-treated diamond surfaces. These treatments were required to eliminate the graphitized surface of diamond. On the other hand, ‘‘unpinned’’ results have also been reported for the surface of semiconductor diamond by several researchers and there have been several discussions. These inconsistent results have been discussed for a long time and are now considered to be due to a dependence on the surface treatment. In particular, surface treatment with oxygen and hydrogen affects the surface characteristics. Oxygen treatment by both wet and dry processes has been carried out, such as boiling in a saturated solution of CrO in H 2SO 4 and O 2 plasma, respectively. It was observed that when oxygen was adsorbed on diamond surfaces, the metal dependence of the Schottky barrier height vanished (23,24). The Schottky barrier height of various kinds of metals on homoepitaxial CVD diamond on a hydrogen-terminated surface has been measured and plotted as a function of metal electronegativity. This is shown in Fig. 4 (25,26). As the metal electronegativity increases, the barrier height decreases. The S factor, which is given in Eq. (3), is 0.7, which indicate that the surface is almost unpinned. As shown in Fig. 5 (27), the surface Fermi level position has been estimated by electrical and Xray photoelectron spectrocopy (XPS) measurements. The oxygenated surface was estimated to be depleted due to Fermi level pinning. It was also stated that remote hydrogen plasma treatment of an oxygenated surface can only partially replace the adsorbed oxygen with hydrogen, whereas the as-grown surface is considered to have an accumulation layer. This has been proposed to explain the ‘‘surface conduction layer’’ of hydrogen-terminated diamond. The surface-depleted layer has been confirmed to be p-type (28). The actual Schottky characteristics of diamond have been intensively studied by Waseda’s group and the results are shown in Table 2. Most Schottky metals show fine ideality factors with their own barrier height, which can be estimated from their electronegativities. Recent results indicate that the Schottky contact for diamond can be controlled by appropriate surface treatment to achieve the fine characteristics that are required for MESFET applications. The interface of SiO 2 and diamond has been studied by several research groups associated with FET fabrication, looking for MOSFET applications. The first paper on MOS on diamond

Figure 4 Schottky barrier height dependence of metals on diamond as a function of metal electronegativity. (From Ref. 26.)

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Figure 5 Position of Fermi level estimated from Kelvin probe and XPS measurements. (From Ref. 27.)

was by Grot et al. in 1990 (29). A sputtered film was used for SiO 2. They have obtained device operation but without saturation. The first study of MOS interfaces was by Geis et al. in 1991 (30). The C-V characteristics were measured and the experimental results almost coincided with the theoretical curve at 10 kHz. Results for a MOSFET with a hydrogen-terminated surface associated with evaporated SiO 2 (31) seem to indicate a high-quality interface. Among insulators other than SiO 2, a CaF 2 film was studied by Maid et al. (32). They observed MISFET operation without an imperfect surface state measured by C-V characteristics. At present, the surface state has not been intensively studied for diamond and the surface state density is still unknown. Intensive investigations associated with surface physics are expected from the device viewpoint.

B.

Ohmic Contact

A low-resistivity p-type ohmic contact to diamond is essential technology for reduction of series resistance in order to realize a high-performance transistor. And a temperature-stable ohmic contact is extremely important for diamond for high-temperature applications. It is well known that for ohmic contacts of semiconductors, two solutions are provided. The first one is heavy doping of the contact region, which enables an increase in the tunneling probability of electrons or holes. The other is to prepare low-resistivity contacts to reduce the barrier height at the interface, including an intermediate low-barrier-height semiconductor layer. For the first solution, an ohmic contact with heavy doping of the semiconductor is realized

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Table 2 Summary of FET Development Studies Early studies Bipolar transistor Point-contact transistor Permeable base transistor MESFET p-MESFET p-MESFET p-MESFET with i-diamond p-MESFET with i-diamond p-MESFET p-MESFET with i-diamond p-MESFET p-MESFET with i-diamond p-MESFET with SCL p-MESFET with SCL p-MESFET with i-diamond MOSFET p-MOSFET with SiO 2 p-MOSFET with SiO 2 p-MOSFET with SiO 2 p-MOSFET with SiO 2 p-MOSFET with SiO 2 p-MOSFET with SiO 2 p-MOSFET with SCL

Comment

Year

Center

1992 1987 1988

University of Witwatersrand MIT MIT

First paper First paper First paper for i-diamond 310°C operation Diffusion and RTA Polycrystal Gate-recessed Polycrystal First paper for SCL Highest gm Pulse-doped

1989 1989 1990 1991 1991 1991 1994 1994 1994 1994 1995

Sumitomo Penn State University Sumitomo Sumitomo Varian Research Center Kobe Steel Sumitomo Kobe Steel Waseda University Waseda University Sumitomo

First paper Selective growth Ion-implanted channel Gate-recessed 350°C operation Polycrystal 400°C operation Highest gm (trans conductance)

1990 1991 1991 1992

Penn State University MIT Naval Ocean System Center Penn State University

1992 1994 1996

Kobe Steel Kobe Steel Waseda University

by doping diamond with B. For the latter, there are two methods for obtaining low-barrierheight materials. One is to insert a low-energy-gap intermediate semiconductor layer such as InAs in the case of GaAs. The second is to have low-barrier-height metals. The first method cannot be achieved for diamond, because of its lattice constant. However, a graded band gap contact from Si to diamond, which, exactly speaking, is not a real semiconductor band gap grading, has been investigated (33). This is formed by ion mixing with Kr ion implantation and annealing at 1200°C to form an SiC layer. The contact resistance obtained was 5 ⫻ 10 ⫺3 cm 2. In most of the studies, low-barrier-height materials associated with heavy doping are considered as ohmic contacts for diamond. In the early stage of the research looking for devices, low-barrier-height metals such as Au (34–36) and Pt (37) were used for the ohmic metal. This type is called a ‘‘nonalloy-type ohmic metal.’’ The contact resistance of Pt was 3.3 ⫻ 10 ⫺3 cm 2. The refractory metal–transition metal systems to p-type diamond are well known as ohmic metals, such as Au/Ti (38), Au/Mo (39), Au/Ta (38), Mo/Ni/Au (40), TiC/Au (41), and TaSi 2 / Au (41). These are ‘‘alloy-type ohmic metals.’’ For these ohmic metal systems, low contact resistances of 10 ⫺5 to 10 ⫺6 Ω cm 2 have been obtained with highly doped channels. The dependence of contact resistance on diborane doping concentration for Ti/Mo/Au metal is shown in Fig. 6 (42). A contact resistance of order 10 ⫺6 Ω cm 2 is obtained. This is the same as that of other semiconductor contacts and is low enough for device operation for integrated circuits. For Ti-based contacts, a TiC layer is observed to be formed by the contact alloy. As is well known in semiconductor devices, temperature degradation is determined by

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Figure 6 Dependence of the contact resistance of Ti/Mo/Au ohmic metal on diamond on doping concentration. (From Ref. 42.)

the temperature durability of the ohmic contact. Thus, for high-temperature operation of diamond devices, high thermal stability of ohmic metals is required as well as low resistivity (42,43). The aging characteristics of Ti/Mo/Au were studied and it was found that this system is superdurable for high-temperature aging; that is, there was no degradation for 400 h at 800°C as shown in Fig. 7 (42). Compared with GaAs and SiC, which have durabilities of 10 h at 650°C and 100 h at 500°C, respectively, diamond has far better temperature durability. This indicates that diamond will be able to find high-temperature applications with superhigh temperature stability.

Figure 7 Aging characteristics of Ti/Mo/Au ohmic metal on diamond. (From Ref. 42.)

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IV. GROWTH AND PROCESSING Despite the purpose of this chapter, short descriptions of selective growth and heteroepitaxial growth for band gap engineering will be given here.

A.

Selective Growth of Diamond

Selective growth is important for the fabrication of device structures, especially for quite complicated structures of high-performance devices. For diamond, various kind of insulators and metals can be used for the mask in selective growth, because diamond is inert to acid and alkali solvents as well as etching gas plasma, and there are few problems related to the fabrication of mask materials on diamond. It has been reported that the SiO 2 was sputtered and patterned into a mask by lithography and subsequent etching by buffered HF. Diamond 0.15 µm thick was selectively grown for a 60 ⫻ 200 µm window (44). The evaporated tungsten metals have also been used for the mask to grow diamond selectively for a 30 µm window (45). These are successfully utilized in the fabrication of FETs.

B.

Heteroepitaxial Growth for Band Gap Engineering

Heteroepitaxial growth of diamond for band gap engineering is limited to cubic BN (cBN). The ˚ and the lattice mismatch to cBN (3.615 A ˚ ) is 1.3%. Thus, lattice constant of diamond is 3.267 A it is possible to grow diamond epitaxially on cBN. Koizumi et al. (46) succeeded in growing diamond on cBN in 1990. This was followed by Tomikawa and Shikata (47), who found that the lattice spacing of the diamond (111) plane on cBN is the same as that of the bulk crystal. They also observed dislocations once in 82 planes, which almost correspond to lattice mismatch. These results indicate that when cBN vapor-phase growth is achieved in the future, band gap engineering is available for diamond, and various kinds of devices such as HBT, HEMT, and QW devices will be possible using heterojunctions.

C.

Etching

In order to enhance the characteristics of FETs, the series resistance and contact resistance might be reduced with less effect of the surface depletion layer. For these purposes, microfabrication technologies are essential to meet the requirements for the fabrication of devices, such as a small size gate with a self-aligned structure, recessed structure, and so on. Several techniques that are already used in Si large-scale integration (LSI) processes such as ion beam–assisted etching, reactive ion etching, and electron cyclotron resonance (ECR)– assisted etching have been adopted for the dry etching of diamond (48–51). Typically, NO 2, O 2, and inert gases are used for the etching gas with SiO 2 and Al as etching masks. An etching selectivity of 38 for diamond to SiO 2 is obtained with a gas composite of Ar with 1% O 2, which is high enough for high-aspect-ratio etching of diamond with a high process margin. Also, by using pure Ar, an etching selectivity of about 1 is obtained. The wide range of etching selectivities from 1 to 38 enables complex fabrication processes of devices using diamond. Utilizing this dry etching technique for diamond, microfabrication of diamond

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Figure 8 Overview of diamond etched by RIE. (From Ref. 51.)

was carried out. Figure 8 shows an overview of etched diamond surfaces for various sizes of lines and spaces. With regard to their lithography resolution, up to 1-µm line and space patterns of diamond are fabricated. The minimum size of lines and spaces will be improved to the halfto quarter-micrometer level by utilizing further lithography techniques such as i-line or excimer laser stepper and electron beam exposure. As can be seen from the foregoing studies, diamond can be fabricated by dry etching, despite its inertness to wet etching by acid and alkali.

V.

TRANSISTORS AND INTEGRATED CIRCUITS

A.

Early Studies

Transistors of diamond have been investigated mainly with the p-channel MES type and pchannel MOS type, because the only reproducible channels are available for B-doped p-type diamond. However, from a historical viewpoint, research activities on MESFETs and MOSFETs were preceded by several pioneering studies with other device structures. The first work that utilized a bipolar transistor was that of Prins (52). Using a natural ptype diamond bulk crystal as a substrate, carbon ions are ion implanted to form n-type-like regions with 3.2-µm-diameter wire as a implant mask. The energy level and mechanism of the carbon implantation cannot be estimated; however, bipolar transistor behavior was achieved. The I-V characteristics are shown in Fig. 9. Although the current gain of h F ⫽ I C /I B is only 0.11, the impact on researchers in this field was not insignificant. This was followed by several research activities, such as work on npn bipolar transistors with As implanted n-type-like regions and a point contact bipolar-like transistor (53). In 1987, the first high-temperature operation up to 500°C was achieved by Geis et al. (54) using a point contact transistor. A permeable base transistor with an Al metal base was the next type of the device tried

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Figure 9 I-V characteristics of the first FET of Prins. (From Ref. 52.)

for diamond. This device is fabricated with ion beam etching to form the structure. A transconductance of 30 µS/mm was exhibited (55). B.

MESFETs

MESFETs are promising devices for diamond because of the characteristics obtained with unipolar semiconductors associated with their simplified fabrication process. The device characteristics of MESFETs depend highly on the device size, especially the gate length, and surfacerelated characteristics. The first papers on MESFETs were published in 1989 by Shiomi et al. of Sumitomo Electric Industries (56) and by Gildenblat et al. of Pennsylvania State University (57). In the former work, a p-channel of 2.0 µm was obtained with a B-doped epitaxial diamond layer on an insulating bulk crystal. Al and Ti were employed directly on the p-channel for gate and ohmic electrodes, respectively. The structure and I-V characteristics are shown in Fig. 10. The gate length was 140 µm. Although the drain current saturation and pinch-off characteristics were not observed, the drain current changed slightly with gate bias. These studies were followed by improvement of structures as well as sophisticated fabrication processes. In order to improve Schottky characteristics, intrinsic diamond was inserted between the p-channel and gate metal (58). Intrinsic diamond of 0.23 µm was applied and improved characteristics of 2 µS/mm were obtained. These structures are known in compound semiconductor devices and are sometimes classified as MISFETs the ‘‘I’’ standing for insulating semiconductor. In this chapter, these structures are classified as MESFETs regarding the general knowledge of

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Figure 10 I-V characteristics of one of the first MESFETs. (From Ref. 56.)

silicon technology. Such a structure was also applied to high-temperature operation by Nishibayashi et al. (59,60) utilizing selective epitaxy of intrinsic diamond, and they obtained high-temperature operation at 310°C. The rapid thermal annealing associated with B doping by thermal diffusion was employed for a MESFET by Tsai et al. (15); this is the only FET operation result obtained with diffusion doping. To improve MESFET characteristics, several techniques have already been introduced in III-V compound semiconductor devices. There are two major directions for improvement. The first one is to reduce gate length with fine lithography technique. The second is to reduce series resistance. Reducing the spatial distance between the gate and a low-resistance region such as a p⫹ doped region is a promising technique for the reduction of series resistance. An extreme structure can be found in a self-aligned structure. The reduction of ohmic contact resistance is also an important technique for reducing series resistance. It is also important to avoid influence of the surface state. Utilizing some of these techniques, such as low ohmic contact and a gate recessed structure associated with reduced gate length, the first pinch-off characteristics of a diamond MESFET were observed by Sumitomo’s group (61). The structure and I-V characteristics are shown in Fig. 11. For the recess etching process in this work, reactive ion etching (RIE) was employed (51). A shallow channel is also a promising approach to enhancing MESFET characteristics. A pulse-doped (delta-doped) structure was applied for diamond by Shiomi et al. in 1995 (62). By secondary ion mass spectroscopy (SIMS) measurement of the pulse-doped structure, the ˚ , and they observed a drain current channel thickness can be estimated to be less than 400 A saturation characteristic with a high transconductance of 116 µS/mm with a 4-µm gate length MESFET. This structure is promising for a diamond FET utilizing degeneracy of doping that can avoid the difficulties caused by a deep acceptor level of 370 meV. A unique MESFET utilizing a ‘‘surface conducting layer’’ as a channel was developed at Waseda University (63,64). As described earlier in Sec. III, the hydrogenated surface of diamond is known to behave as p-type. Using this layer as a channel, a MESFET has successfully

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Figure 11 I-V characteristics of MESFET for first pinch-off. (From Ref. 61.)

been fabricated. The pinch-off characteristics and high transconductance of 200 µS/mm were observed for FETs of gate length 10 µm (65). These characteristics have been improved and the highest transconductances of 2.5 mS/mm obtained by a 7-µm gate length FET with pinchoff and 4.1 mS/mm for a non-pinch-off FET (66). These are also shown in Fig. 12. This is the highest transconductance of diamond ever reported for a diamond MESFET. The preceding results were obtained with single-crystal diamond. However, a single crystal is far from real applications because of the crystal size and cost. Thus, the fabrication of FETs has been performed using polycrystalline diamond film. In particular, the advanced technology of heteroepitaxial growth, which can provide a large-area crystal, is expected to be promising (67,68). The first FET operation using polycrystalline diamond was reported by Nishimura et al. in 1991 (69). Silicon nitride (Si 3N 4 ) was used as a substrate. A MiSFET structure with intrinsic diamond as the Hayer was fabricated, and it was observed that the drain current changed slightly with gate bias.

Figure 12 Cross section and I-V characteristics of a MESFET using a surface conductive layer. (From Ref. 64.)

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MOSFETs (MISFETs)

For MOSFETs, inversion-type and non-inversion-type FETs are known for various types of semiconductors; however, an inversion-type MOSFET had not been realized for diamond, because of the poor characteristics of the MOS interface. Thus, all of the reports on diamond MOSFETs given here are for non-inversion-type FETs. The first paper on MOSFET was by Grot et al. in 1990 (70). Silicon dioxide 0.1 µm thick was employed for the insulator, which was deposited by sputtering with Ar and oxygen plasma. The channel thickness was 0.1 µm. The device structure and FET characteristics for operation at 300°C are shown in Fig. 13. The gate leakage current was as small as 10 pA at 300°C operation, which indicates an advantage of MOSFETs compared with MESFETs. To improve this FET, a gate recess structure was introduced by electron cyclotron resonance (ECR) etching and high-temperature operation up to 300°C was achieved. The maximum transconductance was 87 µS/mm (71,72). The first pinch-off characteristics of MOSFETs were achieved by Zeisse et al. in 1991 (73). They introduced a sophisticated process of ion implantation of boron. Implantation was carried out at 80 K with a multiple scheme to provide a uniform layer 210 nm thickn. After implantation, the substrate was annealed to 1263 K to activate ions. The I-V curve shows fine pinch-off characteristics with 3.9 µS/mm transconductance, which is shown in Fig. 14. This is first report on pinch-off characteristics of a diamond MOSFET. Pinch-off characteristics have also been reported for a MOSFET by Glass et al. (74), with an epitaxially doped channel MOSFET. As can be seen in Fig. 15, they observed fine characteristics at 400°C with transconductance of 0.26 mS/mm. The Waseda University group have obtained high transconductance of 16.4 mS/mm for a 6 µm gate length MOSFET with evaporated SiO 2 associated with a hydrogenterminated surface (75). This is the highest transconductance ever reported for diamond, including various types of FET structures. This FET has been confirmed to operate at 327°C. For polycrystalline diamond, a MOSFET with SiO 2 was reported by Tessmer et al. (75) in 1992 (76). These results for FETs, including early studies, MESFETs, and MOSFETs, are summarized in Table 2. D.

Heterojunction Devices

As shown in a previous subsection, it is possible to grow diamond epitaxially on cBN with a lattice mismatch of 1.3% (47). Utilizing this growth, a heterojunction of p-type diamond–n-

Figure 13 The first MOSFET characteristics operating at 300°C. (From Ref. 70.)

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Figure 14 I-V characteristics of MOSFET for first pinch-off. (From Ref. 73.)

type cBN has been grown successfully, and using this junction, a heterojunction diode was fabricated and operated up to a temperature of 500°C (76,77). E.

Integrated Circuit

For integrated circuits using p-channel diamond, bipolar logics and the complementary MOS (CMOS) logic are not available and the circuits are limited to the logics of unipolar FETs, which are familiar with compound semiconductor devices. The typical unipolar FET logics are summarized in Table 3. Integrated circuits using diamond are under investigation because of the progress in FET characteristics. The first trial was by Zeiss and colleagues (78) using ion-impanted channel

Figure 15 I-V characteristics of a MOSFET operated at 400°C. (From Ref. 74.)

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Table 3 Typical Logics of Unipolar FET Mode Enhancement mode Depletion mode

Logic DCFL (direct coupled FET logic) LPFL (low pinch-off voltage FET logic) SDFL (Schottky diode FET logic) BFL (buffered FET logic) CCL (capacitor-coupled FET logic) SCFL (source-coupled FET logic) SSFL (Schottky-coupled Schottky FET logic)

MESFETs with a transconductance of 3.9 µS/mm. Two MESFETs were connected, including one FET as a current source, to observe a gain (V out /V in ) of approximately 2. Using a logic analyzer, two FETs were connected with load resistance to observe NAND operation in 1994 by Glass et al. (74). A series of logics was successfully demonstrated by the Waseda University group using a MESFET with a surface conductive layer in 1995 (66,80). The logics consist of enhancement mode MESFETs with a MESFET load. The gate length of the FET was 5 µm and transconductances of FETs were from 1.5 to 2.2 mS/mm. They had fabricated logics of NAND, NOR, NOT, and RS flip-flop. The logic operations were obtained up to 20 kHz and the RS flip-flop was operated up to 5 kHz. An overview and I/O characteristics of the RS flip-flop are shown in Fig. 16. This series comprises the first logic and memory operations (RS flip-flop) of diamond devices. More recently, the Waseda group have succeeded in fabricating logic with the enhancement/depletion (E/D) type of FETs (79) and observed fine logic operation. These results indicate that diamond is available for logic operations when these are applied to a specified field such as a high-temperature environment where conventional device operations are not available. F.

Applications in Future

As described in this chapter progress in semiconductor diamond is likely to verify the possibilities of diamond devices. The applications of diamond for active devices are to be realized; the

Figure 16 Overview and I/O characteristics of an RS flip-flop. (From Ref. 74.)

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distinction between diamond and conventional semiconductor devices should be the critical point. High-temperature operation and durability in harsh environments are considered to be prospects for diamond. Specifications of environmental conditions and related reliability and temperature ranges of industrial applications are shown in Table 4 and Fig. 17 (81). Oil well equipment electronics, military electronics, and space electronics are thought to be the applications that will be realized shortly due to their harsh environmental requirements, which cannot be met with Si-based devices. The possible products for those applications include sensors, devices for high-temperature operation, and power devices. Radiation-durable devices are also candidates, finding applications in space and electric generation by atomic power (82). With regard to the cost problem, the progress in heteroepitaxial growth on Si substrates is promising for diamond device applications (67,68). This technique offers diamond crystals of several micrometers with almost the same crystal configurations, as they are coalesced. This is not a single crystal but can be used as almost a single crystal; that is, devices can be fabricated on each diamond crystal and interconnected, crossing over the crystal boundaries. Utilizing this technique, large waters of diamond-silicon are available at low cost due to the established Si substrate.

VI. SUMMARY The semiconductor characteristics of diamond and its device applications including recent progress have been reviewed in this chapter. Concerning channel formation, B is the only atom used successfully for the formation of channels in diamond with a deep acceptor level of 370 meV. Successful doping is available mainly by vapor-phase doping during deposition. For the surface properties related to device application, the Schottky and MOS characteristics of diamond have been summarized. The hydrogenated surface of diamond has been investigated; diamond was found to have a fine surface and the Fermi level is thought to be unpinned. Thus, fine Schottky characteristics are available with a small ideality factor. The ohmic contact plays an important role in device characteristics. For diamond, Ti-based metal with a highly doped layer can provide a low-resistivity ohmic contact. The aging characteristics of Ti/Mo/Au were studied and it was found that this system is superdurable for high-temperature aging, that is, no degradation for 400 h at 800°C. For the fabrication process, the selective growth and dry etching technologies are now possible for diamond. Diamond has small lattice constant and band gap engineering ulitizing heteroepitaxial growth is not available. The only exception is diamond on cBN, and this system is now undergoing basic research. For semiconductor devices, MESFETs and MOSFETs have been developed using unipolar channels. Several techniques have been performed for MESFETs and fine characteristics have been reported. Also, utilizing unipolar MESFET logic, several logic circuits such as NAND, NOR, and RS flip-flop were developed. For MOSFETs, a high transconductance of 16.4 mS/mm (6 µm gate length) has been achieved using evaporated SiO 2 associated with a hydrogen-terminated surface. For both FETs, high-temperature operations were achieved up to 300–400°C. The characteristics of diamond, include high durabilities for temperature and radiation associated with high thermal conductivity, oil well equipment electronics, military electronics, and space electronics, and it is thought that these applications will be realized shortly because their harsh environmental requirements cannot be met with Si-based devices. The possible products for those applications include sensors, devices for high-temperature operation, and power devices.

⫺65 to ⫹125 (⫹175) 40 g random at 10 to 2000 Hz 300 g/3 mS ⫹10% Good and up

⫺55 to ⫹85 (⫹150) 20 g sinus at 10 to 2000 Hz 30 g/3 mS ⫹10% Good and up sharply

Operation Temp. (°C) (max) Vibrations

Mech. shock Power supply EMI tendency

Source: From Ref. 81.

Military

Civil

Property

1g ⫹10% Medium and up

5 g sinus at 10 to 200 Hz

0 to ⫹40 (⫹60)

Instrumentation

Table 4 Specifications of Future Trends in Harsh Environment Applications

30 g ⫹30% Poor and up

⫺45 to ⫹85 (⫹280) 15 g sinus at 10 to 500 Hz

Automotive

500 g/5 mS ⫹10% Medium and up

⫺45 to ⫹300 (⫹400) 10 g sinus at 10 to 300 Hz

Oil well equipment

300 g ⫹10% Good and up

⫺65 to ⫹125 (⫹175) 20 g sinus at 10 to 2000 Hz

Space

Future tendency Going up

Upper limit will go up

Remarks

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Figure 17 Temperature ranges for industrial applications. (From Ref. 81.)

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57. GS Gildenblat, SA Grot, CW Hatfield, CR Wronski, AR Badzian, T Badzian, R Messier. Proceedings MRS Fall Meeting, 1989, p 297. 58. H Shiomi, Y Nishibayashi, N Fujimori. Second International Conference on New Diamond Science and Technology, 1990, p 976. 59. Y Nishibayashi, H Shiomi, N Fujimori. First International Conference on Applications of Diamond Films and Related Materials, 1991, p 295. 60. N Fujimori, Y Nishibayashi. Diamond Related Materials 1:665, 1992. 61. H Shiomi, Y Nishibayashi, N Toda, S Shikata; N Fujimori. Fourth International Conference on New Diamond Science and Technology, 1994, p 661. 62. H Shiomi, Y Nishibayashi, N Toda, S Shikata. IEEE Electron Device Lett EDL-16:36, 1995. 63. N Nakamura, M Aoki, M Itoh, N Jin, H Kawarada. Fourth International Conference on New Diamond Science and Technology, 1994, p 729. 64. H Kawarada, M Aoki, M Ito. Appl Phys Lett 65:1563, 1994. 65. M Ito, N Nakamura, N Jin, H Noda, A, Hokazono, N Nagai, H Kawarada. Eighth Diamond Symposium Japan New Diamond Forum, 1994, p 12. 66. M Ito, A Hokazono, N Jin, H Noda, K Nakamura, T lshikura, S Yamashita, H Kawarada. Ninth Diamond Symposium Japan New Diamond Forum, 1995, p 138. 67. S Yugo, T Kanai, T Kimura, T Muto. Appl Phys Lett 58:1036, 1991. 68. BR Stoner, JT Glass. Appl Phys Lett 60:698, 1992. 69. K Nishimura, R Kato, S Miyauchi, K Kobashi. Fifth Diamond Symposium Japan New Diamond Forum, 1991, p 34. 70. SA Grot, CW Hatfield, GS Gildenblat, AR Badzian, T Badzian. Second International Conference on New Diamond Science and Technology, 1990, p 949. 71. GS Gildenblat, SA Grot, AR Badzian. IEEE Electron Dev Lett EDL-12:37, 1991. 72. GS Gildenblat, SA Grot, AR Badzian. IEEE Electron Dev Lett EDL-13:462, 1992. 73. CR Zeisse, CA Hewett, R Nguyen, JR Zeidler, RG Wilson. IEEE Electron Dev Lett EDL-12:602, 1991. 74. JT Glass, DL Dreifus, RE Fauber, BA Fox, ML Hartsell, RB Henard, JS Holmes, D Malta, LS Plano, AJ Tessmer, GJ Tessmer, HA Wynands. Fourth International Conference on New Diamond Science and Technology, 1994, p 355. 75. AJ Tessmer, LS Plano, DL Dreifus. Proceedings Device Research Conference, 1992. 76. T Tomikawa, Y Nishibayashi, S Shikata. Diamond Related Materials 3:1389, 1994. 77. Y Nishibayashi, T Tomikawa, S Shikata. 42nd Conference on Applied Physics, Japan, 1995. 78. JR Zeidler, CA Hewett, R Nguyen, CR Zeiss. Diamond Related Materials 2:1341, 1993. 79. A Hokazono, H Noda, T Uemoto, K Kitatani, T lshikura, K Nakamura, S Yamashita, H Kawarada. 10th Diamond Symposium Japan New Diamond Forum, 1996, p 164. 80. H Kawarada, M Itoh, A Hokazono. Jpn J Appl Phys 35:L1165, 1996. 81. IM Buckley-Golder, PR Chalker, C Johnston, S Romaini. Fourth International Conference on New Diamond Science and Technology, 1994, p 669. 82. J Levy. First European Conference on High Temperature Electronics, 1993.

18 SiC Boule Growth Yuri M. Tairov St. Petersburg Electrotechnical University, St. Petersburg, Russia

I.

INTRODUCTION

SiC is the only semiconductor compound of subgroup IV elements—silicon and carbon. SiC is a diamond-like semiconductor and is an electronic analogue of an elementary IVB semiconductor: diamond, silicon, germanium, and α-tin. Silicon carbide exists in a large number of structural forms called polytypes (more than 140), which represent modifications of hexagonal (wurtzite) and cubic (sphalerite) close-packed crystal structures. Polytypism is a special one-dimensional case of polymorphism. All polytypes consist of identical close-packed Si-C double layers, whose stacking sequences differ along a certain direction. The nearest neighbor arrangement of atoms is identical in all crystal structures. Because of the structural identity of layers, different polytypes have the same lattice parameters in the perpendicular direction. The unit cell dimension along the normal to layers or unit cell height can vary in the range from several parts to several hundred nm. And because of the identity of the elementary layers the unit cell height is equal to the product of the height of the elementary layers and their number in the cell. More precise investigations show that elementary layers of different polytypes of the same substance are not completely identical. Their composition and lattice parameters can vary from polytype to polytype. There are several forms of polytype notation in scientific publications. For describing three-dimensional closely packed crystalline structures, a classical ABC scheme is widely used in which the alternation sequence of two-dimensional layers is shown. Three positions of layers in the most closely packed arrangement of hard-sphere atoms are denoted by A, B, and C. They differ from each other by a translation period ⫾(1/3; 2/3) or by an angle ⫾60° (Fig. 1). Each subsequent identical layer of spheres, if closely packed on layer A, can occupy positions of either B or C type. Similarly, a layer in either position C or A can be placed on layer B or else a layer in position A or B on layer C. Hence, any sequence of letters A, B, and C in which no letter is immediately followed by the same one characterizes the most closely packed arrangement. The height of a unit cell depends on the number of layers after which the packing sequence is repeated. This number of layers, n, defines the identity period and varies from 2 up to infinity for different closely packed arrangements. The mutual arrangement of atoms in layers is clearly seen from the structure of the crystallographic plane (1120). The arrangement of atoms in this plane for some silicon carbide structures is shown in Fig. 2. A structure of the wurtzite type is represented by the sequence (AB)AB . . . with a repetition of two layers, that of a sphalerite 409

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Figure 1 Three possible positions (A, B, C) of layers in close-packed atom arrangement.

type by the sequence (ABC)ABCABC . . . with a repetition of three layers. A six-layer structure is represented by the sequence (ABCACB)ABCACB . . . etc. The disadvantage of this notation is that it is too bulky for long-period structures. More conveniently, polytypic structures are described with Zhdanov symbols. The symbol consists of numbers of which the first one indicates the number of successive cyclic A → B → C → A . . . packing arrangements, and the second one indicates that of anticyclic A → C → B → A . . . packings. The same numbers characterize the sequence of zigzags formed by atoms in the (1120) plane (Fig.2). Often, if a preceding and a succeeding layer have a similar orientation, the intermediate one is designated with the letter h (e.g., the layer is in a hexagonal position), whereas a layer on both sides of which the adjacent layers have a different orientation is denoted with the letter k (e.g., the layer is in a cubic position). Consequently, the hexagonality D ⫽ n h /(n h ⫹ n k ), where n h and n k are the numbers of layers in hexagonal and cubic positions, respectively, is more convenient for characterization of polytype structures. Ramsdell’s notation includes the number of layers in a unit cell, which is followed by a Latin letter indicating the crystallographic system to which the given structure belongs. It is recommended that the letters C, T1, O, H, R M, and Tc be used to denote the cubic, tetragonal,

Figure 2 Arrangements of silicon (small circles) and carbon (big circles) atoms in (1120) plane of some silicon carbide polytypes.

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orthorhombic, hexagonal, rhombohedral, monoclinic, and triclinic crystallographic systems, respectively. For instance, a 6-layer hexagonal and 15-layer rhombohedral polytype with layerpacking sequences ABCACB and ABCBACABACBCACB or hkkhkk and hkhkkhkhkkhkhkk, respectively, are represented as (33) and (32)3 with Zhdanov symbols and as 6H and 15R with Ramsdell symbols. Polytypes having similar dimensions of the unit cell but different sequences of packing arrangements of ABC are distinguished by subscripts, e.g., nH 1 and nH 2 . These designations of polytypic structures of elementary matter are also applicable to chemical compounds. In this case the elemental layers of the structure A, B, and C characterize the positions of atoms of one type in the elemental layer, whereas the positions of the other atoms in these layers are determined relative to these. For example, in SiC the elemental layer of the structure consists of closely packed Si atoms, and above each of them one C atom is located at a distance of 0.189 nm (Fig.2). The arrangements of atoms in the first and second coordination spheres are identical in all polytypes of silicon carbide and other diamond-like semiconductors. Each atom is tetrahedrally surrounded by four nearest atoms of another type. The second coordinational sphere consists of 12 atoms of the initial type. For most polytypes, surroundings of atoms of the same type in the lattice can differ; e.g., nonequivalent atom states are probable. It is possible to define them in the (1120) plane by use of the difference of the distances between atoms in the C-axis direction (vertical lines in Fig. 2). In cubic SiC and in the 2H polytype the distances between two atoms of the same type along the C-axis are the same and equal to heights of three and two layers, respectively. There are two such nonequivalent positions in the 4H polytype (h, k), three of them (h 1 , k 1 , k 2) in 6H, five (h 1 , k 1 , k 2 , h 2 , k 3) in 15R, etc. (Fig. 2). According to symmetry groups, all polytypes are distinguished as follows: 3C-SiC of cubic syngony has the symmetry group T 2d (F43m), polytypes of hexagonal syngony C 46v (P6 3mc), polytypes of trigonal syngony C 13v (P3ml), and polytypes of rhombohedral syngony C 53v (R3m).

II. PROPERTIES OF SiC POLYTYPES Up to now, more than 140 SiC polytypes have been reported, but their number seems to be unlimited. Improvements in structural analysis have revealed new polytypes that differ from each other by the number of layers and order in the unit cell. For instance, polytype 1200R has parameter c ⫽ 301.56 nm. It is found that the presence of different polytypes in SiC and other materials is caused by solid-state transformations caused by internal and external sources of strain. Phase transformations of this type are observed for many types of matter, and as shown by investigations polytypism is comparatively widely distributed in nature. The most important physical-chemical parameters of the main SiC polytype structures are shown in Table 1. It is clearly seen from the table that there is a linear correlation with the hexagonality for most of the parameters. The SiC phase diagram has a peritectical character (Fig. 3). The temperature of peritectical transformation T p ⫽ 3103 K. The SiC compound is the only solid phase for the Si-C binary system. Figure 3b and c represent parts of the diagram that border with silicon and carbon. In the part of the diagram that borders with Si (Fig. 3b) is a decrease in the liquidus temperature ∆T l versus increasing carbon concentration C 1c in the solution. The equilibrium distribution coefficient of carbon in silicon is k 0 ⫽ 0.07. It is hard to define phase diagrams for different polytype structures because the physical-chemical analysis is not sufficiently accurate. The incongruent melting of SiC at temperature T p can be described by the following peritectic reaction:

0 0.25 0.29 0.33 0.36 0.40 0.40 0.44 0.5 1

Source: From Ref. 1.

3C 8H 21R 6H 33R 15R 10H 27H 4H 2H

Polytype

Hexagonality D 0.2 0.26 — 0.33 — 0.32 — 0.35 0.37 —

Chemical shift W SiKB (eV) 0.74 0.96 — 1.22 — 1.19 — 1.30 1.37 —

Effective charge q 1.046 1.029 — 1.022 — 1.012 — 1.008 1.001 —

Ratio of silicon and carbon concentrations C Si /C c 0.308269 0.308130 0.308111 0.308086 0.308075 0.308043 0.308049 0.308028 0.307997 0.30763

a(nm) 0.755124 2.01516 5.29034 1.51174 8.31534 3.78014 2.52011 6.80495 1.00830 0.50480

c(nm) 0.251708 0.251895 0.251921 0.251955 0.251980 0.252009 0.252011 0.252035 0.252076 0.2524

c/n(nm)

Lattice parameters

Table 1 Crystallochemical Parameters of Silicon Carbide Polytype Structures

3.2154 3.2159 3.2159 3.2160 3.2159 3.2162 3.2161 3.2162 3.2163 3.2151

α xg/CM 3 3.1584 3.1657 — 3.1661 — 3.1665 — 3.1665 3.1673 —

α pg/CM 3

X-ray and practical density

2.0 3.3 — 4.3 — 5.7 — 6.2 7.1 —

C SiB 10 ⫺20CM ⫺3

2.3 1.7 — 1.5 — 1.1 — 1.0 0.7 —

C BC 10 ⫺20CM ⫺3

Carbon and silicon vacancy concentration

1093 866 — 907 — 841 926 891 1297 —

Debyetemperature ΘD

⫺65.6 — — ⫺66.5 —

⫺65.2

⫺62.7 ⫺64.4

Formation enthalpy ∆H° 298 (kJ/mol)

14.88 23.28 — 21.61 — 24.70 20.69 22.28 10.62

Entropy S° 298 (J/mol K)

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Figure 3 Phase diagram of silicon carbide: (a) big scale; (b) silicon side of the phase diagram; (c) carbon side of the phase diagram; (d) liquid line of the SiC-Si system; (e) silicon and carbon interaction parameter α L in the solution-melt; (f ) temperature dependences of vapor pressures of main components over 6HSiC (SiC-Si, ⋅  ⋅  -SiC-C).

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SiC s ⇔ [1/(1 ⫺ C p )] (Si 1⫺Cp C Cp )L ⫹ [(1 ⫺ 2C p )/(1 ⫺ C p )]C s where C p ⫽ 0.19 is the molar part of the carbon in the melt at temperature T p . The liquidus equation in the regular solutions approximation is T l ⫽ (⫺∆H p ⫹ 0.76 ∆H m (c) ⫹ α L [0.19 ⫺ (C Lc )2 ⫺ (1 ⫺ C Lc )2]}/ {⫺∆S p ⫹ 0.76 ∆S m (c) ⫺ R ln 0.55 ⫹ R ln[(1 ⫺ C Lc )C Lc]} where ∆H m (c) ⫽ 100 kJ/mol and ∆S m (c) ⫽ 24 J/(K mol) are the enthalpy and entropy of carbon melting, respectively; ∆H p ⫽ 65 kJ/mol and ∆S p ⫽ 20.95 J/mol are the enthalpy and entropy of the peritectic reaction; C Lc is the atom part of carbon in the melt at temperature T L; α L is the interaction parameter of the components in the liquid phase; and R is the universal gas constant; values of C Lc and α L are given in Fig. 3d and e. The activity coefficient of silicon in the solutionmelt at temperatures under 2400 K is equal to unity and at temperatures from 2600 to 3100 K varies in the range 1.003 to 1.085. The native stoichiometric composition of silicon carbide melt can exist at temperature 3460 K and pressure 1010 Pa. Reactions of SiC dissociative evaporation (taking into account the main components of the gas phase) are 1. SiC s ⇔ Si g,s ⫹ C s ; k 1 ⫽ p Si 2. SiC s ⫹ Si g,L ⇔ Si 2C g; k 2 ⫽ p Si2C /p Si 3. 2SiC s ⇔ SiC 2g ⫹ Si g,L ; k 3 ⫽ p SiC2 p Si , where k 1 , k 2 , k 3 are equilibrium constants The temperature dependences of the vapor pressures of the main components in the gas phase for the temperature range 1300–3103 K are described by the equation lg p i ⫽ A i ⫺ B i /T The values of A i and B i for different systems are presented in Table 2. This equation describes vapor pressure with good accuracy for the system SiC-Si. When approaching the temperature of peritectic transformation T p the curves deviate from linear ones in the coordinates lg p ⫽ f (1/T) (Fig. 3f ). The silicon vapor pressure data presented are approximately two times higher than the most reliable experimental data. Vapor pressures over other polytypes can be calculated using the expression lg p i(D) ⫽ lg p i(3C) ⫺ a j D The values of a i are shown in Table 3. Vapor pressures of Si 2 C and SiC 2 according to the constants of dissociative evaporation reactions depend on silicon vapor pressure. In order to control the vapor composition over silicon carbide, it is extremely important to know the equations P Si2C ⫽ 2.85 10 2 exp(⫺1.79 ⫻ 10 4 /T)P Si P SiC 2 ⫽ 9.41 10 28 exp(⫺14.35 ⫻ 10 4 /T)/P Si Similar equations for vapor pressures over other silicon carbide polytypes can be defined with the help of Table 3. The ratio of silicon and carbon concentrations in the gas phase, N Si / N C , for most temperature values is greater than unity and can be estimated using the equation C Si /C C ⫽ (P Si ⫹ 2P Si2C ⫹ PSiC2 )/(P Si 2 C ⫹ 2P SiC2 ) There are two types of deviations from the stoichiometric composition in the crystals of silicon carbide polytypes. The first one is characterized by big deviations (Table 1), and it is supposed that it is caused by structural regulation of silicon and carbon vacancies in the crystal lattice. The SiC layers in cubic and hexagonal positions keep their composition in different

12.74 2.66

Si 15.10 3.42

Si 2 C

6H-SiC-C

15.98 3.53

SiC 2 10.82 2.04

Si 13.23 2.81

Si 2 C

6H-SiC-Si

18.05 4.18

SiC 2 12.89 2.68

Si

15.35 3.45

Si 2 C

3C-SiC-C

16.11 3.54

SiC 2

10.82 2.04

Si

13.28 2.81

Si 2 C

3C-SiC-Si

Values of Constants in the Temperature Dependences of Vapor Pressures of Main Components Over 6H- and 3C-SiC Polytypes

Source: From Ref. 1.

A1 B1

Constant

Table 2

18.18 4.18

SiC 2

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Table 3 Values of a i Parameter for Calculation of Components of Vapor Pressures Over Different SiC Polytypes ai a Si a SiC 2 a Si 2C

SiC-C

SiC-Si

0.75–6 ⫻ 10 /T 0.38–3 ⫻ 10 2 /T 0.75–9 ⫻ 10 2 /T 2

0.00 0.38 0.14

Source: From Ref. 1.

polytypes. This causes linear variation of the general composition, practical density, and other physical-chemical parameters of crystals versus hexagonality (see Table 1). The second type of deviation from stoichiometry has a small value 10 ⫺4 –10 ⫺3% (atomic) and is characterized by the accidental distribution of silicon and carbon vacancies in the lattice. According to experimental data on 6H-SiC crystal quenching, the concentration of paramagnetic vacancies in the carbon sublattice in the temperature range 1900–2450°C is C vC ⫽ 1.5 10 20 exp(⫺∆W/kT) where ∆W is the activation energy, equal to 2.1 eV. Theoretical values for vacancy formation in the silicon and carbon sublattices are ∆W BSi ⫽ 4.93 eV and ∆W vC ⫽ 2.92 eV, respectively; energies of antisite defect formation are ∆W SiC ⫽ 3.2 eV and ∆W CSi ⫽ 2.9 eV. The experimental value of the carbon vacancy migration energy is 1.2 eV for temperatures 1080–1300 K. X-ray and practical density, lattice parameters a and c, interlayer distances c/n (n ⫽ number of layers in the unit cell), and enthalpy and entropy of formation (∆H°298 and S2°98 ) are presented in Table 1. Values of the chemical shift of the analytical line Sikα1.2 (W Sikα) in SiC polytypes referring to pure silicon measured by X-ray spectral analysis are shown in Table 1. The chemical shift of the analytical line observed in silicon carbide polytypes gives evidence of the presence of positive charge on silicon atoms, values of which are given in Table 1. This charge is caused by the fact that the carbon atom has greater electronegativity (2.5) than silicon (1.8). An increase of the effective charge leads to increased ionicity of chemical bonds of polytypes with increased hexagonality. This is caused by the difference in the coordinational spheres’ configuration. Ionicity of chemical bonding for SiC is 12% according to Poling. Anisotropy of the temperature expansion coefficient for SiC polytypes at temperatures 100–1500 K is insignificant (α11 /α 芯 ) ⫽ 1–1.07. For some polytypes temperature dependences α11 are known only for lattice parameter c/n and are described at temperatures 18–1000°C as follows: α3C ⫽ α11 8H ⫽ α11 6H ⫽ α11 15H ⫽

(3.2 (2.8 (2.3 (2.3

⫹ ⫹ ⫹ ⫹

4.1 6.6 8.9 9.0

⫻ ⫻ ⫻ ⫻

10 ⫺3 t 10 ⫺3 t 10 ⫺3 t 10 ⫺3 t

⫺ ⫺ ⫺ ⫺

2.6 3.8 7.0 7.9

⫻ ⫻ ⫻ ⫻

10 ⫺6 t 2 ) 10 ⫺6 t 2 ) 10 ⫺6 t 2 ) 10 ⫺6 t 2 )

10 ⫺6 10 ⫺6 10 ⫺6 10 ⫺6

α11 10H ⫽ (2.8 ⫹ 6.6 ⫻ 10 ⫺3 t ⫺ 5.1 ⫻ 10 ⫺6 t 2 ) 10 ⫺6 α11 27R ⫽ (2.3 ⫹ 8.3 ⫻ 10 ⫺3 t ⫺ 6.7 ⫻ 10 ⫺6 t 2 ) 10 ⫺6 α11 4H ⫽ (2.9 ⫹ 4.6 10 ⫺3 t ⫺ 2.3 10 ⫺6 t 2 ) 10 ⫺6 Because of the absence of experimental data on α, one can suppose that α11 ⫽α芯 ⫽ α.

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Table 4 Activation Energy and Frequency Parameters of Parabolic and Linear Components of Oxidation Equation for (0001)C Facet of 6H-SiC Atmosphere

P H 2O(Pa)

∆W 1 (kJ/mol)

R1 0 (nm 2 /c)

∆W 2 (kJ/mol)

R2 0 (nm/c)

Wet oxygen Dry oxygen

5 ⫻ 10 3 ⬍10

58.5 ⫾ 0.8 62.7 ⫾ 0.8

(2.0 ⫾ 0.2)10 3 (8.5 ⫾ 0.3)10 2

276 ⫾ 13 146 ⫾ 8

(3 ⫾ 1)10 9 (3 ⫾ 1)10 4

Source: From Ref. 1.

Debye characteristic temperatures of polytypes, Θ D , obtained from the α temperature dependences, are shown in Table 1. Silicon carbide is chemically extremely stable. It does not interact with concentrated and dilute acids, their mixtures, and water solutions of alkalides. The only exceptions are heated orthophosphorous acid and a mixture of HNO 3 and HF. SiC interacts with chlor, melts of alkali salts, and peroxides of alkali metals at the temperatures 400–900°C. SiC reacts with the vapors of water and hydrogen at temperatures higher than 1500°C (Fig. 4). This is useful for crystal etching and mass transfer intensification during vapor-phase growth of epitaxial layers. The SiC etching rate in liquid and gaseous etchants depends on the crystallographic orientation and conductance type of crystals. This fact is useful for facet identification, mesa structure production, revealing p-n junctions, etc. Dependences of thermal oxidation rates are of great importance for silicon carbide device technology. It is not necessary to elaborate special technology for the oxidation of SiC monocrystals. It can be carried out using silicon technology but at higher temperatures. In general, the oxidation process can be described by a linear-parabolic equation. h 2 /k 1 ⫹ h/k 2 ⫽ t where h is the thickness of oxide layers; t is the oxidation time; k 1 ⫽ k 10 exp(⫺∆W 1 /RT) is the constant of the equations parabolic component; and k 2 ⫽ k 20 exp(⫺∆W 2 /RT) is the constant of the equations linear component. The oxidation rate of (0001)C is 5–10 times higher than of (0001)Si in the temperature range 1000–1300°C in dry and wet hydrogen flow at 15 liters per minute (Fig. 5). The oxidation rate of other facets, for instance, (1120), has an intermediate value compared with {0001} facets. The oxidation process of the (0001)C facet is limited by diffusion of the reaction components through the growing oxide film. Hence the oxidation rate of this facet does not depend on the crystal surface treatment, type and level of doping, or polytype structure. The constants of the linear-parabolic equation for (0001)C oxidation are shown in Table 4. The oxidation rate of (0001)Si is limited by chemical reactions at the oxide-SiC interface and, for oxidation for more than 30 minutes, kinetic dependences became linear. Values of the linear equation for 6H-SiC (0001)Si oxidation are shown in Table 5. The oxidation rate depends on preliminary facet surface treatment, type of conductivity (the oxidation Table 5 Activation Energy and Frequency Parameters of Oxidation Equation for (0001) Si Facet of 6H-SiC Monocrystals Atmosphere

P H2O(Pa)

∆W 2 (kJ/mol)

k 20 (Nm/c)

Wet oxygen Dry oxygen

5 ⫻ 10 ⬍10

145.5 ⫾ 0.4 91.5 ⫾ 0.4

(9.5 ⫾ 0.15)10 2 9.3 ⫾ 0.5

Source: From Ref. 1.

3

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Figure 4 6H-SiC etching rate dependences on the melt temperature for (a) different compositions and (b) different planes. ● KOH ⫹ Na 2 O 2 (9: 1); 䊊 KOH ⫹ K 2 O 4 (9 : 1); ∆ KOH; 䊐 NaOH ⫹ Na 2 O 2 (9 : 1).

constant is 5% different for p- and n-type), and polytype structure. The hexagonality dependence of the oxidation rate linear component (in nm/s) in dry hydrogen for (0001)Si is k 2 ⫽ (10 ⫾ 0.5) exp{⫺[∆W 2 0 ⫹ (dW/dD)D]/RT} where ∆W 2 0 ⫽ 89.0 ⫹ 0.4 kJ/mol—activation energy of 3C-SiC oxidation; dW/dD ⫽ (75 ⫾ 1)102 J/mol. Differences in SiC polytype formation enthalpies can be estimated using this dependence (Table 1). The parameters of the layers obtained on silicon carbide crystals by oxidation are similar to those on silicon. The thickness of these layers can be estimated using color tests elaborated for silicon. Temperature dependences of the thermal conductivity coefficient (perpendicular to the c axis) of 6H-SiC monocrystals for different doping levels are shown in Fig. 6. The 3C-SiC microhardness according to Moos is 9.2 to 9.3 and it is strongly dependent on facet and indenter orientation. Values of the microhardness according to Knoop are shown in Table 6. As follows from the 6H- and 3C-SiC microhardness temperature dependences, there is a local phase transition at temperatures lower than 40°C and pressure about 29 GPa with the formation of closely packed and more plastic phases. The activation energy of dislocation move-

Figure 5 Kinetic dependences of 6H-SiC oxide layer growth at 1180°C in dry oxygen (PH 2 O ⬍ 10 Pa) on (0001)C plane (curve 1) and (0001)Si plane (curve 2).

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Figure 6 Temperature dependences of 6H-SiC thermoconductivity coefficient perpendicular to c-axis (n- and p-concentrations in samples are for T ⫽ 293 K): (a) low temperatures; (b) high temperatures.

ment in 6H-SiC, equal to 1.7 ⫾ 0.1 eV, was estimated using this dependence in the temperature range 500–1400°C. 6H-SiC has an exteremely high hardness, close to that of diamond, at temperatures higher than 1300°C. Destruction strain of bulk α-SiC monocrystals is lower than 0.98 GPa at room temperature. This is due to the presence of defects. The strain for high-quality α-SiC whiskers is up to 21 GPa. The stacking fault formation energy in 3C-SiC is 6.1 mJ/m 2 (3.1 MeV). Table 6 SiC Microhardness According to Knoop at 20°C and 0.98 N Load

Polytype

Facet

6H

(0001) (1010) (1120)

3C

(111) (001)

Source: From Ref. 1.

Indentor orientation to c-axis

Microhardness (GPa)

储 (1010) 储 (1020) 储 [0001] 芯 [0001] 储 [0001] 芯 [0001) 储 [110] 芯 [110] 储 [110] 储 [100]

28.62 28.98 20.89 27.03 23.45 27.03 26.00 27.27 25.65 26.44

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Table 7 Mechanical Properties of Silicon Carbide Properties

Polytypes

Value

Temperature (K)

Shift modulus, GPa All-side press modulus, GPa Ung modulus, GPa

α α α

168 96.1 385 350

300 300 300 1500

Plastic constants, ⫻10 2 GPa C 11 C 12 C 33 C 44 C 66 ⫽ (C 11 ⫺ C 11 ) ⫻ 2 C 11 C 12 C 44 Pressing ability (up to 5 ⫻ 10 7Pa)

6H 6H 6H 6H 6H 3C 3C 3C

5.00 0.92 5.64 1.68 2.04 2.89 2.34 0.55 20.6

70–300 70–300 70–300 70–300 70–300 300 300 300 300

Source: From Ref. 1.

Some other important mechanical properties of silicon carbide are shown in Table 7. Electronic and optical properties of silicon carbide are described in Ref. 1.

III. DIFFUSION AND SOLUBILITY OF DOPANTS IN SILICON CARBIDE It is necessary to know the main components of self-diffusion coefficients for understanding of diffusion in silicon carbide and a scientific approach to crystal growth technology. Temperature dependences of self-diffusion coefficients of silicon and carbon in pure and doped n-type 6HSiC crystals obtained using isotopes 14C and 30Si are shown in Fig. 7. These dependences can be written in the following form: D i ⫽ D 0i exp(⫺W i /kT ) The parameters D 0i and W i are given in Table 8. It is clear from Fig. 7 that the silicon self-diffusion coefficient in undoped crystals is lower than in doped crystals. An opposite dependence was observed for the carbon self-diffusion coefficient. According to the law of acting masses, the silicon vacancy (acceptor) concentration increases with increasing donor dopant concentration (nitrogen). All this leads to an increase in the diffusion coefficient in the presence of a vacancy mechanism of self-diffusion. Carbon vacancies are donors, and their concentration decreases when the donor concentration is increased. This leads to a decrease in the carbon self-diffusion coefficient. The diffusive distribution of acceptor dopants has the following peculiarities: 1. Presence of near-surface (high concentration, low effective diffusion coefficients) and volume (lower concentrations, high diffusion coefficients) regions (Fig. 8). 2. Presence of an abnormal layer on the border of volume and near-surface regions. This layer is compensated p- and more often n-type in the case of Al and Be diffusion. This layer is is low-doped and low-compensated (compared with neighboring ones) p-type in the case of boron diffusion (Fig. 8).

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Figure 7 Temperature dependences of 14 C qnd 30 Si self-diffusion coefficients in pure (curves 1, 4) and nitrogen-doped (curves 2, 3) silicon carbide

Table 8 Parameters of Diffusion Coefficients of Different Atoms in 6H-SiC a Element 30

Temperature (K)

Si Si 14 C 14 C B B(1) B(T) B* Al

2273–2563 2273–2563 2321–2453 2321–2453 2273–2673 1873–2823 1873–2823 1873–2823 2073–2723

Ga Be Be Be* Li O

2173–2623 1873–2573 1873–2573 1873–2573 1773–2473 2073–2623

30

a p-type crystal, volume region. Source: From Ref. 1.

Coefficient, D oi (sm 2 /S) (5.01 (5.01 (5.01 (5.01

Activation energy (eV)

⫾ 1.71)10 ⫾ 1.71)10 5 ⫾ 1.71)10 5 ⫾ 1.71)10 7 50.00 3.20 0.70 0.12 8.00

0.17 0.3 32.00 10 ⫺4 1.2 ⫻ 10 ⫺3 11.00

2

⫺7.22 ⫾ 0.07 ⫺8.18 ⫾ 0.10 ⫺7.41 ⫾ 0.05 ⫺8.20 ⫾ 0.08 ⫺5.6 ⫺5.1 ⫺5.1 ⫺3.4 ⫺6.1 ⫺5.5 ⫾ 0.02 ⫺3.1 ⫺5.2 ⫺1.5 ⫺1.7 ⫺6.9

Dopant concentration N Nitrogen 10 16 –10 17 cm ⫺3 Nitrogen 3 ⫻ 10 19cm ⫺3 Nitrogen 10 16 –10 17 cm ⫺3 Nitrogen 3 ⫻ 10 19 cm ⫺3 N s B ⱕ 3 ⫻ 10 18cm ⫺3 N s B ⫽ (2–5) ⫻ 10 18cm ⫺3 N S B ⫽ (2–5) ⫻ 10 18cm ⫺3 N s Al ⫽ (1–1.5) ⫻ 10 18cm. ⫺3 volume region N s Ga ⱕ (3–5) ⫻ 10 17 cm ⫺3 N s Be ⬎ 2 ⫻ 10 18 cm ⫺3 volume region N s Be ⬍ 2 ⫻ 10 18 cm ⫺3 surface region — — N s O ⫽ (1–2) ⫻ 10 18

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Figure 8 Dopant concentration profiles for acceptor (Al, B, Be) diffusion in silicon carbide crystals (hatched parts, compensated regions of the crystals).

3. Effective diffusion coefficients strongly depend on the annealing conditions of crystals: N Si /N C ratio in the gas phase and on the surface, dopant concentration, presence of a third component. These pecularities are caused mostly by carbon vacancy (donor) generation near the crystal surface and also by the formation of complexes by dopants and vacancies. Acceptor dopant temperature dependences are shown in Fig. 9. Their parameters are given in Table 8. Diffusion profiles of acceptor dopants have a standard form and can be described by one diffusion coefficient when boron surface concentrations are low (N Bs ⬍ 3 ⫻ 10 18 cm ⫺3 ). Diffusion profiles became more complicated with increasing boron concentration. A steep region

Figure 9 Temperature dependences of dopant diffusion coefficients in 6H-SiC.

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Table 9 Ratios of Boron Diffusion Coefficients in Doped (N and Al) and Pure SiC Temperature (K)

D BN /D Bi

D BAl / D Bi

N N ⫽ 5 ⫻ 10 18 cm ⫺3 N N ⫽ 3 ⫻ 10 19 cm ⫺3 N Al ⫽ 5 ⫻ 10 19 cm ⫺3 N N ⫽ 5 ⫻ 10 18 cm ⫺3

2300 2150 1850

0.9 0.6 0.3

0.3 0.2 0.08

1.0 3.0 10.0

4.0 10.0 18.0

Source: From Ref. 1.

appears near the surface, and the diffusion rate increases significantly in the ‘‘volume’’ region of the crystal. The volume region became stepwise at diffusion temperatures over 2100°C. It is not possible to describe the near-surface region by one diffusion coefficient. Boron diffusion is practically equal in polar directions [0001]C and [0001]Si. However, it is 1.2–1.3 times higher in directions perpendicular to the c-axis. The rate of diffusion is slightly lower in the case of diffusion perpendicular to dislocation lines. Boron diffusion in Al-doped p-type crystals is higher, and diffusion to n-doped n-type crystals is lower than to undoped single crystals (N DN A ⬍ 10 17 cm ⫺3 ) (Table 9). Boron diffusion profiles depend strongly on the vapor phase composition. A significant increase (two to four times) in the diffusion coefficient is observed (especially in the near-surface region) with an N Si /N C ratio increase. In the volume region this effect is not so strong. The rate of boron diffusion from the boron-doped epitaxial layer is lower than from the vapor phase, especially at low values of N Bs . However, at N Bs close to the boron solubility limit, a decrease of the diffusion coefficient is observed only in the near-surface region. The boron diffusion coefficient also depends on the polytype. The diffusion rate increases with decreasing polytype hexagonality in the row 4H, 15R, 6H, 21R, 8H, 3C (Fig. 10). All the characteristics described are in good agreement with the vacancy diffusion model referring to boron atom–carbon vacancy complexes. Aluminum diffusion distributions also have complicated profiles consisting of an abrupt near-surface region and a less sharp volume region. Parameters of diffusion depend on surface concentration, and there is a slight increase of the diffusion coefficient with decreasing Al concentration from 5 ⫻ 10 20 to 10 19 cm ⫺3 . The rate of aluminum diffusion from the Al-doped epitaxial layer is lower than from the vapor phase. It is assumed that Al diffuses via silicon vacancies. The beryllium distribution at low concentrations (N Bes ⬍ 2 ⫻ 10 18 cm ⫺3 ) has the form of a standard profile. At higher concentrations the Be distribution has a sharp form near the surface

Figure 10 Dependence of relative boron diffusion coefficient on polytype hexagonality.

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Table 10 Ratios of Beryllium Diffusion Coefficients in Doped (Nitrogen, Aluminum, Boron) and Pure SiC Temperature (K) 2323 2123

D NBe / D iBe N N ⫽ 4 ⫻ 10 19 cm ⫺3

Be D Be Al /D i N Al ⫽ 2 ⫻ 10 20 cm ⫺3

D BBe /D iBe N B ⫽ 1.5 ⫻ 10 20 cm ⫺3

0.6 0.4

40 50

10 15

Source: From Ref. 1.

and a less sharp one in the volume region. Both of these regions can be described by an erfc function. In the near-surface region Be diffuses via carbon vacancies; in the volume region a significant part of the dopant diffuses via interstitials as Be 2⫹ ions. This leads to high diffusion coefficients and low activation energies of the process. Beryllium in the silicon carbide interstitials is a donor. Diffusion of Be in SiC heavily doped with nitrogen is slightly slowed down. Beryllium mobility is significantly higher in crystals doped with aluminum and boron (Table 10). The diffusion coefficient of scandium is very low and for temperatures lower than 2673 K does not exceed 10–12 cm 2 /s. As to donor dopants, only the diffusion of N, O, and Li has been investigated (see Fig. 9 and Table 8). The uncertainty in N diffusion coefficients is caused by problems of measurement due to their low values. For instance, the N diffusion coefficient at 2550°C is about 10–12 cm 2 ⁄s. Lithium has the highest diffusion coefficient among the investigated dopants. Lithium diffusion is observed even at room temperature. Ion implantation of SiC is also actively developed. This method is especially important for SiC because of the high temperatures and durations of diffusion annealing. Also diffusion of the most important dopant—nitrogen—is an extremely complicated problem. Now ion implantation is used for doping with nearly all important donor and acceptor dopants. Parameters of ion implantation with different ions are shown in Fig. 11. Radiation defect annealing is carried out by either thermal (1400–1800°C) or laser annealing. SiC crystal doping in vapor-phase crystal growth can be carried out with or without equi-

Figure 11 Dependence of the average run projection R p (a) and the average normal deviation of the run projection ∆R p (b) in SiC on energy for different ions: 1, Be; 2, B; 3, N; 4, Al; 5, P.

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Table 11 Limits of Dopant Concentrations in SiC Crystals Doped During Growth Element

T (K)

Li Cu Au Be B Al Ga In Sc Y

2400 2600 2600 2600 2600 2600 2600 2600 2600 2600

Concentration

Element

T (K)

⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻

Ho Ge Ti N P As Sb Ta Cr W Mn

2600 2600 2600 2500 2100 2100 2100 2100 2600 2600 2600

1.2 1.2 4.9 8.0 2.5 2.0 1.8 9.5 2 2.0

10 18 10 17 10 16 10 20 10 20 10 21 10 19 10 15 10 17 10 16

Concentration 6.0 3.0 3.0 5.0 2.8 5.0 8.0 2.4 3.0 2.5 3.0

⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻

10 16 10 19 10 18 10 20 10 18 10 16 10 15 10 17 10 17 10 17 10 17

Source: From Ref. 1.

librium of dopant states in the source phase and in the volume of the crystal. The first case is realized when growth rates are much lower than the diffusion rate in the crystal. In this case, the dopant concentration depends only on the growth temperature and does not depend on the growth rate and crystallographic orientation of the growing surface. The second case takes place with growth rates comparable to dopant diffusion rates. In this case, the concentration of dopant depends on the growth rate, temperature, and crystallographic orientation of the growth surface. These cases can be described using the dopant distribution coefficient: k ⫽ k 0 ⫹ (k s ⫺ k 0 ) exp(⫺v D /v) where k 0 is the equilibrium distribution coefficient, k s is the ratio of the concentration of adsorbed dopant atoms to their concentration in the vapor phase, v D ⫽ D/h is the dopant diffusion rate in the crystal, D is the dopant diffusion coefficient, h is the thickness of a unit growing layer, and v is the normal growth rate. The same correlation governs concentrations of the main components (silicon and carbon) and the deviation from stoichiometry of the growing crystal as a function of growth rate. Maximal concentrations of dopants achieved in silicon carbide are shown in Table 11.

Figure 12 Dependences of lattice parameter at 300 K (a), temperature linear expansion coefficient at 573–1073 K (b), and thermoconductivity coefficient (T ⫽ 300 K) (c) on (SiC) x (AIN)1⫺x solid solution composition.

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IV. METHODS OF SILICON CARBIDE CRYSTAL GROWTH Classical methods of crystal growth from melt are not applicable to silicon carbide because a silicon carbide melt can exist only at extremely high pressure and temperature. Therefore methods of crystal growth from the vapor phase and from solutions in the melt are used. In the second method Si; Si ⫹ Co; Si ⫹ Cr; and Si ⫹ rare earth metals Ge, Sn, Ga, Cr, Sc, Dy, Nd, Pr, and others are used. Rates of growth from solutions in a melt are defined by the angles of liquidus bending (Fig. 13). Using rare earth metals in the melting zone method, it is possible to grow single crystals of 10 ⫻ 10 ⫻ 3 mm 3 with a growth rate over 1 mm/hr. But at such growth rates droplets of melt are captured by crystals and the number of defects is increased. For this reason, the method of growth from solution in a melt is used in silicon carbide semiconductor technology only for epitaxial layer growth with low growth rates in order to avoid formation of inclusions of the second phase. There are three methods of vapor-phase growth: 1. Method of thermal decomposition of carbon-silicon–containing compounds in hydrogen on graphite at a temperature of about 1700–1800°C. For this purpose one can use siliconorganic compounds that contain silicon and carbon in moleculas in a certain ratio [CH 3 SiCl 3 , (CH 3 )2SiCl 2 , CH 3 SiHCl 2 , etc.] or a mixture of components containing either silicon or carbon, for instance, SiCl 4 and CCl 4 . In the last case it is possible to control the silicon-carbon ratio in the vapor phase. With this method it is possible to grow α-SiC whiskers including 2H (with length up to 3 mm and diameter up to 0.5 mm) and plates of 3C-SiC with basal plane (111), hexagonal habitus, and dimensions up to 5–7 mm. The crystals obtained by this method have a high defect density due to spontaneous nucleation. Low growth temperature and polyfacet growth cause a sectorial distribution of dopants and probably of deviation from stoichiometry. Because of these disadvantages, this method is used mostly for epitaxial layer growth for both α-SiC and 3C-SiC. 2. Sublimation method with spontaneous nucleation (mass crystallization). Crystal growth is carried out in cylindrical graphite crucibles (Fig. 14). Powder silicon carbide is used as a source material. Crucibles are heated in cylindrical furnaces with resistive or inductive heating. Growth proceeds in an inert atmosphere (argon, helium) at a temperature of 2500–

Figure 13 Silicon carbide solubility in low-temperature (a) and high-temperature (b) solvents: 1, Yb; 2, Sn; 3, Ge; 4, Ga.

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Figure 14 Growth cell for SiC spontaneous growth. 1, graphite cylinder; 2, source material; 3, inside graphite cylinder.

2600°C. Nucleation takes place both on the inside surface of the crucible and, most probably, on silicon carbide grains in holes on the inside part of the crucible (Fig. 14). Crystals are obtained in the form of plates with basal plane (0001) and a hexagonal habitus. Most of the crystals have across dimensions of about 3 mm; some of them reach 30 mm. Crystals have a large scatter (comparing different crystals or different parts of the same crystal) of dopant concentrations and dislocation densities due to polyfacet growth and spontaneous nucleation. Every crystal contains one or more disordered layers of thickness 4–50 µm parallel to the basal plane (0001). There is also a big scatter in polytypes among one set of crystals. Moreover, crystals often have different polytype structures on different sides from the disordered layer. One method of this type is direct synthesis. In this case silicon is loaded in the lowtemperature part (2000–2200°C) of the crucible. Silicon vapors react with the crucible walls and form Si 2 C, SiC 2 , and SiC molecules. These molecules form nuclei of silicon carbide crystals and then crystal growth takes place. This method also has disadvantages mentioned above. 3. Sublimation method with seeded growth. The main advantage of this method is the control of crystal nucleation (Fig. 15). Mass transfer is formed by the flows of the gas-phase components Si, Si 2 C, and SiC 2 . These components are formed in the first stage by decomposition of polycrystalline source material. In the next stage silicon vapor, which has the highest pressure, interacts with colder graphite walls of the crucible and forms additional components SiC 2 and Si 2 C: C s ⫹ 2Si g ⫽ Si 2 C g 2C g ⫹ Si g ⫽ SiC 2g So silicon transfers carbon in Si 2 C and SiC 2 molecules, and the graphite crucible is a source of carbon and takes part in the formation of flows to the growing crystal. Crystal growth is carried out in vacuum or an inert atmosphere (argon, helium) sometimes with additional hydrogen at a temperature of 1800–2600°C. Mass transfer and growth rate are controlled by the inert gas pressure. This is a very efficient method (growth rate up to 10 mm/h). Crystal lengths and diameters are 50 mm or more, and there are no significant limitations to further enlargement of crystals. Doping levels are controlled by controlling the amounts of dopants in the source material or gas phase. For instance, concentrations of important donor and acceptor dopants can be varied in the range 10 16 –10 21 cm ⫺3. It is possible to grow single crystals of silicon carbide–alluminum nitride solid solution using the mixture (SiC) x (AlN)1⫺x as the source material. Detailed investigations of the process of mass transfer of SiC vapor in vacuum and different gaseous media (argon, helium, hydrogen, carbon oxide) showed that it is possible to produce

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Figure 15 Growth cells for SiC crystal growth: (a) in patterned graphite channels; (b) in thin-wall graphite crucible; (c) under pulling out of crucible.

bulk SiC single crystals at as low a temperature as 1800°C provided the process is performed in vacuum. Depending on the composition and pressure of the gaseous medium in the growth region, production of SiC single crystals with rather high deposition rates (up to 1–10 mm/h) is possible in the temperature range 1800–2600°C. We note the most important features of the method developed. The main stages of bulk SiC single-crystal growth are the following: dissociative sublimation of an original charge, mass transfer in the gas phase, and crystallization onto a seed. Figure 16 shows a growth cell schematically.

Figure 16 Growth cell for growing bulk SiC single crystals. Reactions of charge dissociations:SiC(s) → 1/2Si 2 C(v) ⫹ 1/2C(s); SiC(s) → 1/2 SiC 2 (v) ⫹ 1/2Si(v). Reactions on the crucible surface: C(s) ⫹ 2Si(v) → Si 2 (v); 2C(s) ⫹ Si(v) → SiC 2 (v).

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Investigations of SiC source sublimation in growing crystals and epitaxial layers demonstrated that the composition of the vapor phase, in particular the ratio of silicon to carbon atoms, N Si /N C , depends significantly on the preparation conditions and polytype composition of the original source. If the charge is obtained by milling previously synthesized SiC cakes, the total pressure of vapor and the ratio N Si /N c in the vapor phase are a strong function of the size of the charge grains (Fig. 17). This phenomenon can be accounted for in terms of the mechanical activation of chemical processes. The plastic strain of a material during milling results in accumulation of an energy H, whose value can be estimated as ∆H ⫽ E(∆a/a)V where E ⫽ 3 ⫻ 10 11 Pa is Young’s modulus of silicon carbide, ∆a/a is the relative variation of the lattice parameters caused by strain, and V is the molar volume of SiC. Since Young’s modulus of SiC is large and molecules containing both silicon and carbon are present in the vapor phase, shift of the reaction equilibrium due to the appearance of marked additional free energy leads to variation of the ratio of silicon to carbon atoms in the vapor. The increase in defectiveness of SiC grains with increasing milling duration and, accordingly, with decreasing grain fraction size (8,9) was established by electron spin resonance (ESR) and X-ray measurements of the powder lattice parameters. The values of N Si /N C calculated on the basis of the measurements made are in good agreement with the experimental results (see Fig. 17). This, in turn, affects the mass transfer rate and can result in the formation of a silicon melt film on the crystal surface and thereby induce the vapor-liquid-solid (VLS) growth mechanism, which can influence the polytypism of growing crystals as well as the concentration of point and linear defects. All these phenomena are observed experimentally (10–13). In addition to mechanochemical activation of the original charge, the polytype structure of the charge powders exerts an influence on the partial pressure of vapor components and, consequently, the ratio N Si /N C in the vapor phase. From the results for precision oxidation of SiC crystals of various polytype structures, the thermodynamic characteristics of the polytypes have been evaluated, from which the partial pressures of basic components of the vapor phase were calculated as a function of the degree of hexagonality of the polytype D (14). Within error, the experimental results agree reasonably well with the calculated data. As a result of studies of vapor compositions above the SiC charge, a basic conclusion

Figure 17 Temperature dependence of the ratio of Si and C atoms in the vapor phase on the grain size of the original charge (dissociative process occurs in vacuum). Grain dimensions: (䉭) 0.065–0.2 mm; (䊊) 0.2–1 mm; (䉲) 2–3 mm.

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can be drawn: reproducible production of the SiC single crystals of a specified shape, growth rate, polytype and dislocation structure, stoichiometric composition, doping level, etc. requires careful control of the preparation of the original source and its composition. During research on the mass transfer of SiC vapor from the source to the seed in a growth cell with graphite walls, it was established that graphite can act as a catalyst. The main point of the phenomenon is as follows. In dissociative sublimation of the charge, the vapor phase is enriched with silicon atoms, i.e., N Si /N C ⬎ 1. When the vapor interacts with the graphite walls of the growth cell, the excess silicon atoms are bound to carbon atoms. This raises the value of N C in the vapor phase and, accordingly, increases the mass transfer rate, since one of the limiting conditions of mass transfer when N Si /N C ⬎ 1 is the transport of the carbon component. At a low crystal growth temperature, 1800°C, when N Si /N C ⬎ 1 the graphite walls of the growth cell exhibit maximum catalytic properties, but they do not show them at 2600°C (by the Lely method), because at these temperatures N SiC /N C approaches unity. Thus, in the method we have developed the shape of the growth cell and the mutual arrangement of the growing crystal and graphite walls permit precise control of the effectiveness of bulk SiC crystal growth processes. Using this phenomenon, it is possible to control the processes of enlargement and profiling of single crystals by varying the graphite cell geometry and, accordingly, the mass transports of vapor phase components toward the growing crystal. In addition, this effect enables us to lower the growth temperature, to obtain epitaxial layers at temperatures up to 1300°C. The processes of SiC crystal growth can be intensified, making use of the effect of the difference in the pressures of vapors above the SiC polytypes. An alternative implementation of this effect is the joint growth of a single crystal of α-SiC (on seed) and of a polycrystal of 3C-SiC (on graphite) by condensing supersaturated vapor (Fig. 18). Under particular conditions nucleation occurs on graphite. The curves of the growth rate of the [0001]-oriented single crystal and the polycrystal versus supersaturation are shifted relative to each other owing to heterogeneous nucleation on graphite and are represented in Fig. 19. The value of the critical supersaturation σ cr is dependent on the temperature, the conditions of graphite preparation, and a number of other factors. Figure 19 shows the dependences of this effect. The variation in supersaturation between the vapor source and graphite substrate was produced by changing the distance between the source and substrate at a temperature gradient of 20°C/cm. With an increase in process temperature, the critical distance, and consequently the critical level of supersaturation below which deposition of SiC onto graphite is not observed, is seen to be reduced. At values of supersaturation up to α cr , the single crystal leads to growth of polycrystal and will enlarge over the area owing to the tangential component of the growth rate. Hence, because of its defects and metastable structure, the 3C-SiC polycrystal deposited on graphite exhibits a higher vapor pressure than the σ-SiC single crystals growing nearby do at the same temperature. So, the 3CSiC polycrystal is a side source of vapor for growing single crystals. When the front of singlecrystal growth lays behind the front of polycrystal growth, the polycrystal is enlarged because

Figure 18 Joint growth of SiC single crystals and polycrystals.

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Figure 19 Growth rate of SiC single crystals and polycrystals versus supersaturation.

of substitution of the single crystal. Also, the single-crystal parts that are closer to the polycrystal are fed better then the center, resulting in the formation of a pit in the center of the growing crystal. If the growth rate of the single crystal drastically exceeds that of the polycrystal and the single crystal begins to project above the polycrystal by a considerable height, the feed to the periphery of the growth front deteriorates because it is distant from the polycrystal, which gives rise to loss of stability of the flat growth front of these parts and faceting of the single crystal. In particular, in growing the [0001]-oriented crystal, faceting occurs with pyramid faces of type (1011), (1012), etc. This in turn eliminates further enlargement of the single crystal. The best results are observed at the ratio V p /V s ⫽ 0.95–0.98. The investigation of vapor deposition and crystallization on seeds has revealed the following features. Because with dissociative components in the vapor phase N Si /N C ⬎ 1, whereas with crystallization on seed the crystal has a more nearly stoichiometric composition, accumulation of silicon atoms can take place in the vapor phase in a quasi-closed system, which both retards mass transfer and leads to the formation of a silicon melt on the growing surface of the film. As silicon is an SiC solvent, the creation of a melt film results in the vapor-liquid-solid (VLS) growth mechanism. Theoretical and experimental studies of these processes (10) indicated that the formation of a silicon melt film depends on the closure (quasi-closure) of a system as well as on its volume, temperature, gaseous medium, and type of vapor source (single crystals, powder, the polytype, and mechanical activation of the powder). Figure 20 represents the experimental dependence of the deposition rate of silicon film growing epitaxial SiC layers in a sandwich system in a vacuum of 10 ⫺2 Pa in the temperature range 1800–2100 K at a difference in temperature between the SiC crystal vapor source and the crystal substrate of 0.5–3 K. The gap between the source and the substrate amounted to 3 µm, and the sandwich on the edges was sealed with dense carbon residue, formed as a result of phenolformaldehyde resin film annealing. From the dependence it is seen that under the given conditions the crystal growth follows the VLS mechanism at temperatures below 2030 K and the vapor-solid (VS) mechanism above this. As already mentioned, the temperature of this boundary between growth mechanisms is dependent on the parameters of the growth process. The base and impurity compositions of crystals are influenced by the crystal growth kinetics. Growth by sublimation is performed at rather low temperatures, below 0.7 T m . In addition, the normal growth rates are considerably higher than those of self-diffusion of the components, i.e., of silicon and carbon, in the lattice. It follows that SiC crystal growth takes place in the

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Figure 20 Experimental dependence of the deposition rates of SiC and Si on temperature.

absence of equilibrium between the crystal bulk and vapor phase, which leads to the dependence of the base composition of the crystal on its growth rate. The investigations undertaken have confirmed these considerations (14). Figure 21 shows the dependence of the difference between the equilibrium (C Si and C C ) and real (C Si and C C ) concentrations of silicon and carbon in 4HSiC crystals on their reverse growth rate. The coefficients of silicon and carbon self-diffusion

Figure 21 Deviation from stoichiometry in SiC crystals versus the growth rate.

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in the lattice determined from the slope of the curves agree closely with the data reported in Ref. 15. Again, regular variations in lattice parameters, crystal density, and luminescent properties sensitive to point defects (13) are observed. Similar regularities, but now for the impurity composition, are also observed for slowly diffusing impurities of nitrogen and aluminum. The N or Al doping yields a specific crystal color (green or blue, respectively), and when a visual sectorial nonuniformity over the base composition of crystals can be observed, when growing faceted crystals, or when growing epitaxial layers on different crystallographic planes of seeds, this is observed indirectly in terms of electrophysical properties [manifested more distinctly in luminescent properties (13)]. Thus, for producing uniform SiC crystals (over the base and impurity compositions) it is necessary to achieve one-face crystal growth. We now consider the problems connected with control of the polytype structure of the crystals being grown. As a result of investigations of the nature of polytypism (14), the following methods of controllable production of crystals and layers of specified polytype structure have been developed: (a) growth under close-to-equilibrium conditions of the desired polytype structure on the faces of seeds able to transfer structural information and (b) the formation of the specified polytype strucure by control of the growth kinetics in the initial stage of crystallization. Let us briefly characterize these methods. In growing SiC crystals on seed with different crystallographic orientations in both ‘‘vapor-bulk crystal’’ equilibrium conditions (the normal growth rate is much less than that of the component diffusion) and ‘‘vapor-growth surface’’ equilibrium conditions, it was shown that all faces of the seed except (0001)C exhibit good stability for structural information transfer. On the basis of the investigations undertaken, a bank of SiC seeds of various polytype structures has been created. In this case the growth of a crystal or epitaxial layer of a desired polytype structure is conducted on seeds of the same polytype structure on the (1100), (1120) faces or on the planes deflected from (0001)C by a small angle (up to 10°). The angle is determined mainly by requirements of the morphology of the growing space: Control of the polytype structure of the crystals and layers grown using the crystallization kinetics is applied when it is necessary to develop heteropolytype structures, i.e., on seeds of one to obtain a layer of another polytype stucture or in the process of crystal growth changing periodically the polytype structure of the growing crystal. To change the polytype structure of a growing crystal it is necessary, according to conclusions on the nature of polytypism (16) to provide conditions in the crystal for initiating solid-phase transition in the initial stage. The solid-phase transition can be initiated by mechanical stresses, e.g., by virtue of the layer-bylayer change in the base or impurity composition of building up layers and, accordingly, lattice parameters. To control the base composition of a growing crystal, the growth should take place at rates comparable to or greater than the diffusion rate of the base components, silicon and carbon. Consider the example of experimental implementation of this method. SiC single crystals were grown on the (0001)C face of chemically well etched seeds of 6H-SiC. In order to outgas the graphite armature of the furnace, it was heated in vacuum at 1500°C and then argon was introduced into the furnace up to a definite pressure P 0 . Further heating of the furnace was carried out up to the growth temperature T 0 . The value of argon pressure P 0 was chosen so that the rate of SiC vapor diffusion mass transfer in argon and the rate of crystal growth were negligibly small. Then argon was pumped off down to a certain pressure P 1 defined by the rate of crystal growth. In the simplest pumping out, the variation in argon pressure with time follows an exponential law with time constant τ. Because in an argon atmosphere the crystal growth is limited by the rate of vapor diffusion mass transfer, during pumping out the rate of crystal growth will be inversely proportional to the argon pressure and hence will also follow an exponential law with time. The growth temperature T 0 and operating growth rate were chosen such that the self-

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diffusion rate of silicon in SiC was three to five times less than the growth rate. On pumping out with an increase in growth rate up to the operating level, the crystal layers building up have a different ratio N Si /N C and, accordingly, different lattice constants. As a result, a layered structure is produced with composition and lattice parameter gradients normal to the growth surface, which, along with the seed, forms a stressed composition. When the value of the shear stress is reached, the solid-phase transition occurs in this composition, resulting in the formation of dislocation centers on the growth surface, step sources defining the further growth of a crystal of a certain polytype structure. Figure 22 represents the dependences of the polytype structure yields in the initial stage of growth on the pumping time constant τ for T 0 ⫽ 2220 K, P 0 ⫽ 4 ⫻ 10 4 Pa, and P 0 ⫽ 10 ⫺1 Pa. The yield S/S 0 is the ratio of the area S of an initial crystal layer of a particular polytype to the entire area of the growing crystal S 0 . The averaged value for four crystals growing simultaneously corresponds to each point of Fig. 7. The spread in values of S/S 0 did not exceed 20% from crystal to crystal. As the crystal is growing, enlargement of the main polytype modification takes place at the expense of the accompanying modifications, depending on the value of vapor supersaturation. As a consequence, a crystal of only one polytype structure is formed at appropriate values of τ and supersaturation. With fast pumping out, i.e., at small values of τ, the 4H-SiC structure is primarily formed. With slow pumping out, i.e., at large values of τ, crystals of polytype modification 3C-SiC are grown. At intermediate values of τ the growth of 6H-SiC crystals occurs. If required to produce a crystal of a layer-bylayer structure with alteration of different polytypes, in particular for obtaining periodic polytype structures, the crystal growth process is interrupted periodically by introducing argon up to pressure P 0 , and then the pumping process is repeated again with the desired value of τ. If it is necessary to obtain local epitaxial heteropolytype structures, the surface of the seed crystal is treated in advance according to a specified topological pattern (e.g., by polishing with diamond paste, by particle irradiation, by impurity deposition). For this problem we choose the boundary value of τ between the polytype structures needed for a heteropolytype composition. The impurity (N, Sc, Al, group IV elements Ge, Sn, Pb, etc.) doping of growing layers results in a significant change in the shape of the kinetic diagram shown in Fig. 22 and the appearance of more complex polytype structures. This is due to a different influence of doping impurities on the lattice and, accordingly, the energy of packing defect formation during solid-phase transition in the initial stages of crystallization. Also, it was established that the more the covalent radius

Figure 22 Dependences of SiC crystal yield of 3C, 6H, and 4H polytypes on the deposition kinetics in the initial stage of growth.

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of the impurity differs from that of the substituted atom (of silicon or carbon), the lower its solubility in Si; at smaller concentrations of impurity an influence on the polytype structure of the layers being grown is observed. As a rule, the most dramatic effect of the impurity is manifested when its concentration is close to the solubility limit in the SiC lattice. Analysis of the data reported in the literature on the influence of the impurity on the polytypism in other materials, in particular, in metals (14), has revealed a similar tendency. The possibility of device fabrication based on SiC depends on defects such as micropipes in crystals and layers. Hence the investigation and control of the problem of micropipes are of extreme significance. The first step of our laboratory in this direction is to study the micropipe behavior in 6H-SiC single crystalls under high-temperature annealing (19).

REFERENCES 1. YM Tairov, VF Tsvetkov. In: VP Korizkiei, VV Pasynkov, BV Tareev, eds. Reference book on Electrotechnical Materials. Vol 3. Moscow: Energoatomizdat, 1986, pp 446–457. 2. A Lely. Ber Dtsch Keram Ges 32: 229, 1955. 3. YM Tairov. Rost Krist 6:199, 1965. 4. DR Hamilton J Electrochem Soc 105:735, 1958. 5. WF Knippenberg. Philos Res Rep 18:16, 1963. 6. YM Tairov, VF Tsvetkov. Silicon Carbide 1973:146, 1973. 7. YM Tairov, VF Tsvetkov. Rost Krist 13:14, 1980. 8. YM Tairov, AA Kalnin, NA Smirnova. Neorg Mater 9:125, 1973. 9. VA Ilyin, VI Kolynina, YM Tairov, VF Tsvetkov. Zh Prikl Khim (J Appl Chem Sov) 5: 1205, 1987. 10. YM Tairov, EG Ivanov, VF Tsvetkov. Neorg Mater 21:588, 1985. 11. F Raihel, YM Tairov, TVF Travadzhyan. Neorg Mater 16:1011, 1980. 12. YM Tairov, MA Chernov, VF Tsvetkov. Kristallogr (Crystallogr Sov) 24:772, 1979. 13. LI Levin, YM Tairov, VF Tsvetkov. Tech Poluprovodnikov (Phys Tech Semicond Sov) 14:1194, 1984. 14. YM Tairov, VF Tsvetkov. In: Progress in Crystal Growth and Characterization. Vol 7. London: Pergamon, 1983, p 2485. 15. JD Hong, RF Davis. J Mater Sci 16:2485, 1981. 16. JE Gegusin. Physics of Sintering. Moscow: Nauka, 1984, pp 149–234. 17. JD Hong, RF Davis, DE Newberry. J Mater Sci 16:2485–2494, 1981. 18. DL Barret, JP McHugh, HM Hobgood, RH Hopkins, PG McMullin, RC Clarke, WJ Choyke. J Cryst Growth 128:358–362, 1993. 19. AS Bakin, SI Dorozhkin. Transactions Second International High Temperature Electronics Conference (HiTEC) Charlotte, NC, June 5–10, 1994, p 169.

19 Epitaxial Growth, Characterization, and Properties of SiC Sadafumi Yoshida Saitama University, Urawa, Saitama, Japan

I.

INTRODUCTION

There is no SiC crystal in the natural world except in meteoric stones. However, historically, SiC is rather an old semiconductor, which has been known since the beginning of the 19th century. Since Acheson succeeded in synthesizing SiC powder industrially in 1892, SiC has been used as a grinding powder and for high-temperature heaters and firebricks because of its thermal and chemical stability and hard nature. However, research on SiC as a semiconducting material started after the development in 1955 of the Lely method, by which high-purity singlecrystal platelets of SiC can be obtained. In the 1960s and 1970s, physical and chemical properties of SiC were studied using Lely crystals and their excellent properties for electronic and optical device applications were shown. Based on these properties, many attempts have been made to fabricate devices (1,2). However, because it was difficult to make electronic devices using small Lely crystals in industry, the research on SiC declined in the latter half of the 1970s. In the early 1980s, two important advances were made to break through the problems of SiC research, which again stimulated the research on SiC. As a result, SiC has attracted much interest again since the middle of the 1980s. One is the development of a growth method for large-area 3CSiC epilayers on Si substrates by chemical vapor deposition. The other is the growth of bulk SiC, which makes it possible to obtain SiC wafers. By using homoepitaxially grown layers of 6H and 4H-SiC and heteroepitaxially grown layers of 3C-SiC, more precise studies of the properties of SiC have been done (3), as well as the fabrication of electronic devices, such as diodes and transistors, and optical devices, such as light-emitting diodes and optical detectors. In this chapter, the epitaxial growth techniques are reviewed in Sec. II, the characterization of single crystals and epilayers is discussed in Sec. III, and finally the physical properties of SiC are summarized in Sec. IV.

II. EPITAXIAL GROWTH SiC has been grown epitaxially by the methods of liquid-phase epitaxy (LPE), chemical vapor deposition (CVD), and molecular beam epitaxy (MBE). Because the epitaxial growth temperature of SiC is very high compared with other semiconductors, the materials suitable for the substrates are restricted to refractory crystals. SiC itself (homoepitaxial growth) and other materials, such as Si and TiC (heteroepitaxial growth), have been used as substrates. 437

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Figure 1 Schematic diagram of the dipping method for liquid-phase epitaxy (LPE) growth of SiC.

A.

Methods of Epitaxial Growth

1. Liquid-Phase Epitaxy (LPE) As a liquid phase of SiC cannot exist under atmospheric pressure, LPE of SiC has been carried out using the dissolution of SiC into molten metals, such as Fe, Ni, or Cr (4,5). However, SiC crystals grown from metal solution contain a high density of metal impurities. Comparatively high purity 6H-SiC crystals have been grown using the Si–Sc–C system (6). To avoid unintentionally doping with impurities, Si solution has been used (7), although the solubility limit of carbon in Si is not so high, for example, compared with Si–Fe alloy solution (8). When Si is melted in a graphite crucible, carbon atoms dissolved in the higher temperature part of the crucible are transferred toward the lower temperature part by thermal convection and supersaturated carbon reacts with Si to form SiC on the substrates immersed in the Si melt. Usually, α-SiC (6H-, 4H-, and 15R) itself is used as a substrate material for the growth of αSiC. The dipping method (9), in which SiC substrates are dipped in Si melt to grow SiC and then pulled up, has been used. Figure 1 shows a schematic diagram of the dipping method for the LPE growth of SiC. Growth rates are typically in the range between 5 and 12 µm/h at a

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substrate temperature of 1600°C. Unintentionally doped epilayers show n-type conduction. Ptype epilayers are obtained by adding Al into Si melt. Low conductivity n-type epilayers are grown in an N 2 atmosphere. Using three crucibles, for the growth of p-type and n-type layers and for rinsing, epilayers with pn junctions can be obtained. This method has been used to produce SiC light-emitting diodes (10). 2. Chemical Vapor Deposition (CVD) For the growth of SiC by CVD, many kinds of reaction gases have been used (11). As the source gas for Si, SiH 4 , SiH 2 Cl 2 , SiHCl 3 , and SiCl 4 have been used. As the source gas for carbon, hydrocarbon gases such as CH 4 , C 2 H 6 , C 3 H 8 , C 2 H 4 and C 2 H 2 have been used. As single source gases for SiC growth, organosilane gases having Si–C bonds, such as methyltrichrolosilane CH 3SiCl 3 (12) and silacyclobutane c–C 3 H 6SiH 2 (13), have been reported. Hydrogen is usually used as a carrier gas. Figure 2 shows a schematic diagram of a CVD system for the growth of SiC. A graphite plate coated with SiC is used as a susceptor and heated inductively by a radio frequency (RF) generator. SiH 4 diluted with H 2 or 100% SiH 4 , C 3 H 8 diluted with H 2 or 100% C 3 H 8 , and H 2 carrier gas purified by a palladium-silver alloy cell are introduced into a water-cooled, quartz reaction tube previously evacuated to a vacuum below 10⫺6 torr. The flow rate of each reaction gas is controlled by using a mass flow controller. For doping, Al(CH 3 ) 3 (trimethylaluminum, TMA), Al(C 2 H 5 ) 3 (triethylalumium, TEA) (14), or B 2 H 6 for ptype dopant and N 2 or NH 3 for n-type dopant are added in the reaction gases. The amount of TMA(TEA) is controlled both by the H 2 flow rate for bubbling TMA(TEA) and by the temperature of a TMA(TEA) cylinder. Usually, CVD has been carried out at atmospheric pressure. Reduced-pressure CVD has been reported to improve the thickness uniformity of the epilayers (15). Growth by alternative supply of SiH 2 Cl 2 and C 2 H 2 has also been reported to reduce growth temperatures (16). A typical growth temperature for 3C-SiC is 1300–1400°C and for 4H and 6H-SiC, 1600– 1800°C. By using off-axis (0001) SiC substrates, the epitaxial growth temperature for α-SiC has been reduced to around 1500°C, which will be described in Sec. II. B on homoepitaxy. High-temperature CVD growth at around 1800–2300°C (HTCVD) has been reported (17). Very high growth rates, as high as 0.5 mm/h, have been achieved by HTCVD, whose growth mechanism may include usual chemical vapor transport and sublimation. 3. Molecular Beam Epitaxy (MBE) The MBE technique attracts much interest because of its low growth temperatures compared with LPE and CVD and its feasibility of in situ observation of crystal structures during growth. As sources for Si and C, Si and C molecular beams obtained by thermal evaporation of solid Si and C have been used (18). An electron beam gun is used for the evaporation of carbon. Instead of solid sources for carbon, gas sources such as C 2 H 4 and C 2 H 2 have also been used, which is called gas source MBE (19). In the case of using Si and C solid sources, as sticking coefficients of Si and C at around 1000–1200°C are both almost unity, it is hard to control the stoichiometric composition of the films deposited. On the other hand, in the case of using hydrocarbon as a C source, films with stoichiometric composition can easily be obtained, because, at around 1000°C, these hydrocarbon molecules do not dissociate thermally, but react only with Si to form SiC and the remains reevaporate. For an Si source, gas sources such as Si 2 H 6 and SiHCl 3 have been used (20). To realize atomic layer epitaxy, it is important to study the surface structures under an Si source beam and a C source beam. 3C-SiC (001) surfaces were investigated by medium energy ion scattering spectroscopy (MEISS), Auger electron spectroscopy (AES), low-electron

Figure 2

Schematic diagram of a chemical vapor deposition (CVD) system for the growth of SiC.

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energy diffraction (LEED), and scanning tunneling microscopy (STM) (21). Several kinds of surface structures, i.e., surface reconstruction patterns, have been reported (22). 3C-SiC surfaces were cleaned with an Si beam at 900°C, at which oxides evaporate by the reaction with an Si beam. Then a (3 ⫻ 2) surface reconstruction pattern was observed. After stopping the Si beam, the surfaces were heated up to 1065°C and kept at this temperature in high vacuum below 10⫺10 torr. The surface structure changed from (3 ⫻ 2) to c(2 ⫻ 2) via (5 ⫻ 2), (2 ⫻ 1), and (1 ⫻ 1). By Auger electron spectroscopy, the surface with (3 ⫻ 2) is assigned as Si terminated and that with c(2 ⫻2) as C-terminated. Figure 3 is an STM image of a 3C-SiC (001)-(3 ⫻ 2) surface. Each oval-shaped atom group consisting of the whole surface is the (3 ⫻ 2) unit cell, which includes the Si dimers, that is, four Si atoms. When an Si 2 H 6 beam was applied to a c(2 ⫻ 2) C-terminated surface, the Si/C AES peak ratio increased with exposure time and the surface structure changed from c(2 ⫻ 2) to (3 ⫻ 2) via (1 ⫻ 1) and (2 ⫻ 1), which shows that the surface became Si-terminated. When the surface shows (3 ⫻ 2) structure, the Si/C ratio saturates, as shown in Fig. 4a, which indicates self-limiting of Si monolayer absorption. On the contrary, when a C 2 H 2 beam was supplied to a (3 ⫻ 2) Si-terminated surface, the Si/C AES peak ratio decreased with exposure time and the surface structure changed from (3 ⫻ 2) to c(2 ⫻ 2), which indicates that the surface became C terminated. When the surface shows c(2 ⫻ 2) structure, the Si/C ratio saturates as shown in Fig. 4b, which also indicates self-limiting of C monolayer absorption. These results suggest the possibility of atomic layer epitaxy of SiC by alternative supply of Si 2 H 6 and C 2 H 2 . It has been reported that epitaxial growth temperature can be reduced to around 800°C by using a mass-separated C⫹ ion beam (23) or a C-related beam from a C 3 H 8 thermal cracker cell (1200°C) (24).

Figure 3 Scanning tunneling microscopy (STM) image of a 3C-SiC (001)-(3 ⫻ 2) reconstructed surface.

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Figure 4 Transition of elemental composition (a) from carbon-terminated to silicon-covered surface by exposing disilane and (b) from silicon-covered to carbon-terminated surface by exposing acetylene at 1050°C. (From Ref. 21.)

B.

Homoepitaxy

Bulk SiC substrates made by the Acheson method or the Lely method have been used as the substrates for growth of α-SiC. Recently, SiC wafers sliced from an SiC ingot grown by the modified Lely method have been used. Usually, (0001) Si or (0001) C surfaces are used, Here, homoepitaxial growth of SiC by CVD using an SiH 4 –C 3 H 8 –H 2 reaction gas system is illustrated as an example. SiC substrates are etched with HF solution to remove oxide layers and are then set in the reaction tube. Prior to the growth, the surfaces are etched with HCl gas at around 1500°C. SiH 4 and C 3 H 8 reaction gases with typical flow rates of 0.1–5 sccm and H 2 carrier gas of 3–10 slm are introduced in the reaction tube. Growth rates are in the range of 1–3 µm/h. At 1600– 1800°C, epilayers with the same polytype as the substrates grow; i.e., 6H-SiC grows on 6HSiC substrates, 4H- on 4H-SiC, and 15R- on 15R-SiC. However, when (0001) on-axis surfaces of 6H-SiC are used as substrates, 3C-SiC grows on them at 1500°C. The 3C-SiC epilayers contain many twins, resulting in a mosaic patterned surface morphology. On the contrary, when off-axis surfaces toward the [1120] direction, about 3–6 degrees, are used as substrates, 6HSiC epilayers with smooth surfaces grow even at 1500°C (25,26). These results have been explained as follows. It is plausible that nucleation tends to occur at the atomic steps rather than at the terrace. In the case of on-axis substrates, as there are few steps, three-dimensional nucleation occurs at the terrace. As the stable polytype is 3C type at 1500°C, 3C-SiC clusters nucleate and grow. When adjacent nuclei with the stacking sequences ABCABC and ACBACB grow, touch each other, and coalesce, a twin boundary is introduced at the boundary, as shown in Fig. 5a and b. To obtain 6H-SiC epilayers, temperatures above 1700°C are needed in the case of on-axis substrates, where 6H-SiC is a stable polytype. On the contrary, on off-axis substrates,

Figure 5 Schematic image of the relationship between growth modes and polytypes of grown layers. (a) On an on-axis 6H-SiC (0001) surface, 3C-SiC grows through three-dimensional nucleation and (b) an antiphase boundary is introduced when the islands coalesce. (c) On an off-axis 6H-SiC (0001) surface, on the contrary, homoepitaxial growth of 6H-SiC is achieved by step-flow growth.

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there exist many atomic steps, and thus the nucleation occurs at the steps, not at the terrace. In this case, called step growth mode, as films grow laterally, the stacking sequence follows that of substrates, and thus the same polytype as that of the substrate grows as shown in Fig. 5c. Therefore, 6H-SiC grows on 6H-SiC substrates even at 1500°C. C.

Heteroepitaxy

For heteroepitaxial growth, the selection of substrates is important, not only from the point of view of matching the lattice constant and thermal expansion coefficient but also in terms of the thermal and chemical stability of the surfaces at the growth temperatures. As the epitaxial growth temperatures of SiC are very high, the materials suitable for the substrates are restricted essentially to refractory materials. In the case of CVD, hydrogen is used as a carrier gas, and oxide materials cannot be used as substrates. Usually, Si has been used as the substrate for the growth of SiC. As the growth temperature of α-SiC is higher than 1500°C, only 3C-SiC is grown on Si substrates, whose melting point is about 1420°C. For the growth of 3C-SiC on Si, there exist serious problems. Mismatching of lattice constants and thermal expansion coefficients between SiC and Si has been believed to be the reason why SiC with good crystalline quality cannot be grown on Si (27). In 1983, Nishino et al. (28) succeeded in growing good quality 3C-SiC epilayers on Si by CVD by using a carbonization process for Si surfaces before SiC growth. The typical growth sequence in CVD is as follows. The Si surfaces are etched with HCl at around 1200°C to remove surface oxide layers. Then the substrates are heated up to 1300–1400°C within a couple of minutes under the flow of a hydrocarbon gas, where the surfaces are carbonized and covered with thin SiC layers about 10 nm thick. After the carbonization process, SiC layers are grown on the carbonized Si substrates with SiH 4 and C 3 H 8 reaction gases. A typical growth rate is about 2 µm/h. Using 3CSiC epilayers on Si, Schottky barrier diodes (29), Schottky gate field effect transistors (MESFETs) and metal-oxide-semiconductor field effect transistors (MOSFETs) (30,31) were fabricated in the 1980s, and the operation of MOSFETs up to high temperatures was demonstrated (32). The carbonized layers on Si substrates were thought to act as buffer layers for lattice mismatch between SiC and Si (33). However, by cross-sectional transmission electron microscopy (TEM) of the interface between SiC and Si, there exists no interface layer between SiC and Si and four Si lattices are commensurate with five SiC lattices (34,35), as shown in Fig. 6. It is hard to distinguish between a carbonized layer and a grown layer, although there exist many crystal defects such as stacking faults and dislocations near the interface. Reflection highenergy electron diffraction measurements for carbonized Si surfaces also indicate that the carbonized layer is stoichiometric SiC, not a mixed phase of SiC and Si. These results indicate that the carbonized layers cannot relax the lattice mismatch between SiC and Si. However, without the carbonization process, 3C-SiC epilayers with good crystalline quality cannot be obtained. The role of the carbonized layers is thought to be to prevent the diffusion of Si atoms to the surface of SiC (36). At the growth temperature of SiC, 1300–1400°C, which is just below the melting point of Si, the Si atoms are very mobile. As SiC grows after the manner of a threedimensional nucleation and growth mode on Si, the grown SiC layers do not cover whole the Si surfaces in the early stage of the growth, and thus Si atoms in the substrates move through the uncovered part (SiC holes) to the surface. At the surface, SiC grows with Si and C from reaction gases, which changes the Si/C ratio, and SiC with good crystalline quality cannot be obtained. However, when Si surfaces are covered with SiC layers, Si atoms are not supplied from Si substrates by diffusion, because the diffusion constant of Si in SiC is very low (37).

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Figure 6 Lattice image of a 3C-SiC/Si interface obtained by cross-sectional transmission electron microscopy (TEM).

Therefore, carbonized SiC layers are thought to act as diffusion barriers for Si atoms from Si substrates. The important point is how to cover Si surfaces with thin dense SiC layers before the substrate temperature reaches the growth temperature, 1300–1400°C. If the substrate temperature rises in a hydrocarbon atmosphere, Si surfaces react with hydrocarbon gas molecules to form uniform and dense SiC layers around 800°C. These layers are thought to prevent the diffusion of Si from the substrates. Therefore, two-step growth has been proposed (38), where polycrystalline SiC layers are grown first at around 800°C and then heated up to 1300–1400°C to grow SiC single crystals. It is noted that although the SiC layers grown at around 800°C are polycrystalline or amorphous, they change to single crystals after heating at the growth temperature of 1300–1400°C. Compared with the growth of SiC epilayers on Si (001), it is hard to grow SiC with good crystalline quality on Si (111) surfaces, where substrates sometimes bend due to the difference in thermal expansion coefficient between SiC and Si and many cracks are introduced in the epilayers. For the use of an SiC/Si heterointerface as the emitter of heterobipolar transistors (HBTs), low-temperature growth of SiC on Si has been tried using an SiH 2 Cl 2-C 2 H 2 reaction gas system (39). However, it is hard to reduce the growth temperature well below 1000°C for the accommodation to an Si large-scale integration (LSI) process. Antiphase boundaries (APBs) are seen in the epilayers on Si (001) substrates, as in the case of GaAs on Si. APBs can be observed by the etching pattern of the epilayers or by the boron decoration method (40). The formation of APBs can be avoided by using off-axis (001) surfaces of Si substrates instead of on-axis surfaces (41).

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Another substrate for the heteroepitaxial growth of SiC is TiC (42), whose lattice constant is only 0.8% different from that of SiC. However, large single crystals of TiC are difficult to produce. The technique for growing 3C-SiC epilayers heteroepitaxially on Si substrates is attractive from the viewpoint of obtaining large-area single-crystal substrates. And 3C-SiC is the most attractive polytype, because of its isotropic properties and large electron mobility compared with other SiC polytypes. However, at present, the quality of the epilayers is inferior to that of homoepilayers on modified Lely crystals due to the heteroepitaxial growth with large mismatch in lattice constants and thermal expansion coefficients between SiC and Si. More research to find methods for improving the crystal quality is needed. Kitabatake et al. (43) studied the mechanism of SiC heteroepitaxial growth by the carbonization of Si (001) surfaces at the atomic scale using molecular dynamics (MD) simulations. Possible heteroepitaxial growth mechanisms of 3C-SiC on Si (001) surface are elucidated by the MD simulations as shrinkage of the [110] rows of the Si lattice atoms with the C adatoms and breaking of the deeper Si–Si bonds in the Si lattice. The carbonization process in this model results in clear and abrupt interface formation (not a buffer layer) between the carbonized 3CSiC crystalline and the Si substrate lattice. This agrees with cross-sectional TEM images of 3CSiC/Si interfaces.

III. CHARACTERIZATION A.

Crystal Structures (Polytype Identification)

One of the most prominent characteristics of SiC is the existence of more than 100 kinds of polytypes. Therefore, the control of polytypes is very important for the growth of SiC. There are several methods for identifying SiC polytypes: X-ray diffraction (XRD); Raman scattering, high-resolution transmission electron microscopy (HRTEM); reflection high-energy electron diffraction (RHEED); and measurements of optical absorption and luminescence spectra. It is easy to identify the polytypes by the lattice images observed using the HRTEM method. However, for TEM observation, very thin samples on the order of 10 nm thick are required, and thus this method is not convenient for the identification of SiC polytypes. By RHEED observation, it is possible to identify polytypes of thin films in the growth chamber. However, if the surface is flat, distinction of the polytypes is rather hard because of their streaky diffraction patterns. Compared with these methods, Raman scattering measurements are useful for identifying SiC polytypes without pretreatment of the samples. Many Raman lines peculiar to the polytypes are observed in the Raman spectra of SiC crystals. The spectra can be explained by using the concept ‘‘large zone and zone folding.’’ When the period of the polytype is n times that of 3C-SiC, the size of its Brillouin zone is 1/n that of 3C-SiC, resulting in n times folded modes of the phonon dispersion curve as shown in the insets in Fig. 7. Each phonon branch in the large zone is folded into the real Brillouin zone. In the case of 3C-SiC, the large zone is the real Brillouin zone itself; in the case of 6H-SiC, the large zone is six times larger than the real Brillouin zone and the Γ point in the real Brillouin zone corresponds to the position of k ⫽ 0.00 (the original mode), 0.33, 0.67, and 1.00 in the large zone. Therefore, the folded modes can be observed for SiC polytypes with longer periods in Raman scattering spectra. Nakashima et al. (44,45) have calculated relative intensities of Raman lines for several polytypes, 6H, 8H, 15R, 21R, 27R, and 33R, using a linear chain model, and shown the calculated results are in good agreement with the experimental results. These results suggest that the polytypes can be identified by measurements of Raman scattering. Both

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Figure 7 Raman spectra from (a) a 3C-SiC epilayer and (b) a 6H-SiC bulk crystal. The position and the symmetry of each peak are shown. The insets show schematic diagrams of the large zone and the zone folding. (From Ref. 46.)

transverse optical and acoustic modes are folded. To identify the polytypes, observation of the folded transverse acoustic (TA) modes in the lower frequency region is useful because the Raman lines are sharper than those of the folded transverse optical (TO) modes in the highfrequency region. Figure 7 shows the observed Raman spectra for typical SiC polytypes, 3Cand 6H-SiC. In case of 6H-SiC, we can see Raman peaks corresponding to the folded modes in the regions 140–150 cm⫺1 (TA region) and 760–800 cm⫺1 (TO region), which are not seen in the case of 3C-SiC. Okumura et al. (46) and Yoshida et al. (47) have identified the polytypes of the SiC epilayers grown on 6H-SiC (0001) and 3C-SiC (111) and (001) surfaces by CVD using Raman scattering. The distribution of the polytypes can be obtained by using Raman scattering measurements with micrometer-size focused laser beams. Measurements of optical absorption and luminescent spectra can be used to identify the polytypes based on the difference in the band gaps between polytypes. Because of the band gap energy difference, it is easy to distinguish between 3C- and 6H-SiC from the absorption edge and/or luminescence peaks. By using a focused light beam for absorption measurements or a narrow laser beam for excitation in photoluminescence (PL) measurements, the distribution of the polytypes can be obtained. Mapping of an SiC wafer to separate 4H and 6H modifications has been carried out using the deference of band gaps between 4H (3.2eV) and 6H (2.9eV) polytypes (48). It is easy to separate with a bandpass filter around 400 nm (3eV). A more highresolution distribution of polytypes can be obtained using a focused electron beam in cathodoluminescence measurements.

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Crystal Defects

The methods for characterizing crystal defects can be divided into two categories: direct observation of crystal structures, i.e., TEM, Rutherford backscattering (RBS), and XRD, and indirect characterization through measurements of physical properties, i.e., Raman scattering, PL, and electrical measurements. Crystal imperfections can be divided into three categories: points defects (vacancies, interstitial atoms, antisite atoms, and impurities), structural defects (dislocations, stacking faults, and grain boundaries), and combined defects. The defects can also be classified by their origins—those due to crystal growth, those induced by the device process such as like etching and polishing, and those induced by irradiation with energetic particles. Characterizations of the crystal defects in SiC have been done in all these categories. The defects in bulk crystals are described in another chapter in this book. Radiation damages are discussed in Sec. IV.D of this chapter. Here, the crystal defects in 3C-SiC epilayers grown on Si by CVD are described. Lattice imperfection, i.e., displacement of atoms from the lattice sites and the existence of interstitial atoms, has been studied by using RBS measurements. The ratio between the yield for the channeling direction and that for random directions, χ min ⫽ 1.8%, has been reported for 3C-SiC epilayers grown on Si by CVD (49) and is almost the same as the theoretical value. This indicates that the 3C-SiC epilayers have excellent crystallographic structures. However, as the atomic mass of carbon is much different from that of Si, the scattering peaks from the carbon sublattice overlap those from the Si sublattice in usual RBS measurements using an He⫹ beam. Therefore, information about the carbon sublattice cannot be obtained. Nashiyama et al. (49) have proposed a new method in which D⫹ ions are used and information about the Si sublattice and carbon sublattice can be obtained independently from the RBS signal of D⫹ and from the nuclear reaction 12 C(d, p)13C, respectively. Using this method, they found that about 5% of C atoms shift from the lattice sites to the tetrahedral-like interstitial sites, although the Si sublattice is almost perfect. As shown by the cross-sectional TEM image in Fig. 6, there exist many stacking faults and misfit dislocations near the SiC/Si interfaces. The densities of these defects decrease with distance from the interface. Yoshida et al. (36) have shown that the electron mobility increases from 750 to 850 cm 2 /Vs at room temperature when the substrate side of the epilayers is etched away. This indicates that the substrate side of the epilayers has poor crystalline quality.

C.

Internal Stress

Because of the difference in thermal expansion coefficients between SiC and Si substrate, the 3C-SiC epilayers grown on Si may come under stress in the process of cooling from the growth temperature to room temperature. Large lattice mismatch between SiC and Si may also bring about internal stress in the epilayers. The existence of tensile stress is obvious from the fact that the substrates bend toward the epilayer side after deposition and sometimes the epilayers crack. Mukaida et al. (50) have estimated the internal stress by using Raman scattering measurements. When a Si substrate was etched away, the peak corresponding to the LO phonon shifted by 1.4 cm ⫺1 toward the higher energy side. Annealing in an H 2 atmosphere at 1750°C brought about a further 0.3 cm ⫺1 shift. The internal stress in SiC epilayers on Si was estimated assuming that the annealed sample has no internal stress. The stress in the epilayers was estimated to be 5.4 ⫻ 10 9 dyn/cm 2 tensile using the results of a study of the pressure dependence of Raman phonons (51). This value cannot be explained only by the thermal stress due to the difference in shrinking between SiC and Si during cooling from the growth temperature (1350°C) to room temperature after deposition, ⬃1 ⫻ 10 9 dyn/cm 2, which suggests the existence of other intrinsic

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internal stress. Feng et al. (52) studied the thickness dependence of internal stress in 3C-SiC on Si (100) and obtained a tensile stress of 3–11 ⫻ 10 9 dyn/cm 2 and strain of 0.1–0.2% for 3C-SiC epilayers 4–17 µm thick. These values are less than 1/1000 of that estimated from the difference in lattice constants between SiC and Si. This is considered to be due to almost perfect lattice relaxation at the interface on introducing misfit dislocations at every four Si lattices and five SiC lattices, as shown in the TEM images of SiC/Si interfaces (Fig. 6). The difference between four Si lattices and five SiC lattices is only 0.3%, which is the same order as in the case of GaAs/AlAs interfaces. Mukaida et al. (50) observed the Raman peak corresponding to the TO phonon for 3C-SiC self-standing epilayers, which should not be observed in the backscattering configuration for (001)-oriented epilayers according to the selection rule. Feng et al. (52) also reported the observation of forbidden TO lines, which they explained as follows. When an Si substrate is etched away, the reflectance at the back surface increases from 4.7% (SiC/Si interface) to 21% (SiC/air interface). This brings about scattering of light for the forward scattering configuration, which has different selection rules from backscattering and thus could lead to the appearance of the forbidden TO line from 3C-SiC self-standing films. D.

Impurities

Impurities in SiC crystals have been estimated from PL, electron spin resonance (ESR), electron nuclear double resonance (ENDOR), and Hall measurements and more directly by secondary ion mass spectroscopy (SIMS) measurements. It is well known that the unintentionally doped SiC epilayers show n-type conduction with a residual carrier density of the order of 10 15 –10 16 cm ⫺3. The residual carriers in SiC epilayers have been attributed to nitrogen impurities, which is strongly supported by the observation of three-line electron spin resonance (ESR) signals related to nitrogen impurities in 6H- (53) and 3C-SiC (54). However, it is hard to explain the temperature dependence of carrier density and ESR signals only by the nitrogen impurities. Here, the methods for studying nitrogen impurities in SiC crystals will be described. The origin of the residual carriers will be discussed in Sec. IV.B. Figure 8 shows ESR spectra observed in nondoped 3C-SiC epilayers at various temperatures (55). Below 30 K, a three-line ESR signal can be seen in the spectra, which decreases with temperature and disappears at 40 K. This three-line structure can be decomposed into a nitrogen-related hyperfine structure with equally spaced three-line structure (g ⫽ 2.0049, hfs ⫽ 1.08G, line width ⫽ 0.56G) and a narrow one-line structure with the same g value (line width ⫽ 2.2G), as shown in Fig. 9 (56). The figures suggest that the nitrogen impurities exist in the epilayers. Spin densities estimated from the three-line nitrogen-related structure at 4.2 K are on the order of 10 15 cm ⫺3, which is one order smaller than that of residual carriers. ESR signals can be observed for unpaired electrons quenched at donor levels. Above 40 K, unpaired electrons at the nitrogen impurity level may ionize, and thus the three-line signal is not observed, which is also different from the temperature dependence of the carrier concentrations. Density of nitrogen impurities can be estimated directly by SIMS measurements. However, it is hard to estimate nitrogen density below 10 16 cm ⫺3, because of the very low sensitivity of nitrogen in SIMS measurements and difficulty of distinguishing adsorbed nitrogen from residual gas in the SIMS chamber. Moreover, in the case of nitrogen in SiC, the overlapping of the signals from 14N ⫺ and 28Si 2 ⫺ makes SIMS measurements difficult. In the case of nitrogen in Si, the detection of N is estimated from the signals for compounds such as SiN. However, in the case of SiC, a mass resolution M/∆M of more than 300,000 is required to separate 29Si 13C ⫺ and 28 14 ⫺ Si N . Nashiyama et al. (57) used a high-resolution and high-vacuum (⬍10 ⫺10 torr) SIMS system, in which CN signals were used to detect nitrogen impurities. In this case, M/∆M more than 7,000 is required to separate 12 C 14N ⫺ and 13C 2 ⫺. For the calibration of nitrogen content, 3C-

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Figure 8 Electron spin resonance (ESR) signals observed in undoped 3C-SiC epilayers at low temperature.

Figure 9 Decomposition of the three-line structure into a nitrogen-related hyperfine structure with an equally spaced three-line structure and a narrow one-line structure with the same g value. (a) Nitrogenrelated hyperfine structure, (b) one-line structure, (c) added spectrum of (a) and (b), and (d) observed ESR spectrum.

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Figure 10 Depth profile of nitrogen impurity concentration in a 3C-SiC epilayer implanted with 60and 160-keV nitrogen ions. (From Ref. 57.)

SiC epilayers were implanted with nitrogen ions at 2.5 ⫻ 10 15 cm ⫺2. Figure 10 shows the depth profile of the nitrogen content in 3C-SiC implanted with nitrogen ions. For depth above about 0.6 µm, values about 4 ⫻ 10 15 cm ⫺3 are attributed to the residual nitrogen impurities in undoped 3C-SiC epilayers. The background level of the nitrogen in the measurements is 1 ⫻ 10 15 cm ⫺3. 3C-SiC epilayers grown with very pure reaction gases have a nitrogen content below the background level of ⬃1 ⫻ 10 15 cm ⫺3, although their residual carrier concentrations are in the range 10 15 –10 16 cm ⫺3. IV. PHYSICAL AND CHEMICAL PROPERTIES A.

Optical and Luminescent Properties

1. Optical Absorption SiC polytypes show different optical absorption spectra due to differences in the band gap energies (58,59). SiC crystals other than 3C type have anisotropic crystal symmetry and show dichroism for light with the electric field E储 c-axis and E 芯 c. The shapes of the absorption curves are characteristics of indirect transition, with shoulders due to phonon emission. The reported values of the exciton energy gap and the exciton binding energy are listed in Table 1. The values of phonon energies related to the optical absorption are shown in Ref. 3. It is well known that nitrogen-doped SiC crystals show characteristic colors, green in 6H, yellow in 15R, and greenyellow in 4H polytypes. These colors are attributed to direct optical transitions from the lowest conduction band to higher empty bands (60). 3C-SiC shows a pale canary yellow color due to the band edge absorption at 2.2 eV.

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Table 1 Low-Temperature Band Gap Energies (E g ), Exciton Energy Gap (E gx ), and Exciton Binding Energies (E x ) of Various SiC Polytypes Polytype 3C 4H 6H 15R 2H 21R 33R

E g (eV)

E gx (eV)

E x (meV)

2.403 3.285 3.101 2.946

2.390 3.265 3.023 2.906 3.330 2.853 3.003

13.5 20.0 78.0 40.0

2. Refractive Index The refractive indices of SiC are also different for light with E储 c-axis and E 芯 c. As the wave at normal incidence to the c-plane, E 芯 c, is called the ordinary ray and that for E储 c the extraordinary ray, the refractive index for E 芯 c is denoted as n o and that for E储c as n e. The refractive indices of several polytypes have been measured. Powell (61) measured the refractive indices of 2H-SiC in the wavelength range 435.8–650.9 nm by the method of minimum deviation. He obtained a Cauchy dispersion equation by curve fitting of the experimental data. The empirical fitting equations, as well as the values at wavelength λ ⫽ 515 nm, are listed in Table 2 (60). An attempt has been made to relate the birefringence of SiC to the crystal structure. Figure 11 shows the birefringence δ at wavelength λ ⫽ 584 nm of several SiC polytypes as a function of the hexagonality h (61). The figure shows the linear relation between δ and h as in the case of ZnS polytypes, except for 3C and 2H.

Table 2 Refractive Indices of SiC Polytypes a Parameters for empirical fitting equation Polytype 3C 2H n0 ne 4H n0 ne 6H n0 ne 15R n0 ne a

at 515 nm

C0

C ⫻ 10 4

2.6823

2.55378

3.417

2.6615 2.7389

2.5513 2.6161

2.585 2.823

2.6881 2.7450

2.5610 2.6041

3.40 3.75

2.6789 2.7236

2.5531 2.5852

3.34 3.68

2.6800 2.7297

2.558 2.5889

3.31 3.74

C 2 ⫻ 10 8

8.928 11.49

Empirical fitting equation: n(λ) ⫽ C 0 ⫹ C 1 /λ 2 ⫹ c 2 /λ 4; n 0 , refractive index for ordinary ray; n e , refractive index for extraordinary ray.

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Figure 11 Birefringence versus hexagonal fraction h of SiC polytypes at 584 nm. (From Ref. 61.)

3. Luminescence Luminescence spectra have peaks related to the excitons near the band edge, peaks related to donor and acceptor impurity levels, and peaks related to deep levels due to impurities and defects. From measurements of luminescence, therefore, much information about the exciton band gap, impurity levels, and deep levels can be obtained. For SiC, many luminescence measurements have been made by photoluminescence, cathodoluminescence, and electroluminescence at low temperatures, as well as at room temperature, and analyzed to determine the band structures and identify the impurities and defects contained (62). However, in the case of SiC, the existence of many polytypes and site-dependent impurity levels resulting from the lattice site inequivalence, cubic sites, and hexagonal sites make the luminescence very complicated. Moreover, it has been difficult to analyze the luminescence spectra because of the lack of perfect crystals with very low defect densities and background impurity concentrations. Recently, both highly pure and intentionally doped epilayers have been obtained by CVD. The measurements on these have made it possible to discuss the origins of the luminescence peaks more precisely, which is of interest from the viewpoint of the origin of residual carriers in unintentionally doped SiC. Studies of radiation damage using luminescence measurements have been done because of the interest in damage due to ion implantation and in device tolerance for nuclear irradiation. Luminescence related to irradiation-induced defects will be described in Sec. IV.D. a. Exciton-Related Emission Relatively sharp luminescence lines observed near the band edge arise from the recombination of electron-hole pairs that form bound excitons (BEs) at impurity sites or free-to-bound (FB) transitions that involve the recombination of free electrons (holes) with holes (electrons) bound at neutral acceptors (donors). Figure 12 shows the PL spectrum at 1.96 K for an undoped 3CSiC epilayer grown on Si by CVD (63). In the energy range 2.4–2.2 eV, five sharp lines are seen. Choyke et al. (64) have observed five similar sharp luminescence peaks for a 3C-SiC crystal grown by the Lely method. These peaks have been assigned as the zero phonon line (ZPL, 2.379 eV) and its phonon replicas TA, LA, TO, and LO. They attributed these lines to

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Figure 12 Photoluminescence spectrum of an undoped CVD-grown epilayer of 3C-SiC at 1.96 K. (From Ref. 63.)

recombination of excitons bound at neutral nitrogen donors (nitrogen at carbon site N c ) from the analogy with PL spectra of nitrogen-doped 6H-SiC and 15R-SiC. From the value of the exciton energy gap of 3C-SiC, E gx ⫽ 2.390 eV, determined from the optical absorption measurements, the bound exciton binding energy to N c , E bx ⫽ 11 meV, and the phonon energies for TA, LA, TO, and LO of 46, 79, 94, and 103 meV were obtained (65). Nedzvetskii et al. (66) studied the temperature dependence of optical absorption and luminescence of 3C-SiC and obtained the fundamental energy gap E g ⫽ 2.4018 eV, exciton binding energy E x ⫽ 13.5 meV, and E bx ⫽ 9.1 meV at 4.2 K. Dean et al. (67) obtained the donor ionization energy as 53.6 ⫾ 0.5 meV. However, there is no evidence for the attribution of these five-line PL peaks to nitrogen donors. High-purity 3C-SiC epilayers on Si have been grown by CVD, and their PL spectra have been reported, which are essentially the same as that for bulk 3C-SiC reported by Choyke et al. (64). PL spectra of nitrogen-doped 3C-SiC epilayers have been measured (68). As seen in Fig. 13, weak shoulders are observed on the low-energy side of each phonon replica, which increase with nitrogen doping concentration. Similar peaks have been observed for undoped 3C-SiC epilayers grown with a lower C/Si ratio in the reaction gases in CVD growth (69). These results suggest that the five-line peaks observed for nondoped 3C-SiC cannot be attributed simply to nitrogen-bound excitons (70). The origin of the five lines is still unclear. In the spectra of nitrogen-doped 6H-SiC, several tens of peaks are observed near the band edge around 3 eV (71). These peaks have been attributed to excitons bound at neutral and ionized nitrogen donors and their complexes. Because of the existence of three inequivalent carbon sites, one hexagonal site and two cubic sites, three ZPLs are observed at 3.008, 2.993, and 2.991 eV, respectively. The value for the free exciton band gap is obtained as 3.024 eV at 4.2 K. The values of the exciton binding energy E x; the bound exciton binding energy to N c , E bx; the exciton energy gap E gx; the fundamental energy gap E g; and the exciton binding energy at 4.2 K have been measured for several polytypes and are listed in Table 1 (63). b. Luminescence Related to Donor-Acceptor Pairs It is well known that nitrogen impurities at carbon sites in SiC bring about donor levels and aluminum, gallium, and boron impurities at Si sites bring about acceptor levels. In samples with both donor and acceptor impurities, electrons bound at neutral donors recombine with holes

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Figure 13 Photoluminescence spectra of nitrogen-doped 3C-SiC epilayers at 4.2 K. (From Ref. 68.)

bound at neutral acceptors, which is called donor-acceptor pair (DA pair) recombination. The photon energy of the luminescence for a DA pair is given by (72) E(r) ⫽ E g ⫺ (E D ⫹ E A ) ⫹ (e 2 /εr) ⫺ (e 2 /ε) (a 5 /r 6 )

(1)

where E g is the fundamental energy gap, E D and E A are the isolated donor and acceptor binding energies, respectively, ε is the static dielectric constant, a is the effective van der Waals coefficient for the interaction between a neutral donor and a neutral acceptor, and r is the distance between an isolated neutral donor and acceptor. According to Eq. (1), a series of luminescence peaks are observed and their low-energy limit, r → ∞ in Eq. (1), gives E min ⫽ E g ⫺ (E D ⫹ E A )

(2)

Figure 14 shows the PL spectrum for Al-doped 3C-SiC around 2.2 eV at 6 K (63). Choyke (59) attributed the sharp peaks observed in the figure to nitrogen donor–Al acceptor pair recombinations and obtained E D ⫹ E A ⫽ 310 meV from E g ⫽ 2.4034 meV and E min ⫽ 2.0934 eV. From the measurements at higher temperatures, an emission peak due to the recombination of a free

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Figure 14 Photoluminescence spectrum of an Al-doped 3C-SiC epilayer at 6 K, showing a series of peaks due to DA pair recombination. (From Ref. 63.)

electron with holes bound to Al acceptors (free-to-bound transition), the value E A ⫽ 257 meV has been obtained. From Eq. (2), E D ⫽ 53 meV is obtained, which Choyke and Patrick (73) denoted as the binding energy for nitrogen donors. In cases of polytypes other than 3C, the spectra due to DA pair recombination consist of several series of DA pair luminescences resulting from the inequivalence of the impurity sites. Ikeda et al. (74) have analyzed DA pair luminescence for 3C, 15R, 6H, and 4H-SiC and obtained the donor and the acceptor binding energies. c. Luminescence Related to Deep Levels Due to Transition Metal Impurities Luminescence spectra for 6H-, 4H-, and 15R-SiC doped with Ti and V have been reported (48). The PL spectra of Ti in SiC have been explained by a model in which the silicon-substitutional, isoelectronic neutral Ti (3d 0 ) impurities bind excitons (75). It is expected that Ti impurities act as isoelectronic traps as in the case of nitrogen impurities in GaP, which bring about bright luminescence of GaP emitting diodes. In the 1.3–1.5 µm near-infrared spectral range, emission related to vanadium impurities substituting the various Si sites in the lattice was observed (76,77). The spectra arise from the intra-3d-shell transitions 2E(3d 1 )→ 2T 2 (3d 1 ) of V Si 4⫹. Vanadium impurities have attracted much interest in the role of minority-carrier lifetime killer. d. Raman Scattering and Infrared Absorption Many Raman scattering lines are observed for SiC, reflecting zone folding effects in phonon dispersion curves. These lines can be used to identify the polytype of SiC crystals, as mentioned in Sec. III.A. From the shift of the Raman peaks and the discrepancy of the selection rules in optical transitions, information about the internal stress and crystallinity of SiC crystals, respectively, can be obtained, as mentioned in Sec. III.B. Free carriers from plasmons in semiconductors, which interact with LO phonon modes and form LO phonon–plasmon coupled modes. Figure 15 shows the Raman peak positions for the TO and LO modes as a function of carrier concentration in 3C-SiC epilayers. The frequency of the LO band increases with increasing free carrier density, which shows that the LO-phonon band is coupled with the overdamped plasmon. Yugami et al. (78) have obtained the carrier concentrations by line shape fitting of the coupled modes and compared them with the values derived from Hall measurements. They found good agreement between the values derived by

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Figure 15 Variation of the Raman peak positions for the TO- and LO-plasmon modes with the carrier concentration in 3C-SiC epilayers. The solid lines show the values calculated using the equation driven mainly by the deformation potential and electro-optic mechanisms. (From Ref. 78.)

the two methods. This result suggests that the free carrier concentrations can be estimated by observing LO phonon–plasmon coupled modes in Raman scattering in the carrier concentration range between 10 16 and 10 19 cm ⫺3. B.

Electrical Properties

1. Parameters for the Electrical Properties of SiC SiC has a moderate value of carrier mobility (⬃1,000 cm 2 /V s for electrons at room temperature), which is of the same order as that of Si; a large saturation drift velocity (2.7 ⫻ 10 7 cm/s), which is twice as that of Si and the same as that of GaAs; and a large breakdown field (5 ⫻ 10 6 V/cm), which is one order of magnitude larger than that of Si. The values of some electrical parameters are listed in Table 3, compared with those for Si, GaAs, GaN, and diamond. Values of the saturation electron drift velocity V s for 6H-SiC have been measured by Berman et al. (79) and Muench and Pettenpaul (80). Ferry (81) has calculated theoretically the values of V s for various semiconductors in terms of phonon frequency, as shown in Fig. 16. Figure 17 shows the electric field dependence of electron drift velocity for SiC and various semiconductors. The open circles denote the breakdown field for the respective semiconductor. The figure shows that the breakdown field of SiC is one order of magnitude larger than those for Si and GaAs, and the saturation drift velocity is same as that of GaAs and twice of that of Si. 2. Polytype Dependence of Electrical Properties The values of carrier mobility for n- and p- types and effective mass for electrons and holes in various SiC polytypes are tabulated in the literature (82). The electron mobility differs between

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Table 3 Properties of SiC Compared with Those of Si, GaAs, GaN, and Diamond (Room Temperature) SiC Material

3C

6H

Si

Band gap energy E g (eV) Thermal conductivity κ (W/cm ⋅ K) Mobility (cm 2 /V ⋅ s) µe µh Dielectric constant ε0 ε∞ Electron saturation Drift velocity V s (⫻10 9cm/s) Breakdown field E B (⫻10 5V/cm)

2.20

2.86

1.113

1.428

3.39

4.9

4.9

1.51

0.54

1.3

800 70 9.72 6.52 2.7

40

460 60 9.66a,10.03c 6.52a,6.70c 2.0

25

1500 450 11.4 11.6 1.0

3

GaAs

8500 420 12.91 11.10 2.0

4

GaN

600 100 10.4c,9.5a 5.8c,5.35a 2.7

40

Diamond 5.470 20.9

1800 1600 5.93 5.76 2.5

35

Figure 16 Saturation electron drift velocities of various semiconductors versus the parameter related to energy relaxation. The solid line represents the calculated values. (From Ref. 81.)

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Figure 17 Electric field dependence of electron drift velocity for various semiconductors. The open circles denote the breakdown fields.

the polytypes as a result of the different number of conduction band minima lying at the Brilloiun zone boundary and the difference in effective masses. At around room temperature, the electron mobility is dominated by acoustic phonon and intervalley scattering. 3C-SiC has the highest mobility in SiC polytypes (83), which was expected from its small intervalley scattering and high energy of longitudinal acoustic phonons (84). Except for the neutral impurity scattering, generally, the larger the effective masses, the larger the scattering is. The larger mobility of 15R-SiC compared with 6H is explained by the smaller effective mass of 15R than of 6HSiC (85). High-quality 4H-SiC epilayers have been grown homoepitaxially by chemical vapor deposition (86), and a mobility of 800 cm 2 /V s was obtained (87), which is twice that for 6HSiC. Reflecting the different values of effective masses in different crystal directions, anisotropic electric properties of SiC except for the 3C type have been observed. For 4H-SiC, however, a nearly isotropic electron mobility, µ 芯 /µ 储 , was reported (88). Because of its wide band gap, high, nearly isotropic electron mobility, and the highest breakdown field, the 4H polytype is believed to be superior in applications for electronic devices, compared with 6H polytypes (89,90). The hole mobility, in contrast, does not vary strongly with the polytypes, because the valence band maximum is located at the Γ point for all polytypes. Temperature dependences of intrinsic carrier mobilities for 3C- and 6H-SiC have been calculated theoretically (91,92). Figure 18 shows the calculated and observed values of the electron mobility for 6H-SiC (91). At low temperatures, ionized impurity scattering and neutral impurity scattering dominate the mobility. At around room temperature, piezophonon scattering, acoustic phonon scattering, and intervalley scattering dominate it, and optical phonon scattering dominates it at high temperatures. In the case of SiC, the effect of piezophonon scattering is

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Figure 18 Temperature dependence of the electron mobility for 6H-SiC. The broken lines show the calculated values of the mobility determined by the impurity scattering µ imp , by the piezophonon scattering µ piez , by polar optical phonon scattering µ pol , and by acoustic phonon scattering µ ac . The solid line shows the values for the mobility determined by acoustic phonon and optical phonon scatterings, which is in good agreement with the observed values above room temperature (m* ⫽ 0.2m 0 , N A ⫽ 10 14cm ⫺3, N A /N D ⫽ 0.5). (From Ref. 91.)

small and acoustic phonon scattering and intervalley scattering mainly dominate the mobility at around room temperature. Quantitative fits of the theoretical scattering mechanisms to the experimentally obtained values of the carrier concentrations and mobility as a function of temperature have been carried out for undoped 3C-SiC (93,94). By using a compensation model and assuming Matthiessen’s rule for scattering mechanisms, curve fitting for the temperature dependence of carrier concentration gave an ionization energy of donors of about 20 meV (94–96), which is about a half of that for nitrogen impurities determined by luminescence measurements. This discrepancy will

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be discussed in subsection. 3. Yamanaka et al. (97) reported that the temperature dependence of the Hall mobility µ H (T) cannot be fit by using values of the donor activation energy E d , donor concentration N D , and compensated acceptor concentration N A obtained by fitting the temperature dependence of carrier densities, especially at low temperatures. Tsukioka (98) reported that the introduction of dipole scattering may be able to resolve the contradiction between experimental data for µ H (T) and n(T ). Quantitative fits of theoretical curves to the experimentally obtained n(T ) values have also been carried out for nitrogen-doped 6H- and 4H-SiC (87,99). The presence of two donor levels (∆E N , 1 , N N , 1 ) and (∆E N , 2 ,N N , 2 ) is required to fit the experimental electron concentrations over the entire temperature range. The ionization energies of the donor levels are ∆E N , 1 ⫽ 85.5 meV and ∆E N , 2 ⫽ 125 meV. The ratio of the concentrations of these donors, N N ,1 /N N , 2 is approximately 1 : 2. Hexagonal (h) and cubic (k 1 , k 2 ) lattice sites have a relative abundance of 1 : 2 in the 6H polytype, which is in good agreement with N N , 1 /N N , 2 . Therefore, we can speculate that nitrogen atoms on h sites give donor level 1 and nitrogen on k 1 and k 2 sites give donor level 2. For 4H- SiC, ∆E N , 1 ⫽ 45 meV and ∆E N , 2 ⫽ 100 meV are obtained, and N N , 1 /N N , 2 is approximately 1 : 1, which is in good agreement with a relative abundance of h sites and k sites of 1 :1 in the 4H polytype. The mobilities of 6H and 15R-SiC change with temperature as T ⫺2.0 –T ⫺2.6 (87,100) above room temperature. These changes are steeper than that due to acoustic phonon scattering, T ⫺1.5. This is considered to be due to the contribution of intervalley scattering (100). While 3C-SiC has cubic symmetry, higher crystal symmetry than 6H and 15R, intervalley scattering is restricted by a selection rule (84), and the mobility of 3C-SiC changes with temperature as T ⫺1.5 (101), which is slower in the reduction of mobility at high temperatures. As a result, at high temperatures, 3C-SiC has greater mobility than other polytypes, which is attractive from the viewpoint of the use of SiC devices at high temperatures. 3. Doping Properties One of the attractive characteristics of SiC for device application is easy control of the conduction type by doping, which is different from the situation with other wide band gap semiconductors, such as III-V nitrides, II-VI compounds, and diamond. n-type crystals can be obtained by doping with nitrogen in the range between 2 ⫻ 10 16 and 1 ⫻ 10 19cm ⫺3 and p-type crystals by doping with column III elements, B, Al, and Ga, in the range between 2 ⫻ 10 16 and 1 ⫻ 10 18 cm ⫺3 for 4H and 6H-SiC (102). As the diffusion coefficient of impurities in SiC crystals is very low, doping is done by introducing impurities in the reaction chambers or crucibles during growth. Ion implantation is an attractive doping method for device processes. However, annealing at high temperatures, more than 1500°C, is required to recover the crystallinity (103), which prevents the use of ion implantation as a doping process. Implantation at temperatures around 500°C, called ‘‘hot implantation,’’ has been reported to be useful in reducing radiation damage by ion implantation, as shown in Fig. 19 (104). However, to activate the impurities, annealing at temperatures higher than 1400°C is required (105). Acceptor levels with Al, B, and Ga in SiC are so deep that the activation rates at room temperature are very low. For example, in the case of Al, the activation energy of acceptor levels is around 160 meV, which is much larger than kT at room temperature, 25 meV, resulting in a low activation rate, as low as 0.01. Therefore, high levels of doping more than two to three orders of magnitude higher than the carrier density, is required. It has been found that the doping efficiency depends on the C/Si ratio in the reaction gas (106). For nitrogen doping, a smaller ratio brings about a higher doping efficiency, and for Al

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Figure 19 Dependence of the density of residual defects in N 2 ⫹-implanted 3C-SiC on implantation temperature. (From Ref. 104).

doping, a higher ratio brings about a higher doping efficiency. This phenomenon is explained as follows. Nitrogen atoms occupy C sites to form donor levels. When the C concentration at the growth surface is small, nitrogen atoms can easily occupy C sites instead of C atoms. In the case of Al doping, Al atoms occupy Si sites to become acceptor impurities, which is easy when the Si concentration at the surface is low. Therefore, this phenomenon is called ‘‘site competition epitaxy.’’ This technique affords intermediate doping control as well as the production of degenerately doped (⬃10 19 cm ⫺3 ) and very low doped n-type and p-type epilayers (⬃10 14 cm ⫺3 ). Semi-insulating 6H-SiC crystals have been achieved by using controlled doping with deeplevel vanadium impurities (107). The resistively is 10 15 Ω cm at room temperature and 10 7 Ω cm even at 300°C. The semi-insulating behavior is attributed to compensation of residual acceptors by the deep-level vanadium V 4⫹ (3d 1 ) donor located near the middle of the band gap. 4. Origin of the Residual Carriers in SiC It is well known that unintentionally doped SiC crystals grown by LPE, CVD, and the sublimation method show n-type conduction. For example, undoped 3C-SiC epilayers grown by CVD usually have a residual carrier (electron) concentration of the order of 10 16 cm ⫺3. The origin of the residual carriers has been considered to be nitrogen impurities because the existence of nitrogen impurities in SiC crystals has been shown by ESR measurements, which suggest no impurity inclusion other than nitrogen in SiC epilayers. However, some results inconsistent with the attribution to nitrogen impurities have been reported (55,63). Curve fitting for the temperature dependence of the carrier concentration of 3C-SiC epilayers gives a donor ionization energy

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of about 20 meV (94–96), which is far different from that for nitrogen impurities determined by luminescence measurements, 53 meV (64,67). Segall et al. (95) tried to explain this discrepancy by introducing the idea that the ionization energy for the nitrogen impurity level E N depends on the donor concentration N D , as E D (N D ) ⫽ E D ⫺ αN D 1/3, following an empirical rule given by Pearson and Bardeen (108). A curve fit gives α ⫽ 2.6 ⫻ 10 ⫺5 meV cm and E N (0) ⫽ 48 meV, which is nearly the same as the generally accepted value of E D for nitrogen donors. Yamanaka et al.(97), however, measured the temperature dependence of carrier concentrations and mobilities of undoped and nitrogen-doped 3C-SiC and showed that the dependence of ionization energy on carrier concentration is different in undoped and nitrogen-doped SiC. Okumura et al. (68) and Freitas et al. (69) have shown that the nitrogen-doped 3C-SiC epilayers show other PL peaks, about 8 meV lower than that observed in undoped 3C-SiC epilayers as discussed in Sec. IV.A.3. Nashiyama et al. (56,57) and Okumura et al. (55,109) studied the origin of residual carriers in 3C-SiC epitaxially grown by CVD on Si by the Hall effect, ESR, and SIMS methods. Three types of ESR signals were observed in the epilayers, including a three-line and a narrow singleline ESR signal associated with nitrogen impurities and a broad single-line ESR signal, as shown in Fig. 8. An apparent correlation was found between residual carrier density and total spin density. These results suggest that nitrogen impurities exist in the epilayer. However, the total spin density associated nitrogen impurity is usually smaller than the residual carrier density, and a three-line signal disappears at around 40 K, which does not coincide with the temperature dependence of carrier density. Undoped 3C-SiC epilayers with a residual carrier density of about 1 ⫻ 10 15 cm ⫺3 have been obtained by using highly pure SiH 4 (5N) and C 3 H 8 (6N) source gases and a very clean growth system preevacuated below 10 ⫺8 torr (57). Epilayers having carrier densities as low as 10 15 cm ⫺3 showed no significant ESR signals associated with nitrogen. These results indicate that residual carriers in 3C-SiC with carrier concentration higher than 10 16 cm ⫺3 originate partly from nitrogen impurities. ESR centers corresponding to the broad single-line signal, which is presumably associated with some defects, may be the main origin for the residual carriers in 3C-SiC with carrier concentration less than 10 16 cm ⫺3. Nashiyama et al. (56) have explained both the temperature dependence of carrier concentration and the ESR signal in 3CSiC epilayers simultaneously, assuming two donor levels and compensated acceptor levels. C.

Thermal Properties

SiC is thermally stable up to temperatures higher than 1500°C, and thus SiC has been used for heaters and firebricks. At higher temperatures, SiC does not melt but sublimates under atmospheric pressure. The predominant species of evaporated gas molecules from SiC are Si, SiC 2 , and Si 2 C (110). Scace and Slack (111) have reported that SiC possesses a peritectic point at 2830 ⫾ 40°C at 35 atm. The thermal conductivity of SiC is around 5 W/cm K at room temperature, which exceeds that of not only other semiconductors, such as Si and GaAs, but also the good thermal conducting materials Cu, BeO, Al 2 O 3 , and AlN (112). Figure 20 shows the thermal conductivities of various semiconductors as a function of Mδθ 3 , where M is the mean atomic mass, δ 3 the mean volume of atoms in the crystal, and θ the Debye temperature (113). The figure suggests a linear relationship between thermal conductivity κ and Mδθ 3. The thermal conductivity depends on polytype, doping, and temperature. In the low-temperature regime, all of the heat flow is due to phonons, and one expected κ ⬃ T 3. However, the observed κ for SiC is characterized by a T 2 dependence, except for very pure samples. The T 2 dependence is explained by the additional thermal resistance due to scattering of phonons by electrons in an impurity (nitrogen) band (114). The thermal expansion coefficient of SiC also depends on polytype and temperature. Val-

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Figure 20 Variation of thermal conductivities of various semiconductors as a function of Mδθ 3, where M is the mean atomic mass, δ 3 the mean volume of atoms in the crystal, and θ the Debye temperature. (From Ref. 113.)

ues of 3.3–3.7 ⫻ 10 6 deg ⫺1 at room temperature have been reported for 3C and 6H-SiC (115), smaller than the value for Si but larger than that for GaAs. This discrepancy in thermal expansion coefficients of Si and SiC brings about large internal stress in 3C-SiC epilayers grown on Si substrates. D.

Radiation Damage

Studies of radiation damage in semiconductor lattices give information useful not only for investigating device tolerance of nuclear irradiation but also for knowing the radiation damage in device processes, such as ion implantation, e-beam lithography, and reactive ion etching. The studies of radiation damage are also important from the viewpoint of investigating the nature of native crystal defects. SiC has been said to be tolerant of nuclear irradiation compared with Si. However, it has not been clarified why SiC is tolerant and how tolerant it is. In 1954, the first report on radiation damage of SiC was published, and in the latter half of the 1960s many papers appeared on radiation damage, which have been reviewed by Babcock (116), Campbell and Chang (117), and Choyke (118). These papers treated the lattice swelling, changes of carrier concentration, and I-V characteristics of pn junctions on neutron irradiation mainly in bulk α-SiC, from the interest in the use of neutron and charged particle detectors. The data on the carrier removal rate and defect introduction rate for neutron and proton irradiation were rather scattered, and it is hard to insist on the tolerance of SiC for neutron and proton irradiation compared with other

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Figure 21 Electron irradiation effects on the carrier density n and the Hall mobility µ at room temperature for 3C-SiC and Si. n 0 and µ 0 indicate the carrier density and the mobility before irradiation, respectively. (From Ref. 121.)

semiconductors. However, it can be said that SiC is tolerant by one to two orders of magnitude for irradiation with these particles when we use SiC detectors at high temperatures, because SiC is stable up to high temperatures and radiation damage is recovered at high temperatures. High crystalline quality SiC epilayers have been obtained by CVD, and more reliable data have been reported on the radiation damage in SiC using these epilayers (119,120). Figure 21

Figure 22 ESR spectra of 3C-SiC irradiated with 1-MeV electrons at 3 ⫻ 10 18 cm 2. The spectra were observed at room temperature (a) and at 60 K (b), when a magnetic field was applied parallel to the 〈011〉 axis. The arrows indicate five lines of the T1 center.

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Figure 23 Temperature dependence of the Hall mobilities for as-grown, electron-irradiated, and annealed 3C-SiC epilayers. (From Ref. 121.)

shows the changes of carrier density and carrier mobility of 3C-SiC epilayers on irradiation with 1-MeV electrons compared with those for Si (121). The figure suggests that the carrier removal rate and mobility reduction rate of SiC are both smaller than those of Si, which indicates that SiC is more tolerant than Si. The annealing behaviors of the radiation-induced damage have been studied by use of ESR, Hall, and PL measurements (121,122). Five-line isotropic ESR centers as well as four anisotropic centers have been observed for 3C-SiC irradiated with 1MeV electrons, as shown in Fig. 22. Five-line centers, called T1 centers, have three annealing stages, 150, 350, and 750°C, and disappear at around 800°C. As this annealing behavior is similar to that of the carrier removal rate and mobility reduction rate, it is considered that T1 centers introduced by irradiation act as electron traps and the annealing out of T1 centers brings about recovery of the carrier density and mobility. Figure 23 shows the temperature dependence of the mobilities. The mobilities decrease in the low-temperature region, which can be explained in terms of charged electron traps acting as electron scattering centers like ionized impurity centers. T1 centers have been also observed for 3C-SiC irradiated with 2-MeV protons (123). The generation rates of T1 centers per fluence were obtained as 0.02 and 200 cm ⫺3 for 1-MeV electrons and 2-MeV protons, respectively, which are almost the same as the ratio of defects induced by the knock-on of atoms from the lattice sites. The origin of the T1 center has been studied by measurements of the angular dependence

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Figure 24 ESR spectrum at 10 K of 3C-SiC irradiated with 2-MeV protons at 1 ⫻ 10 16cm ⫺2 when the magnetic field was applied parallel to the 〈100〉 axis. The T1 spectrum consists of the five lines (a,b,c) indicated by the solid-line arrows and the satellite five lines (d,e,f) indicated by the broken-line arrows. (From Ref. 124.)

of ESR spectra (124) and positron annihilation measurements (125). Figure 24 shows the widerange ESR spectrum for 3C-SiC irradiated by 2-MeV protons. Three sets of five lines can be seen. From the intensity ratio and the angular dependence of these lines, five lines can be explained quantitatively by the hyperfine interaction of paramagnetic electrons at the Si lattice sites with one or two 29Si (I ⫽ 1/2, existing 4.7%) nuclear spins at 12 Si sites around the Si site and three sets can be explained by the modulation of one 13C (4%) nuclear spin at four C sites around the Si site. In Fig. 25, the calculated values of intensity ratio are given, which are in good agreement with those observed. Therefore, the T1 center is presumably due to electrons trapped at Si vacancies.

Figure 25 Schematic representation of the ESR lines calculated from simultaneous hyperfine interactions of a paramagnetic electron with 13C and 29Si nuclei. Terms in parentheses indicate the interaction types exhibiting each ESR line. (From Ref. 124.)

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Positron annihilation experiments have also supported this conclusion (125). In the fluence range above 5 ⫻ 10 16 e/cm 2, the S parameter, defined as the integral of the γ-ray intensity in the central energy region (511 ⫾ 0.5 keV) divided by the total intensity of annihilation γ-rays, increases with increasing electron fluence; i.e., narrowing of the Doppler-broadened energy spectrum of annihilation γ-rays was observed. This electron fluence dependence of the narrowing is explained by the introduction of monovacancies in 3C-SiC by the irradiation. Radiation damage caused by ion implantation as well as fast particle irradiation has been studied by use of PL measurements. Choyke (118) reviewed the PL spectra observed for SiC samples implanted with a variety of ions and annealed. Two dominant peaks have been observed. These peaks are referred to as D 1 and D 2 ; their wavelengths do not depend on the implanted ion species, and they become large with annealing temperature and dominate the luminescence spectra even above 1600°C. From the stability of these centers at high temperatures, D 1 and D 2 are thought to originate from defect complexes, divacancies, and carbon diinterstitials. Freitas

Figure 26 Photoluminescence spectra at 4.2 K for (a) an as-grown 3C-SiC epilayer and (b) an epilayer irradiated with 1-MeV electrons at 2 ⫻ 10 17 cm ⫺2. The impurity-bound exciton (BE)–related zero-phonon line (ZPL) and its phonon replicas are represented by arrows with the phonon combinations labeled in (a). The defect-related D 1 line and G band in as-grown 3C-SiC are also shown. Irradiation-induced lines labeled E, D 1 , α 1 , α 2 , β 1 , β 2 , and γ are indicated by arrows with the emission energies in (b).

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et al. (126) have reported their relative intensity to the edge emission increase with increasing annealing temperature. Itoh et al. (122) have measured PL spectra of 3C-SiC epilayers irradiated with 1-MeV electrons. They found a pronounced peak at E ⫽ 1.913 eV, as well as a D 1 center, in the PL spectrum for electron-irradiated 3C-SiC (Fig. 26), which disappears on annealing at 700°C. As this annealing behavior is quite similar to that of T1 ESR centers, they attributed the PL peak at 1.913 eV to T1 centers or Si vacancies. With γ-ray irradiation up to 10 7 Gy, no appreciable ESR center has been observed, which

Figure 27 Absorbed dose dependence of the radiation-induced (a) interface traps ∆N it and (b) oxide traps ∆N ot in 3C-SiC MOS capacitors, as well as those of an Si MOS capacitor, irradiated under opencircuit conditions. (From Ref. 128.)

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suggests that no lattice defect is introduced in SiC crystals by γ-ray irradiation up to 10 7 Gy. However, this does not imply radiation hardness of devices using SiC for γ-ray irradiation. Nashiyama et al. (127) have studied the effect of γ-ray irradiation of up to 10 5 Gy for 3C-SiC MOSFETs and MESFETs. In case of MESFETs, little change of drain current was observed with γ-ray irradiation, which suggests that SiC MESFETs are quite tolerant of γ-ray irradiation up to 10 5 Gy. However, in the case of MOSFETs, the drain current and, therefore, transconductance decreased markedly on γ-ray irradiation. These changes are considered to be due to an increase in the interface trap density N it and oxide trapped charges N ot . Yoshikawa et al. (128) have obtained the changes of N it and N ot with absorbed dose, separately, by use of C-V measurement at high frequency and pulsed C-V measurements for 3C-SiC MOS structures. Figure 27 shows the absorbed dose dependence of the radiation-induced interface traps ∆N it and oxide trapped changes ∆N ot in 3C-SiC MOS capacitors irradiated with 60Co γ-rays, as well as those in an Si MOS capacitor. Both ∆N it and ∆N ot start to change at around 10 4 Gy. In the case of Si MOS, they start to increase at around 100 Gy. Radiation effects on 3C-SiC MOS structures depend on the oxidation process. The filled circles in Fig. 27 show those for 3C-SiC MOS capacitors fabricated by pyrogenic oxidation at 1100°C. The generation of interface traps and oxide trapped charges is much suppressed in the case of pyrogenic oxidation. These results suggest that with 3C-SiC MOS structures, especially those with pyrogenic oxide, it is hard to generate interface traps and oxide-trapped charges compared with Si MOS structures. This supports reasonably the fact that 3C-SiC MOSFETs have significant tolerance against γ-ray irradiation compared with Si MOS devices.

V.

CONCLUSION

Epitaxial growth, characterization, and physical properties of SiC have been reviewed. The most pronounced characteristic of SiC is the existence of polytypes, and the proper growth methods and properties depend strongly on the polytypes. High-quality epilayers of 3C, 6H, and 4H-SiC have been grown, mainly by CVD, and by using these epilayers, physical properties have been elucidated. However, the quality of the SiC crystals is still not enough to determine the material parameters. Therefore, the growth of higher quality crystals of SiC is needed, not only for device application but also for the clarification of physical properties. In the case of SiC polytypes other than 3C, 6H, and 4H-SiC, it is necessary to grow single-phase single crystals to elucidate their physical properties.

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86. O Kordina, A Henry, JP Bergman, NT Son, WM Chen, C Hallin, E Janzen. High quality 4H-SiC epitaxial layers grown by chemical vapor deposition. Appl Phys Lett 66:1373, 1995. 87. WJ Schaffer, HS Kong, GH Negley, JW Palmour. Hall effect and CV measurements on epitaxial 6H- and 4H-SiC. Institute of Physics Conference Series No. 137. London: IOP, 1994, p 155. 88. N Son WM Chen, O Kordina, AO Konstantinov, B Monemar, E Janzen. Electron effective masses in 4H SiC. Appl Phys Lett 66:1074, 1995. 89. JW Palmour, CE Weitzel, K Nordquist, CH Carter Jr. Silicon carbide microwave FETs. In: Institute of Physics Conference Series No. 137. London: IOP, 1994, p 495. 90. PA Ivanov, NS Savkina, TP Samsonova, VN Panteleev, VE Chelnokov. Junction field-effect transistor based on 4H-silicon carbide. In: Institute of Physics Conference No. 137. London: IOP, 1994, p 593. 91. HJ van Daal. Mobility of charge carriers in silicon carbide. Philips Res Rep Suppl No 3:1, 1965. 92. A Suzuki, A Uemoto, M Shigeta, K Furukawa, S Nakajima. Temperature dependence of electrical properties of non-doped and nitrogen-doped beta-SiC single crystals grown by chemical vapor deposition. Appl Phys Lett 49:450, 1986. 93. A Suzuki, A Ogura, K Furukawa, Y Fujii, M Shigeta, S Nakajima. Analysis of temperature dependence of Hall mobility of nondoped and nitrogen-doped β-SiC single crystals grown by chemical vapor deposition. J Appl Phys 64:2818, 1988. 94. M Yamanaka, H Daimon, E Sakuma, S Misawa, S Yoshida. Temperture dependence of electrical properties of n- and p-type 3C-SiC. J Appl Phys 61:599, 1987. 95. B Segall, SA Alterovitz, EJ Haugland, LG Matus. Compensation in epitaxial cubic SiC films. Appl Phys Lett 49:584, 1986; comment on ‘‘Temperature dependence of electrical properties of nondoped and nitrogen-doped beta-SiC single crystals grown by chemical vapor deposition,’’ Appl Phys Lett 50:1533, 1987. 96. WE Carlos, WJ Moore, PG Siebenmann, JA Freitas Jr, R Kaplan, SG Bishop, PER Nordquist Jr, M Kong, RF Davis Residual donors in β-SiC films. Mater Res Soc Symp Proc 97:253, 1987. 97. M Yamanaka, H Daimon, E Sakuma, S Misawa, K Endo, S Yoshida. Temperature dependence of electrical properties of nitrogen-doped 3C-SiC. Jpn J Appl Phys 26:L533, 1987. 98. K Tsukioka. Electron scattering mechanisms in β-SiC. Technical Digest of International Conference on SiC and Related Materials, Kyoto, 1995, p 294. 99. G Pensl, WJ Choyke. Electrical and optical characterization of SiC. Physica B185:264, 1993. 100. L Patrick. Electron mobilities in SiC polytypes. J Appl Phys 38:50, 1967. 101. K Sasaki, E Sakuma, S Misawa, S Yoshida, S Gonda. High-temperature electrical properties of 3C-SiC epitaxial layers grown by chemical vapor deposition. Appl Phys Lett 45:72, 1984. 102. RA Stein, R Rupp, KO Dohnke, J Vo¨lkl, D Stephani, C Ha¨ßlen, G Pensl. Recently, control of carrier concentration in the range 5 ⫻ 10 15 –1 ⫻ 10 19cm ⫺3 has been reported (6th International Conference on SiC and Related materials, Kyoto, 1995). 103. OJ Marsh. Ion implantation in SiC. In Ref.2, p 471. 104. H Itoh, Y Aoki, M Yoshikawa, I Nashiyama, H Okumura, S Yoshida. Characterization of deffects in hot-implanted β-SiC. Proceedings of 13th Symposium on Materials Science and Enginering Research Center of Ion Beam Technology, Hosei University, 1994, p 75. 105. M Ghezzo, DM Brown, E Downey, J Kretchmer, W Hennessy, DL Polla, H Bakhru. Nitrogenimplanted SiC diodes using high-temperature implantation. IEEE Electron. Device Lett 13:639, 1992. 106. DJ Larkin, PG Neudeck, JA Powell, LG Matus. Site-competition epitaxy for controlled doping of CVD silicon carbide. Institute of Physics Conference Series No. 137. London IDP, 1994, p 51. 107. HM Hobgood, RG Glass, G Augustine, RH Hopkins, J Jenny, M Skowronski, WC Mitchel, M Roth. Semi-insulating 6H-SiC grown by physical vapor transport. Appl Phys Lett 66:1364, 1995. 108. GL Pearson, J Bardeen. Electrical properties of pure silicon and silicon aloys containing boron and phosphorus. Phys Rev 75:865, 1949. 109. H Okumura, H Itoh, I Nashiyama, S Yamasaki, S Misawa, S Yoshida. Characterization of 3C-SiC epilayers by pulsed electron spin resonance. Mater Sci Eng B11:31, 1992. 110. J Drowart, G De Maria, MG Inghram. Thermodynamic study of SiC utilizing a mass spectrometer. J Chem Phys 29:1015, 1958.

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111. RI Scace, GA Slack. The Si-C and Ge-C phase diagrams. In Ref.1, p 24. 112. GA Slack. Thermal conductivity of pure and impure silicon, silicon carbide and diamond. J Appl Phys 35:3460, 1964. 113. GA Slack. Nonmetallic crystals with high thermal conductivity. J Phys Chem Solids 34:321, 1973. 114. D Morelli, J Heremans, C Beetz, WS Woo, G Harris, C Taylor. Carrier concentration dependence of the thermal conductivity of silicon carbide. In: Institute of Physics Conference Series No. 137. London: IOP, 1994, p 313. 115. A Taylor, RM Jones. The crystal structure and thermal expansion of cubic and hexagonal silicon carbide. In Ref.1, p 147. 116. R Babcock. Radiation damage in SiC. IEEE Trans Nucl Sci NS-12:43, 1965. 117. B Campbell, HC Chang. Silicon carbide junction devices. In: RK Willardson, AC Beer, eds. Semiconductors and Semimetals. Vol 7. New York: Academic Press, 1971, p 625. 118. WJ Choyke. A review of radiation damage in SiC. Inst Phys Conf Ser No. 31:58, 1977. 119. V Nagesh JW Farmer, RF Davis, HS Kong. Defects in neutron irradiated SiC. Appl Phys Lett 50: 1138, 1987. 120. I Nashiyama, T Nishijima, E Sakuma, S Yoshida. Deutron channeling for defect analysis of silicon carbide. Nucl Instrum Methods Phys Res B33:59, 1988. 121. H Itoh, M Yoshikawa, I Nashiyama, S Misawa, H Okumura, S Yoshida. Electron irradiation effects on CVD-grown 3C-SiC epilayers. Springer Proceedings in Physics 56, Amorphous and Crystalline Silicon Carbide III, 1992, p 143. 122. H Itoh, M Yoshikawa, I Nashiyama, H Okumura, S Misawa, S Yoshida. Photoluminescence of radiation induced defects in 3C-SiC epitaxially grown on Si. J Appl Phys 77:837, 1995. 123. H Itoh, M Yoshikawa, I Nashiyama, S Misawa, H Okumura, S Yoshida. Electron spin resonance study of defects in CVD-grown 3C-SiC irradiated with 2MeV protons. J Electron Mater 21:707, 1992. 124. H Itoh, M Yoshikawa, I Nashiyama, S Misawa, H Okumura, S Yoshida. Radiation induced defects in CVD-grown 3C-SiC. IEEE Trans Nucl Sci 37:1732, 1990. 125. H Itoh, M Yoshikawa, L Wei, S Tanigawa, I Nashiyama, S Misawa, H Okumura, S Yoshida. Positron annihilation and electron spin resonance of electron-irradiated 3C-SiC. Mater Res Soc Symp Proc 262:331, 1992. 126. JA Freitas Jr, SG Bishop, JA Edmond, J Ryu, RF Davis. Photoluminescence spectroscopy of ionimplanted 3C-SiC grown by chemical vapor deposition. J Appl Phys 61 : 2011, 1987. 127. I Nashiyama, M Shinohara, T Matsumoto, K Endo, E Sakuma, S Misawa, H Okumura, S Yoshida. Gamma-ray irradiation effects of 3C-SiC devices. In: GL Harris, CYW Yang, ed., Springer Proceedings in Physics 34, Amorphous and Crystalline Silicon Carbide. Berlin: Springer-Verlag, 1989, p 123. 128. M Yoshikawa, H Itoh, Y Morita, I Nashiyama, S Misawa, H Okumura, S Yoshida. Effects of gamma-ray irradiation on cubic silicon carbide metal-oxide-semiconductor structure. J Appl Phys 70:1309, 1991.

20 Silicon Carbide Power Electronic Devices B. Jayant Baliga North Carolina State University, Raleigh, North Carolina

I.

INTRODUCTION

Semiconductor devices are required for a large variety of power electronics applications. In fact, it is recognized by the power electronics community that the growth in ratings and improvements in performance of these systems are strongly dependent on the availability of semiconductor devices with better electrical characteristics. This has motivated enhancement of the performance of devices by the industry. The blocking voltage and current-handling capability demanded from a power semiconductor switch for some prominent applications are shown in Fig. 1. At relatively low blocking voltages (under 100 V) there are important applications in power supplies [e.g., for integrated circuits (ICs) used in computers and their peripherals] and multiplex-bus automotive electronics systems. These applications require significant current levels because a large number of ICs are usually connected to the power supply in computers and because typical lamps and motors in cars demand up to 10 A during operation. The other applications fall on a trajectory of increasing voltage and current. At the low-power end of this spectrum, displays and telecommunication needs can be satisfied by using power ICs that monolithically integrate power devices with their control circuits, as well as CMOS encode-decode and bipolar analog protection circuitry. At medium power levels, the application needs for factory automation (robotics) systems and motor control (heating, ventilating, air-conditioning) systems are satisfied at present by using discrete power devices driven by high-voltage ICs. For the high power levels typical of traction (streetcars and electric locomotives) and HVDC (power transmission and distribution) systems, discrete thyristors have been developed with single devices capable of handling over 1000 A and blocking over 6000 V. From Fig. 1 it is obvious that the demands of power electronic systems require a very broad range of operating voltages and currents for the power switching devices. At present, only silicon devices are available for this purpose. This chapter discusses the benefits of development of power switches from silicon carbide and explores the merits of various device options.

II. FIGURE OF MERIT The forward voltage drop of a device determines its on-state power loss and hence the efficiency of power electronic systems in which it is utilized. It is therefore desirable to reduce the internal 477

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Figure 1 Ratings for power devices required for various power electronic applications.

device resistances to reduce the forward voltage drop. In order to analyze the forward voltage drop of power devices, a fundamental relationship between the specific on-resistance of the drift region of a power semiconductor device and the material properties was first derived more than 15 years ago (1): R on,sp ⫽

4BV 2 εsµE 3c

(1)

Based on this equation, Baliga’s figure of merit (BFOM) has been defined as (2) BFOM ⫽ εsµE 3c

(2)

which can be used to compare the relative merits of various semiconductor materials for power device development. Using the BFOM, it can be concluded that semiconductors with high breakdown electric field strength are favored.

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Figure 2 Comparison of the critical electric field for silicon carbide and silicon.

III. RELEVANT PROPERTIES OF SILICON CARBIDE One attractive property of silicon carbide is the relatively high breakdown electric field strength for the various polytypes. The critical electric field for breakdown is a function of the doping concentration in the drift region (3). A comparison of the reported (4,5) variation of the critical electric field (E c ) for the primary polytypes (6H, 4H, and 3C) and silicon is provided in Fig. 2. In general, the breakdown electric field for SiC is a factor of 7 to 8 times larger than for silicon at the same doping concentration. However, it is misleading to use this ratio in Eq. (2) because the doping concentration for the SiC device is much higher than for the silicon device for the same breakdown voltage. When this is taken into account, a much larger figure of merit is predicted (5). The other important semiconductor material parameter required for analysis of the R on,sp and BFOM is the mobility. Because the electron mobility is larger than that of holes, it is relevant to consider only n-type drift regions. A comparison of the mobility of electrons in the three SiC polytypes (6) with that in silicon is provided in Fig. 3. In general, the mobilities in SiC are lower than those in silicon, offsetting some of the benefits of the higher breakdown electric field strength.

IV. SPECIFIC ON-RESISTANCE OF DRIFT REGION Using the critical electric field and mobility values shown in the figures, the specific on-resistance can be calculated for each breakdown voltage. A comparison of the specific on-resistance

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Figure 3 Comparison of the electron mobility for silicon carbide and silicon.

calculated for the three polytypes with that for silicon is provided in Fig. 4. From this plot, it can be concluded that the specific on-resistance of the drift region for all three polytypes lies within a factor of 2, which is within the range of uncertainty created by the relatively sparse data reported for E c and mobility for the SiC polytypes. More important, a conclusion that can be derived from this plot is that the specific on-resistance of the drift region for SiC is about 200-fold smaller than that for silicon devices with the same breakdown voltage. In order to gain a good perspective on the implications of the lower specific on-resistance for SiC drift regions, it is beneficial to compare the on-state voltage drop for a 5000-V SiC field effect transistor (FET) with that for the silicon Gate Turn-Off Thyristor (GTO) (the best commercially available silicon bipolar power switch). The on-state operating point for any power switch is decided by the maximum power loss that can be tolerated. For silicon devices in typical packages, this power dissipation is about 100 W/cm 2. Although a higher value may be anticipated for SiC because of the lower leakage currents arising from its wider band gap structure, it will be assumed here that the power dissipation is the same as for a silicon device. The operating points for the SiC FET and the silicon GTO can then be compared with the aid of Fig. 5. The silicon GTO operates at a current density of 35 A/cm 2 with an on-state voltage drop of 3.5 V. In comparison, the SiC FET operates at a current density of 100 A/cm 2 with an onstate voltage drop of only 1 V. Thus, the analysis predicts a greatly reduced on-state power loss (factor of 3.5) in systems together with the benefits of a smaller (factor of 3.5) device area. In addition, the SiC FET will be much easier to control because it does not require the large

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Figure 4 Comparison of the specific on-resistance of the drift region for silicon carbide and silicon.

(typically one-third of the on-state current) gate drive current of the GTO, it will have a very fast switching time (0.1 µs versus 10 µs for the GTO) because of majority carrier transport, and it will have a very large forward-biased safe operating area allowing snubberless operation in hard switching Pulse Width Modulation (PWM) circuit topologies. For high-voltage applications, the silicon Insulated Gate Bipolar Transistor (IGBT) structure has been widely accepted for applications, and many MOS-gated thyristors are under development (3). Although development of similar MOS-bipolar structures from SiC has been proposed (7), this approach is flawed because of the very large built-in potential of the P-N junction in SiC, which makes the onstate voltage drop for these structures much larger than for the SiC field effect transistors.

V.

IDEAL EDGE TERMINATION

In the preceding section, the SiC FET was compared with a silicon GTO using the ideal specific on-resistance of the drift region. In order to be able to exploit the benefits of the low drift region resistance for SiC, it is essential that the breakdown voltage of devices not become limited by the edge termination. Many edge terminations have been proposed and examined for silicon devices that allow nearly ideal breakdown voltages to be achieved (3). In principle, the same techniques should also work with SiC. However, the low diffusion coefficients for dopants in

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Figure 5 Comparison of the forward conduction characteristics of a 5000-V SiC FET with that of a silicon 5000-V GTO.

SiC and the small depletion region widths preclude the development of the commonly used multiple floating diffused field rings for silicon devices. Experiments performed using multiple floating metal field rings and the resistive field plate structure have succeeded is producing only 50% of the ideal breakdown voltage (8). A nearly ideal breakdown voltage was achieved in SiC Schottky barrier rectifiers by ion implantation of argon at the periphery to create a high-resistivity amorphous layer (9) as shown in Figs. 6 and 7. The presence of the high-resistivity layer reduces electric field crowding at the edges of the metal because of lateral spreading of the potential as indicated by the depletion layer boundary. This potential spreading has been confirmed by Electron Beam Induced Current (EBIC) measurements (10). Numerical simulations of this edge termination structure indicate that deep-level acceptor centers formed by the ion implant damage are responsible for the formation of the high-resistivity layer. The deep acceptor level must be located at least 0.6 eV below the conduction band with a concentration several orders of magnitude greater than the doping concentration for the potential spreading to occur. Such deep acceptor levels have indeed been detected in the argon-implanted layer by Deep Level Transient Spectroscopy (DLTS) measurements (11). This edge termination should be effective in all wide band gap semiconductors and be generally applicable to rectifiers, FETs, and other high-voltage devices.

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Figure 6 Argon-implanted edge termination for SiC devices for obtaining nearly ideal breakdown voltages.

Figure 7 Measured breakdown voltage as a function of the argon ion implantation dose.

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VI. UMOSFET STRUCTURE AND DESIGN The DMOS structure (3) is at present the most widely commercially available silicon power MOSFET. The silicon UMOSFET structure (3) has been commercially introduced because of its significantly superior specific on-resistance. This improvement arises from a combination of the higher channel density and the elimination of the JFET component of the on-resistance within the DMOS structure. In the case of SiC, the fabrication of the DMOS structure is not practical because of the very low diffusion coefficients for dopants at temperatures at which the refractory gate (polysilicon) is stable. The most viable power MOSFET structure from SiC is therefore the UMOS structure shown in Fig. 8. In the case of SiC devices, the P-base and N⫹ source regions can be fabricated using multiple epitaxial growth steps. The electric field distribution in the UMOSFET during the blocking mode of operation is depicted on the left-hand side in Fig. 8. Note that peak electric field occurs at the junction with the depletion layer extending into the P-base and N-drift regions. In the case of silicon devices, the doping concentration of the N-drift region must be low to obtain even relatively small breakdown voltages. For example, a breakdown voltage of 100 V requires a doping concentration of the N-drift region below 5 ⫻ 10 15 cm ⫺3. Because the peak P-base doping concentration must be 1 ⫻ 10 17 cm ⫺3 to obtain an acceptable threshold voltage of 2 V, most of the depletion extends in the N-drift region. In contrast, the doping concentration in the N-drift region for SiC devices is much larger, leading to large depletion extension into the P-base region. In order to prevent reach-through breakdown, the thickness of the P-base region must be made larger than for a silicon device. This can add a significant channel resistance contribution to the SiC UMOSFET, as discussed later. Another important consideration during the design of the SiC UMOSFET is the high electric field created at the sharp corners located at the bottom of the U-shaped gate regions. In addition to producing premature breakdown in the semiconductor, this produces a high electric field in the gate insulator (typically silicon dioxide). In accordance with Gauss’s law, the electric field in the oxide will be higher than that in the semiconductor by a factor of 3. When the maximum electric field (E m ) approaches the critical electric field (about 2 ⫻ 10 5 V/cm) for silicon devices, the electric field in the gate oxide remains below its breakdown field strength

Figure 8 The power UMOSFET structure and the electric field profile in the blocking state.

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(about 1 ⫻ 10 7 V/cm). However, in the case of SiC, when the maximum electric field approaches the critical electric field (about 3 to 4 ⫻ 10 6 V/cm), the electric field in the oxide can exceed its breakdown strength, leading to catastrophic failure. It is therefore imperative that the gate insulator have a large dielectric constant to reduce the electric field. The specific on-resistance of the UMOSFET can be analyzed by taking into account the various components of the resistance in the current flow path between the source and the drain electrodes. These components are (a) the resistance at the source and drain metal contacts; (b) the resistance within the N⫹ source region and, more important, the thicker N⫹ substrate that serves as the drain region; (c) the resistance of the inversion layer that serves as the channel in the P-base region; and (d) the resistance of the drift region including the effect of current spreading as shown in Fig. 9. The current spreading effect increases the specific resistance of the drift region to a value greater than in the ideal case in which the current is assumed to flow uniformly. It can be shown that the predominant components of the on-resistance are the channel and drift region if the substrate component is reduced by thinning it. As an example, the specific on-resistance calculated for the case of a 1000-V UMOSFET is provided in Fig. 10 as a function of the inversion layer mobility (12). It can be seen that the specific resistance approaches the ideal value for the drift region only when the inversion layer mobility exceeds 200 cm 2 /V s. Unfortunately, the best reported value for the inversion layer mobility in SiC is only 15 cm 2 /V s. Consequently, the channel resistance becomes dominant with a contribution of 90% of the total resistance and the specific on-resistance is nine times greater than the ideal value. The impact of poor inversion layer mobility for devices with other breakdown voltages can be assessed by using Fig. 11. For the case of the measured inversion layer mobility of 15 cm 2 /V s, much of the improved performance projected for SiC FETs is lost unless the breakdown voltage exceeds 1000 V. Attempts at fabrication of SiC UMOSFETs from 6H and 4H polytypes have produced very disappointing results with specific on-resistances larger than those for silicon and breakdown voltages limited to less than 200 V (13).

Figure 9 Current flow path in the UMOSFET in the on state with the primary resistances in the current flow path between source and drain.

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Figure 10 Impact of inversion layer mobility on the specific on-resistance of a 1000-V SiC UMOSFET. The percentage contributed by the channel resistance can be read from the right-hand side.

Figure 11 Impact of inversion layer mobility on the specific on-resistance of SiC UMOSFETs with various breakdown voltages.

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Figure 12 Impact of cell pitch on the specific on-resistance of a 1000-V SiC UMOSFET for the case of an inversion layer mobility of 15 cm 2 /V s.

One approach to solving this problem is to increase the channel density by using a smaller cell pitch. The calculated specific on-resistance with an inversion layer mobility of 15 cm 2 / V s for cell pitches reduced from 6 to 1 µ is plotted in Fig. 12, where the components of the resistance are included for comparison. It is worth pointing out that the calculated drift region resistance is smaller than the ideal value. This unusual result is due to the fact that a substantial fraction of the blocking voltage is supported within the P-base region in the SiC UMOSFET, allowing higher doping and a smaller thickness to be used for the drift region than in the ‘‘ideal case.’’ It should be noted that the specific on-resistance becomes close to the ideal value only when the cell pitch becomes close to 1 µm. This imposes severe technological challenges for the development of high-performance SiC UMOSFETs because of the high-resolution lithography and the very small trench width that must be etched and refilled with polysilicon.

VII. ALTERNATIVE SILICON CARBIDE POWER SWITCH STRUCTURES Because of the problems with SiC UMOSFETs pointed out in the previous section, it becomes important to consider alternative device embodiments. Two device structures described in this section make it possible to circumvent these issues. A.

High-Voltage ACCUFET Structure

The problems with the poor inversion layer mobility in SiC can be addressed by using the ACCUFET structure shown in Fig. 13 (14). Here, the P-base region has been replaced with a very lightly doped N-region. If the spacing between the trench sidewalls is chosen so that the

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Figure 13 The power ACCUFET structure.

N-region is depleted at zero gate bias, a potential barrier is formed below the N⫹ source region that prevents the transport of electrons between the source and drain. This allows the structure to block current flow even at large drain voltages, providing its forward blocking capability. When a positive bias is applied to the gate electrode, an accumulation layer is formed at the sidewalls of the trenches, allowing the transport of electrons from the source to the drain. In the case of silicon, it has been demonstrated that the accumulation layer mobility is close to the bulk values (3). If this is applicable to SiC, the ACCUFET can be shown to have a smaller specific on-resistance. As an example, the specific on-resistance is shown in Fig. 14 for the case of a channel mobility of 100 cm 2 /V s for cell pitch ranging from 6 to 1 µm. It can be seen that the specific on-resistance is now close to the ideal value even for a cell pitch of 6 µm. This indicates that the ACCUFET is more technologically feasible.

B.

The Baliga Pair Configuration

In the case of silicon bipolar transistors, the Darlington pair is a well-know configuration for obtaining a higher current gain. In the same vein, it is possible to create an attractive power switch configuration with a silicon carbide MESFET or JFET and a silicon MOSFET. This circuit configuration, which will be referred to as the Baliga pair configuration for convenience, is shown in Fig. 15. It consists of an Si power MOSFET connected in series with the source region of an SiC high-voltage power MESFET or JFET. Either vertical channel or a lateral SiC FET structures can be utilized. It is important to note that the gate region of the SiC MESFET is connected to the reference terminal (or source region of the silicon power MOSFET) and the composite switch is controlled by a signal applied only to the gate of the silicon power MOSFET. The basic operating principles of this switch are discussed in the following. If the half-width a of the MESFET channel is designed to be larger than the zero bias depletion width of the MESFET gate structure, the MESFET behaves as a depletion-mode (or normally on) device structure. When an increasing positive bias is applied to the drain (D B ) of the Baliga pair with gate (G B ) shorted to the source (S B ), the voltage is initially supported by

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Figure 14 Impact of cell pitch on the specific on-resistance of a 1000-V SiC UMOSFET for the case of a channel mobility of 100 cm 2 /V s.

Figure 15 The Baliga pair power switch configuration utilizing a high-voltage SiC MESFET and a lowvoltage silicon MOSFET.

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Baliga

the silicon MOSFET because the MESFET channel is not depleted. This results in an increase in the potential of the source region S SiC of the SiC MESFET. Because the gate G SiC of the silicon carbide MESFET is at zero potential, this produces a reverse bias across the gate-source junction of the MESFET. As the voltage applied to the drain D B is increased, this reverse bias produces pinch-off of the MESFET channel by the extension of a depletion region from the gate contact. Once the MESFET channel pinches off, any further increase in the voltage applied to the drain D B is supported by the extension of a depletion region in the drift region of the SiC MESFET. It has been shown by two-dimensional numerical simulations that, once the channel is pinched off, the potential at the drain D M of the MOSFET remains relatively constant and independent of the voltage applied to the drain D B of the composite switch. Since a channel pinchoff voltage of less than 25 V can easily be designed, this implies that a silicon power MOSFET with relatively low breakdown voltage can be used in conjunction with a high-voltage silicon carbide MESFET to form the Baliga pair. This is important from the point of view of obtaining a low total on-state voltage drop for the composite switch. In order to turn on the Baliga pair, a positive gate bias is applied to the gate G M of the silicon power MOSFET, which also serves as the gate G B of the composite switch. This switches the silicon MOSFET to its highly conductive state. When a positive voltage is applied to the drain D B, current can now flow through the undepleted MESFET channel and the silicon MOSFET. The simulations have demonstrated that the specific on-resistance of the SiC MESFET is very close to the ideal specific on-resistance for the drift region because of a uniform current distribution in the drift region. The resistance contribution from the MESFET channel increases the specific on-resistance by less than 25% because the current is transported in the bulk and not along a surface. Thus, the Baliga pair is projected to have on-state voltage drops of only 0.1 V when the SiC MESFET is designed to block up to 1000 V. The Baliga pair has several other important attributes. The first is an excellent forwardbiased safe operating area. This is achieved by simply reducing the gate bias applied to the switch until it approaches the threshold voltage for the silicon power MOSFET. In this case, when a voltage is applied to the drain D B, the MOSFET operates in its current saturation regime. This limits the current flowing through the composite switch. When the voltage applied to the drain D B is increased, the voltage across the MOSFET increases until the channel of the MESFET is pinched off, allowing high voltages to be sustained with a current flow dictated by the MOSFET channel. Numerical simulations indicate a square Forward Biased Safe Operating Area (FBSOA) for the Baliga pair because no minority carrier transport is involved. The absence of minority carrier transport in the Baliga pair is also important in obtaining a high switching speed. As both the silicon MOSFET and the silicon carbide MESFET are unipolar devices, the turn-off time for the composite switch is determined by the charging and discharging time constants for the silicon MOSFET. Well-optimized silicon power MOSFETs can be designed at the required low breakdown voltages, resulting in a very high switching speed for the Baliga pair. This is attractive for the reduction of power losses in medium- to high-voltage power electronic systems operating at high frequencies. Another attribute of the Baliga pair is that it incorporates an excellent integral flyback diode. In the case of the silicon power MOSFET, the junction between the P-base region and the N-drift region can be utilized as a reverse conducting (flyback) diode. However, this diode operates with the injection of minority carriers into the drift region, which compromises the switching speed and power losses in the devices. In the case of the SiC MOSFET structure, there is an additional disadvantage that the potential required for the injection of minority carriers is much larger (typically 3 V) when compared with silicon (typically 1 V) because of its larger energy band gap. This results in a severe increase in the power losses for the flyback rectifier. In contrast to this, in the case of the Baliga pair, the application of a negative bias to the drain D B forward biases the Schottky barrier gate structure. The SiC Schottky barrier rectifier has

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been demonstrated to have excellent on-state and switching characteristics because it is a unipolar device. Thus, the Baliga pair also contains an excellent flyback diode if implemented by using a high-voltage SiC MESFET structure.

VIII.

POWER RECTIFIERS

In conjunction with power switches, high-performance power rectifiers are required in all power electronics systems. The most commonly used high-voltage power rectifier today is the silicon P-i-N structure (3). A major problem with utilizing this device in circuits is the large reverse recovery transient that occurs due to the stored charge within the i-region. This reverse recovery produces significant power losses in the rectifier and the switches at each switching cycle. Improvements in silicon high-voltage power rectifiers have been achieved by combining a Schottky contact region with the P-i-N region, but the reverse recovery current is not eliminated. Although high-voltage P-N junctions have been reported in SiC (15), the large band gap for SiC results in a very large on-state voltage drop (⬎3 V), making these devices unattractive compared with silicon devices. The development of SiC Schottky barrier rectifiers can provide a much superior highvoltage power rectifier for applications. The basic structure of the high-voltage Schottky rectifier is shown in Fig. 16 together with the band diagram and equivalent circuit. A unique feature of the high-voltage Schottky rectifier is the lightly doped drift region needed to support high blocking voltages. The on-state voltage drop in the high-voltage Schottky rectifier then consists of the voltage drop across the metal-semiconductor barrier and that across the N-drift region (assuming that the voltage drop across the N⫹ substrate can be neglected) (3): VF ⫽

冢冣

J KT ln F ⫹ R on,sp J F q Js

(3)

Figure 16 Basic structure of a high-voltage Schottky barrier rectifier with its band diagram and equivalent circuit.

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Figure 17 Calculated forward conduction characteristics of SiC Schottky barrier rectifiers with various breakdown voltages.

As discussed earlier in conjunction with the SiC FETs, the specific on-resistance of the drift region for SiC is 200-fold smaller than for the silicon device with the same breakdown voltage. This makes it possible to design SiC Schottky rectifiers with high blocking voltages and low on-state voltage drop. The forward conduction characteristics of SiC Schottky barrier rectifiers can be calculated for various breakdown voltages by taking into account the resistance of the drift region. In Fig. 17, the calculated forward characteristics are provided for breakdown voltages ranging from 200 to 5000 V for the case of a Schottky barrier height of 1.2 eV (3). This relatively large barrier height was chosen to make the reverse leakage current small. From these plots, it can be concluded that SiC Schottky barrier rectifiers with blocking voltages as high as 5000 V may be feasible because their on-state voltage drop will be less than 2 V. This is superior to that of silicon P-i-N rectifiers. The main benefit of such devices would be the elimination of the reverse recovery transient in power circuits. Experimental verification of the feasibility of fabricating high-voltage SiC-based Schottky rectifiers was first reported in 1992 with the fabrication of a 450-V device with an on-state voltage drop of only 1 V (16). These devices exhibited fast switching with no reverse recovery transient as expected. Subsequently, the breakdown voltage of SiC Schottky barrier rectifiers has been extended to above 1000 V (17). These rectifiers already exhibit excellent performance for power electronic applications.

IX. CONCLUSIONS Theoretical analysis indicates very positive prospects for the development of SiC power devices that can outperform silicon power devices. High-voltage Schottky rectifiers have already been fabricated with excellent performance. Although problems have been encountered with the de-

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velopment of high-performance SiC power MOSFETs, it has been demonstrated in this chapter that a high-voltage SiC MESFET can be used together with an Si power MOSFET to create an excellent power switch with an integral flyback diode. Although the demonstration of highperformance SiC MESFETs can be expected shortly, the commercialization of SiC technology will require an increase in wafer size with a significant reduction in cost.

ACKNOWLEDGMENTS The author wishes to acknowledge the encouragement and support of the sponsors of the Power Semiconductor Research Center, which has enabled significant advances to be made in SiC device and process technologies over the past 4 years.

REFERENCES 1. BJ Baliga. Semiconductors for high voltage vertical channel field effect transistors. J Appl Phys 53: 1759, 1982. 2. BJ Baliga. Power semiconductor device figure of merit for high frequency applications. IEEE Electron Device Lett 10:455, 1989. 3. BJ Baliga. Power Semiconductor Devices. Boston: PWS Publishers, 1995. 4. JW Palmour, CH Carter, CE Weitzel, KJ Nordquist. High power and high frequency silicon carbide devices. Materials Research Society Meeting, 1994, p 133. 5. M Bhatnagar, BJ Baliga. Comparison of 6H-SiC, 3C-SiC, and Si for power devices. IEEE Trans Electron Devices ED-40:645, 1993. 6. WJ Schaffer, HS Kong, GH Negley, JW Palmour. Hall effect and C-V measurements on epitaxial 6H- and 4H-SiC. Proceedings 5th Conference on Silicon Carbide and Related Materials, 1993, p 155. 7. A Bhalla, TP Chow. Bipolar power device performance: dependence on materials, lifetime, and device ratings. International Symposium on Power Semiconductor Devices and ICs, 1994, p 287. 8. M Bhatnagar, H Nakanishi, S Bothra, PM McLarty, BJ Baliga. Edge terminations for SiC high voltage Schottky rectifiers. International Symposium on Power Semiconductor Devices and ICs, 1993, p 89. 9. D Alok, BJ Baliga, PM McLarty. A simple edge termination for silicon carbide devices with nearly ideal breakdown voltage. IEEE Electron Device Lett 15:394, 1994. 10. D Alok, BJ Baliga. A planar, nearly ideal, SiC device edge termination. International Symposium on Power Semiconductor Devices and ICs, 1995, p 96. 11. D Alok, BJ Bliga, M Kothandaraman, PK McLarty. Argon implanted SiC device edge termination: Modelling, analysis and experimental results. Sixth International Conference on Silicon Carbide and Related Materials, Paper ThA-I-5, 1995. 12. M Bhatnagar, D Alok, BJ Baliga. SiC Power UMOSFET: Design, Analysis, and Technological Feasibility. Proceedings 5th Conference on Silicon Carbide and Related Materials, 1993, p 703. 13. JW Palmour. Vertical power devices in silicon carbide. Inst Phys Conf Ser 137:499, 1994. 14. BJ Baliga. Silicon carbide field effect device. U.S. Patent 5,323,040, June 21, 1994. 15. LG Matus, JA Powell, CS Salupo. High voltage 6H-SiC p-n junction diodes. Appl Phys Lett 59: 1770, 1991. 16. M Bhatnagar, PK McLarty, BJ Baliga. Silicon carbide high voltage (400V) Schottky barrier diodes. IEEE Electron Device Lett 13:501, 1992. 17. T Kimoto, T Urushidani, H Matsunami. High voltage (⬎ 1 kV) SiC Schottky barrier diodes with low on-resistance. IEEE Electron Device Lett 14:548, 1993.

21 Science and Technology of Boron Nitride Osamu Mishima National Institute for Research in Inorganic Materials, Tsukuba, Ibaraki, Japan

Koh Era Helios Optical Science Laboratory, Inc., Tsukuba, Ibaraki, Japan

I.

INTRODUCTION

The compound boron nitride (BN) has no counterpart in nature on the earth. Up to the present various types of BN have been synthesized, starting with the synthesis of a hexagonal layered compound in 1842 (1). In 1957, boron nitride with the zinc blende (sphalerite) structure was synthesized, by Robert H. Wentorf, Jr. (2) of General Electric Company, under high-pressure and high-temperature conditions using an apparatus similar to that developed by his group for the synthesis of diamond. This opened a field of important applications similar to those of diamond (3). Since then, powders, grains, and sintered compacts of the compound have been mass produced in high-pressure factories and have become very important materials for grinding and cutting applications, supporting modern industries. This compound has been mainly called cubic boron nitride (cubic BN) after Wentorf (3) (see also Table 1 for various names) and usually abbreviated cBN. (CBN or C-BN with capital letter C may be confused with the material carbon-boron-nitrogen, usually written as BCN, or a C/BN heterojunction and should be used with care.) The potential of cBN as a semiconductor was also shown by Wentorf (4). cBN can be regarded as the extreme of III-V compounds from the viewpoint of periodic table systematics. Indeed, its band gap energy (estimated to be 6.3 eV; see Sec. III.A) is the widest among known semiconductors including diamond. This fact gives us a hint that cBN has new potential in electronic applications. The present chapter deals mainly with cBN on the basis of references published up to 1995. Other phases of BN are described only in conjunction with cBN. The main body was written by Mishima and revised and edited by Era. Studies of cBN have also been reviewed in handbooks, conference proceedings, and journals (5–14).

II. STRUCTURE OF BN PHASES Boron nitride has many names: hBN, rBN, cBN, wBN, zBN, αBN, βBN, γBN, tBN, pBN, iBN, aBN, EBN, ABN, SBN, BORAZON, elbor, cubonite, and more. Although many names are 495

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Table 1 Names of BN Phases Crystal Hexagonal BN (hBN)

Amorphous Pyrolytic BN (pBN)

Turbostratic BN (tBN)

αBN Graphite-like BN (BNg)

BN

Rhombohedral BN (rBN) Ion-bombarded BN (iBN) Cubic BN (cBN) Zinc blende BN (zBN), βBN Borazon, sphalerite BN (BNsp) Elbor, cubonite, okmal [Trademark: powder] BORAZON (GE) SBN (Showa Denko) ABN (DeBeers)

sp 3-amorphous BN (aBN)

Wurtzite BN (wBN) γBN, BNw, hexanite BN?

Explosion BN (EBN)

confusing, we can simply group these boron nitrides into four crystalline phases, amorphous BN and their mixed states as shown in Table 1. These BN phases can exist at room temperature at 1 atm. The atomic and molecular weights of these boron nitrides are listed in Table 2. Note that 10 B has a large cross section for thermal neutron capture and changes to 7Li with the emission of an alpha-particle [ 10B(n, α) 7Li]. A.

Crystalline BN Phases

The structures of the four crystalline BN phases are shown in Figs. 1 and 2. Lattice data are given in Table 3. The cBN (2,15) and wBN (16) have tetrahedral sp 3 BEN bonding and their structures correspond to those of cubic and hexagonal diamond, respectively. Table 2 Atomic and Molecular Weights of BN Property Atomic number Atomic weight ( 12 C ⫽ 12.000)

Boron (B)

Nitrogen (N)

5 10.81 10 B ⫽ 10.013 (19.7%) 11 B ⫽ 11.009 (80.3%)

7 14.0067

Boron nitride (BN) Molar weight

24.82 g (B, 43.6%; N, 56.4%) (Avogadro’s number: 6.0225 ⫻ 1023 mol⫺1 )

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Figure 1 The four BN crystals.

The hBN (17) and rBN (18–20) have trigonal sp 2 bonding and their structures are similar to, but not the same as, the graphite structure. The densities of sp 3 crystals (cBN and wBN) are 1.5 times larger than those of sp 2 crystals (hBN and rBN) under normal pressure-temperature conditions. These four crystalline structures of BN have hexagonal rings made of three boron atoms and three nitrogen atoms, as shown in Fig. 2. Both hBN and rBN have flat sp 2 6-rings, and cBN and wBN have puckered sp 3 6-rings. The BEN distance in the sp 2 6-rings (144 pm) is shorter by ⬃8% than that in the sp 3 6-rings (157 pm), which indicates that the BEN bonding in the 6-ring plane of hBN and rBN is stronger than that in cBN and wBN. In contrast, the distance (333 pm) between the layers of sp 2 6-rings in hBN and rBN is relatively long, indicating that the binding force between the layers is weak. Hence, hBN and rBN may be regarded as molecular crystals made of layers of a flat sp 2-network ‘‘molecule.’’ Roughly speaking, when molecular crystals are subjected to high pressures, their structures generally change to more atomic forms.

Figure 2 Structural relations among the four BN crystals.

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Table 3 Lattice Data for BN Crystals hBN a ⫽ 250.441(7) pm c ⫽ 665.62 (4) pm ρ ⫽ 2.34 g/cm 3 P63 /mmc

rBN

cBN

wBN

a ⫽ 250.4 pm c ⫽ 1001 pm ρ ⫽ 2.2 g/cm 3 (cal.) R3m

a ⫽ 361.58 pm (BEN: 156.56 pm) ρ ⫽ 3.49 g/cm 3 F43m

a ⫽ 255.3 pm c ⫽ 422 pm ρ ⫽ 3.45 g/cm 3 P63 mc

That is, the distance between the molecules contracts and the distance between the atoms in the molecule expands relatively. When the sp 2 ‘‘molecular’’ BN crystals are subjected to high pressures, they change to the atomic sp 3 crystals and we can see the common pressure-induced structural conversion from molecular to atomic crystals. The reported X-ray diffraction spectra of BN phases are reproduced in Fig. 3. The X-ray diffraction data are given in Refs. 17 and 19 and Joint Committee on Powder Diffraction Standards (JCPDS): 34-421 for hBN; in Refs. 18–20 for rBN; in Refs. 16, 25, 27, and 59, JCPDS: 35-1365 and 25-1033, for cBN; and in Refs. 16, 25, 27, and 59, JCPDS:26-772 for wBN. The spectral peaks around 2θ ⫽ 25° correspond to the distance (⬃333 pm) between the layers of the sp 2 networks. Some peaks around 2θ ⫽ 40°–50° are due to the atoms in the sp 2 or sp 3 6-rings. The lattice data are summarized in Table 3.

Figure 3 Schematic X-ray diffraction patterns of BN phases. (Data from Refs. 20, 32, 42, 45, 61, 62.)

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Regarding wBN, which can be made by compression of hBN at low temperatures (16,21,23–25) or by shock wave compression (22,27–33), the cell constant along the c-axis of wBN (421–422 pm, depending on defects in wBN) is reported to be ⬃1% longer (c/a ⫽ 1.653) than that of the ideal tetrahedral structure (418 pm, c/a ⫽ 1.633) (21,33,35). Hence, the density of wBN (3.45 g/cm 3) is thought to be ⬃1% lower than that of cBN (3.49 g/cm 3) (35). Besides the four crystalline BN phases already mentioned, there is a crystalline material called EBN. EBN was found in shock-compressed BN samples and was reported to have a facecentered cubic structure with lattice constant a0 ⫽ 840.5 pm and a density ρ ⫽ 2.55 g/cm 3 (5,29–31,36) (JCPDS:18-251). A material having an X-ray diffraction pattern similar to that of EBN has also been synthesized by the vapor deposition method (37,38). However, an unambiguous structural analysis, using samples of an EBN single phase, has not been carried out and the chemical composition of EBN is also unknown and may be different from that of stoichiometric BN. There is a report indicating that EBN is BN1⫺xOx (39). B.

Noncrystalline BN

In this chapter, we define amorphous BN as the material having halo diffraction patterns. This implies that amorphous BN has no translational long-range order and is either truly amorphous (without lattice periodicity) or microcrystalline (from the presence of halo patterns ⬍⬃2 nm in size). Generally, it is difficult to distinguish experimentally between the truly amorphous states and the microcrystalline states. Although high-resolution electron microscopy can provide atomic-level information, knowledge of the detailed amorphous structure of BN is vague. Nevertheless, we usually think of two kinds of amorphous BN, tBN (sp 2-amorphous BN) and aBN (sp 3-amorphous BN), by analogy with amorphous graphite and diamond-like amorphous (DLA) carbon (Table 1 and Fig. 4). According to Biscoe and Warren (40,41), the turbostratic structure (unordered layers), first found in carbon black (amorphous graphite), consists of roughly parallel ⬃6-ring layers that are piled up at translational and rotational random about the layer normal. The material called tBN shows the halo X-ray diffraction pattern characteristic of this turbostratic structure (Fig. 4). It has a broad diffraction peak around 2 θ ⫽ 25° to the distance between the layers (⬃333 pm) (Fig. 3) (42). Analysis of the diffraction patterns of tBN indicated that the average group of parallel layers had several sp 2 sheets and had a thin ‘‘wafer’’ shape, although other tBN structures may

Figure 4 Plausible amorphous BN structures.

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be possible depending on the conditions of synthesis. For example, we can expect a fine granular group of parallel turbostratic layers and even a fully disordered sp 2 structure (isotropic tBN?— see Fig. 4). However, these amorphous BN phases have not been observed to date. The tBN can have a variety of macroscopic structures (43) (A, B, and C in Fig. 4). For example, a hollow tubular shape with turbostratic BN walls (micron-tubes: C in Fig. 4) has been made upon heating some amorphous BN material. When these turbostratic layers become ordered, the tBN becomes so-called pBN. The pBN is highly oriented tBN or tBN⫹hBN and is produced, for example, at high temperatures and low pressures by the chemical vapor deposition (CVD) method (probably the D region of Fig. 3 of Ref. 43) (A in Fig. 4). When the pBN structure is further ordered, it finally becomes crystalline hBN. The details of how this structural ordering occurs are unknown (42). We can also think of fully disordered ⬃BN structures as similar to diamond-like amorphous carbon (amorphous diamond). Here, we call this sp 3-amorphous BN, aBN. The aBN would have a broad diffraction peak around 2 θ ⫽ 40°–50° and no peak around 2 θ ⫽ 25° because of the absence of the sp 2-layer structure. Actually, there exists amorphous BN whose 2 θ ⫽ 40°–50° peak is relatively strong and its 2 θ ⫽ 25° peak is weak (45). This may be the aBN with a small fraction of tBN. However, preferentially oriented tBN may show a similar diffraction pattern and, therefore, conclusive evidence of the existence of the sp 3 aBN is lacking at present. There is a hard amorphous (or quasi-amorphous) BN that is made by the low-pressure ion-beam deposition method. This amorphous BN is called iBN; the prefix ‘‘i’’ alludes to the essential role of ions in this preparation method. The structure is supposed to have sp 3 and sp 2 bondings (46,47). One may think that the general structure of amorphous BN is a homogeneous mixture of the sp 2-amorphous tBN and the sp 3-amorphous aBN and that the structure changes continuously between these two amorphous states. A first-order phase transition between two amorphous structures of H2O has been reported, showing polymorphism in the amorphous structure of this material (48,49). This idea (polymorphism in an amorphous structure) may be applied to amorphous BN; that is, like crystalline phases, the tBN and the aBN may be distinctly different amorphous phases with well-defined different amorphous structures. Raman, infrared, and electron energy loss spectra (EELS) of BN have shown that vibrational frequencies of sp 2 and sp 3 bonding in all of the BN materials examined (including amorphous BN) were distinctly separated and did not show any clear evidence of sp 2-sp 3 frequency merging. The absence of frequency merging indicates absence of intermediate sp 2-sp 3 states and may suggest the possibility of polymorphism in amorphous BN. It is difficult at present to resolve sp 2 and sp 3 BEN distances in the radial distribution function of the X-ray diffraction pattern of amorphous BN (Fig. 5). Although one diffraction analysis suggested that the amorphous BN has a structure of mixed sp 2(hBN)-sp 3 (cBN) clusters (50), another analysis indicated that the structure is disordered even at short range (52). Further studies are desirable. In this connection, there has been a study of a pressure-induced phase change between a low-density liquid and a high-density liquid of hightemperature carbon (51). If a glass transition were observed in amorphous BN, we could associate the material with supercooled BN liquid and melt-quenched BN glass. However, no glass transition in amorphous BN has been reported so far. C.

Phase Diagram

Experimental results for the observed transitions between the four crystalline BN phases and the amorphous BN are shown in Fig. 6.

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Figure 5 Radial distribution function, G(r), of amorphous BN. (Data from Ref. 52.)

When hBN is compressed at room temperature, it transforms sluggishly to wBN around 10–15 GPa (F in Fig. 6, see also Fig. 7). (7,16,24). When rBN is compressed at room temperature, its structure changes to an unknown form [tBN?, hBN?, wBN? (53), cBN? (54)] at 4–8 GPa (G in Fig. 6). When it is further compressed beyond ⬃20 GPa and recovered at 1 atm, the recovered phase is cBN according to Ref. 54 (E in Fig. 6). Sluggish structural transformations and irreversible phase transitions are common at low temperatures, where thermal agitation is inactive and atomic rearrangement is difficult. These sluggish transformations are affected by kinetic factors and depend on individual experimental conditions such as stress, time scales, and defects in crystals. Therefore, the observed transition pressures and transition temperatures at low temperatures (B, C, D, E, F, and G in Fig. 6) do

Figure 6 The BN phase diagram. (Data from Refs. 16, 22, 23, 42, 45, 54, 61, 62, 65, 66.)

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Figure 7 Transitions in BN during compression and heating. (Data from Refs. 16, 22, 23.)

not mean thermodynamic equilibrium phase boundaries and these transition regions vary with experimental conditions. When hBN with preferential ordering along c-axes (e.g., A in Fig. 4) was compressed at relatively low temperatures and transformed directly to wBN, the preferential crystal orientation in the starting hBN was found to be maintained in transformed wBN. This indicated that the (002) planes of the wBN were parallel to the sp 2 planes of the hBN (24) (see also Ref. 21). This structural relation suggested that the transition was a martensitic diffusionless transition. Besides, some transitions observed in shock experiments (27,28,33,56) suggested that the martensitic transformation occurs from hBN to wBN and from rBN to cBN (Fig. 2). This martensitic transition was also considered (57) and studied theoretically (58). Thus atomic diffusion during the transitions was considered to be suppressed at low temperatures and in the short duration of shock experiments (usually less than 1 µs). On the other hand, some experimental observations contradict this simple martensitic mechanism. Shock experiments showed that transitions occur from hBN to cBN and from rBN to wBN probably via an intermediate phase (59–61). With static compressions of rBN at low temperature, the rBN transformed to wBN (53). Apparently there are multiple transformation paths among these BN phases even if the transitions are martensitic. The structural transformations occur more easily at higher temperatures. Roughly speaking, over the usual time scale and in the 0–10 GPa region, crystallization of tBN usually starts at 1000–1300 K (D in Fig. 6) (42,45,62), crystal-crystal transitions at 1500–2000 K (B and C in Fig. 6 and Fig. 7) (23,63), and sintering and recrystallization at 1700–2200 K (64,65). When cBN is heated at 1 bar, it transforms kinetically to hBN at ⬃1300°C in air and at ⬃1600°C in vacuum (10). Very little is known about the equilibrium pressure-temperature phase diagram of BN (23,66) because of the retardation of the transformation at low temperatures and difficulty in carrying out high-temperature experiments at high pressures. Tentative equilibrium phase boundaries are shown by the dashed lines in Fig. 6. Hexagonal BN and cBN are thermodynamically stable at high temperatures at low and

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high pressures, respectively. The boundary between hBN and cBN is approximately known experimentally between 1500 and 3000 K (A in Fig. 6 is from Ref. 23). Compared with the graphite-diamond boundary, the hBN-cBN boundary is located ⬃2 GPa to the low-pressure side, suggesting that cBN is relatively stable at low pressures compared with diamond. The low-temperature hBN-cBN boundary shown in the figure was obtained by thermodynamic considerations, as mentioned in Sec. III. C. 1. The hBN-cBN boundary extrapolates to nearly zero pressure at 0 K, which gives rise to the possibility of cBN being stabler than hBN at low temperatures and at 1 atm, as has also been suggested by some theoretical studies (58,67) and experimental analyses (68,69). There are discussions of the hBN-cBN equilibrium boundary (70,71), and further study of the boundary is necessary. Other phase boundaries of BN, shown by dashed lines in Fig. 6, are speculated upon by analogy with the carbon phase diagram (72). There is a maximum in the melting curve of graphite, so hBN is supposed to have a melting curve maximum, suggesting the presence of a significant density change in liquid BN. The melting temperature of diamond is considered to increase as pressure increases (73), so the melting temperature of cBN is speculated to increase with pressure. From the Clausius-Clapeyron equation, this suggests that BN liquid is less dense than the cBN crystal and that the melt-quenched BN glass, if obtainable, would also be less dense than cBN. If the structure of sp 3-amorphous BN (aBN) resembles this melt-quenched glass, its density would be lower than cBN’s and the aBN would be softer than cBN. The cBN can exist up to at least ⬃100 GPa as shown by static (74) and shock compression (75) experiments. No new BN phase, except for EBN as discussed in Sec. II.A, has been found in these compression experiments. [Note that EBN, if it is a BN phase, has a low density (2.55 g/cm 3) and should be a low-pressure phase.] Theoretical work suggests that cBN is stable up to about 1 TPa (⫽1000 GPa), where it would change to the rock salt structure (76,77). Theoretical and experimental work (27,78) also suggests that wBN is always thermodynamically metastable. Theoretical work suggests that wBN is stabler than cBN beyond 133 Gpa (78). Regarding the possibility of new BN phases, BN materials with an entirely sp 2-bonded structure (bct-4 and similar crystals) and with unusual mechanical and thermal properties have been theoretically proposed (Fig. 8) (79,80). A BCN material with an sp 2-layered structure is claimed to exist (81,82). The possibility of a solid solution or compound of BC2N (or BCN) with an sp 3-bonded structure was experimentally and theoretically studied; some experimental studies claimed the formation of a BCN compound (see references in Ref. 83), whereas others suggested that mixing of diamond and cBN (or formation of a solid solution) is difficult (83,84).

Figure 8 Hypothetical bct-4 and BN- and BCN-ball structures. (From Refs. 79, 80, 85, 86.)

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There have also been some theoretical studies of BCN (85) and BN (86) balls with structures similar to that of C60 (Fig. 8).

D.

Structure and Polarity of Cubic BN

Is the electric polarity of cBN B ⫺N ⫹ or B 3⫹N 3⫺? As shown in Fig. 9, the B ⫺ and N ⫹ atoms, made by an N-B transfer of an electron to give four electrons each, may have covalent bonding as is the case for diamond. Alternatively, the B 3⫹ and N 3⫺ atoms, resulting from a B-N transfer of three electrons, may have ionic bonding. From an analysis of the (200) X-ray diffraction intensity (85), which reflects any differences in the number of electrons on the B and N atoms, and experimentally obtained electron density distributions (88) as well as theoretical analyses (90–96), cBN was found to have an electric polarity of B ⫹δ N ⫺δ (δ ⬃0.4). Therefore, there is an electron charge transfer of about 0.4e from the B to the N atoms. As shown in Fig. 9, electrons forming covalent bonding shift toward the more electronegative N atoms. This shift of the bonding electrons is characteristic of III-V compound materials and provides properties different from those of diamond, which has a symmetric electron distribution with two electron density peaks. Cubic BN is usually considered to have both covalent (75%) and ionic (25%) aspects. The covalent radius of boron is said to be ⬃20% larger than that of nitrogen in this connection.

Figure 9 Electric polarity of cBN. (Charge density from Ref. 95.)

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1. Crystallographic Polarity As shown in Fig. 10, the zinc blende structure has crystallographic polarity along 〈111〉 axes by nature. That is, there are (111)B and (1¯1¯1¯)N surfaces in cBN crystals, which results in the characteristic crystal habit and surface morphology. The crystallographic polarity of cBN should also affect etching behavior, crystal growth, dislocations, strain and abrading properties, chemical reactivity, impurity concentrations, etc. as observed in other sphalerite compounds (97). Absolute crystallographic polarity of cBN crystals was determined by Rutherford backscattering spectroscopy (RBS) using helium ion beam (98). 2. Habit, Morphology, and Etching Crystal habit, surface morphology, and the etching behavior of cBN crystals made by the solvent method at high pressures are discussed here because crystals made by other methods are too small to be studied at present. a. Habit and Morphology In principle, growth habit and surface morphology depend on individual growth conditions. Besides effects caused by the individual growth conditions, the usual cBN crystals, made by using a solvent (such as Li3BN2 , LiCaBN2, or other boron nitrides) at high pressures, have their own characteristic habit and surface morphology, which are caused by the crystallographic polarity of cBN (10,15,100–103). The growth shape of cBN crystals is essentially tetrahedral, although almost cubic shapes with (100) faces sometimes appear and twins and cleaved faces complicate the crystal shape. The tetrahedral crystals appear because the surface energy is different between (111)B and (1¯1¯1¯)N: low-energy and inactive surfaces dominate during the crystal growth. The (1¯1¯1¯)N faces are usually large, smooth, shiny, and flat (Fig. 11). Growth hillocks and growth layers are observed on (1¯1¯1¯) faces, which make the faces incline from the exact (1¯1¯1¯) and result in a relatively rough appearance. Boundaries between (1¯1¯1¯) and adjoining (100) faces are sometimes vague due to this inclination from the exact (1¯1¯1¯). The (111)B faces usually have a small and rough (or matted) appearance. The (111) faces are flat throughout the face, and boundaries between (111) and adjoining (100) faces are usually distinct. It seems difficult to observe growth layers on (111) faces. The (100) faces are macroscopically nonpolar. There should be no gross differences between opposite (100) faces. (Reconstruction on the surface may change the arrangement.) Calcu-

Figure 10 Crystallographic polarity of cBN.

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Figure 11 Habit, morphology, etching patterns, and polarity of cBN. (Data from Refs. 102, 111.)

lations indicated that 2 ⫻ 2 dimer reconstruction on the B-terminating surface might favor the (100) surfaces (104). However, as seen in many sphalerite compounds (105), real (100) faces of the cBN crystals are usually nonflat and have steps, presumably made of (1¯1¯1¯) faces, forming striations with a 〈110〉 direction (101,106). Distinct striations are wavy looking macroscopically. The striations are always parallel to the boundaries between (100) and adjoining (1¯1¯1¯) faces. These habits and morphologies may be simply realized as overlapped tetragons with (1¯1¯1¯)N faces, as shown in Fig. 12. The cleavage plane of cBN crystals is (110) as in the other III-V sphalerite compounds and different from the (111) cleavage plane of diamond (Fig. 13). When twins exist, they are detectable by observing the (100) faces, because the twins make lines vertical to the growth striations of the (100) faces (Fig. 14) (101). b. Etching Chemical etching studies of cBN crystals have revealed different etching behavior on different kinds of surfaces (10,99,102,107–109). The reported etchants are LiOH, NaOH, KOH, and

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Figure 12 The overlapped tetragons used to illustrate cBN morphology.

Figure 13 Cleavage planes of cBN.

Figure 14 The spinel-type twin.

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Figure 15 Schematic etch pit configuration of (100) faces of cBN.

NaNO3. Note that the solvents (catalysts) of cBN synthesis can dissolve cBN crystals and are, therefore, etchants (110) (see Sec. IV.A.2). When cBN crystals were etched in molten NaOH for a few minutes, hexagonal (or triangular), large, shallow, smooth, flat, and randomly distributed pits were usually observed on (1¯1¯1¯)N (Fig. 11). On the faces, which are inclined from the exact (1¯1¯1¯), rough etch patterns appear. On (111)B, relatively small, triangular pyramids or triangular terraces usually appear. On (100), long and slender pits, parallel to the 〈110〉 striations, are observed (102). Although cBN is insoluble in usual acids at room temperature, it can be etched at high temperatures under high pressures. When cBN crystals were etched in 2HCl ⫹ 2HNO3 ⫹ 5H2O at about 450°C and 2 GPa for ⬃60 minutes (in a Teflon capsule), the etching behaviors were different from that with NaOH etching and similar to the acid-etching character of other III-V compounds (O. Mishima et al; unpublished work; see Ref. 200). That is, the long and slender pits on (100) faces were perpendicular to the 〈110〉 growth striations (Fig. 11). In general, etching patterns depend on the relative etching rates of etch-pit faces (111). Regarding the long and slender pits on (100) faces of the III-V compounds, the pits are usually considered to have two (111)III and two (1¯1¯1¯)V faces (105) (Fig. 15). A difference in the etching rate of III and V faces makes the long pits. When the etchant was NaOH, the B faces reacted rapidly, leaving relatively inert N faces as the dominant etch-pit faces. When HCl ⫹ HNO3 ⫹ H2O was used as the etchant, the N faces reacted rapidly, leaving relatively inert B faces as the dominant etch-pit faces. The relations among surface morphology (of the usual cBN crystals made at high pressures), etching patterns, and polarity are summarized in Fig. 11. From these relations, we can easily identify the polarity by observing the surface morphology of cBN crystals.

III. PROPERTIES OF CUBIC BN From the periodic table systematics, cBN is the lightest III-V compound and has a chemical bond isoelectronic with diamond. Thus, we may expect to have properties of both the III-V compounds and diamond. Difficulties in obtaining large, high-quality cBN crystals prevent precise measurements of the properties of this material. Therefore, many properties of cBN are known with poor precision or even not known with any precision. Recent progress in computational physics has partly supplemented this information. Generally, various properties of crystals may be calculated by using band theories, at least in the framework of one-electron theory (112). Experimental judgments are inevitable, however.

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509

Electronic Band Structure

Many band calculations have been carried out on cBN. Their results mostly agree qualitatively, indicating that the minimal band gap occurs between the X1,c conduction band and the Γ15,v valence band (76,78,89,91,93–96,113–126). The main values related to the cBN energy band obtained from recent calculations lie in rather small ranges; the band gap energies lie in the range 4.2– 5.2 eV, the upper valence band width 10–11 eV, the lower valence band width 5.3–7 eV, the gap between the upper and lower valence bands 3.3–4.0 eV, and the total valence band width 20–23 eV. However, differences between the calculated and experimental values are not small: the calculated band gap (4.2–5.2 eV) and the upper valence band width (10–11 eV) are smaller than the available experimental results (⬃6.3 eV and ⬃14 eV, respectively; see Fig. 17). By using the local-density and GW approximations with the experimental dielectric constant ε ⫽ 4.5, Surh et al. (125) obtained a band gap energy of 6.3 eV. Here, the GW approximation is the one which uses a product of functions usually written as G and W. G is a Green function. W is a symbol of a function which expresses a dynamically screened electron interaction. The above method used by Surh et al. has furnished very good results about band gap energies of several compounds. Indeed, the value, 6.3 eV is very close to the onset of the imaginary part of the complex dielectric function obtained from reflectance spectra explained below (133–135). Using their calculated values at the symmetric points and interpolating them graphically by referring to other researchers’ results, the energy band structure is drawn in Fig. 16. In the same figure, an electronic density of states (DOS) curve is drawn by summing up reported cBN DOS curves (112,121–124,127,128). Effective masses of electrons and holes have not been obtained experimentally and were deduced by a calculation (123). There have been several optical measurements of cBN in the short-wavelength spectral region (127,129–132). Results of the measurements agree with one another, although the exact value of the band gap energy has not been determined with enough accuracy. In Fig. 17, two reflectance spectra are shown (133–135). These spectral profiles are roughly similar to each other. Energy values of spectral peaks and shoulders are close to those

Figure 16 Band structure of cBN. (Data from Refs. 125, 130.)

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Figure 17 The ε2 spectra and reflectance spectra of cBN. Solid line, single crystal; dotted line, polycrystal. (Data from Refs. 125, 133–135.)

of theoretically expected singularities (indicated by arrows in the figure). However, even though the experimental and theoretical results appear to agree (78,112,121,125,134,135), it should be noted that unambiguous assignments of the experimental spectra have not yet been made. The experimental value of the band gap of cBN is 6.2–6.4 eV (130,131,135), which is larger than that of diamond (5.5 eV) and comparable to that of AlN (6.3 eV). Cubic BN, as well as AlN, has the widest band gap among the existing semiconductors as shown in Fig. 18. Note that aBN and wBN are considered to have larger band gaps than cBN [aBN, 7.4 eV (136); wBN, ⬃1.1 ⫻ Eg of cBN (78)]. Both experimental (137) and theoretical (93,95,122) studies show that the indirect band gap energy of cBN increases with pressure. The band gap is theoretically considered to change from indirect to direct at 1.16 TPa (1160 GPa) (138), although cBN may be transformed to the rock salt structure around this pressure (76,77). B.

Mechanical Properties

In general, mechanical or electric displacement in materials induced by an applied mechanical or electric field can be described with a tensor equation that determines the mechanical properties of the material. For weak applied fields, the displacement is approximately proportional to the applied field (Fig. 19). Because of the crystalline symmetry of cBN (F43m), only three elastic constants, one piezoelectric constant, and one dielectric constant in the equation are of importance or have

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Figure 18 Comparison of the band gaps of typical semiconductors.

Figure 19 An example of the tensor equation and its coefficients.

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nonzero values (Fig. 19). Although these coefficients have not yet been determined precisely, the mechanical properties of cBN have been estimated from experiment and theory. It is found that cBN is the second hardest material after diamond. 1.

Elastic Properties

There are various kinds of elastic constants, some of which are illustrated in Fig. 20. They are correlated with one another by their definitions, as shown in Table 4. When two independent kinds of constants are given, we can derive other elastic constants. Plausible elastic constants of cBN are listed in Table 5 by summing up the theoretically expected (10,94–96,124,140,141) and experimentally observed data (74,143–145). Gru¨neisen parameters (143,144) and linear thermal expansion coefficients near room temperature (146,147) are also listed. The elastic constants of cBN are about 20–40% lower than those of diamond and several times larger than those of other covalent crystals such as Si and GaAs. Although cBN is stiff, it is elastic and can be distorted: the volume of cBN decreases elastically by about 20% at 100 Gpa (Fig. 21) (74). When the microscopic force constant along a BEN bond, C0, and the force constant in a BEN bending direction, C1, of cBN are estimated according to Ref. 112 and compared with those of other sphalerite compounds, the ratio C0 /C1 of cBN appears to be relatively small (as is the case for diamond). This indicates that the bonds in cBN and diamond are rather difficult to bend in a circular direction. 2. Hardness When materials are strained beyond their elastic limits, they deform permanently and then fracture. The measurement of hardness is a convenient method with which to evaluate these proper-

Figure 20 Illustration of some elastic constants.

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Table 4 Correlation of Elastic Constants Lame´ constants λ, µ

ε, σ

C11, C12, C44 [C11 ⫽ C12 ⫹ 2C44 ]

εσ (1 ⫹ σ)(1 ⫺ 2 σ)

C12

K, γ 2 γ 3

λ ⫽ C12

λ

K⫺

Shear modulus, µ ⫽ γ ⫽ C44

µ

γ

ε 2(1 ⫹ σ)

C44

K

ε 3(1 ⫺ 2 σ)

C11 ⫹ 2C12 3

λ⫹

Bulk modulus, K

2 µ 3

Young’s modulus, ε

µ (3λ ⫹ 2µ) λ⫹µ

9K γ 3K ⫹ γ

ε

C44 (C11 ⫹ 2C12) C11 ⫺ C44

Poisson’s modulus, σ

λ 2(λ ⫹ µ)

3K ⫺ 2γ 2(3K ⫹ γ)

σ

C12 2(C12 ⫹ C44 )

ties. The definitions of the Vickers hardness and the Knoop hardness are illustrated in Fig. 22. The Knoop hardness is empirically 10–20% lower than the Vickers hardness. The hardness of a crystal depends on its temperature, crystalline orientation, the time scale of measurement, and possibly the defect content. The hardness of cBN is shown in Figs. 23 and 24 (10,100,148–151). Although cBN is the second hardest material after diamond, its hardness (Hk ⬃4000) appears to be only half of that of diamond (Hk ⬃8000) and is close to the hardness of SiC and B4C (Hk ⬃3000). Thus, cBN crystals can be polished rather easily with diamond powders.

Table 5 Estimated and Observed Elastic Constants of cBN C11

7–8 ⫻ 10 11Pa

C12

1–2 ⫻ 10 11Pa

C44

⬃4 ⫻ 10 11Pa

C0 K

⬃3.8 ⫻ 10 11Pa

ε γ: LO(Γ) γ: TO(Γ) a

0.9 (142) 1.2 (142) ⬃3.5 ⫻ 10 ⫺6 /K(0–400°C) (146)

a

Reference numbers in parentheses.

7.12 ⫻ 10 11 Pa (139) a 8.3 ⫻ 10 11Pa (140) 7.83 ⫻ 10 11Pa (144) 4.2 ⫻ 10 11Pa (140) 0.8 ⫻ 10 11Pa (10) 1.46 ⫻ 10 11Pa (144) 4.5 ⫻ 10 11Pa (140) 3.34 ⫻ 10 11Pa (10) 4.18 ⫻ 10 11Pa (144) 3.83 ⫻ 10 11Pa (139) 3.82 ⫻ 10 11Pa (142) 3.69 ⫻ 10 11Pa (74) 3.67 ⫻ 10 11Pa (95, 96, 141) ⬃8.8 ⫻ 10 11Pa (polycrystal) (145) 1.2 (143) 1.5 (143) ⬃4.8 ⫻ 10 ⫺6 /K (430°C) (10) 3.7 ⫻ 10 ⫺6 /K (0–400°C) (polycrystal) (147)

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Figure 21 Compression curves of cBN and hBN. (Data from Refs. 74, 139.)

There are some approximate empirical relations between the hardness and elastic properties of materials (152), and we can speculate upon the elastic constants of cBN from its hardness. 3. Piezoelectricity In principle, cBN should exhibit piezoelectricity because of its crystal structure. That is, when a cBN crystal is located in an electric field, the boron atoms of the crystal with positive charges and the nitrogen atoms with negative charges move in opposite directions. This induces macroscopic strains (and stresses) in the crystal. The induced strains (stresses) are approximately proportional to the electric field. For cBN, there is only one direction in which strains (stresses) are induced by the electric field. This is expressed by TXY ⫽ e14 EZ (SXY ⫽ d14EZ ), where TXY (SXY ) is a stress (strain) along the y axis on the x plane, E Z an electric field along the z axis, and e14 (d14) a piezoelectric constant. Here, e14 ⫽ C44 d14, as deduced from Hooke’s law: TXY (force) ⫽ C44 (a spring constant) ⫻ SXY (displacement). When the electric field is increased along a 〈001〉 direction, the cBN crystal deforms elastically as shown in Fig. 25. The value of e 14 has been estimated theoretically to be ⫺1.36 (C/m2 ), ⫺3.3 (C/m2 ), and ⫺0.2 (C/m2 ) by different researchers (126). As yet, no experimental observation of piezoelectricity from cBN has been reported. 4. Lattice Dynamics Because of the strong covalent bonding of cBN, as suggested by its large elastic constants, and the light masses of B and N atoms, cBN has high-frequency lattice vibrations, large sound velocities, high Debye temperatures, and large thermal conductivities. These lattice properties

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Figure 22 Definitions of the Vickers and Knoop hardnesses.

Figure 23 Surface orientation dependence of hardness of cBN. (Data from Refs. 149, 151.)

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Figure 24 Temperature and time dependence of hardness of cBN. (Data from Ref. 149.)

of cBN are superior to those of all other materials except diamond. It should be noted, however, that the bonding in the flat sp 2 6-rings of hBN is stronger than that in the puckered sp 3 6-rings of cBN, as indicated by the higher frequency BEN vibrations exhibited by hBN [hBN, νLO ⫽ 1610 cm ⫺1, νTO ⫽ 1370 cm ⫺1 (161); cBN, ν LO ⫽ 1304 cm ⫺1, νTO ⫽ 1054 cm ⫺1]. The energy values of lattice vibrations (phonons) of cBN have been determined from measurements of the infrared (IR) absorption (131,146,154) and the Raman effect (143,144,154– 160) (K. Aoki and O. Mishima, unpublished work; see Ref. 106) and are shown in Fig. 26 and Tables 6 and 7. Pressure (89,93) and temperature (158,159) effects on the vibrations have been investigated.

Figure 25 Illustration of a piezoelectric effect of cBN.

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Figure 26 Infrared and Raman spectra and phonon dispersion curves of cBN. (Data from Refs. 106, 131, 141, 146, 164.)

There was an attempt to calculate the phonon dispersion curve of cBN, which is shown in Fig. 26 (141). The derived phonon density of states is also shown. However, the calculated TO and LO modes (1200 and 1260 cm ⫺1, respectively) are quantitatively different from the experimental results (1056 and 1304 cm ⫺1, respectively). Further studies are necessary. Dielectric constants of cBN were derived by fitting experimental results for the infrared reflectivity of cBN to the so-called damped-oscillator model (146). The high-frequency and the low-frequency dielectric constants thus obtained, ε∞ and ε0, are 4.5 and 7.1, respectively. The experimental value for the refractive index n of cBN in the visible region is 2.11 (Fig. 27) (135). The high-frequency dielectric constant estimated from this value by using the relation ε ⫽ n 2 is 4.45, which agrees with the value of 4.5 obtained by the model fitting mentioned previously. Using the Lyddane-Sachs-Teller relation, ε0 /ε∞ ⫽ νLO 2 /νTO 2, with the values ε∞ ⫽ 4.5, νTO ⫽ 1064 cm ⫺1, and νLO ⫽ 1304 cm ⫺1, ε0 is calculated to be 6.9, which is close to the value 7.1 obtained by the model fitting. Thus, we have fairly reliable values (4.5 and ⬃7) for ε∞ and ε0. An experimental value of ε0 for a polycrystalline cBN compact was reported to be 6.5 (147). The bulk crystal is opaque for the light between νTO and νLO because of reflection originat-

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Table 6 IR and Raman Frequencies of cBN IR (from Ref. 146)

IR (from Ref. 131)

Raman (from Ref. 106) 438 694

650 700

1000–1260

884 928 1055 (TO) 1244 1305 (LO)

1000–1300

1370 1580

(1550) (1700) 1785 1818 (1840) 1885 1927 1985 2140 (2330)

1830

1920 2000 2230

1886 1990 2204

2465 2560

2540

2700 2910

ing from the extraordinary dispersion effect of the lattice vibration (Figs. 26 and 28). However, the damping effect makes the reflectance finite. This results in light transmission through thin films. The transmission spectra are often used to identify a cBN phase in low-pressure syntheses. For convenience, typical IR transmission spectra of thin-film cBN and other BN phases are shown in Fig. 29 by summing up reported spectra (161,162,163). The wide-range optical spectrum of cBN is drawn in Fig. 27. The spectrum becomes complex around 10 3 and 10 5 cm ⫺1 because of absorption by phonons and by electrons, respectively. Generally, the difference between LO and TO vibrations of a compound material can reveal its ionicity. The difference between νTO and νLO of cBN decreases slowly with pressure while both νTO and νLO increase with pressure, indicating that the cBN lattice becomes hard and tight under high pressure (143,144). The decrease in the νTO ⫺ νLO difference with pressure indicates that the ionicity of cBN decreases with pressure as observed for other III-V compounds (144).

Table 7 IR and Raman Frequencies of νTO and νLO Bands of cBN ν ν (TO) ν (LO)

IR

Raman

⫺1

1056 cm ⫺1 (active) 1304 cm ⫺1 (active)

1065 cm (active) (inactive)

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Figure 27 Wide-range optical spectra of cBN. (Data from Refs. 135, 146.)

C.

Thermal Properties

1. Thermodynamics The thermal properties of a lattice are generally affected by the anharmonicity of the potential between atoms and are described using lattice dynamic theories. The specific heat capacities (Cp) of cBN (164–167), wBN (164,168,169), and hBN (164,170), as well as their Debye temperatures deduced from the capacities, are shown in Fig.

Figure 28 Reflectivity and optical constants of cBN. (From Ref. 146.)

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Figure 29 Reported IR spectra of thin-film BN phases. (Data from Refs. 161–163.)

30. The compression curves and the linear thermal expansion coefficients (10,146,147,171,172) of these BN phases are also shown in Figs. 21 and 31. Using these experimental data as well as thermodynamic relations, we can estimate differences in the Gibbs free energy among these phases (164,169). The difference, ∆G, between cBN and hBN is shown in Fig. 32. The cBNhBN equilibrium phase boundary corresponds to the line where the difference becomes zero (Figs. 6 and 32). As shown in Fig. 32, Gibbs energy of hBN is lower than that of cBN at 1 atm and,

Figure 30 The heat capacities of cBN, hBN, and wBN. (Data from Refs. 165–171.)

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Figure 31 Linear thermal expansion coefficient of cBN. (Data from Refs. 10, 146, 147, 172.)

therefore, hBN is more stable than cBN at 1 atm, which agrees with theoretical results (78). The difference in the Gibbs energy between hBN and cBN at 1 atm and 0 K was estimated from experimental data to be about 510 cal/mol (169). Because this difference is small (that is, the experimental hBN-cBN boundary at high temperatures extrapolates to nearly zero pressure at 0 K), there is a possibility that cBN is more stable than hBN at low temperatures near 1 bar as described in Sec. II.C. The linear thermal expansion coefficients of materials with a diamond or zinc blende structure (Si, Ge, GaAs, etc.) near 0 K are commonly negative. This is due to the bending action

Figure 32 Calculated Gibbs free energy surfaces of cBN and hBN.

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Figure 33 Thermal conductivities of cBN, diamond, and Si. [cBN: sintered compacts (147,177–179); (⫻) Single crystals (181); (⫹) calculation (181)].

of atomic bonds caused by thermal agitation; that is, as temperature increases from 0 K, bond bending causes slight shrinkage of a lattice as in the case of bellows. For cBN, a negative thermal expansion coefficient was suggested (173); further experimental confirmation is needed. The reported Gru¨neisen parameters (γ) of cBN are listed in Table 5 (143,144,174). 2. Thermal Conductivity If there is a difference in temperature in a material, a flow of thermal energy occurs. The flow of thermal energy, Q, is proportional to the temperature gradient, dT/dx, and the coefficient is called the thermal conductivity, K. Thus, Q ⫽ KdT/dx. The thermal conductivity, K, is approximately proportional to the heat capacity (Cv ), the phonon speed (v), and the mean free path of phonons (l ) of the material; K ⬀ Cvvl (175). At low temperatures, the mean free path (l ) is almost constant and the heat capacity (Cv ) is proportional to T 3. Thus, K is proportional to T 3. At high temperatures, Cv is almost constant and l is proportional to T ⫺1. Thus, K is proportional to T ⫺1. The thermal conductivity of cBN appears to have this general tendency as shown in Fig. 33 (147,176–178). The thermal conductivity of cBN crystals is theoretically estimated to be 13 W cm ⫺1 K ⫺1 at room temperature, the second largest value after diamond (18–20 W cm ⫺1 deg ⫺1) (179). Values of some single crystals (180) and polycrystalline cBN compacts (147,176) (see Fig. 33) are 6–9 W cm ⫺1 deg ⫺1 around room temperature, which are larger than those of SiC (⬃5 W cm ⫺1 deg ⫺1), silver (4.2 W cm ⫺1 deg ⫺1), and copper (3.9 W cm ⫺1 deg ⫺1). Defects in single

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crystals and different phases in sintered polycrystalline compacts reduce the thermal conductivity (181,182).

D.

Optical and Electrical Properties

1. Defect and Optical Properties Crystals of cBN made by the high-pressure synthesis method usually contain twins, cracks, and inclusions. Taking into account the band gap energy, defect-free cBN crystals should be colorless. However, crystals usually exhibit colors: pale yellow, yellow, honey, amber, cinnamon, brown, orange, light blue, blue, blue-black, or almost black. This shows the presence of various lattice defects. Actually, impurities of O, Li, Ca, C, Mg, Si, Be, Al, Fe, P, As, Sb, Bi, etc. are reported. Beryllium doping to form p-type crystals results in blue color (4,184) (see Sec. III.D.2). It is worthwhile to point out here that p-type diamond also exhibits a blue color, suggesting resemblance of the electronic states participating in these optical absorption transitions. As shown by the transmission spectra in the upper graph of Fig. 34, colorless cBN crystals are transparent in the range ⬃1 to ⬃6.3 eV (6.3 eV corresponds to the onset of the fundamental absorption). Thin films of cBN made by a low-pressure method show similar transparency (207). The gradual decrease of transmittance occurring around 3 eV results in a yellow color (131). As the origin of the yellow color, nitrogen vacancies have been speculated (5), because the color appears on crystals that are supposed, from their synthesis conditions, to be nonstoichiometric Brich crystals. The main luminescence bands found in cBN crystals are summarized in Table 8 and Fig. 34. In most cases, the luminescence is excited by electron beams (cathodoluminescence, CL) (185–198). Luminescence caused by recombination of electrons and holes in pn junctions (injection luminescence, IL) has been observed (189,199). The origin of any of the luminescence bands is unknown at present, although there are discussions in the literature. The CL band US-1 (200) [also known as UCL (188)] is commonly observed in cBN crystals of various origins. This band shows a vibrational structure with remarkable anharmonicity. Participating vibrations are at 127–145 meV and correspond to the energies of characteristic cBN optical phonons: TO, 131 meV, and LO, 162 meV (Fig. 26). The band GC-1 (186,187,190,192) appears around 1.76 eV and shows Mo¨ssbauer-type phonon structure. It resembles the CL band, GR-1, of diamond, which is associated with the neutral vacancy. By analogy, GC-1 was then speculated to be related to N vacancies (190). Be-doped and Si-doped crystals showed CL spectra called PCL and NCL, respectively. When a pn junction was made under conditions similar to those for these crystals, two types of IL specta were observed (188,199). Those IL spectra are quite different from the PCL and NCL spectra. In other Si-doped crystals, a CL band called the T band having an oscillating structure has been reported in the region 4–5 eV. Measurements of the nuclear magnetic resonance (NMR) (201,202) and the electron spin resonance (ESR) (156,183,203–205) of cBN treated under various conditions have been reported. The temperature dependence of the magnetic susceptibility of cBN was studied to evaluate the contribution of the lattice impurities and defects (206). In principle, impurities or nonstoichiometry of a crystal should be related to a composition phase diagram as shown in Fig. 35 and should be homogeneously distributed in the crystal if the crystal was annealed at sufficiently high temperatures. However, for example, in a blue Bedoped crystal, the blue color is often inhomogeneously distributed, indicating an inhomogeneous

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Figure 34 Luminescence bands and absorption coefficient of cBN. (Data from Refs. 135, 187–190, 192, 193, 195, 196, 199, 208.)

distribution of Be impurities. The inhomogeneous spatial distribution of cathodoluminescence that has been commonly observed (e.g., Ref. 200) also indicates an inhomogeneous distribution of some defects. Therefore, impurities and defects are not in their thermodynamically equilibrium states. This suggests that these defects are taken into crystals during growth and that they have difficulty diffusing in the crystals at the growth temperature (usually 1500–1700°C). It suggests further that doping of impurities by the diffusion method from crystal surfaces is rather difficult at the growth temperatures commonly used.

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Table 8 Luminescence of cBN Peak energy E (eV)

Peak wavelength (nm) ⫽ 1240/E (eV)

Mark a

Notes

⬃4.8 ⬃4.2 ⬃3.8 ⬃3.5 3.18 ⬃3.0 2.99 2.84 ⬃2.7 ⬃2.45 ⬃2.4 2.33 2.27 ⬃2.2 2.15 1.99 1.86 1.79 1.76 ⬃1.7 1.63 1.55

⬃260 ⬃300 ⬃330 ⬃350 389 ⬃410 414 437 ⬃460 ⬃510 ⬃520 533 546 ⬃560 577 623 669 693 705 ⬃730 761 800

AIL T BIL PCL O US-1 Γ PC-1 NCL B C[EM] PC-2 RC-1 A RC-2 RC-3 RC-4 PC-3 GC-1 C GC-2 GC-3

IL-A CL, Si-doped,4.8eV(max) IL-B CL, Be-doped, p-type CL, Si-doped CL, PL, undoped,(UCL) CL, Si-doped CL CL, Si-doped, n-type CL IL,CL CL CL,(RK-1?) CL CL,(RK-2?) CL,(RK-3?) CL CL CL CL CL CL

a

Ref. 189, 199 189, 189, 199 189, 199 196 189 196 189, 196 193, 196 193, 193, 200 196 187, 196 187, 192

201 201 201 191

201 195 195 195

188, 192, 194 188, 192, 194

CL, Cathodoluminescence; PL, photoluminescence; IL, injection luminescence of pn diodes; PC, CL of pressuretreated crystals (pressure cubic, from Ref. 196); RC (RK), CL of electron (ion)-irradiated crystals (radiation cubic, from Ref. 193); GC, CL of common crystals (general cubic, from Ref. 187).

2. Semiconducting Properties As pointed out in Sec. III.A, cBN has the widest band gap (⬃6.3 eV) among known semiconductors. Of course, undoped pure cBN crystals should be good electrical insulators at room temperature. However, the crystals usually made by the high-pressure method are slightly conductive, having resistivities of 10 9 –10 10 Ω cm, due to unknown defects in the crystals (4,10,208). The semiconducting properties of cBN were demonstrated in early cBN studies from measurements of the thermoelectric power, resistivity, and temperature dependence of the resistivity (4). Since then, upon doping with impurities such as Be, Si, S, C, As, P, Se, and Te, cBN has been reported to have semiconducting properties (4,65,177,183,184,209). Be doping results in p-type conduction and Si doping in n-type conduction. Although, to date, there has been no convincing paper on the Hall effect and conduction types, the fact that light emission around 5.8 eV occurs in a forward-biased pn junction that consists of Be-doped p-type and Si-doped n-type (199), as described later in Sec. VI.B, supports the existence of both Be-doped p-type and Si-doped n-type crystals. The spatial inhomogeneity of resistance in semiconducting cBN single crystals has thus far prevented detailed measurement of their electrical properties. The large and unstable contact resistances at the electrodes of cBN are also troublesome. Reported resistances of semiconduct-

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Figure 35 Plausible phase diagrams of stoichiometry, (a) Ref. 5 and (b) Be doping of cBN.

ing cBN are summed up in Fig. 36. The resistance of n-type crystals is usually higher than that of Be-doped p-type crystals. The activation energy of resistance of Be- (and Si-doped crystals has been measured as ⬃0.23 and ⬃0.24 eV in the range 20–600°C, respectively (184). Semiconducting cBN polycrystalline compacts, made by sintering Be-doped cBN powders, generally showed higher resistivity than Be-doped single crystals (65,210). The activation energy of resistance (20–600°C) of these p-type compacts was similar to that of p-type single crystals. The voltage-current (V-I ) relation of these compacts was found to be nonlinear, having the characteristics of that of varistors. That is, the resistance of the compacts decreased with applied voltage. With the Si-doped n-type compacts, the resistance was too large to obtain reliable results. The contact resistance between cBN and electrodes of conventional materials is usually 10 4 –10 6 Ω at room temperature (184). Although the contact resistance decreases at high temperatures, it is still quite large. In order to form an ohmic contact and reduce the contact resistance, a few materials have been examined. Trials of materials such as Cu (208), Ag (4,184), Au (210), Al (210), Cr-Ni (177), and Mo and Pt (200) have been reported in the literature and patents. Ohmic electrodes with relatively low contact resistance have been made using Ti-Au and AlAu on Be-doped p-type crystals (210). The contact resistance of Ti-Au was 10 2 –10 3 Ω at room temperature. Annealing procedures are considered to be effective. Formation of Ti or Al nitride probably occurred. E.

Chemical Properties and Thermal Stability

The chemical reactions of cBN are an important consideration when synthesizing cBN with solvents, cutting materials with cBN tools, forming electrodes on cBN surfaces and so on. Generally, wetting between a material and a molten metal depends on various conditions such as the surface conditions of the metal and the material (e.g., the presence of oxidized films). According to a study of the wetting between hBN and molten Al (211), interfacial reactions such as the formation of nitride or boride films of metal components in contact control the

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Figure 36 Electric resistance of cBN. (Data from Refs. 64, 178, 185, 210.)

wetting behavior. A similar mechanism presumably works in cases involving cBN. For example, in cases of Ti and Al with cBN, TiN and AlN, respectively, or metal borides such as AlB12 are considered to be formed at high temperatures. Metals Fe, Ni, Co, and Mo have been reported to react with cBN above 1300–1400°C and Si above ⬃1500°C (10). Metals Sn, In, Ga, Ge, Cu, Ag, Au, and Pb do not wet cBN below ⬃1200°C (10,212,213). Etchants and catalysts (or solvents) of cBN also react with cBN (see Secs. II.D.2.b. and IV.A.2). They are alkaline or alkaline earth metals, their nitrides and boron nitrides, H2O, alkaline salt etchants (NaOH, LiOH, KOH, Na2CO3, NaNO3), and acid etchants (HNO3 ⫹ H2O). The reaction occurs promptly at high temperatures (usually above 1300–1400°C at high pressures). As described in Sec. II.D.2.b, some base etchants appear to react more rapidly with (111) nitrogen surfaces of cBN crystals and acid etchants with (111) boron surfaces. When cBN crystals are heated in air, oxidation occurs above ⬃900°C accompanied by removal of nitrogen gas. Thus, B2O3 (melting point ⬃580°C and boiling point ⬎1500°C; glassy at low temperatures) forms on the surfaces of cBN (10,214). If the heating is done quickly (or in vacuum or in nitrogen gas), cBN is converted above 1400–1600°C to a black graphitic BN phase (which may not be hBN) (10,215) or white hBN. Cubic BN may also react with its container (or decompose) with formation of a boron-rich material and removal of nitrogen gas,

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Figure 37 Change of cBN at high temperatures at 1 bar.

as observed in a vacuum-heating experiment with hBN in a carbon container (215). The conversion of cBN occurs kinetically depending on the crystal quality and contaminants (Fig. 37) (214).

IV. SYNTHESIS OF CUBIC BN Because the structure and the properties of cBN resemble those of diamond, the synthesis of cBN may also resemble that of diamond. Indeed, we can make cBN crystals with methods similar to those used for synthesis of diamond, that is, the high-pressure method and the lowpressure vapor deposition method (see Ref. 13 for a review). Cubic BN, a two-element compound, is apparently more difficult to synthesize than diamond because of problems of stoichiometry, antiphases, and so on. A.

High-Pressure Synthesis

We can make cBN crystals by subjecting a source BN material (hBN, tBN, etc.) to high-pressure and high-temperature conditions in which cBN is thermodynamically stable. For example, hBN, tBN, or wBN transforms directly to cBN (see Sec. II.C). Generally, we have difficulty in controlling nucleation and crystal growth in direct solid-solid transformations. Cubic BN crystallizes when liquid BN freezes at high pressures (216). It is, however, experimentally difficult to keep the high-temperature liquid state (⬎⬃3000 K) under high pressures for a long time. Cubic BN may be obtained by decomposition of materials containing B and N atoms. It was reported that cBN crystals appeared when Mg3BN3 reacted with H2O at high pressures (218). Cubic BN crystals can be grown under relatively low-pressure and low-temperature conditions (P⬃5 GPa, T⬃1500°C) when suitable catalysts are used, as described in the following sections (for a review, see Refs. 11 and 218). Because the pressures and temperatures used for the catalyst method are similar to those used for diamond synthesis, we can appropriate the relatively well established high-pressure technology of diamond synthesis. Two types of high-pressure apparatus are schematically illustrated in Fig. 38. They are the so-called belt-type apparatus and the multianvil apparatus, both used in diamond and cBN factories. The belt type is a modified piston-cylinder apparatus. There is also an apparatus called the toroid type, which is a modified Bridgman-type anvil apparatus. Materials held in the central chamber of these apparatuses are squeezed with anvils made of tungsten carbide. To prevent outflow of the materials between the anvils, pressure-sealing

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Figure 38 The belt type and the multianvil type of high-pressure apparatus.

gaskets are placed between them. High pressure is generated in the central chamber, whereas the ends of the gaskets are at 1 bar. Therefore, a large pressure gradient exists in the gaskets. The temperature is increased by having an electric current flow through a graphite (or metal) heater located inside the chamber while the surrounding anvils are cooled with water.

1.

The Catalyst (Solvent) Method: Principle

Spiral growth layers (219) and etching patterns (110) were observed on surfaces of cBN crystals made by the catalyst method. This suggests that crystals grew in a liquid state and that the catalyst acted as a solvent or a flux. As in the case of diamond synthesis with a catalyst, cBN crystals are usually considered to precipitate in a molten catalyst (or solvent) when B and N atoms in the liquid are supersaturated (220) [the liquid ⫹ cBN (‘‘liquid’’ abbreviated L hereafter) region of Fig. 39]. Actually, phase diagrams of some BN-solvent systems have been reported (220–223). Other reported catalysts are generally assumed to act as solvents even though their solvent action has not been confirmed. In accordance with the experience gained with diamond synthesis, we can think of two solvent methods: the so-called high-pressure film method (224) and the temperature difference (or temperature gradient) method (225,226). Both methods provide supersaturation of B and N atoms in a solvent from which BN crystals are precipitated. The high-pressure film method may be regarded as a solvent-mediated phase transition in which hBN dissolves in a solvent and cBN crystals precipitate from it. Because hBN is metastable and cBN is stable at high pressures, hBN should dissolve more in a high-pressure solvent than cBN (Fig. 39). Therefore, B and N atoms supersaturate for cBN; as a result, deposition of cBN crystals occurs. The temperature difference method utilizes the difference in solubility at different temperatures. Consider a solvent with high- and low-temperature regions. Generally, a material dissolves more easily in a higher temperature region than in a lower temperature region. Then, in the low-temperature region, the material becomes supersaturated in the solvent and precipitates. When this general method is applied for cBN growth at high pressures, the BN source material dissolves in the high-temperature region and cBN crystals precipitate in the low-temperature region.

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Figure 39 Pressure-temperature-solvent composition phase diagram of cBN.

2.

Catalysts (or Solvents)

Many catalysts are known for the synthesis of cBN at high pressures (7,13) (Table 9). They are alkali metals (15), alkaline earth metals (15,219), their hydrides (236), their nitrides (15,219– 221,228,230,235), their borides (234) and boron nitrides (101,110,219–221,223,235), other metals (15,83), water (237–240,245), fluoride and fluoronitride compositions (241), ammonia compounds (240,241,244,245), hydrochloric acid (246), aluminum nitride (247–250,251), and silicon and its compounds (251,252). Other materials such as Al-Ni, Al-Co, Al-Mn, inconel, Si3N4, ZnO, and LiSrBN2 have been reported in patents. The pressure-temperature cBN synthesis conditions for some catalysts (or solvents) are shown in Fig. 40. The best catalyst (or solvent) for providing good cBN crystals under relatively low-pressure, low-temperature conditions is unknown at present. Alkali boron nitrides or alkaline earth boron nitrides (Li3BN2, Mg3BN3, LiCaBN2, etc.) appear to be better solvents than alkali or alkaline earth metals and their nitrides (Mg, Mg3N2, etc.) because the former boron nitrides already contain adequate B and N atoms in their compositions and are ready to provide supersaturation of B and N atoms (Fig. 41a: X ⫽ Mg3N2, Y ⫽ Mg2BN3, etc.). The reported Mg3B2N4 (or Ca3B2N4) solvent (47,219,223) is probably Mg3BN3 (or Ca3BN3) as shown by chemical and X-ray analyses of Mg3BN3 (253). When cBN crystals were grown at high pressure using an LiCaBN2 solvent and then cooled slowly at high pressure and recovered to 1 bar, erosive patterns were observed on the surfaces of the recovered cBN crystals (110). This suggests complexity in the BN-solvent phase diagram and indicates the existence of a peritectic relation in the LiCaBN2-BN system (Fig. 41b). Thus, when cBN crystals made in the L⫹cBN region of Fig. 41b were cooled, the crystals were thought to dissolve in the L⫹Y region of the figure. Boron nitride solvents also dissolve carbon, AlN, and BP. If a sufficient amount of AlN (or BP) is dissolved with BN in a solvent such as Li3BN2 at high pressure, crystals of AlN (or

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Table 9 Solvents for cBN Synthesis at High Pressures and Their References (LiEBEN) Li (15) Li3N (15, 220) Li3BN2 (101, 220)

(HELiEBEN) LiH (236) LiNH2 (236) (HENaEBEN)

(MgEBEN) Mg (15) Mg3N2(220, 228, 230) Mg3B2N4 (219, 221) MgB2 (⫹Bi) (234)

(CaEBEN) Ca (15) Ca3N2 (15, 220, 235) Ca3B2N4 (223, 235) (LiECaEBEN) LiCaBN2 (110) (AlEBEN) AlN (247, 249, 251) (other metals) Sb, Sn, Pb (15) Co (83) AgECd, SnECu, Fe3Al

(HEBENEF) NH4F (241)

(LiEBENEF) LiBF4 (241) (NaEBENEF) NaF (241)

NaH (236)

(HEBENECl) HCl (246) NH4Cl (241)

(HECaEBEN) CaH2 (236)

(FEBENEBr) NH4Br (241)

(HEBaEBEN) BaH2 (236)

(HEBENEO) H2O (237–240, 245) H3BO3 (240, 244) NH4NO3 (244) (NH4)2B4O7 ⋅ 4H2O (244, 245) (HEBECENEO) (NH2)2CO (240, 244)

(MgEBENEF) MgF2 (241) (CaEBENEF) CaF2 (241) (GaEBENEF) GaF3 (241) (BiEBENEF) BiF3 (241) (HELiEBENEF) LiHF2 (241) (HEBESiENEF) (NH4)2SiF6 (241) (NaEBESiENEF) Na2SiF6 (241) (BaEBESiENEF) BaSiF6 (241)

Figure 40 Phase diagram for cBN synthesis using solvents. (Data from Table 10.)

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Figure 41 Proposed BN-solvent phase diagrams.

BP) grow with the cBN crystals (O. Mishima, unpublished work). The existence of compounds such as Li3BN2, Li3AlN2, and Li3GaN2 suggests chemical similarity among BN, AlN, and GaN. 3.

Preparation and Analysis

a. Powders Cubic BN powders (usually ⬍⬃0.5 mm in size) are produced when hBN powders mixed with solvent powders are subjected to pressure ⬎⬃5 GPa and temperatures ⬎⬃1500°C for several minutes. Commercial cBN powders are mass produced in this way. For diamond synthesis by the high-pressure film method, described in Sec. IV.A.1, a thin solvent film always exists between the graphite source material and the diamond crystal produced. The formation mechanism of cBN powders is believed to be the same as that for the synthesis of diamond by the highpressure film method, although a solvent film between the hBN source material and the cBN crystal produced has not been observed as clearly as it has been for diamond (223). If the mechanism of the high-pressure film method is assumed, the degree of supersaturation of B and N atoms in the solvent is determined from the solvent-BN phase diagram if pressure, temperature, and solvent material are fixed (Fig. 42). Generally, the degree of supersaturation affects the nucleation and growth of crystals. If a pressure-temperature condition for cBN synthesis is chosen near the hBN-cBN equilibrium boundary, the degree of supersaturation of B and N atoms for the cBN phase is small (Figs. 39 and 42). Spontaneous nucleation is then suppressed and the crystals grow slowly, producing relatively large, high-quality crystals. To date, cBN crystals up to about 1 mm in size have been obtained by keeping the growth condition near the hBN-cBN equilibrium boundary. When a small amount of a semiconductor impurity is added to the solvent, semiconducting cBN powders (p- and n-type powders) are obtained (4). By growing an n-type cBN crystal on a p-type cBN seed, a functional pn-junction crystal (⬍⬃1 mm in size) was made using this high-pressure film method [T. Okubo, private Communication; the diodes were described in his patent (254)]. b. Larger Crystals We can grow crystals larger than 1 mm using the temperature difference method (101,110) (Fig. 43). Growth of crystals by this method is controlled by the temperature and the temperature

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Figure 42 Cubic BN formation by the high-pressure film method.

difference. When the temperature difference is small and thus the degree of supersaturation of B and N atoms is small, spontaneous nucleation is suppressed and cBN crystals grow slowly on seed crystals. High temperatures induce rapid growth of the crystals, providing relatively large but low-quality crystals with cracks and solvent inclusions. At low temperatures, the crystals grow very slowly. Under appropriate growth conditions, cBN crystals up to ⬃3 mm in size grow in several tens of hours (5,101,110). Naturally, the size of the crystals produced is ultimately limited by the size of high-pressure apparatuses, which is restricted to be smaller than the size of synthesis apparatuses at normal pressure. Using this temperature difference method, we can obtain semiconducting crystals by adding a small amount of a suitable impurity to the solvent (184,201). To make a pn-junction crystal, two compressions were carried out. In the first compression, a p-type crystal was made by adding a small amount of beryllium (p-type dopant) to the solvent. In the second compression, the p-type crystal was located at the low-temperature end of the growth cell as a seed crystal. By adding silicon (n-type dopant) to the solvent, an n-type crystal was grown on top of the ptype seed. A functional pn crystal was thus fabricated (184,199). Regarding homoepitaxial growth of cBN on a cBN seed, a clear boundary between the grown crystal and the seed crystal was obtained when LiCaBN2 was used as a solvent (184,199). When Li3BN2 was used, it appeared difficult to make a clear interface.

Figure 43 Cubic BN formation by the temperature difference method.

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c. Sintered Polycrystals At high temperatures close to the melting point of materials (or at temperatures above about two thirds of their melting temperature), atomic diffusion in a crystal becomes active and sintering, recrystallization and plastic deformation occur. Cubic BN powders are thus sintered without any sintering aid when they are subjected to high enough temperatures at high pressures (usually, E in Fig. 40) (23,63–65,176,255,257). Sintering aids (or solvents) assist in sintering cBN powders at lower temperatures. Cubic BN compacts are also produced from an hBN starting material by a simultaneous hBN-cBN conversion and sintering process using a small amount of solvent (256). When cBN powders are well sintered, with or without a sintering aid, transparent (or translucent) cBN compacts are obtainable (246,257). Cubic BN composite materials with TiC, TiN, Al2O3, AlN, Si3N4, WC, etc. are also produced. The mechanical properties of these materials depend on their microstructure such as grain size distribution and voids in the composites (258). Because these composite compacts are useful as cutting tools, they are usually described in the patent literature. Some reported elements for these composites are listed in Table 10 (7). A BN material is sintered with these elements and/or their nitrides, carbides, borides, and carbonitrides. Sintering of carbon precoated cBN grains and formation of BX CY NZ grain boundaries were claimed in a patent, as quoted in Ref. 7. Polycrystalline compacts with a S, Se, or Te dopant have been reported (259). When Bedoped cBN semiconducting powders were sintered without any sintering aid, semiconducting compacts were obtained (65). Cubic BN compacts were also reported to be made by shock wave compaction (260,261). The properties of the compacts depended on the grain size of the starting cBN powders, and coarse cBN powders were shown to be desirable for producing a consolidated compact. 4. Problems in Crystal Growth at High Pressures Synthesis of cBN at lower pressures and lower temperatures may improve the productivity of cBN and its cost performance. A method for growing large crystals quickly is also desirable. A search for new solvents, as well as new synthesis methods, has therefore been carried out. For diamond growth at high pressures, it seems to be possible to obtain a perfect diamond crystal, as revealed by X-ray topography. Large single-crystal diamonds up to 17 mm in size have been grown and 10-mm diamond crystals are now commercially available. Because the high-pressure synthesis methods for cBN are similar to those used for diamond, perfect and large cBN crystals may also be expected. However, growth of large cBN crystals is proving more difficult than growth of large diamonds. Large and good cBN crystals are reproducibly obtained but productivity is low at present. This is because of immature growth techniques in areas such as controlling nucleation, pressure, temperature, solvent, and purity. Cubic BN, a two-element compound, also has intrinsic problems, notably with easy cleavage, difficult control of stoichiometry, and so on. Fine cracks, solvent-trapped pools, and twins, which are probably caused by rapid crystal growth, are often observed in cBN crystals made at high pressures. An inhomogeneous distribution of body color is usually observed in cBN single crystals, Table 10 Some Reported Elements for cBN Composite Compacts Transition elements

Y

Ti Zr Hf

V Nb Ta

Cr

Mn

W

Zr

Fe

Co

Ni

Cu

Zn

3a

4a

Al

Si

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Figure 44 Schematic potential surface and formation of a metastable phase.

indicating an inhomogeneous distribution of defects in the crystal. To date, precise control of doping levels and the distribution of impurities in cBN crystals, which determine semiconducting properties, has not been achieved with high-pressure methods. Also, complicated devices are obviously difficult to make under high pressures. B.

Low-Pressure Synthesis

Although cBN is metastable at low pressures, it can be synthesized below 1 bar in a manner similar to the formation of diamond at low pressures. In the early 1980s, a small amount of cBN was claimed to exist with a large amount of hBN (or tBN) in a BN deposited film. At present, a small amount of hBN (or tBN) remains in a cBN polycrystalline film although the cBN crystals forming the film are extremely small (⬍⬃0.1 µm). Studies of low-pressure methods for producing cBN films are continuing with a view to future applications. 1. Principle Under conditions in which hBN is thermodynamically stable, we can synthesize metastable cBN. As mentioned in Sec. IV.A.1 on the high-pressure film method, a metastable material should dissolve more in its solvent than its stable phase. A stable material usually grows on the stable-phase substrate. However, in hydrogen-mediated diamond synthesis at pressures below 1 bar, stable graphite crystals were etched by hydrogen (or hydrocarbon) gas while metastable diamond crystals grew at the site where the graphite crystals were located. This phenomenon (namely, etching of graphite and growth of diamond at low pressures) is apparently different from the usual solution phenomenon, where metastable materials should dissolve easily. The surface energy difference between a small nucleus of graphite and a small nucleus of diamond in the presence of hydrogen (or the difference in their nucleation processes) is not influential in the growth process because graphite crystals of stable phase already exist as the substrate. From common thermodynamic phase diagram such as Fig. 39, we cannot explain this graphite → diamond change and the corresponding hBN → cBN change (263) at low pressures. Low-pressure synthesis of diamond and cBN involves growth under thermodynamically nonequilibrium conditions. The formation of the nonequilibrium phase cBN may be understood in terms of a schematic potential diagram of low-pressure conditions (Fig. 44). The Gibbs free

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Figure 45 A schematic graph of the Gibbs free energy of stable, metastable, and liquid phases versus temperature.

energy of the high-pressure phase is higher than that of the low-pressure phase. In other words, cBN is in the metastable state. When a certain amount of energy is absorbed by the low energy and equilibrium substance, hBN, a certain concentration of the metastable substance cBN is formed through the excitation of route A in Fig. 44 beyond the concentration determined according to the thermal equilibrium between the both states. Part of the metastable state substance reverts back to the stable hBN through route B. The metastable state is prevented from staying there by the peak (so-called transition state) in the middle of both states. If a certain concentration of the metastable state substance thus formed is kept until it is taken out of the synthesis system, one can obtain it as the product. Thus, excitation beyond the thermal equilibrium of the stable state substance is a necessary condition for obtaining cBN by low-pressure methods. Actually, various experiments on low-pressure cBN synthesis suggest that excitation of the surface of a growing film, for example, by a ion beam, is important. Experimental data are usually restricted to measurements of properties such as the deposition rate and film composition. It is difficult to clarify the underlying low-pressure synthesis mechanisms from these measurements because the elementary reactions involved in the methods are quite complex. We can think of various mechanisms for the reaction in the low-pressure methods: for example, generation of high pressure and high temperature or generation of compressive stresses in a ion-bombarded film (265,266), induced by thermal spikes due to impinging ions (47,265). However, conclusive and detailed mechanisms have not yet been elucidated. Generally, the low-pressure methods have the potential to produce new metastable materials with novel structures and properties. The melting temperature of any metastable phase (Tm2 in Fig. 45) must be lower than that of a stable phase (Tm1 in Fig. 45). A new BN phase obtainable by novel processes using the low-pressure method should have a lower melting temperature than that of hBN near 1 atm. 2. Preparation and Analysis There are some review articles on low-pressure syntheses of cBN (8,9,12). The reported lowpressure methods have usually been named according to the techniques involved, and the variety

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of the names has caused some confusion. Reported experiments can be categorized as employing CVD and PVD methods. The CVD method is chemical vapor deposition in a reactive hydrogen gas atmosphere. The PVD method is physical vapor deposition in vacuum or in a rather nonreactive gas atmosphere. The PVD method can be further categorized into four types: (a) B deposition and simultaneous N (and Ar) ion bombardment, (b) B evaporation in reactive N (and Ar) gas, (c) radio-frequency (RF) sputtered BN deposition in N and Ar sputtering gas, and (d) laserablated BN deposition with or without N ion bombardment. Synthesis of cBN by a low-pressure method was claimed by Vickery in 1959 without any detailed description of his experiment or analysis (267). Around 1980, Sokolowski et al. (268,269) and Weissmantel et al. (47,264,270) reported the synthesis of cBN (or iBN) and showed electron diffraction patterns of the material so produced. Since then, confirmation of cBN synthesis have been attempted by many researchers. Efforts to increase the cBN yield have also been made. Nevertheless, clear identification of cBN formation has not been made because of the smallness of BN grains and difficulty in distinguishing cBN from hBN, tBN, pBN, or even from surrounding materials by IR (271,272) and diffraction methods (273–275) (Y. Matsui, private communication). Combined analyses of the structure, the composition, and the atomic bonding of the films produced by IR, diffraction, and electron spectroscopy etc. could improve the situation. In 1987, Inagawa et al. (276) and Chayahara et al. (277,278) succeeded in increasing the cBN yield by applying a negative bias potential to the substrate. The importance of biasing to the substrate has been confirmed by other researchers. At present, PVD and CVD methods can provide films made of an apparently almost single (80–100%) cBN phase. Some important factors to increase the cBN yield are a negative bias of the substrate, ion beam bombardment of the growing surface, dilution with Ar gas, and so on. The necessity for proper bias to the substrate has been well confirmed in CVD and PVD (RF sputtering) methods (162,279–283). Ion bombardment by a bias potential during film growth was often speculated to be important for cBN formation. Ions were accelerated by an externally applied voltage or a negative self-bias of the substrate (which is caused by the higher mobility of electrons than ions). However, films would be etched by sputtering if the bias potential was too large (162). The true mechanism of cBN formation with a negative bias of the substrate is unknown. By using B (or BN) deposition with simultaneous N (⫹ Ar) beam bombardment, cBN was formed reproducibly without bias control (284–289). a. Chemical Vapor Deposition It seems to have been established that the bias to the substrate is important in increasing the cBN yield in the case of RF plasma CVD (277), electron cyclotron resonance (ECR) plasma CVD (277,280,290,291), and inductively coupled RF plasma (ICP) CVD (279,292). A suitable amount of dilution gas such as Ar and a high ion flux to the substrate promote cBN formation (263,280). The hydrogen content in the gas needs to be small because BN deposition with a bias was difficult due to etching of the film by the gas (Fig. 46) (292). Without the bias, formation of cBN (or hard BN) was reported with ECR plasma CVD (293), microwave plasma CVD (275,294), RF plasma CVD with a thermal activation filament (295), and reactive evaporation of B or H3BO3 in an NH3 discharge (296–298). The amount of cBN in an hBN or tBN matrix of these films appears to be smaller than that of the films made with bias control. Ion beam deposition from a borazine (B3N3H) plasma (299) or from ionized borazine (264,270,300) was also reported to produce a hard BN material. Formation of a cBN film by the DC plasma CVD method has also been claimed (301). Laser-assisted plasma CVD, in which an excimer laser beam irradiated a growing film, was reported to be effective for growing cBN crystals (302,303).

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Figure 46 Chemical vapor deposition; parameters for growth of cBN. (Data from Refs. 278, 280, 281, 291, 293.)

b. Physical Vapor Deposition B deposition and simultaneous N beam bombardment on a growing film. Films of an almost single phase of cBN were reproducibly formed when evaporated or sputtered B atoms were deposited with simultaneous bombardment by N and Ar ions. The Ar content and the ion beam energy were shown to be important parameters for the formation of cBN (Fig. 47)

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(284,285,288,289,304,305). [However, there is a report which suggests that the addition of Ar plays an insignificant role when neutralized N atoms are bombarded (306).] Without Ar ion bombardment or when the beam energy was not appropriate, deposited films were mainly hBN, tBN, or iBN (47,264,270–272,308–310). Implantation of N ions in a boron substrate did not result in any clear evidence of cBN formation (311–313). B evaporation in reactive N and Ar gas. Nearly single-phase films of cBN were reproducibly formed when B atoms were evaporated in a N and Ar plasma and B and N atoms were deposited on a bias-controlled substrate (162,266,276,281,314). Formation of cBN was pro-

Figure 47 B deposition and simultaneous N beam bombardment. (Data from Refs. 285, 286, 289, 305.)

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moted by mixing Ar gas and by controlling a negative RF self-bias potential of the substrate (Fig. 48). Radio-frequency sputtered BN deposition in an N and Ar sputtering gas. Radio-frequency sputtered BN deposition in an N (and Ar) plasma without any proper control of the substrate bias potential or the gas composition resulted in the formation of mainly hBN (or tBN) (315– 317). In 1987, a role of the negative bias potential of the substrate in cBN formation was suggested (318). In 1990, films of an almost single phase of cBN were successfully obtained by sputtering hBN in an Ar-rich gas and depositing B and N atoms on a sufficiently negatively biased substrate. An additional magnetic field assisted cBN formation (282,283,319). Sputtered matter from a BN target was suggested to be in an atomic state, not in a BN molecular state (Fig. 49) (282). Laser-ablated BN (or B) deposition with or without simultaneous N beam bombardment

Figure 48 B evaporation in reactive N ⫹ Ar gases. (Data from Refs. 163, 208, 277, 314.)

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Figure 49 The RF sputtered BN deposition in N ⫹ Ar gases. (Data from Refs. 283, 284.)

on the growing films. When a BN material was evaporated by irradiation with a CO2 laser (λ ⫽ 10.6 µm) (286), a KrF laser (λ ⫽ 248 nm) (285,287,320–322), or a Q-switched ruby (λ ⫽ 694 nm) or neodymium (λ ⫽ 1.06 µm) (163) laser in vacuum, the deposited films were tBN or hBN and were nitrogen deficient. In the initial stage of deposition, epitaxial growth of a cBN thin film on a Si crystal substrate up to ⬃10 nm and successive growth of a polycrystalline hBN or tBN film on this cBN layer were indicated (321,323). Laser-ablated BN deposition with a simultaneous supply of N ions on the growing film was found to be successful in making cBN-rich films (Fig. 50) (286,287,320). Laser-ablated BN (or B) deposition in N2 or NH3 (plasma) gas has shown, so far, no evidence of cBN formation (163,322,324).

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Figure 50 The laser ablation method. (Data from Refs. 287, 288.)

3. Problems in the Low-Pressure Synthesis The size of the cBN crystals made at low pressures has been too small (⬍100 nm) for us to observe the growth surfaces. The small size of the cBN crystals causes a slight suspicion that the deposited microscopic (or nanoscopic) cBN might be different from the macroscopic cBN bulk crystal. Growth of larger cBN crystals is a current problem. There is a paper that details the growth of large cBN single crystals (⬎1 µm). The crystals were grown by a CVD method with simultaneous laser irradiation of the growing film (302,303). Epitaxial growth of a cBN film on a single-crystal substrate is another problem. Although there have been reports of deposition of preferentially oriented cBN crystals on a Si substrate (287,302,321), good growth of a cBN film on a single-crystal substrate has not yet been attained.

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Another problem is the poor adhesion strength of cBN films on the usual substrates (e.g., Si crystals), which causes flaking and peeling off of the film with time when the film is exposed to air. High residual compressive stresses in the deposited film were thought to be the reason for the degradation (300). Unwanted trapping of gases might cause the degradation. Selection of suitable substrate materials (or buffer layers) reduces the degradation of films. Use of a diamond substrate hindered the peeling off of a cBN film (291). Buffer layers between a cBN film and a Si substrate, such as B-rich layers (290,325,326) and SiNx layers, were reported to be effective in preventing the peeling off. The usefulness of a thin hBN interlayer is a subject of controversy at present (282,283).

V.

HETEROJUNCTIONS

A heterojunction between cBN and diamond is possible (327,328), and theoretical calculations (329,330) suggest that the junction has a type II alignment of the band-offset diagram (Fig. 51). Geometric considerations are discussed in Ref. 330. Regarding the formation of a diamond-cBN junction at high pressures, cBN can grow epitaxially on a diamond seed when a suitable solvent, such as Li3BN2, is used (328). Generally, growth of cBN, which is a two-element material, on a diamond lattice causes an antiphase problem (Figs. 52 and 53). The surface morphology of a cBN crystal that was grown on a diamond seed exhibited characteristic features of the antiphase (328) (see Sec. II.D.2.a). To date, growth of diamond on a cBN seed by the high-pressure method has not been reported. Synthesis experiments for the formation of a diamond-cBN junction are listed in Table 11. Regarding formation of the junction at low pressures, diamond was used as a substrate for cBN deposition in order to improve adhesion of the cBN film to the substrate (291,294,313). A low-pressure diamond film was also deposited on a substrate of a cBN single crystal (or polycrystal) that was made at high pressures (275,329,332–335) or on a polycrystalline cBN film made at low pressures (336–338). The diamond film could grow epitaxially on some kinds of cBN surfaces (35,332,339). The (111)B surface of a cBN crystal was believed to be more useful as a substrate for diamond growth than the (111)N surface (332). High-resolution electron microscopy confirmed the diamond-cBN parallel epitaxy (335,339), showing almost no misfit

Figure 51 The type II alignment of the band-offset diagram for a C/BN (110) heterojunction. (From Ref. 330.)

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Figure 52 Formation of an antiphase at the C-BN interface.

Figure 53 The (100) surface morphology of cBN grown on a diamond single crystal.

Table 11 Methods of Synthesis for the Formation of a Diamond-cBN Heterojunction and Their References Diamond on cBN

cBN on diamond

LP method

HP method

LP method

HP method

cBN substrate

cBN substrate

Diamond substrate

Diamond substrate

Film

Bulk

Film

280 297

263 260

Film

Bulk

302 303 304

298 292 299 300 245

Film

Bulk

Bulk 293

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dislocation at the diamond-cBN interface (one dislocation per 82–84 diamond lattice planes) due to the small lattice mismatch of ⬃1.3% (339). Epitaxial low-pressure deposition of cBN on a Si substrate (lattice mismatch ⬃33%) was reported (321). Because further deposition layers consisted of an amorphous tBN phase, it was suggested that, when the deposited BN layer became thicker than ⬃10 nm, the BN layer changed from a cBN phase to an amorphous tBN phase (323).

VI. APPLICATIONS OF CUBIC BN Because of the similarity of the properties and syntheses of cBN and diamond, the applications of cBN resemble those of diamond. Possible applications of cBN, which are also applications expected for diamond, are listed in Table 12. There exist some differences in properties between the two materials, such as their chemical constituents, electronic band structure, chemical reactions, ionicity, neutron absorption, and impurities. Because of these differences, cBN is superior to diamond for some applications. Diamond, having perfect covalent bonding, is the hardest material and may be interesting in mechanical and thermal applications. On the other hand, cBN, having about half as much ionic character in its chemical bonding, has the largest band gap among existing semiconductors with tetrahedral chemical bonding. These features of cBN may lead to novel optical and electronic applications.

A.

Mechanical and Thermal Applications

Because diamond is harder than cBN, it should exhibit higher performance in grinding and cutting than cBN. However, diamond reacts with some metals at high temperatures and forms metal carbides. The reaction appears to occur more easily than the reaction of cBN, which forms metal nitrides. Thus, tools made of cBN are preferable for cutting or grinding metals with which diamond reacts seriously. Today, an estimated ⬃20,000 kg/year (or ⬃100 million carat/year; 1 carat ⫽ 0.2 g) of cBN powders is mass produced in high-pressure factories and used mostly for mechanical applications around the world (Fig. 54) (340,341). Cubic BN tools are used to grind and to cut hardened steel or chilled cast irons, for which diamond tools are not usually applied. Use of cBN tools has been growing in parallel with the growth of hard Fe-rich materials, in order to fulfill the requirements for precise finishing and high productivity of these materials in automated

Table 12 (Potential) Applications of cBN Abrasive Cutting Drill Blade Hard lubrication Wear resistance Electric insulator Substrate Heat sink

Diode, transistor High-T device Harsh conditions device Light emitter Light detector High-E particle detector Neutron detector Dosimeter Photovoltaic device Photochemical device

Optical window Optical protector X-ray lithograph Atomic reactor window Spacecraft window Piezoelectric device Speaker Oscillator High-pressure anvils, etc.

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Figure 54 Estimated consumption of cBN in the world. (Data from Refs. 341, 342.)

large-scale factories (such as automobile factories). Tools made of cBN have taken the place of other nondiamond ceramic tools in these factories. Abrasive cBN powders are used mainly for grinding, whereas cBN compacts, made by sintering cBN powders with or without TiC, TiN, Al2O3, etc., are used for cutting (342). To find the optimal operation conditions for an individual grinding or cutting application, the performances of various tools are tested and compared by changing the tool materials, materials to be machined, speed of grinding or cutting, operation time, and so on. The application of a cBN single crystal for precise cutting of hard steel has been reported, indicating that the cBN crystal can make mirror-finished surfaces of a steel material, eliminating further grinding processes (343). However, the cBN crystal was severely worn and practical applications for machining of hard steel appear to be difficult because of the lack of endurance of the tool. Films of cBN made at low pressures may be useful for mechanical application when good cBN films are manufactured. Trial applications of cBN films for cutting materials may have been carried out, but results are unclear at present (313). The possibility of a tribologic application for cBN films has been suggested (344). Because cBN is a good thermal conductor and has a thermal expansion coefficient close to that of Si near room temperature, cBN is suitable as a substrate material for Si-based electronic devices. Thus, sintered polycrystalline cBN has been made as a heat sink substrate (147). Polycrystalline cBN is also used in the tape-automated bonding (TAB) tool (147). B.

Electronic and Optical Applications

The band gap energy of cBN is the largest among those of existing IV, III-V, and II-VI semiconductors and cBN can be doped, forming both p and n types. Because of these characteristics, as well as other properties such as hardness and chemical stability, cBN is expected to have potential as a wide-gap semiconductor that can be used under severe, extreme, or refractory

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Figure 55 Rectification characteristics of a cBN pn-junction diode. [T. Tomikawa, private communication; the diodes were described in his patent (347).]

conditions. For example, cBN may be used as a high-temperature device, a short-wavelength light emitter or detector, and so on (for a review, see Refs. 345 and 346). Fabrication of a cBN pn-junction diode was first attempted by Wentorf (4) using a highpressure method, but the pn composites he made were too small for the junction characteristics to be examined. A cBN pn junction large enough for some fundamental characteristics to be measured was fabricated by a high-pressure method in 1987 by one of the authors (O.M.) and others (184). Formation of the pn junction was clearly demonstrated by showing the existence of the space charge layer in the junction region through electron beam–induced current (EBIC)

Figure 56 Injection luminescence spectra of a cBN pn-junction diode. (Data from Ref. 189.)

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images and by observing the rectification characteristics (20–650°C) (Fig. 55) (347). The cBN pn diode was also functional as an ultraviolet light–emitting diode (Fig. 56) (189,199,200). These cBN diodes were, however, primitive prototypes, and improvements in many areas such as synthesis methods, ohmic contacts, and doping control need to be achieved before various applications are realized. Semiconducting cBN polycrystalline compacts containing Be impurities may be used as varistors, as memtioned in Sec. III.D.2.

VII. PROBLEMS AND PROSPECTS One of the most important problems confronting cBN research is the synthesis of single crystals of good and controlled quality and a certain size. This is particularly true for electronic applications and for elucidating detailed fundamental properties. For this purpose, improvement of the high-pressure methods is important and very desirable. This might be accomplished by the lowpressure methods in the future. For electronic applications, lowering the resistivity of cBN (especially that of the n-type crystal) is desirable. In conjunction with this, sulfur doping (4) is attractive and should be tested. Forming ohmic electrodes is the important problem to be solved. When light-emitting diode (LED) action of cBN was reported, there appeared expectations for blue LEDs. However, the success of GaN systems has lowered the expectations for cBN. Applications of cBN as electronic devices have not been developed. We must expect them in the future. Utilizing unique properties of cBN, such as the large band gap energy, mechanical hardness, good chemical stability, high thermal conductivity, large cross section for slow neutrons, and their combinations, may bring about new and novel applications in the field of electronics. Although cBN has been used widely as an abrasive and cutting material for ferrous metals, a cBN single crystal appears to be worn out easily for reasons that are as yet unclear. Metastability of cBN at 1 bar limits any use of cBN at very high temperatures. ACKNOWLEDGMENTS The authors would like to acknowledge Drs. M. Kamo, H. Kanda, S. Komatsu, M. Mieno, S. Nakano, T. Sekine, T. Taniguchi, S. Yamaoka, and many other NIRIM researchers for various discussions. The authors also thank Dr. R. C. DeVries for information concerning some literature and Dr. S. Lawson for advice on the English of the original manuscript by one of the authors (O.M.). REFERENCES 1. WA Balmain. J Prakt Chem 27:422, 1842. 2. RH Wentorf Jr. J Chem Phys 26:956, 1957. 3. About the research and development of cubic BN, see, for example, HP Bovenkerk. New Diamond 29:36, 1993 (in Japanese) and (on diamond) HP Bovenkerk et al. Nature 365:19, 1993. 4. RH Wentorf Jr. J Chem Phys 36:1990, 1962. 5. RC DeVries. In: RE Clausing et al, eds. Diamond and Diamond-Like Films and Coatings. New York: Plenum, 1991, p 151. 6. OA Golikova. Phys Status Solidi (a) 51:11, 1979.

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22 Boron Phosphide Yukinobu Kumashiro Yokohama National University, Hodogaya-ku, Yokohama, Japan

I.

INTRODUCTION

Boron phosphide (BP) is a III-V compound semiconductor with zinc blende structure and displays rather peculiar behavior compared with other compounds of the III-V family. The constituent atoms of BP are the light elements, and especially boron belongs to the first law of group III of the periodic table, those with small inner shells, and exhibits strong covalent bonding with small ionicity, as may be seen from its electronegativity difference of 0.1 eV. The ionization energy of boron I(B) strongly deviates from that of Ga and In (P and As having quite comparable ionization energies), which is believed to be the origin of the differences between BP and the other III-V materials. BP has the most compact crystal structure because of the small atomic radius of boron. Consequently, the overlap of atomic orbitals in BP exceeds the overlap in the other III-V semiconductors and stabilizes BP to a larger extent (1). The other stabilizing factor is the small energy difference between the atomic orbitals that constitute the valence band of BP. The difference between energies of molecule ∆I(BP) is much smaller than ∆I for the other III-V materials. Both stabilizing effects can be thought of as originating from the small atomic radius of boron, which leads to both a larger orbital overlap and a higher ionization energy. When log ν t is plotted against log a where a is the lattice constant and ν t is the vibrational frequency, approximately straight lines are obtained for the heavier III-V compounds but the plot is no longer linear for boron phosphide, indicating that the nearest-neighbor force constants are considerably larger in boron phosphide than in the heavier III-V compounds (2). Boron phosphide is also known as a refractory semiconductor with a wide band gap and has the potential for application in electronic devices in extreme conditions such as high-temperature, radiation, and high-energy environments (3,4). However, BP has been considered to have few outstanding features in comparison with other III-V compound semiconductors for three basic reasons. First, it is difficult to prepare wellcharacterized single crystals because of high melting points (⬎3000°C) and high decomposition pressures (⬃10 5 atm at 2500°C) (5). Second, the material handling process is complicated because of its refractory hardness and brittleness. Third, it has lower electron mobility (6) than other III-V compound semiconductors. The mobility of BP at a lower carrier concentration might be slightly greater than that of Si; hence, BP can become a useful semiconductor material if controlled doping can be achieved. A few studies were reported concerning device fabrication, i.e., BP-Si heterostructures for wide gap window solar cells and wide gap emitter transistors 557

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(7). An Si-BP-Si double heterojunction prepared by alternate growth of BP and Si on an Si substrate (8) and a p-n junction in BP prepared by use of B⫹ ion implantation (9) were reported. In this chapter, first various band calculations in relation to intrinsic properties and crystal growth by various methods to clarify electrical, optical, and mechanical properties at room temperature are reviewed. Second, high-temperature properties, which are indispensable with the development of high-temperature devices, clarify impurity levels and lattice scattering processes. Finally, the applications of new refractory semiconductors to electronic devices such as junction devices and energy-related applications of photocathode and thermoelectric devices are reviewed.

II. BAND STRUCTURE There are limited experimental data on the electronic structure of boron phosphide. Although several theoretical calculations are available, their results differ considerably. The existing theoretical data cannot be relied upon to provide accurate estimates of excitation energies, because most band structure calculations performed to date rely on the Xα method (10) and the local density approximation (LDA) to the density-functional theory (11–13). These theoretical methods can yield errors of up to several eV in band gaps or other excitation energies when compared with reliable experimental results. It has become possible to compute with great accuracy a number of electronic and structural properties from first-principles calculations. Among the quantities obtainable with this kind of calculation are crystal structures, phonon spectra, lattice constants, bulk and shear moduli, and other static and dynamical properties. The unusual behavior appears to originate from the small core size and the absence of p electrons in the cores of the atoms in the first row of the periodic table. These atoms are expected to have deep and localized pseudopotentials compared with the atoms in other rows. Wentzcovitch et al. (12) used the total-energy pseudopotential technique employing the LDA for electronelectron interactions to calculate the following ground-state properties of BP: bulk moduli, lattice constants, cohesive energies, frequencies of the TO(Γ) phonon mode, and total electronic charge densities. The computed equilibrium lattice constant a, elastic constant C ij , bulk modulus B, frequency of the transverse optical vibrational mode at q ⫽ 0, TO (Γ), and shear modulus Cs are given in Table 1. The calculated lattice constants are in good agreement with the measured

Table 1 Experimentaland CalculatedLattice Constant a, theElastic ConstantsC ij ofBP, the Elastic Constant C 044, the Optical Γ-Phonon Frequency ω Γ , the Bulk Modulus B, and the Shear Modulus C s Reference

˚) a(A

Exp. (14) Exp. (15) Exp. (16) Exp. (17) Calc. (12) Calc. (18)

4.538

a b

C 11 (Mbar)

C 12 (Mbar)

C 44 (Mbar)

3.15

1.0

1.6

4.558 4.474

B ⫽ (C 11 ⫹ 2C 12 )/3. From Murnaghan’s equation.

3.59

0.81

2.02

C 44 0 (Mbar)

ωΓ (THz)

2.10

23.9 24.6 23.0 24.6

B (Mbar)

Cs (Mbar)

1.73

1.65 1.73a 1.72b

1.39

Boron Phosphide

559

values to within 0.4%. Comparisons with available reported data for the bulk moduli suggest that the theoretical results are underestimated. Using the empirical relation B0 ⫽ 1761d⫺3.5 (19), where d is the nearest-neighbor distance, gives B0 ⫽ 166 GPa, in excellent agreement with their results. Pseudopotential calculations (12,20) of the electronic structure confirm the lack of p character of B in the bottom of the conduction bands and suggest that a large amount of character is associated with the B atom in the top of the valence bands, as generally happens with a typical anion. These studies (12,20) also indicated that in the formation of the bonds in BP the charge moves from the antibonding region associated with the group V element to the bonding region. Usually this rearrangement of charge in zinc blende semiconductors is observed to proceed in the opposite way, with the charge leaving the antibonding region associated with the group III element and going to the bonding region. Herna´ndez et al. (18) obtained highly converged total energies, forces, and stresses in BP to arrive at the elastic modulus, frequencies of the TO(Γ) phonon mode, and electronic band structures. For all the calculations they used ab initio self-consistent pseudopotential calculations in the framework of the LDA with a plane-wave basis. The equilibrium lattice constants, a 0 ⫽ ˚ , were determined by fitting the total energy to the empirical Murnaghan equation of 4.474 A state. The calculated bulk modulus B and the frequency ωΓ agree remarkably well with the experimental data (15–17). The calculated elastic constants (C 11 ⫽ 3.59 Mbar and C 12 ⫽ 0.81 Mbar) compare well with the Brillouin scattering results (15) (Table 1). Their results for BP compare remarkably well with experiment. The calculated band structure is shown in Fig. 1a. Although this approach fails to describe accurately the energy of the excited states, it usually provides a qualitative description of these

Figure 1 Band structures of BP by (a) total-energy pseudopotential technique within the local density approximation (18), and (b) GW approximation (21).

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states. Advances have made it feasible to perform ab initio calculations with enough quantitative accuracy to provide information on the excitation energies. These calculations employ the GW approximation to include properly the effects of exchange and correlation on the quasi-particle energies (21). The GW approach has resulted in calculated band gaps with 0.1 eV accuracy when a random phase approximation (RPA) dielectric matrix is used or with 0.1–0.3 eV accuracy with use of an appropriate model dielectric matrix. Surh et al. (21) examined the electronic excitation energies for high-symmetry points Γ, X, and L for BP in the GW approximation using a model dielectric function (Fig. 1b). A model for the static screening matrix makes use of the ab initio ground-state charge density and either experimental values or empirical estimates for ε∞ the electronic contribution to the macroscopic dielectric constant. Wave functions from an ab initio local density approximation calculation with norm-conserving pseudopotentials are employed along with the self-consistent quasi-particle spectrum to obtain the energy-dependent one-particle Green function G. The results of the LDA and GW calculations for BP are listed in Table 2 along with experimental data. The reported reflectivity spectrum of BP (26) has three main peaks at ⬃5.0, 6.9, and 8.0 eV, which were tentatively assigned to direct transitions Γ v15 → Γ c15 , X v5 → X 1c , and L v3 → L c3 , respectively. An indirect gap of 2 eV was obtained by optical absorption experiments (24). The direct band gaps for BP are 4.4, 6.5, and 6.5 eV at Γ, X, and L, respectively; they are all approximately 1.0 eV larger than the LDA values. An empirical pseudopotential method (EPM) calculation (23) was done to reproduce the gap and the reflectivity spectrum adjusting the pseudopotential form factors. This study led to a minimum direct gap at L and the lowest conduction state was obtained at Γ 1c . A band structure calculation using a semi–ab initio approach (10) obtained an indirect gap (Γ v15 → Γ 1c ) of 2.0 eV and a comparable direct gap (Γ v15 → Γ c1 ) of approximately 2.0 eV. The minimum band gaps of BP have been reliably estimated from the experimental optical absorption. However, the direct band gaps and other excitation energies must be estimated from structure in the optical response versus frequency. The accuracy of the resulting experimental values depends on the correct identification of features in, e.g., the reflectivity with particular transitions between band states. Then the GW results may be more reliable estimates than the experimental direct band gaps.

Table 2 Summary of Important Features of the Band Structure of BP Minimum gap (eV) Method and reference Theoretical Quantum dielectric theory (22) EPM (23) LDA (12) LDA (18) LDA (21) Semi–ab initio approach (10) GW (21) Experimental Optical absorption (24) Ultrasoft X-ray spectroscopy (25) Reflectivity spectrum (26)

Indirect

Direct

2.19 (Γ v15 → X c 1 ) 1.2 (Γ v15 → ∆ min ) 1.14 (Γ v15 → ∆ min ) 1.2 (Γ v15 → ∆c min ) ⬇2.0 (Γ v15 → L c1 ) 1.9 (Γ v15 → ∆ min )

4.9 (Γ v15 → Γ c15 ) 5.0 (L v3 → L c1 ) 3.3 (Γ v15 → Γ c15 ) 3.45 (Γ v15 → Γ c15 ) 3.4 (Γ v15 → Γ c15 ) ⬇2.0 (Γ v15 → Γ c1 ) 4.4 (Γ v15 → Γ c15 )

2.02 ⫾ 0.05 2.1 ⫾ 0.2 2.0 (Γ v15 → χc 1 )

5.0 (Γ v15 → Γ c15 )

Valence bandwidth (eV)

17.9 15.3 15.75 15.5 11.8 16.8 16.5 ⫾ 0.5

Boron Phosphide

561

III. CRYSTAL GROWTH AND CHARACTERIZATION A.

Crystal Growth

First, the preparations of powder and sintered specimens are mentioned. Polycrystalline boron phosphide powder (27) material was prepared by the reduction of a boron tribromide–phosphorus trichloride mixture with hydrogen in a gas flow system in a fused silica tube furnace at about 1100°C. An excess of phosphorus trichloride was used to maintain the stoichiometry of the deposit. The deposition rate was approximately 2 g/h. High-purity BP powders are prepared by hydroisostatic pressing. Boron and red phosphor were mixed in a fused silica tube evacuated to less than 10 ⫺3 torr and sealed. The ampule was hydrostatically pressed to 1300°C under pressure of 1.8 ton/cm 2 for 2 h. The BP powders thus prepared are far purer than commercial ones. The specimens were sintered at 1300°C at a hydrostatic pressure of 2 ton/cm 2 for 1 h (28). BP is a difficult material to sinter because of the high dissociation pressure of phosphorus. Radio frequency (RF) hot pressing would be applicable (29). The powders were pressed up to 19.6 MPa at room temperature and the temperature was raised to 1000°C by RF heating with a maximum applied pressure of 78.4 MPa. Subsequently, the temperature was kept at sintering temperatures (1500–1800°C) for 1 h and then reduced to room temperature for 1 h. The density of the specimen increases from 60 to 65% of the theoretical value with increasing sintering temperature. Kobayashi et al. (30) synthesized BP at high temperatures and high pressures with a girdletype high-pressure cell having a bore diameter of 15 mm and determined the temperature and pressure conditions for the synthesis of BP (Fig. 2). Solid circles correspond to the case in which BP was successfully synthesized. At relatively low pressure and low temperature no crystalline materials could be observed, but at low pressure and high temperature the B 6P phase was detected. A upper temperature limit for the synthesis and stability of BP is drawn as a solid line. The lower temperature boundary line for the synthesis has a negative slope in a pressure-temperature diagram, indicating that the reaction B ⫹ P → BP is promoted by the application of pressure. Crystalline BP powder less than 100 µm in diameter was produced. The B 6P phase in the hightemperature region shows a dissociation reaction. The dissociation pressure at 2000°C is as high as 8 kbar.

Figure 2 P-T conditions for synthesis of BP. (From Ref. 30.)

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Kumashiro

Niemyski et al. (31) also synthesized BP using an autoclave furnace under a high pressure of 1.5 Mbar at a temperature of 1200–1300°C. Crystallization occurred with a temperature gradient inside the chamber, and prolongation of the reaction time resulted in the formation of larger crystals. The growth of BP single crystals by conventional techniques such as zone melting and growth from the melt is impossible, so preparation methods are limited to chemical vapor deposition (CVD), chemical vapor transport (CVT), and flux methods. Among these, the flux method would produce comparatively large single crystals. A requirement for the flux material was to have a eutectic temperature with B and P lower than the softening temperature of fused silica (⬃1300°C). Iwami et al. (32) grew large single crystals of dimensions 5 ⫻ 2 ⫻ 2 mm 3 from B-Ni-P solution. Chu et al: (33) tried to grow large crystals 2–4 mm in size by means of recrystallization in metal phosphide solution of nickel phosphide and copper subphosphide solutions. Kato et al. (34) obtained larger and better crystals than those grown from Ni-fluxed melt and also succeeded in growing crystals on a seed crystal by the supersaturation with a temperature gradient in the Cu-fluxed melt. The minimum temperature of the low-temperature zone was kept at about 400°C to maintain the phosphorus pressure in the ampule at about 1 atm by maintaining the top of the solution at the highest temperature (1200°C) and the bottom at a temperature a few tens of degrees lower than the top temperature. The crystals had a maximum size of 4 ⫻ 3 ⫻ 0.2 mm 3 and were in the form of planets with a small number of funnel-shaped and needle-shaped ones. Crystals grown from the Cu-fluxed melt were always n-type, and those grown from the Ni-fluxed melt were always p-type with a room temperature resistivity of about 0.5 Ω cm and a dopant concentration of about 10 18 /cm 3. Using a unique high-pressure flux method (35), which is a modification of Chu’s method (33), large BP single crystals would be obtained. Instead of a fused quartz tube, the crystal growth was carried out in an RF induction furnace with a graphite crucible containing the crushed BP-Cu 3P melt under a high pressure of 18 atm. The top of the solution was maintained at about 1400°C for 20 h and the bottom was approximately 10–20 degrees cooler. Then the crucible was slowly cooled down to room temperature. Dark reddish BP single crystals were extracted from HF-HNO 3 solution to confirm that BP was recrystallized and coalesced in the bottom of the crucible. The single crystals obtained (5 ⫻ 5 ⫻ 3 mm 3 ) are the largest with a smooth main face of (111). The X-ray powder diffraction pattern shows small amounts of B 6P ˚, and Cu 3P precipitate in the crystals, but the crystals have a lattice constant of a ⫽ 4.539 A which is in good agreement with the value reported. The crystals exhibit p-type conduction due to copper. Their electrical resistivity, carrier concentration, and mobility are 1.5 Ω cm, 1.67 ⫻ 10 18 /cm 3, and 1.77 cm 2 /V s, respectively. The photoluminescence spectrum at 4.2 K excited by a Cd-He laser (Fig. 3) has five peaks (denoted as A, B, C, D, and E). Peak C corresponds to an LO-phonon replica of peak A, peak E to a second LO-phonon replica of peak A, and peak D to an LO-phonon replica of peak B. Furthermore, the spectra caused by donor-acceptor pairs are observed (not shown here) on the higher energy side than peak A and are in good agreement with the theoretical value of type II in the zinc blende structure (34,36). The crystal growth of boron phosphide by CVT (27) is based on the reversible reaction between boron phosphide and the transport agent. Boron phosphide is transported from a hightemperature source (1270–1290°C) to lower temperature regions in fused silica tubes of 10 mm inner diameter, 16 mm outer diameter, and 12 cm long. The important parameters affecting the quality of the transported crystals include the source temperature, the temperature gradient along the reaction tube, the nature and pressure of the transport agent, and the surface condition in the deposition region of the reaction tube. A phosphorus pressure of 3 atm and a transport agent pressure of 1 atm were optimal for the transport process. The temperature gradient between hot

Boron Phosphide

563

Figure 3 Photoluminescence spectrum of BP single crystal at 4.2 K. (From Ref. 35.)

and cold regions should be as small as possible to approach equilibrium. Phosphorus trichloride was found to be the fastest transport agent, but the transported material consisted of loosely bound aggregates of small crystals. Iodine or bromine as a transport agent has produced better results in the form of disks of about 5 mm diameter and 1–2 mm thickness and in the form of polyhedrons. The deposition region flame-worked to remove any surface irregularities produced only one tightly bound single crystal up to 2 mm at the tip of the reaction tube. Flame working of the fused silica tube is a critical factor in achieving control of nucleation in the closed-tube transport process. The transported boron phosphide crystals were p-type with a room temperature resistivity of approximately 0.5 Ω cm. The deposition of boron phosphide by CVD was carried out in a gas flow system by the thermal decomposition of diborane-phosphine mixtures in a hydrogen atmosphere and the thermal reduction of boron tribromide–phosphorus trichloride mixtures with hydrogen (37). The hydrides are thermodynamically unstable at room temperature and decompose rapidly at above 500°C, which tends to promote homogeneous nucleation by pyrolysis in the gas phase. The halides are thermally more stable than the hydrides, and higher substrate temperatures may be used in the thermal reduction process with essentially no gas-phase reactions. At high substrate temperatures, a phosphorus pressure equal to or greater than the vapor pressure of boron phosphide must be present over the substrate surface to maintain the stoichiometry of the deposit. The reaction tube was water cooled to minimize the gas-phase reactions. For crystalline cubic BP from BBr 3 and PBr 3 in a hydrogen atmosphere a narrow regime of temperature and molar ratios of reactions is available (38). Furthermore, BP whiskers (39) were synthesized on seed metals in the temperature range 850–1000°C. Nickel and silver acted as liquid forming agents in a vapor-liquid-solid (VLS) growth mechanism (40). When saturation is reached, crystallization of the product starts at the liquid-solid interface and after a while the formed crystallite pushes the seed metal droplet away from the substrate, which results in whisker formation. The

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whiskers are of highly twinned single crystallinity, with preferred growth along the (111) direction. High-resolution transmission electron microscopy (TEM) pictures reveal a high density of twin planes, spaced approximately 10–20 nm apart. Energy dispersive X-ray (EDX) element analysis of the whisker tips did not reveal any traces of nickel, and X-rays attributed to nickel were found when the electron beam grazed the graphite surface. Although SiC substrates are most suitable from the viewpoint of lattice matching (37) in the CVD process, the difficult etching of SiC prevents the removal of substrates from BP layers; Si substrates are desirable for this purpose. Nishinaga et al. (41) reported the first experiments on the growth of epitaxial BP layers on Si substrates, with a thermal reduction of the halide system despite larger lattice mismatch of 16.5%. The crystals grown on Si{111} surfaces were found to be monocrystalline with a zinc blende structure for a certain narrow temperature range. Just outside this range, the grains of which the film is composed begin to rotate to take optimal positions with respect to each other. Single-crystal BP layers have not been grown on Si{100} surfaces. Takigawa et al. (42) performed thermal decomposition of diborane and phosphine and concluded that Si{100} was the most favorable surface orientation for the hydride system in contrast to the halogen system (41). One of the important differences between these two experiments is the growth rate of BP. Takigawa et al. (42) employed a very low growth rate, as low ˚ /min. Nishinaga and Mizutani (43) used a rate of approximately 1 µm/min, more than as 700 A 10 times as high. When Nishinaga and Mizutani (43) performed experiments with growth rates ˚ /min, they confirmed that the arrangement of the three {100}, {110}, and as low as 1000 A {111} substrates was the same and the best BP crystal was grown on the {100} substrate, in agreement with Takigawa et al. (42). The conclusion of Nishinaga and Mizutani (43) should be restricted to the case of high growth rates. The TEM image of a BP layer grown on the Si(100) substrate indicates that the BP layer is epitaxial with respect with a [100] surface normal, as evident from the superimposed fourfold configuration visible in the selected area electron diffraction (SAED) pattern. However, fine lines are observed along the (110) plane, showing a high density of planar defects primarily originating at the substrate-epitaxial interface. These defects are mostly stacking faults and microtwins lying along the four equivalent {100} planes. High-resolution electron microscopy (HREM) of the BP/Si interface (Fig. 4) shows a microtwin and misfit line. A huge lattice misfit between BP and Si (⬃16%) produces no continuity of lattice planes across the interface. The BP layer and Si substrate would match with misfit and microtwin. During the epitaxial growth of n- or p-type boron phosphide (BP) on Si substrates using a B 2 H 6-PH 3-H 2 system, either n-type (phosphorus) or p-type (boron) diffused layers are formed on the Si substrate. At an early growth stage of BP on Si substrates a very small amount of boron and phosphorus covers the substrate surface, which serves as a diffusion source (7). The properties of the diffused layers are dependent on substrate temperatures and reactant gas flow rates. The deviation from stoichiometry of boron monophosphide (BP) was controlled by heat treatment of the BP surface cover with Si 3 N 4 (44). Qualitative characteristics of BP according to the heat treatment are summarized in Fig. 5. The as-grown n-BP shows a high resistivity for 8 min of heat treatment at 1200°C and for 30 min at 1100°C. Longer heat treatment times result in a change to p-BP. The resistivity of the p-BP becomes as low as 10 ⫺2 Ω cm as the heat treatment time increases. With treatment times greater than 8 min at 1200°C and 30 min at 1100°C, in as-grown p-BP, the resistivity decreased as the heat treatment time increased. The final value of the resistivity was less than 10 ⫺2 Ω cm. At 1050°C, a resistivity of more than 10 10 Ω cm was obtained for a heat treatment time of more than 2–3 h in both conduction types. The stoichiometric BP after a preliminary heat treatment for 30 min at 1100°C of as-grown nor p-BP finally changed to n-BP after several hours of heat treatment at 1000°C. The CVD growth of BP on a near (1120) oriented sapphire substrate (45) was conducted

Boron Phosphide

565

Figure 4 HREM feature of the BP-Si interface in our specimen. (Courtesy of Dr. Y. Fujita, Itami Laboratory, Sumitomo Electric Industries.)

Figure 5 Qualitative characteristics of BP due to heat treatment. (From Ref. 44.)

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by a two-step method: (a) predeposition of amorphous BP with 40 nm on the substrate at a lower temperature of 550°C and (b) epitaxial growth on the substrate with buffer layers at a higher temperature of 1000°C. The RHEED pattern for the [112] incident direction (Fig. 6) is not the same for every 120° rotation in the same plane but has a periodicity of 60° rotation, indicating the existence of a twin structure with sixfold symmetry. The RHEED patterns for the [110] direction (Fig. 6) are composed of [110] and [110] patterns, showing the existence of the twin. The twin would be at 180° rotation with respect to the perpendicular to the (111) plane and in mirror relation with respect to the twinning plane. The film thus grown has n-type conduction with a resistivity of 3.1 ⫻ 10 ⫺2 Ω cm, a carrier concentration of 4.8 ⫻ 10 18 /cm 3, and a mobility of 37.7 cm 2 /V s, which is consistent with the plot of electron concentration in the range of 5 ⫻ 10 19 to 1 ⫻ 10 22 /cm 3 versus Hall mobility (42). A serious problem with the CVD process is the high carrier concentration and low electrical resistivity arising from contamination with a substrate material. Gas-source molecular beam deposition (GS-MBD) allows control of the flow rates of reactant gases at a lower growth temperature, so that a high-purity boron phosphide film (46) can be obtained. A high-purity film could be prepared on a sapphire crystal using cracked B 2 H 6 (2% in H 2 ) at 300°C and cracked PH 3 (20% in H 2 ) at 900°C under a vacuum of 5 ⫻ 10 ⫺4 torr with an incident ratio of ν PH3 / ν BZ2H6 of 12.7. The boron phosphide film grown at 600°C has the highest resistivity of 4.0 ⫻ 10 4 Ω cm and lowest electron concentration of 6.0 ⫻ 10 10 /cm 3 ever obtained. B.

Fundamental Properties

The CVD BP wafers with an area of 10 ⫻ 20 mm and a thickness of 200–300 µm (47) for long deposition times (24–28 h) were obtained by dissolving away the silicon substrate in an HF-HNO 3 solution. From the back face of the BP, a characteristic diffraction pattern with extra

Figure 6 RHEED and indexed patterns for BP (111) plane with incident beam along the [112] and [110] azimuth of BP. (From Ref. 45.)

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567

Table 3 Semiconducting Properties of BP Wafers Orientation No. No. No. No.

1 2 3 4

(100) (111) (100) (100)

Type

(Ωcm)

n p n p

0.15 12.5 0.25 10.0

ρ(cm ⫺3 )

µ (cm 2 /V s)

Si content by SIMS (atoms/cm 3 )

⫻ ⫻ ⫻ ⫻

120 36.5 107 20.0

⬃10 18 5 ⫻ 10 18 5 ⫻ 10 19 ⬃10 20

3.7 1.6 2.5 3.1

10 17 10 16 10 16 10 16

Source: From Refs. 3, 5, 8.

spots represents twinned lattices {111} (48). BP grows epitaxially on the (100) Si substrate, but the (111) wafer inclines to the (100) plane with respect to the [110] direction, confirmed by a back-reflection Laue photograph and the RHEED pattern. The majority of the impurities consist of silicon, as determined by secondary ion mass spectroscopy (SIMS) analysis. The electrical resistivity ρ, carrier concentration n, and mobility µ of CVD wafers measured by the van der Pauw method are shown in Table 3. The carrier concentration decreases with increasing silicon content for the n-type specimens (samples 1 and 3) and increases for the p-type materials (samples 2 and 4). The silicon atoms act as acceptors and are incorporated at the phosphorus sites in BP. Results of measurements of the lattice constants by the Bond method are shown in Table 4; they were obtained after calibration, using the thermal expansion coefficient (49). The conduction types of the BP wafers were determined using excess boron or phosphorus and were found to be either p- or n-type (50). The excess phosphorus atoms occupy the boron sites in the BP lattice in the n-type material and vice versa for the p-type material (44). The ionic radii of boron and phosphorus in BP are expected to be 0.88 and 1.10 ˚ , respectively. The lattice shrinks in the p-type materials (sample 4), whereas it expands in A the n-type materials (sample 3). The difference in the ionic radii of phosphor and silicon is not so large and no appreciable effect of Si on the lattice constant could be detected. The Vickers microhardness of the BP wafers varies from 3000 to 4000 kg/mm 2, depending on orientation (47,51). The periodicity of the hardness curve of the (100) plane shows fourfold symmetry (Fig. 7). Minimum and maximum hardnesses in the (100) plane correspond to the 〈110〉 and 〈001〉 directions, respectively. By analogy to the anisotropy of hardness in the (001) plane of cubic boron nitride (52) compared with resolved shear stress curves, the primary slip systems of BP are {111} 〈110〉. The elastic constants C 11, C 12 , and C 44 were determined by Brillouin scattering (18) as given in Table 1. The transmission spectra of polycrystalline and epitaxial BP layers are plotted as (αhν)1/2 versus hν to give a linear relationship (Fig. 8) (53), where α is the absorption coefficient. The optical transition in crystalline BP is indirect and allowed. The optical band gap E g is derived

Table 4 The Precise Lattice Constant of BP Wafers Orientation No. No. No. No.

1 2 3 4

(100) (111) (100) (100)

Type

Reflection

Half bandwidth

n p n p

(400) (333) (400) (400)

0.13° 0.14° 0.15° 0.14°

Source: From Refs. 3, 5, 8.

˚) Lattice constant (A 4.538675 4.537983 4.538467 4.538205

⫾ ⫾ ⫾ ⫾

3 3 7 6

⫻ ⫻ ⫻ ⫻

10 ⫺6 10 ⫺6 10 ⫺6 10 ⫺5

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Figure 7 Vickers microhardness anisotropy of BP (100) wafers. (From Ref. 47.)

from the energy axis intercept of the extrapolated line. Absorption in polycrystalline and epitaxial BP extrapolates to an optical band gap E g of 1.8 and 2.0 eV, respectively. The refractive index of BP was measured in the visible spectral range by the Brewster angle method (Fig. 9) (15) and was in good agreement with the value of Takenaka et al. (54) taken at 589.3 nm. The values of n are seen to be fairly large and increasing toward the band edge. GaAs (E g ⫽ 1.47 eV) has n ⫽ 3.3–3.36 and ε ⫽ 12.5–12.9, and GaP (E g ⫽ 2.25 eV)

Figure 8 Determination of the band gap of polycrystalline and epitaxial layers of BP. (From Ref. 53.)

Boron Phosphide

569

Figure 9 Refractive index of BP (15). The data point at 589.3 nm is from Ref. 54.

has n ⫽ 2.9 and ε ⫽ 10–10.2. In the case of BP (E g ⫽ 2.0 eV), values of n ⫽ 3.1 and ε ⫽ 11 would well satisfy the relation of III–V compounds that the dielectric constant is slightly larger than the square of the refractive index. Raman spectra of natural and isotope-enriched boron phosphide single-crystal wafers indicate one strong band at 828.6 cm ⫺1 and 846.2 cm ⫺1, respectively (Fig. 10) (55). The former is in good agreement with 829 cm ⫺1 for BP powder (56) and a strong infrared absorption band at 12.1 µ 17. The frequency shift can be described by the change in mass of the isotopes: ν(10 BP) ⫽ ν(11 BP) [m(11 BP)/m(10 BP)] 1/2

(1)

The Raman frequency in 10 BP is expected to be 833.9 cm ⫺1. The difference between this value and the calibrated value of 847.4 cm ⫺1 is due to the volume decrease between 10 BP and 11 BP:

Figure 10 Raman spectra of isotopically enriched 10 BP and natural BP single crystal (From Ref. 55.)

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∆ν ⫽ ⫺13.5 cm ⫺1

(2)

The volume change ∆V/V required to produce this shift is obtainable from the measured effect of pressure on the Raman line. The pressure dependences of the Raman shift indicate that (57) ∆ν ⫽ ⫺2794(∆a/a)

(3)

Equations (2) and (3) result in ∆a/a ⫽ ⫺1.7 ⫻ 10 ⫺3. The lattice constants of pure 11 BP and 10 BP result in ∆a/a ⫽ ⫺1.2 ⫻ 10 ⫺4, one order smaller than that from the Raman shift, which would be due to such crystal imperfections (57) as lattice distortions and low-angle grains.

IV. HIGH-TEMPERATURE TRANSPORT PROPERTIES A.

Electrical Properties

The temperature dependence of the conductivity for n-type samples (Fig. 11) can be understood as a competition between the decrease in mobility and the increase in carrier concentration (58). The donor energies of 0.1 eV for sample 1 and 0.25 eV for sample 3 seem to correspond to

Figure 11 Temperature dependences of the conductivity σ, the carrier concentration n, and the Hall mobility µ n of n-BP (100) (58). The result of conductivity for polycrystal is also shown (59).

Boron Phosphide

571

the doubly charged donors of phosphorus (P 2⫹ ) and to impurity donors such as magnesium, manganese, and cobalt, respectively. Sample 3 contains more impurities than sample 1, corresponding to the data showing that the mobility in sample 3 is lower than that in sample 1. The result for a polycrystalline BP wafer (59) is shown for comparison as indicated by a smooth line. The conductivity of the polycrystalline wafer shows steep rise at 900 K. The activation energy at lower temperatures is 0.08 eV, corresponding to doubly charged phosphorus (P 2⫹ ). A low carrier concentration of 9 ⫻ 10 15 cm ⫺3 at room temperature (59) would produce a steep rise in the electrical conductivity at high temperature with an activation energy of 0.3 eV, which would be due to the formation of impurity states and crystal defects and the contribution to conduction by the excitation of carriers trapped by impurities and defect levels (60). The mobility in the p-type wafers (Fig. 12) is lower than that in the n-type wafers. The activation energy in sample 2 is calculated to be 1.8 eV for temperatures above 650°C, which is nearly equivalent to a band gap of 2.0 eV and corresponds to the intrinsic conduction region (37). This is a result of the fact that the carrier concentration in sample 2 is lower than that in the n-type samples (Fig. 11). The activation energies associated with the acceptor levels are 0.20 and 0.32 eV for samples 2 and 4, respectively. Above 600 K the value α in the relation µ ⬃ T α, determined from the slope of plots of log µ versus log T, is ⫺1.5, so that lattice-phonon scattering prevails in the scattering process in these temperature ranges. High-temperature electrical properties for the (111) planes before and after irradiation with a thermal neutron dose of 1.449 ⫻ 10 4 n/cm 2 s are shown in Fig. 13 (61). No appreciable

Figure 12 Temperature dependences of the conductivity σ, the carrier concentration ρ, and the Hall mobility µ p of p-BP. (From Ref. 58.)

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Figure 13 Electrical properties of n- and p-10 BP (111) wafers before and after irradiation by thermal neutrons. The temperature dependence of carrier densities with calculated values is denoted by dashed curves. (From Ref. 61.)

change in electrical properties in the (100) plane is observed during irradiation because of no blocking effect and high crystal perfection. A noticeable change in carrier concentration is a typical characteristic of radiation damage in semiconductors. Alpha particles produced by nuclear reaction occur to a depth of about 15 µm in the boron phosphide wafer. The carrier concentration for the n type increases and that for the p type decreases on thermal neutron irradiation because of the formation of donors. The temperature dependence of the carrier concentration of wafers with calculated values is denoted by the dashed curves in Fig. 13. The ionization energies and density of donors or acceptors are estimated by fitting the calculated carrier densities to the experimental results. To estimate the ionization energies (E d and E a ) and density of donors (N D ) or acceptors (N A ), the general formulas were used (3). The calculation indicates that the ionization energies of donors and acceptors are independent of the irradiation, but the increase in donor concentration is clarified quantitatively after irradiation by thermal neutrons (3). The temperature dependence of the thermoelectric power is shown in Fig. 14. In general, the thermoelectric power is described by the following expression:

冢

冣

k (r ⫹ 2)F r⫹1 (η) S(T) ⫽ ⫺ ⫺η e (r ⫹ 1)F r (η)

(4)

where F r (η) is the Fermi integral, r is the scattering parameter, and η is the reduced Fermi level. The S(T ) for an n-BP single crystal (solid and dotted lines in Fig. 14) was calculated

Boron Phosphide

573

Figure 14 Temperature dependences of the thermoelectric power S of BP single-crystal wafers (58). Temperature dependences of experimental (smooth line) and calculated (dashed line) curves (62) and polycrystal (59) are also shown.

with a scattering factor r ⫽ 3/2 (phonon scattering), a donor concentration N d ⫽ 5 ⫻ 10 18 cm ⫺3, and the energy level E d ⫽ 0.02 eV (62). The thermoelectric powers of the BP wafers are similarly high with the exception of sample 3 (58). Sample 3 is compensated by silicon acceptors, which raise the thermoelectric power. The thermoelectric power of the other n-type sample (sample 1) tends to saturate up to 650°C and then increase with increasing temperature owing to the formation of acceptors. The higher the donor concentration, the higher the transition temperature. The behavior of polycrystalline wafers (59) is similar to that of single crystalline wafers. B.

Thermal Properties

The specific heat capacity of BP single crystals (63,64) increases with increasing temperature (Fig. 15). The Debye temperature and its temperature dependence reflect features of boron phosphide (65). A high Debye temperature indicates low atomic mass and strong interatomic bonding in boron phosphide. The Gru¨neisen parameter γ is calculated as a function of the reduced temperature T/θ (65). High γ means high anharmonicity, and a small variation would be attributed to low ionicity (64,65). The thermal diffusivity of a wafer is measured using a ring flash light, which originates from multivariable analysis in a two-dimensional model (66). The temperature dependences of thermal diffusivity together with the results of the photo-AC method show fairly good agreement between the two methods (63), which justifies the ring flash light method. The thermal diffusivity of a single crystal has a large value of 1.8 cm 2 s⫺1 at room temperature and shows a pronounced decrease with increasing temperature, due to phonon scattering, and the thermal diffusivity at room temperature of 0.06 cm 2 /s decreases to 0.04 cm 2 /s at 800 K for a polycrystalline wafer (59).

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Figure 15 Temperature dependences of specific heat capacity and Debye temperature of BP (63,64).

The temperature dependence of thermal conductivity, as calculated from the product of the thermal diffusivity, specific heat capacity, and density, is shown in Fig. 16. The thermal conductivity of boron phosphide single-crystalline wafers is ⬃ 4.0 W/cm K at room temperature, which is in good agreement with Slack’s data (67) and is comparable to the value for boron nitride. Boron phosphide single crystal is thus a promising material for heat sink substrates for semiconductor devices. The electric contribution to thermal conductivity in a single crystal is small and the thermal conductivity in Fig. 16 should correspond to the lattice thermal conductivity, being in very good agreement with the calculation by the three-phonon process (68), where M is the mean atomic mass and δ is the cubic root of the atomic volume. In contrast, the thermal conductivity of polycrystalline BP shows a weak temperature dependence over the entire temperature range, so that thermal conduction is performed by phonon scattering at grain boundaries with a weak temperature dependence of the mean free path of phonons (59). In the case of heteroepitaxial growth of BP on Si substrates, a difference in thermal expansions between two materials is very important in addition to a lattice mismatch. The thermal expansion coefficient α is given by α⫽

1 ∂a ∂(lna) ⫽ a ∂T ∂T

(5)

where a is the lattice constant. The values of α at each temperature are calculated from the gradients of the curves between ln a and T. Thermal expansion of BP epitaxially grown on Si {100} substrates has been investigated by using a high-temperature X-ray diffractometer (49) (Fig. 17). The coefficient α varies from (4.0 ⫾ 0.3) ⫻ 10 ⫺6 to (6.2 ⫾ 0.3) ⫻ 10 ⫺6 K⫺1 in the temperature range 400–800 K. The α value of BP is about 1.3 times as large as that of Si through the whole range investigated, which explains well the phenomena of bending or cracking of grown BP films with Si substrates on cooling after the reaction.

Boron Phosphide

575

Figure 16 Temperature dependences of thermal conductivity of BP wafers (64). The solid line represents values calculated from the equation; the dashed line shows a T⫺1 dependence. The result for the polycrystal is also shown (59).

Figure 17 Temperature dependences of the thermal expansion coefficient α of BP; α for Si is also shown for comparison. (From Ref. 49.)

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V.

APPLICATION AS ELECTRONIC MATERIALS

A.

Electronics Devices

Diffusion layers formed in Si substrates during the epitaxial growth of BP realize various junctions related to devices (Table 5) (7). Of these combinations, a wide gap window solar cell and a wide gap emitter transistor have been fabricated. The current-voltage characteristic of the nBP-pSi heterostructures obtained in growth region A suggests the existence of interface states in the BP-Si heterojunction. The forward current has a region proportional to exp(eV/nkT) with n ⫽ 6 ⫾ 2. The backward current is large and does not saturate. Spectral photocurrents excited with monochromatic light at temperature (Fig. 18) indicate that the spectrum broadens toward the short wavelength region compared with the spectrum of an Si cell, which is attributed to BP having a wider forbidden energy gap than Si. Many recombination states in the BP-Si interface due to the differences in lattice constants and thermal expansion coefficients would reduce the conversion efficiency of the cell. The short-circuit current with an nBP layer is apparently larger than that without an nBP layer, because of a difference in reflectivity of BP and Si. The conversion efficiencies of solar cell with an nBP layer and without an nBP layer are η ⫽ 8.3% and η ⫽ 6.5%, respectively. Two types of wide gap emitter transistors—an nBP-pSi-nSi structure and an nBP ⋅ nSipSi-nSi structure having a cascade junction nBP ⋅ nSi-pSi emitter—were fabricated. The common emitter current gain β in the latter transistor is about 16 and the injection efficiency of the Table 5 Eight Junctions Realized by Combining Conducting Type of BP, Diffusion Layer, and Si Substrate Region A

B

C

D

BP crystal

Diffusion layer

Si substrate

n

p

n

Transistor

p

Diode

n

Ohmic

p

Diode

n

Diode

p

Ohmic

n

Diode

p

Transistor

n

p

p

Source: From Ref. 7.

n

p

n

Energy band structure

Device

Boron Phosphide

577

Figure 18 Spectral photocurrent of wide gap window solar cells with nBP-pSi and nBP ⋅ nSi-pSi structure. That of an nSi-pSi cell after removing the nBP layer from an nBP ⋅ nSi-pSi cell is shown for comparison. (From Ref. 7.)

emitter heterojunction is about 0.94 if the other gain factors are assumed to be unity. The forward current of the emitter junction has two regions proportional to exp(eV/nkT) with n ⫽ 2.6 and 1.6. The backward current of the junction does not saturate and similarly to that of an Si p-n junction was about 250 V. By using the method in Fig. 5, an Si-BP-Si double heterojunction was obtained through the alternate growth of BP and Si on an Si substrate. After BP was grown epitaxially and then covered with Si 3 N 4 , it was heat treated at the stoichiometric temperature of 1050°C. Some typical current-voltage characteristics of the n ⫹Si(epi)-BP-n ⫹Si (sub) structure are shown in Fig. 19. The heat treatment time to obtain highly resistive BP at the stoichiometric temperature of 1050°C was 1 h for sample A, 3 h for B, and 5 h for C. The same barrier height is formed at both the n ⫹Si(epi)-BP and the BP-n ⫹Si(sub) heterojunctions. When a voltage of less than 0.1 V is applied, an ohmic current is observed. If the donor concentration in the BP is less than 10 18 cm ⫺3, BP as thin as 50 nm is depleted. The characteristic values of the Si-BP-Si heterojunctions are summarized in Table 6. The observed resistivity was determined in the ohmic region of current-voltage characteristics. The barrier height V 0 obtained by extrapolating to V 1/2 ⫽ 0 was given by reducing by half the forbidden energy gap of BP to keep the electronic neutrality condition between ionized impurities in the depleted BP and the accumulated carriers at the Si surface. The donor or acceptor concentration N BP was controlled by the length of the heat treatment time at the stoichiometric temperature of 1050°C. The value of thermal emission over the barrier height was calculated from n or p exp(⫺ qV 0 /kT ), where n ⫽ p ⫽ 5 ⫻ 10 19 cm ⫺3.

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Figure 19 Current as a function of the square root of applied voltage V 1/2 in the n ⫹ Si(epi)-BP-n ⫹ Si(sub) structure. The heat treatment time is 1 h for A, 3 h for B, and 5 h for C. The transition voltage V T of 1.4 V is marked. (From Ref. 8.)

BP p-n junctions are especially desired for their potential application in electronic devices to be used in an ambient high temperature. A step (one side) BP p-n junction was formed by B⫹ implantation and subsequent annealing (Fig. 20). In the forward current of a semilog plot of the forward direction, the factor n, the exponential ideality factor of the junction, decreases gradually from n ⫽ 1.8 at V ⫽ 0.2 V to n ⫽ 1.4 at V ⫽ 0.5 V as the applied bias increases. The backward current increases in proportion to the square root of the applied bias. The step (one-side) p ⫹-n junction is formed by B⫹ ion implantation. A breakdown voltage of 160 to 170

Table 6 Characteristics of Si-BP-Si Heterojunctions

Sample A B C D

Heat treatment time (h)

Observed resistivity ⫻ 10 6 (Ω cm)

Barrier height V 0 (V)

Value of thermal emission ⫻ 10 10 (cm ⫺3 )

Electron or hole mobility µ (cm 2 /V s)

Donor or acceptor density N BP ⫻ 10 17 (cm ⫺3 )

1 3 5 6

0.12 3.5 48 13

0.45 0.52 0.59 0.55

60 3 0.2 0.7

— 70 70 70

2.4 2.1 1.8 20

Source: From Ref. 8.

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Figure 20 Typical current-voltage characteristics of a BP p-n junction. (From Ref. 9.)

V was observed. The depletion width spreading in n-BP (N D ⫽ 5 ⫻ 10 17 cm ⫺3 ) at the breakdown is 0.6 µm and the electric field strength is 3 ⫻ 10 6 V/cm. A large current density extrapolated to the zero bias of J 0 ⫽ 2.0 ⫻ 10 ⫺7 A/cm 2 is due to a short minority-carrier lifetime for the electrons injected into the p-BP layer formed by B⫹ implantation. The p-BP works just as a metal electrode. By taking into account the recombination in the depletion layer spreading in the n-BP, the thermionic emission current of a metal-semiconductor contact is calculated. The barrier height V 0 of 0.80 ⫾ 0.02 V is in good agreement with a built-in voltage from the junction capacitance measurement as a function of an applied bias (54). As for BP Schottky diodes, there has been only one study of the n-BP-Sb type (54) to determine a dielectric constant of BP. Heat treatment of the wafer is an important process in evaporating the Schottky metal (69). The n-BP-Sb diode with heat treatment exhibits excellent I-V characteristics, which might be a result of the Sb-BP interface cleaning caused by Sb diffusion into the BP wafer during heat treatment. Extrapolating the curve of 1/C 2 versus V from the near-zero voltage region deduces the diffusion potential V 1 of 1.3 V (69). GaAs and InP,

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being isomorphic with BP, form Schottky barriers with gold (Au) for both n- and p-type materials (70,71), so that Au works on n-type BP. In the forward direction, the turn-on voltage is about 0.6 V, and in the reverse direction soft breakdown occurs at about ⫺5 V (Fig. 21) (72). The capacitance plot is almost linear with V i of 1.2 V, and the depth profile of the carrier concentration calculated from the plot is uniform within the depleted depth. The barrier height (φ B ) is estimated from the following equation (71): φ B ⫽ V i ⫹ V R ⫹ kT/q ⫺ ∆φ

(6)

where V R is the depth of the Fermi level below the conduction band, kT the thermal energy, and ∆φ the image force lowering of the barrier height at the interface. Measurements of the temperature dependence of the carrier concentration (Fig. 11) indicate that the V R values of nBP-Sb and n-BP-Au are 0.09 and 0.23 eV, respectively. The value of kT is 25 meV at room temperature and that of ∆φ ⬍ 10 meV (71). Therefore, the barrier height evaluated from the capacitance measurement is 1.40 eV for n-BP-Sb diodes and 1.45 eV for n-BP-Au diodes, coinciding with the (2/3)E g (E g ⫽ 2.1 eV) rule. The electron transport though the interface is governed not by the metal work function but by the intrinsic nature of BP, so that the Fermi level is pinned by intrinsic defects introduced in the vicinity of the surface of a semiconductor during metal deposition. It is convenient for device processes to use Au for both n- and p-type BP. The BP-on-silicon devices (73) were tested as radiation detectors by irradiating them with 5.5-MeV alpha particles from an Am isotopic source and interrogating the current pulses arising in the detector with conventional nuclear pulse height analysis. Figure 22 shows pulse height spectra obtained by irradiating a BP-Si device both with and without the alpha particle source present. Detection of the alpha particles is clearly indicated, but subsequent testing with a thermal neutron reactor did not occur because of the high carrier concentration in the BP films. For thermoelectric devices, thermal conductivity should be low to reduce loss of thermal energy by thermal conduction between the hot and cold sides. The efficiency of energy conversion of a thermoelectric device becomes high at a larger figure of merit and at high temperature. A single crystalline wafer has comparatively high thermoelectric power, as shown in Fig. 14, but the thermal conductivity is also high (Fig. 16), which reduces the thermoelectric figure of

Figure 21 I-V characteristics and 1/C 2 versus applied bias voltage for nBP-Au Schottky barrier diode. (From Ref. 72.)

Boron Phosphide

Figure 22 Pulse height spectra obtained with a BP-on-Si device with and without an alpha particle source present. (From Ref. 73.)

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241

Am 5.5-MeV

merit Z (⫽ S 2σ/κ); then the BP single crystalline wafer is not applicable for thermoelectric devices. In contrast, the thermal conductivity of a BP sintered polycrystal is smaller than that of a single crystalline wafer by two orders of magnitude (29), which would result in increasing the figure of merit. The thermoelectric power of the BP sintered specimen, however, depends on the purity of the starting powder. Commercially available BP powder contains many impurities that compensate each other, reducing the thermoelectric power to ⬃ 20 µV/K over the entire temperature range (29). The Z value for a CVD boron phosphide polycrystalline wafer calculated from Figs. 11, 14, and 16 increases with increasing temperature, reaching 10 ⫺7 /K at 800 K (59). However it would be ⬃10 ⫺6 /K if the thermal conductivity could be reduced as low as that of a sintered specimen by introducing porosity and a disordered state. B.

Photoelectrochemical (PEC) Cells

BP is an intrinsically stable material, so it is a promising material for photocathodes. One of the major requirements in practical application to photoassisted electrolysis of water using semiconductor electrodes (74) is that the semiconductor should be stable in any electrolyte environment. The attainment of quite stable photocurrents resulting in hydrogen production from a pBP electrode in acidic solution has been reported (75). The effect of ruthenium concentration on the photocurrent-potential curves for BP treated with ruthenium (III) chloride in 0.5 M H 2 SO 4 indicates that the surface treatment should be carried out with a suitable ruthenium concentration and treatment time. The wavelength dependence of the photocurrent for p-BP shows a threshold of the photocurrent response of 600 nm (2.0 eV), in agreement with the direct band gap calculation, responding to sunlight of wavelength shorter than 600 nm. The photocurrent-irradiation time profile for a p-BP photocathode shows no evidence of deterioration. Figure 23 shows the power characteristic in a photoelectrochemical cell (PEC), Pt(H 2 )/0.5 M H 2 SO 4 (1 M ⫽ 1 mol dm ⫺3 )/ /0.5 M H 2 SO 4 /p-BP. Curve 2 indicates that the open-circuit photovoltage is 0.45 V, the

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Figure 23 Photocurrent-photovoltage characteristic of the cell Pt (H 2 )/0.5 M H 2 SO 4 / /0.5 M H 2 SO 4 / p-BP irradiation with 500 xenon lamp. (From Ref. 75.)

short-circuit photocurrent density is 2.4 mA/cm 2, and the fill factor is 0.25. The overall conversion efficiency of optical to electrical energy for the PEC photovoltaic cell is still low with respect to the case of InP. Therefore, improvement of the conversion efficiency is necessary for a more practical device. An attempt to use a large band gap semiconductor of BP on a smaller band gap semiconductor of Si was proposed on the basis of significant stability and conversion efficiency as a photoelectrochemical device (76), serving as a protective optical window by Takenaka et al. (7). The utilization of degenerate single crystalline n-type BP as window material on n-type Si and n-type GaAs electrodes has been proposed (76). The n-Si/n-BP system was stable in a ferriferrocyanide redox couple and more than 10 4 Q charge could be passed through PEC cells without a significant loss of efficiency of the cell. Their device basically resembled a metal-coated semiconductor electrode. Hence, the band bending in the substrate material is in principle determined entirely by the work function of the coating material, and the electrolyte serves only as an electrical contact between the counterelectrode and the ‘‘metal’’-coated photoelectrode. In the band diagram that was derived from their semiempirical electronegativity model, the conduction bands of Si and BP are at about the same energy level, and a small band bending in the Si substrate must be expected for n-Si/n-BP structures. Then the flat-band potential could not be determined experimentally. Also, the Schottky barrier heterojunction could not be characterized electrochemically. Structural, optical, and electronic properties of n-Si/n-BP and p-Si/n-BP heterojunctions have been investigated by Goossens et al. (77,78). Impedance spectroscopy has been used to obtain Mott-Schottky (MS) plots of (C SC )⫺2 versus DC bias, V (Fig. 24). The slope of the MS plot was positive and concordant with an effective donor density N D ⫺ N A of about 5 ⫻ 10 19 cm ⫺3 for all studied samples. For crystalline CVD layers of BP (100), the flat-band potential was ⫺0.55 V versus SCE at pH 4.6 and was observed to show a Nernstian ⫺60 mV/pH dependence. The energy of the conduction band and that of the valence band of crystalline BP were determined on the absolute energy scale with an experimental accuracy of 0.05 eV; that is, versus vacuum: E c (BP) ⫽ (⫹0.32 ⫹ 0.06 ⋅ pH) eV versus SCE E v (BP) ⫽ (⫺1.68 ⫹ 0.06 ⋅ pH) eV versus SCE

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Figure 24 Mott-Schottky plot of C ⫺2 versus electrode potential for a shunted substrate electrode recorded in the dark with KOH (1 M) as an electrolyte (78); when measured through the complete heterojunction, identical MS-plots were obtained. The surface area of the electrodes was 7 mm 2.

The point of zero charge (PZC) (BP) lies at pH 6.4 and SCE ⬃ 4.75 eV below vacuum level. The conduction band of Si matches excellently the conduction band of BP, allowing conduction band electrons to pass easily through the Si-BP junction. However, the valence bands of Si and BP differ considerably. Valence band holes in Si face a 0.9-eV potential barrier at the Si-BP junction and recombine with electrons instead of crossing. The band structures of the n-Si/n-BP and p-Si/n-BP heterojunction configurations are presented in Fig. 25. When the electrode potential is changed by means of an externally applied potential or by addition of a redox couple to the electrolyte, an additional electric field is created in the space charge region of BP at the BP/electrolyte interface. The electric field at the Si-BP junction, however, is not influenced by external applied potential differences. The band structure of the heterojunction agrees with optical features. The n-Si/n-BP electrodes reveal an anodic photocurrent that was generated by photons with hν ⬎ 2.0 eV and was generated only in the window material n-BP. Holes created in the Si are unable to reach the BP-electrolyte interface, so that annihilation of the photoholes by conduction band electrons of Si must occur at the n-Si/n-BP interface. Configurations comprising p-Si/n-BP electrodes produce large cathodic photocurrents when irradiated with low-energy photons, i.e., hν ⬎ 1.1 eV. The photogenerated electrons in Si do cross the Si/BP interface and reach the electrolyte to drive a reduction reaction there. The band structure of the Si/BP heterojunction prevents Si holes crossing the Si/BP junction but does make it possible for conduction band electrons of

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Figure 25 Band structure of n-Si/n-BP and p-Si/n-BP heterojunction photoelectrodes (78). The redox potentials of H⫹ /H 2 and OH-/O 2 are 4.5 and 5.73 eV respectively, below vacuum level.

Si to cross the window and reach the electrolyte. The p-Si/n-BP heterojunction photoelectrodes produce large and stable photocurrents up to 15 mA/cm 2 when applied in liquid junction solar cells. A maximum short-circuit photocurrent, i sc , of 15 mA/cm 2 could be reached with 80 mW/ cm 2 irradiation power. The open-circuit potential, V oc , was about 0.5 V and the fill factor, η, about 0.5. The maximal gained power at 80 mW/cm 2 irradiation power equals (V ⫻ i)max ⫽ η (V oc ⫹ i sc ) ⫽ 3.75 mW/cm 2, which yields a conversion efficiency of tungsten-halogen light of 4 to 5%. The characteristics of photoelectrochemical cells have been greatly improved in comparison with those of fluxed BP crystals (75). In neutral and alkaline electrolytes the surface of BP is free of native oxide and the surface state density is low, but native oxide is present on the surface of BP in acid electrolytes. The presence of an oxide film in acid electrolytes explains the large potential shift in the observed Mott-Schottky plots. Graphs of capacitance as a function of the cell potential (V versus SCE) showed a peaked structure in acid electrolytes that are denoted as ‘‘modified,’’ since a native oxide is present on the surface of BP and surface trapping or recombination is present on these electrodes to a large extent (1). Reliable values for the flat-band potential could not be obtained from these plots. Two additive contributions of the space charge capacitance and a superimposed second capacitive component due to charge trapping in surface states would be suggested. Photoholes at the BP/electrolyte interface give rise to surface recombination in optically created surface states, which are assumed to be a consequence of photoanodic dissolution of n-type BP. Oxygen formation is observed at irradiated n-type BP electrodes, and a competition between the oxidation of the solid and of OH⫺ species occurs, reflecting the lower valence band position of BP and the concomitant larger stability of BP against photoanodic oxidation.

VI. CONCLUSION Semiconducting properties of BP have been clarified to some extent. Theoretical band calculations yield very useful information so that optical properties of BP should be clarified by comparing calculation with experimental data. Theoretical band calculations also indicate that the fundamental gap in BP decreases with increasing pressure (12,79) as in most III-V compound semiconductors, which should be confirmed by high-pressure experiment.

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Thermal conductivity is of technological importance. High thermal conductivity values in single crystals are useful for power-dissipating devices such as diodes, transistors, or lasers to assist in device and circuit design. A low thermal conductivity value is necessary to prompt thermoelectric figure of merit at high temperatures so that the establishment of preparation of sintered polycrystal controlling grain size should be performed by high-temperature and highpressure technologies. The mobility µ and mean trapping lifetime τ of the charge carrier are critical to the operation of a BP neutron detector. The product µτ should exceed ⬃10 ⫺6 cm 2 /V in order to obtain pulses of detectable magnitude for BP detectors (73). For this purpose the growth of high-quality semi-insulating BP with stoichiometric film would be necessary in addition to the GS-MBE process. New film growth techniques such as ion, plasma, and photo CVD methods would be promising for low-temperature growth. Ion beam–induced epitaxial crystallization (IBIEC) has been observed to occur at temperatures much below the thermally induced crystallization temperature and to have a much smaller activation energy than in the pure thermal solid-phase epitaxy (SPE) process. Epitaxial regrowth in BP was induced in the temperatures range 300– 400°C (80). A plasma CVD process would suppress the escape of phosphorus in BP by radicals formed in the plasma atmosphere. The photoexcited CVD process, being free of ion bombardment damage, allows selective excitation of reactant gas in a surface process only. Then the film growth process would treat as heterogeneous gas-phase reactions on the solid surface, which consist of series processes, i.e., surface chemical reaction of adsorption species and transportation of gas phase. We would control each process independently to grow stoichiometric BP films. Investigation of the mechanism of reaction of metal with BP by Rutherford backscattering (RBS) measurements (81) would be useful for the technological aspects of device applications of BP. Nanostructured BP film would be interesting as a new material, and high-surface-area electrodes of the chemically stable BP would be applicable as gas sensors, in photocatalysis, and for energy conversion (39).

ACKNOWLEDGMENTS A number of figures and tables have been taken from the literature. The author would like to thank the authors and publishers of these materials for permission to reproduce them here, expecially the American Physical Society (Fig. 1 (Ref. 18)), the American Institute of Physics (Fig. 19 and Table 6 (Ref. 8)), the Electrochemical Society, Inc. (Fig. 5 (Ref. 44), Fig. 21 (Ref. 72) and Table 5 and Fig. 18 (Ref. 7)), Elsevier Science Ltd. (Fig. 2 (Ref. 30), Fig. 3 (Ref. 35), Fig. 7 (Ref. 47), Fig. 9 (Ref. 15), Fig. 10 (Ref. 55), Fig. 11 and Fig. 12 (Ref. 58) and Fig. 13 (Ref. 61)), and Wiley-VCH (Fig. 24 (Ref. 78) and Fig. 25 (Ref. 78)).

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59. Y Kumashirro, T Yokoyama, A Sato, Y Ando. Thermoelectric properties of boron and boron phosphide CVD wafers. J Solid State Chem 133:314, 1997. 60. S Yugo, T Kimura. Thermoelectric power of boron phosphide at high temperatures. Phys Status Solidi (a) 59:363, 1980. 61. Y Kumashiro, K Kudo, K Matsumoto, Y Okada, T Koshiro. Thermal neutron irradiation experiments on 10 BP single crystal wafers. J Less Common Met 143:71, 1988. 62. S Yugo, T Sato, T Kimura. Thermoelectric figure of merit of boron phosphide. Appl Phys Lett 46: 842, 1985. 63. Y Kumashiro, T Mitsuhashi, S Okaya, F Muta, T Koshiro, Y Takahashi, M Hirabayashi. Thermal conductivity of a boron phosphide single-crystal wafer up to high temperature. J Appl Phys 65:2147, 1989. 64. Y Kumashiro, T Mitsuhashi, S Okaya, F Muta, T Koshiro, Y Takahashi, M Hirabayashi, Y Okada. Thermophysical properties of thick wafers of boron phosphide. High Temp High Press 21:105, 1989. 65. J Ohsawa, T Nishinaga, S Uchiyama. Measurement of specific heat of boron monophosphide by AC calorimetry. Jpn J Phys 17:1059, 1978. 66. DA Watt. Theory of thermal diffusivity by pulse technique. Br J Appl Phys 17:231, 1966. 67. GA Slack. Nonmetallic crystals with high thermal conductivity. J Phys Chem Solids 34:32, 1973. 68. EF Steigmeir, I Kudman. Thermal conductivity of III-V compounds at high temperatures. Phys Rev 132:508, 1963. 69. Y Kumashiro, Y Okada. Schottky barrier diodes using thick, well-characterized boron phosphide wafers. Appl Phys Lett 47:64, 1985. 70. CA Mead. Metal-semiconductor surface barriers. Solid State Electron 9:1023, 1966. 71. SM Sze. Physics of Semiconductor Devices. 2nd ed. New York: Wiley, 1981, chap 5. 72. Y Kumashiro, T Koshiro, Y Okada. Schottky barrier diodes of n-BP-Au. J Electrochem Soc 136: 1830, 1989. 73. JC Lund, F Olschner, F Ahmed, KS Shah. Boron phosphide on silicon for radiation detectors. Same as Ref. 28, p 601. 74. A Fujishima, K Honda. Electrochemical photolysis of water at a semiconductor electrode. Nature 238:37, 1972. 75. JS Lee, A Fujishima, K Honda, Y Kumashiro. Photoelectrochemical behavior of p-type boron phosphide photoelectrode in acidic solution. Bull Chem Soc Jpn 58:2634, 1985. 76. DS Ginley, RJ Baughman, MA Butler. BP-stabilized n-Si and n-GaAs photoanodes. J Electrochem Soc 130:1999, 1983. 77. A Goossens, EM Kelder, J Schoonman. Polycrystalline boron phosphide semiconductor electrodes. Ber Bunsenges Phys Chem 93:1109, 1989. 78. A Goossens, EM Kelder, RJM Beeren, CJG Bartels, J Schoonman. Structural, optical and electronic properties of silicon/boron phosphide heterojunction photoelectrodes. Ber Bunsenges Phys Chem 95:503, 1991. 79. RM Wentzcovitch, ML Cohen, PK Lam. Theoretical study of BN, BP and BAs at high pressure. Phys Rev B36:6058, 1995. 80. N Kobayashi, H Kobayashi, Y Kumashiro. Ion beam induced crystallization in BP. Nucl Instrum Methods B40/41:550, 1989. 81. N Kobayashi, Y Kumashiro, P Revesz, J Li, JW Mayer. Thermal and ion beam induced reactions in Ni thin films on BP (100). Appl Phys Lett 54:1914, 1989.

23 Boron and Boron-Rich Compounds Helmut Werheit Solid State Physics Laboratory, Gerhard Mercator University, Duisburg, Germany

ABSTRACT Outstanding properties of the boron-rich solids in general include their high melting temperatures, their extraordinary hardnesses, their small extension coefficients, and their high chemical resistivity, which predestine them for technical application under conditions that are hardly accessible for most other materials. The aim of this chapter is to describe the relationship of structures, the interrelation of structural and electronic properties, and the possibilities for their modification to tailor boron-rich solids for specific, in particular electronic, applications. The complex structures of the different modifications of elementary boron and of the boron-rich borides are essentially composed of nearly regular B 12 icosahedra and related structural elements, which consist of fragments or condensed systems of icosahedra. These structural elements are bonded directly to one another or via single boron or foreign atoms, thus forming a large variety of open frameworks. The icosahedra as common structural features are the reason for more or less close relationships of the properties and distinguish the boron-rich solids qualitatively from crystals with periodic arrangements of single atoms. Nevertheless, translational symmetry is maintained in these complex crystal structures, and therefore the boron-rich solids must be distinguished from amorphous solids, although early measurements suggested certain similarities of properties. The boron-rich solids are semiconductors with unique electronic properties that are essentially determined by the icosahedra. This implies an interrelation of these properties as well, which can be modified within sometimes large homogeneity ranges of chemical compositions, by forming ternary compounds, by changing the chemical composition within the specific structure groups, and by going to the different structure groups. Accordingly, the icosahedral boron-rich solids offer an excellent chance to study the electronic properties of complex structures and their modification by slight and considerable changes of composition and structure. Some properties of particular interest for fundamental research are the Jahn-Teller effect in the icosahedra; the formation of intrinsic traps by electron-phonon interaction; the soliton-type transport of electrons and holes; the very long lifetime of electrons under specific, externally controllable conditions; the electronic interaction between foreign atoms and the boron framework; and the high, monotonously (up to very high temperatures) increasing Seebeck coefficient of boron carbide. The specific electronic structures make the boron-rich solids rather insensitive to influences of foreign atoms at concentrations that change the semiconductor properties of classical 589

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semiconductors decisively. Nevertheless, doping is possible in principle, indeed at higher concentration levels. This makes the material preparation much easier and less expensive than in the case of the classical semiconductors, demanding extremely high purity. The only electronic property that is at the threshold of technical application at present is the high Seebeck coefficient for high-efficiency direct thermoelectric energy conversion and measurement of very high temperatures under extreme conditions. Moreover, general application for high-temperature electronic devices and at least in some structure groups for wide-gap semiconductors seems promising.

I.

INTRODUCTION

The different modifications of elementary boron and the boron-rich borides exhibit complex structures that are essentially composed of nearly regular B 12 icosahedra and related structural elements consisting of fragments or condensed systems of icosahedra. These structural elements are bonded directly to one another or via single boron or foreign atoms, thus forming comparably open frameworks with a large variety of structures. The common structural features are the reason for more or less close relationships of the properties (1–6) and distinguish the boronrich solids qualitatively from solids with simple periodic arrangements of atoms. Nevertheless, translational symmetry is maintained in these complex crystal structures and therefore the boronrich solids must be distinguished from amorphous solids as well, although early measurements suggested certain similarities of properties. The simplest structure of this series of complex crystals is the α-rhombohedral modification of elementary boron with 12 boron atoms arranged in one B 12 icosahedron per rhombohedral unit cell. The most complex structure known up to now has been found in YB 66-type borides with 1584 boron and 24 metal atoms; the boron atoms are arranged in eight (B 12 ) 13 supericosahedra and eight noncosahedral B 42 units per cubic unit cell. In between there are several further structural groups with different degrees of complexity. All of these structure groups allow the insertion of foreign atoms by substitution or by interstitial accommodation, in many cases in more or less extended homogeneity ranges. Scientifically, these extraordinarily extended possibilities for modifying related structures of solids offer excellent prerequisites for a systematic research on complex crystal structures and on the interrelation between the degree of complexity and the physical properties. With respect to technical applications, this variety promises the possibility of developing compounds with optimized properties for specific applications, while the generally favorable basic properties of the boron-rich solids (e.g., very high melting points, great hardness, low density, small thermal extension coefficient, high resistance to chemical attack), allowing their use under conditions inaccessible for most other solids, remain largely unchanged. Besides of the common mechanical, thermal, and chemical properties of the boron-rich solids, the following largely common structural and electronic properties of icosahedral boron structures attract attention: 1. Common structural properties: (a) In spite of the I h symmetry of the icosahedra forming the structural framework, the space group R 3 m is obviously preferred in the crystal structures. This holds not only for all representatives of the α-rhombohedral boron and the β-rhombohedral boron structure group but also for most of the ion crystals based on [B 12H 12]2⫺ ions as well, where the icosahedral arrangement of the 12 B atoms

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is assumed to be only insignificantly affected by the covalently bonded H atoms (7). (b) In all reliable structure investigations of the covalent and ionic crystals mentioned in 1. (a) and many other structures based on B 12 icosahedra, it was found that the icosahedra are slightly distorted. This distortion was ascribed to steric interactions with cations (7) and influences of the crystal field, respectively; however, initially little attention was paid to the fact that this distortion is very similar in all these cases (8). (c) Except for the ionic crystals, the phonon bands in the infrared (IR) spectrum are weak, indicating a low degree of ionicity of the bonds, and the Raman effect is weak, indicating small polarizability of the structures. 2. Common electronic properties: (a) The semiconducting icosahedral boron-rich solids are not in accordance with the rule, which holds for simple periodic crystal structures in general, that atoms with odd electron numbers form metals in the condensed state. (b) The band gaps of the boron-rich solids do not depend essentially on the crystal structure. (c) In many cases of icosahedral boron-rich solids, a split-off valence band 0.19 eV above the valence band edge has been found. (d) Icosahedral boron-rich solids are p-type semiconductors. Overcompensation to ntype demands donor densities of the order of 10 20 cm⫺3 (9–11). (e) The mechanism of electronic transport is essentially determined by hopping with an activation energy of about 0.2 eV. Even if these general statements on common properties of the boron-rich solids are largely reliable, at present the research on these very promising materials is far from complete. In particular, systematic investigations of interrelations between structural and physical properties have remained in their infancy and are largely restricted to a few materials. Therefore the aim of this chapter is to review the results on electronic structure and electronic transport properties, to demonstrate as far as possible with examples such interrelations between structural and electronic modifications, and to point out the possible extensions of such results to other boron-rich materials. For a complete review of data the reader is referred to Refs. 2 and 3 with updates completed in 1998. The approach of the present chapter—considering the boron-rich solids as a unique group of semiconductors with specific properties that are essentially determined by the icosahedra and are different from those of crystalline and amorphous semiconductors—is in contradiction of the ‘‘amorphous’’ concept of Golikova (1,12). She attributes to the different structures of boronrich solids a degree of amorphization that depends on the number of atoms per unit cell. Accordingly, α-rhombohedral boron with 12 atoms per unit cell is assumed to behave nearly like a crystalline semiconductor, whereas YB 66 with more than 1600 atoms per unit cell is assumed to be nearly amorphous. Of the numerous contradictions of experimental results by this model, only one is mentioned: The properties of the rather well-investigated boron carbide, with 15 atoms per unit cell, close to α-rhombohedral boron, are far from those of classical crystalline semiconductors. Another concept for describing the electronic properties of the boron-rich solids was developed by Emin et al. (13–16) on boron carbide. It is based on the assumption of hole bipolarons in B 11C icosahedra, and the essential basis of this theory is the experimental fact of a very low electron spin resonance (ESR) spin density. These authors were able to describe some uncommon electronic properties of boron carbide with their model.

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However, on the one hand, low ESR signals alone are a weak argument for the assumption of hole bipolarons. On the other hand, several experimental results are in contradiction of this model. For example, (a) the electrical conductivity of boron carbide is maximum at the minimum concentration of B 11C icosahedra in the homogeneity range; (b) polaron-type effects are restricted to one electron per icosahedron and no corresponding electron-phonon interaction with holes, in particular not with hole pairs in icosahedra, has been proved experimentally (c) the distortion of the icosahedra in boron carbide depends to only a small degree on electron-phonon interaction; and (d) the electronic transport in boron-rich solids is due to classical band-type conduction and hopping processes side by side. Hence, the hole bipolaron theory for boron-rich solids can hardly be maintained.

II. STRUCTURE GROUPS OF BORON-RICH SOLIDS A.

Icosahedral Structures

1. α-Rhombohedral Boron Structure Group The vertices of the rhombohedral unit cell are occupied by one B 12 icosahedron each. One of its trigonal axes is orientated parallel to the crystallographic c axis, coinciding with the main diagonal of the unit cell. The six boron atoms forming the top and bottom triangles of this oriented icosahedron are called polar; the six remaining ones arranged slightly above and below the equatorial plane of the icosahedron are called equatorial. The unit cell of the α-rhombohedral boron modification of elementary boron, which can be prepared only at temperatures below about 1200°C, does not contain further atoms. The intericosahedral bonds of the polar atoms along the edge of the unit cell are covalent, and the equatorial atoms of three neighboring icosahedra form weak electron-deficient three-center bonds oriented approximately perpendicular to the c axis. The structural variety of this structure group is particularly determined by additional atoms accommodated on the main diagonal of the unit cell (Fig. 1). They form three-atomic chains (e.g., in binary boron carbide), bonded atoms in pairs (e.g., in B 12 P 2, B 12 As 2 ), and noninteracting atoms in pairs (e.g., in B 6 O, B 6 Be, B 6 S) (17,18). The only exception are Al atoms, which are accommodated in sites outside the main cell diagonal (19). In B 2.89Si the Si atoms form bonded pairs and substitute for boron on icosahedral sites as well. Ternary compounds such as BCSi are known, in which unit cells with three-atom chains (CBC and CBB) and bonded Si 2 pairs exist side by side (20,21), or Si-doped B 12P 2 with P 2 and Si 2 pairs (22,23). The arrangement of these additional atoms leads to a qualitative change of bonding within the structure compared with α-rhombohedral boron in cases in which they saturate the outer bonds of the equatorial atoms, thus replacing their weak intericosahedral three-center bond by strong, largely covalent bonds to the end atoms of the chain. With the compounds known up to now, the possible compositional and structural variety within this structure group seems far from being exhausted. 2. β-Rhombohedral Boron Structure Group β-Rhombohedral boron is the high-temperature, thermodynamically stable crystalline modification of elementary boron. Its unit cell consists of essentially 105 atoms (24,25) [106.5 atoms, if some additional sites with very low occupation densities are taken into account (26)]. The structural formula (B 12 ) 4 (B 28 ) 2B exhibits four icosahedra, one positioned at the vertex and three on the edge centers of the unit cell (both sites are crystallographically inequivalent), and two B 28 units, which consist of three condensed icosahedra each, arranged symmetrically around a centered single atom on the main diagonal of the unit cell. For certain descriptions the alternative

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Figure 1 Unit cell of boron carbide as a representative of the α-rhombohedral boron structure group. The unit cell of α-rhombohedral boron contains the B 12 icosahedron only; in the other representatives twoatom or three-atom chains or two single atoms are on the main diagonal. (䊊) Polar atoms; ( ) equatorial atoms; (䊉) chain atoms.

structural formula B 84 (B 10 ) 2B is preferred, with the B 84 unit consisting of the B 12 icosahedron at the vertex of the unit cell radially surrounded by 12 half-icosahedra, which complete each other forming the B 12 icosahedra on the edge centers. Two B 10 units and the single atom on the diagonal complete this structure description. The outer bonds of the icosahedra are largely radially directed and covalently saturated. The essential bases for the structural diversity within this structure group are different holes in the boron framework (Fig. 2), which are large enough to accommodate foreign atoms up to certain solubility limits, which seem to be specifically determined by the number of suitable sites, the size of the foreign atoms, or the degree of electron transfer to the boron framework (see later). Numerous binary and ternary compounds of this type with Mg, Al, Ga, Si, Ge, Cu, Sc, Ti, Zr, Hf, V, Nb, Ta, Cr, Mn, Fe, Co, and Ni atoms have been prepared (e.g., see Ref. 27 and references therein); for LiB 13 with the β-rhombohedral boron structure see (28). Substitutional B 32Al 3 and B 14 Si compounds [structural formulas B 84 (B 6 Al 4 ) 2Al and B 84 (B 7 Si 3 ) 2 Si] were reported by Matkovich et al. (29,30). 3. α-Tetragonal Boron Structure Group The idealized unit cell of α-tetragonal boron (Fig. 3) (31) consists of 50 atoms, which are arranged in four B 12 icosahedra with one of their fivefold axes parallel to the c axis, and of two additional single B atoms on 2(b) sites. In the borides belonging to this structure group these

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Figure 2 Schematic arrangement of the structure elements in the β-rhombohedral boron unit cell. Icosahedra: (䊐) B 28 unit; (䊉) central B atom. Interstitial sites: (䉱) A(1) (Me1); (䊊) D (Me2); (䉲) E (Me3); (䉳) Si.

2(b) sites and also two voids at 2(a) are assumed to be partly or completely occupied by other, preferably metal atoms. Compounds with Be, Al, C, N, Ni, and Cu have been synthesized (for details and references see Refs. 4 and 26). However, in some cases the obvious difference in phonon spectra (4) makes the attribution of the compounds to the same structure group questionable. There are suspicions that α-tetragonal boron cannot be prepared in pure form but that the structure concerned must be stabilized by foreign atoms. Few investigations of physical properties of representatives of this group have been reported (2–4).

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Figure 3 Unit cell of α-tetragonal boron containing B 12 icosahedra and single B atoms in 2(b) position (31).

4. β-Tetragonal Boron Structure Group The three-dimensional framework of this structure with 190 atoms consists of chains of B 12 icosahedra alternately alligned parallel to the a and b axes and of twinned double icosahedra linked to 10 adjacent B 12 icosahedra and to four neighboring double icosahedra (Fig. 4) (32). The remaining B atoms are single. In the related borides, certain sites in the double icosahedra remain unoccupied. The metal atoms are statistically distributed in interstices or replace the single B atoms (for more details see Refs. 3, 4, and 33 and references therein). The best-investigated compound of this structure group is α-AlB 12 (see later). 5. Amorphous Boron Amorphous boron consists of B 12 icosahedra, which are statistically distributed. It has been proved that the narrow-range and the medium-range orders of amorphous boron are closely related to those of crystalline β-rhombohedral boron (34–38). Accordingly, it has been proved that the external bonds of the icosahedra in amorphous boron are largely covalently saturated. Therefore it seems a likely supposition that the electronic properties are closely related to those of β-rhombohedral boron as well, and moreover there may be holes in the structure to accommodate foreign atoms for doping to modify the properties. This would give a favorable chance of future application because well-established techniques could be used to prepare amorphous instead of crystalline material, for example, in thin layers. There are hints that the structure of amorphous boron deposited by evaporation on surfaces at lower temperatures are essentially different from those in thermal equilibrium (see Ref. 38 and compare with Ref. 34). 6. Orthorhombic Borides (MgAlB 14 Type) The boron framework with 64 atoms per unit cell (Fig. 5) (39) consists of B 12 icosahedra arranged in a distorted hexagonal packing. Contrary to those in the rhombohedral modifications of pure

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Figure 4 Unit cell of β-tetragonal boron. (a) Chains of B 12 icosahedra; (b) twinned B 21 double icosahedron and (䊉) single B atoms (32).

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Figure 5 Structure of AlMgB 14 as a representative of the orthorhombic borides. Projection on the (a) ab plane and (b) bc plane (39,40).

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boron, the direct intericosahedral bonds deviate from radial directions. This holds for the indirect bonds via single boron atoms on sites between the icosahedra as well. The metal atoms are accommodated in large holes outside the icosahedra and are rather weakly bonded to the boron framework (40). The structural formula is (B 12 ) 4Me(1) 4Me(2) 4B 8; however, in most cases the metal sites are not completely occupied. As for the α-rhombohedral boron structure group, there are only B 12 icosahedra and single boron atoms in the structure; there are no complex structural units of fused icosahedra as found in the β-rhombohedral boron (B 28 ) and β-tetragonal boron (B 22 ) structural families or giant B 156 icosahedral arrangements as in the YB 66 structural family. As indicated in the structural formula, ternary compounds have usually been prepared. Because in most cases the crystals have been grown in Al 2O 3 crucibles from high-temperature AlB solutions containing small amounts of other metal atoms, Al is usually one of these metals. However, compounds without Al are known as well (NaB 0.8B 14 (41), Mg 2B 14 (42,43)). For reviews of compounds of this structure group see Refs. 44 and 45. 7. YB 66-Type Structures The cubic unit cell of YB 66-type compounds with 1632 boron atoms consists of 13 giant (B 12 ) 13 icosahedra and 8 nonicosahedral B 42 units [structural formula B 12 (B 12 ) 12 (B 42 ) 8] with the metal atoms statistically distributed on defined interstitial sites (Fig. 6) (46,47). The B 42 units are clusters consisting of 80 boron sites with occupancies ranging between 28 and 71% (48). The homogeneity range is assumed to be considerable (YB n, 20 ⬍ n ⬍ 100). Besides Y, most of the lanthanide and some actinide atoms are known to form this structure (see Refs. 3, 49, and 50).

Figure 6 Schematic structure of YB 66 (46,47) consisting of B 156 [(B 12 ) 13] giant icosahedra, B 48 nonicosahedral units, and metal atoms.

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As far as investigations of physical properties are concerned, they are largely restricted to YB 66 (see later). B.

Nonicosahedral Structures

Besides of the icosahedral structures of boron-rich solids, two structure groups based on other polyhedral arrangements of boron atoms are known: 1. Metal Hexaborides The unit cell contains one formula weight of MB 6. The boron atoms form octahedra positioned at the corners of the cubic unit cell, and the metal atoms are in its center. All rare earth metals and Ca, Sr, Ba, Tl, and Pu form these isostructural hexaborides see (3,51–54). 2. Metal Dodecaborides The structure can be described in terms of a modified face-centered cubic (fcc) unit cell with the metal atoms in the center of regular cubo-octahedra consisting of boron atoms at each of their 24 vertices or, alternatively, by a modified NaCl-type structure with metal atoms and cubooctahedral arrangements of 12 boron atoms, each occupying the structure positions. Lanthanides, actinides, and many other metal atoms are able to form this structure (3,53–55). In contrast to the icosahedral structures, which are semiconductors in general, the compounds in these structure groups are preferably metals and will therefore not be discussed in this chapter in detail. In the case of some metal hexaborides, the existence of semiconducting phases seems to depend on the composition. Dodecaborides with divalent metals are expected to be semiconducting or insulating, those with trivalent metals to be metallic (54). C.

Carbon in Boron Structures

Carbon is a very important foreign element for all boron structures. Its chemical affinity for boron is very high. Because both light elements are immediate neighbors in the periodic system, at present the resolving power of even modern imaging, scattering, and analyzing methods is usually not sufficient to discern them directly in the solid structures. Because the solubility coefficients of carbon in the solid and the liquid phase are almost the same, zone melting, which is used to prepare high-purity crystals of many other elements, is not suitable in the case of boron. Technical boron, which is often taken as the ingredient for the preparation of boron compounds, contains up to about 0.5% carbon. However, in several preparative methods for boron compounds the carbon content may be reduced by secondary chemical or physical reactions. The purest β-rhombohedral boron crystals that have become available up to now were produced by Wacker-Chemie, Munich, FRG. Despite the claimed purity of 99.9999% with respect to other elements, even this high-purity boron contains carbon in concentrations of typically 30 to 80 ppm. Therefore, apart from boron carbide containing carbon as a determining bonding partner, in the assessment of the properties of boron and boron compounds attention must be paid to the fact that a certain, usually unknown carbon content could have influenced the properties determined. Quantitative investigations of the effect of the carbon content on the structure and physical properties of boron-rich solids have been restricted to β-rhombohedral boron and boron carbide (56–61). Up to carbon contents of about 1 at.% in β-rhombohedral boron, the carbon atoms substitute statistically for boron atoms at the polar sites of the B 12 icosahedra in the structure with a maximum of one carbon atom per icosahedron. Compared with the boron atom, the

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carbon atom is radially shifted toward the center of the icosahedron by 6.7(3)% (56,57). This distortion of the icosahedra is quantitatively related to the anisotropy of the change of the unit cell parameters depending on the carbon content. For boron carbide it has been assumed that carbon atoms substitute for boron at the polar sites of the icosahedra as well. However, a quantitative correlation with the modification of the unit cell parameters of boron carbide was not possible, because they are considerably influenced by the changes of the interior of the unit cells depending on the carbon content as well. For the influence of the carbon content on the physical properties of β-rhombohedral boron and boron carbide, see later. D.

Accommodation of Foreign Atoms Within the B 12 Icosahedra

For the incorporation of foreign atoms in all the boron-rich structures discussed previously, only interstitial sites between the icosahedra were taken into account. Although the size of the B 12 ˚ should be sufficient to accommodate small atoms within cage with its diameter of about 3.4 A the icosahedra, up to now no compounds of this kind have become known. The question arises whether such compounds are possible or impossible in principle. To answer this question, Beckel and Howard (62) calculated the possible configurations of the complex [Mg⫹B 12H 12] and found one stable position of the magnesium ion in the center of the B 12 cage. They concluded that incorporation inside the icosahedra should be possible for atoms with low single and double ionization energies and sufficiently small steric radii. III. THE B 12 ICOSAHEDRON AND ITS ELECTRONIC STRUCTURE The B 12 icosahedra are periodically arranged in all crystalline boron-rich structures. Nevertheless, these solids differ decisively from molecular crystals. The overlap of intericosahedral and intraicosahedral vibrations in the phonon spectra (see Refs. 27 and 63) proves, in agreement with theoretical calculations (13), that contrary to molecular crystals, the intericosahedral bonds are stronger than the intraicosahedral ones. This leads to a considerable interaction of the electronic states of the icosahedra in the solid structures, whose energy band structures are essentially determined by the overlap of the electronic orbitals of the icosahedra. A.

The Isolated Icosahedron and Its Orbitals

The distortion of the icosahedra, which is largely independent of the specific structures, has been attributed to the Jahn-Teller effect (64). This is a fundamental principle acting in all cases, where in highly symmetrical atomic arrangements the orbit-degenerated electronic states couple with asymmetrical vibrations. The only exceptions, twofold Kramer-degenerated states in arbitrary groupings and twofold orbit-degenerated states in linear arrangements of atoms, do not apply to the B 12 icosahedron. The physical reason for this coupling, which leads to a distortion and in consequence to a reduction of symmetry, is the reduction of total energy of the system in the distorted state compared with the high symmetrical one. By group theoretical methods it was shown (65,66) that by this distortion the icosahedral point group I h is reduced to the subgroup D 3d, which is compatible with the space group R 3 m. This explains why this space group is preferred in icosahedral crystal structures. Of course, this distortion of the icosahedra affects its molecular orbitals as well. From theoretical calculations for the regular icosahedron by Longuet-Higgins and Roberts (67) and Bambakidis and Wagner (68), it is known that the electronic ground state of the boron atom 2s 2 2p 2 is hybridized to 2s 2p x 2p y 2p z with 3 electrons available. For the regular B 12 icosahedron the result is

Boron and Boron-Rich Compounds

25 bonding orbitals 23 antibonding orbitals

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36 electrons 0 electrons

If the external bonds are assumed to be covalent, the electrons are distributed as 12 orbitals of outer bonds 13 orbitals of inner bonds

12 electrons 24 electrons

This electron-deficient structure leads to the intraicosahedral multiple-center bonds of the icosahedron, which, according to Howard et al. (69), is stable in spite of lacking two electrons. The low ionicity of the crystal structures indicated by the small phonon oscillator strengths (see, e.g., Ref. 4) indicates that this electron-deficiency site remains largely uncompensated in the crystal structures. The influence of the Jahn-Teller effect on the intraicosahedral bonding orbitals was qualitatively derived by group theoretical methods for the clearest situation of exclusively covalent external bonds of the icosahedron (64–66). Comparison of the character tables of I h and D 3d yields immediately that all the three-, four- and five-fold degenerated irreducible representations of the icosahedral group I h split, because they are not comprised in the D 3d group (Fig. 7). The fourfold degenerated uppermost G u orbital of the regular icosahedron partly occupied by only six electrons is thus split so that occupied and unoccupied orbitals become separated. The total splitting range of the G u orbital was quantitatively calculated by Hori et al. (70) as 0.5 eV, in rough agreement with the results experimentally obtained for β-rhombohedral boron (71). B.

Icosahedral Crystal Structures

For the case that in condensed matter the bonding conditions of the free icosahedron (covalent intericosahedral bonds, which are weaker than intericosahedral bonds) remain largely unchanged

Figure 7 Jahn-Teller induced splitting of the icosahedral orbitals, when the symmetry is reduced from I h (free icosahedron) to D 3d (icosahedron in rhombohedral crystal structure) (64,65,71).

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compared with the [B 12H 12]2⫺ cluster, the energy scheme of the intraicosahedral bonding orbitals of the free icosahedron can be essentially transferred, although these orbitals will, of course, spread to energy bands. Because the intericosahedral bonds are stronger, the concerned orbitals are comparably lower in energy and do not contribute to the uppermost part of the valence band. Then occupied and unoccupied electronic states of the solid are energetically separated, and accordingly semiconductor behavior results in spite of the odd number of electrons in the single boron atom. For example, this is the case in many representatives of the α-rhombohedral boron structure group, in particular boron carbide (α-rhombohedral boron itself excluded), and all representatives of the β-rhombohedral boron structure group. α-Rhombohedral boron is an example of icosahedral structures with different conditions of outer bonds. Perpendicular to the c axis, the equatorial atoms of the icosahedra form threecenter bonds, which are weaker than the intraicosahedral bonds, and accordingly positioned at higher energies. Hence these orbitals could contribute to the uppermost valence band range and accordingly change the situation described before. Theoretical band structure calculations for such cases taking the Jahn-Teller effect into account are still lacking. However, the experimental fact that all the icosahedral boron-rich solids are semiconductors seems to indicate that the influence of the intraicosahedral bonds also prevails in these cases. The density of states of the B 12 icosahedron in solids determined by cluster calculations of Shirai and Nakamatsu (72) are shown in Fig. 8.

Figure 8 Density of states of the B 12 icosahedron as obtained from cluster calculations by Shirai and Nakamatsu (72).

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IV. PHYSICAL PROPERTIES OF ICOSAHEDRAL BORON-RICH SOLIDS Up to now, the knowledge and understanding of the physical properties of icosahedral boronrich solids have been most extensively elaborated for β-rhombohedral boron and, with some restrictions, boron carbide as well. Therefore these materials will be in the foreground of the following description. Although both semiconductors belong to different structure groups, a comparison of their properties is interesting because in both cases the external bonds of the icosahedra are largely covalently saturated. Subsequently, the limited results available for other structures will be discussed. To understand and describe the electrical and optical properties of a semiconductor, it is essential to have knowledge of its electronic band structure, which exhibits the relation between energy and momentum E(k) of electrons and holes in the different possible states of the conduction and valence bands at the various symmetry points of the first Brillouin zone of the reciprocal lattice. In particular, the band gap between the valence and conduction bands is important, because it determines, e.g., the optical transition energy and the temperature dependence of the intrinsic conductivity. In the case of the complex boron-rich solids with large numbers of atoms per unit cell, the agreement between theoretical calculations of the band gaps and the experimental results has not yet been satisfactory. As a second parameter of the electronic band structure, the curvature of the energy bands is important for the electronic properties because the effective mass is determined by 1/m* ⫽ –h 2 ∂ 2E/∂k 2 In this respect, all theoretical calculations for icosahedral boron-rich solids yield the corresponding result that the energy bands are rather small compared with classical semiconductors and hence the effective masses are expected to be comparably large. A.

␤-Rhombohedral Boron

1. Optical Parameters β-Rhombohedral boron is the only boron-rich icosahedral solid for which the spectra for interaction with electromagnetic radiation are available in a very extended range. In Fig. 9 the reflectivity spectrum and partly the absorption spectrum are shown (73–77). The small change in the reflectivity within the phonon range of the spectrum underlines the weak ionicity of the structure. 2.

Energy Band Structure

a. Density-of-States Distribution Theoretical studies of the electronic structure of β-rhombohedral boron have been performed by Bullett (78,79). The density-of-states distribution reproduced from Ref. 76 is shown in Fig. 10 and reveals a gap close to 3 eV. Qualitative distributions of the density of states obtained by different experimental methods (80–87) are plotted in Fig. 11. b. Interband and Gap-State Related Transitions Precise transition energies between valence and conduction bands of semiconductors have been experimentally obtained by optical measurements in the low-energy limit of the fundamental absorption range, which is called the absorption edge. As usual, this absorption edge is a superposition of several transitions; however, they can be checked and decomposed according to the theories of interband transitions in crystalline semiconductors (direct and indirect, allowed and forbidden) (see Ref. 88) or an Urbach tail as in amorphous semiconductors. In β-rhombohedral boron the slope of the absorption edge is also complicated by optically excited electronic transitions in connection with intrinsic states of high densities in the band gap. The energy dependence

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Figure 9 Reflectivity and absorption index of β-rhombohedral boron (collection of results obtained by different methods and authors) (73–77).

Figure 10 Theoretical density of states of α-rhombohedral boron and β-rhombohedral boron (78,79).

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Figure 11 Qualitative distribution of the density of states as determined by different experimental methods (see Ref. 2 and references therein, and Refs. 80–87).

of the optical absorption processes concerned correspond to Lucovsky’s theory of transitions from deep levels to parabolic bands in semiconductors (89). Figure 12 shows the absorption edge of different high-purity β-rhombohedral boron samples with low carbon contents measured at room temperature (71). The influence of low but different carbon contents can easily be seen. A larger section of the absorption edge is shown in Fig. 9 (90). The band gap is determined by indirect allowed interband transitions. The energies obtained from the decomposition of the absorption edge are listed in Table 1 (71). The essential band gap is 1.50 for E储c and 1.46 eV for E芯c, and the upper valence band with a distance of 1.32 and 1.29 eV, respectively, from the conduction band is identified as the split-off valence band caused by a static Jahn-Teller effect in the icosahedron as described in Sec. II.A. It was shown that this effect acts on the icosahedra at the vertex of the unit cell only, and accordingly the density of states of the band corresponds to the number of rhombohedral unit cells (N ⫽ 1.35 ⫻ 10 20 cm⫺3 ) and is comparably low (56,57). This is important for the electronic transport mechanism described in the following. The temperature dependence of the transition energies can be quantitatively described by the disorder caused by thermal fluctuations of the atomic positions related to phonons according to –Ω phononn(h–Ω phonon ) E g (T) ⫽ E g (T ⫽ 0) ⫺ βh with the temperature coefficient β in units of k B and the Bose-Einstein–type phonon excitation density n(h–Ω phonon ) (91–93); the parameters used for β-rhombohedral boron are listed in Table 2 (68). All phonons implicated in the interband transitions of β-rhombohedral boron and their temperature dependence are present in the IR phonon spectrum (94,95). From the decomposition of the absorption edge tails of pure (71) and carbon-doped βrhombohedral boron (58,59) the energetic positions of six intrinsic trapping levels in the band gap result. They are generated by electron-phonon interaction with intraicosahedral phonons

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Figure 12 Anisotropy of absorption edge and edge tail of high-purity β-rhombohedral boron (carbon content 66 and 92 ppm, respectively) (71).

and are slightly different in energy for B 12 and B 11 C icosahedra (58,96). They are positioned with energies of multiples of 0.188(2) eV for B 12 icosahedra and multiples of 0.208(2) eV for B 11 C icosahedra off the conduction band edge (Fig. 13). The generation of these intrinsic trapping levels by electron-phonon interaction requires free electrons in the conduction band and the excitation of the phonons involved as well. The involved phonons are antisymmetric breathing modes of the icosahedron described by a conTable 1 Anisotropic Optical Transition Energies and Band Gap Parameters of the Indirect Allowed Interband Transitions in β-Rhombohedral Boron, Extrapolated to T ⫽ 0 E储c

No. 1

Transition energy (eV)

E ⊥c

Gap width

IR phonon assigned (cm⫺1)

1.32(1)

476(1)

1.27(1)

2 3

1.37(1) 1.46(1)

4

1.54(1)

Transition energy (eV)

Gap width

IR phonon assigned (cm⫺1)

1.29(1)

478(1)

1.46(1)

(358(1)

1.23(1) 1.34(1) 1.42(1) 1.50(1)

355(1) 1.50(1)

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Table 2 Parameters Used to Describe the TemperatureDependent Shift of the Gap Energies in β-Rhombohedral Boron

βk B ⫺ hΩ phonon

E储c

E ⊥c

1.03 meV K⫺1 121.9 meV/982 cm⫺1

1.25 meV K⫺1 94.1 meV/758 cm⫺1

tracting upper and expanding lower pentagon of the icosahedron (F 1u mode) and an oblate and a prolate hemispheroid (F 2u mode), respectively. The symmetry axes of the atomic movements concerned are the fivefold symmetry axes of the icosahedron. Because the icosahedron exhibits six of these symmetry axes, the interaction of the electron can take place with up to six pairs of phonons and accordingly the number of trapping levels is limited to six. The maximum distortion of the icosahedron caused by such electron-phonon interactions takes place in the equatorial plane perpendicular to the corresponding fivefold symmetry axis. This is the plane of the Landau orbit of the trapped electrons, when the magnetic field is oriented parallel to the fivefold axes of the icosahedron. Accordingly, it was possible to attribute the ESR resonances of β-rhombohedral boron (97,98) to the trapped electrons and to take the ESR line widths (see Fig. 13) as a measure of the distortion in agreement with the model described (58,59). These results led to the energy band scheme of β-rhombohedral boron in Fig. 14. From optical absorption spectra, photoabsorption, photoconductivity, and relaxation after preceding optical excitation, important information on the transition probabilities between the different levels in the band scheme has been derived (65,66,99–103). Optical transitions from the lower into the upper valence band are forbidden. Electrons cannot be directly excited from

Figure 13 Energetic distance of the intrinsic electron traps from the conduction band edge for B 12 and B 11 C icosahedra. ESR line widths demonstrating the degree of distortion of the icosahedra in case the different traps are generated (58,96).

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Figure 14 Energy band scheme of β-rhombohedral boron (65,66,99–103).

the valence band into the electron trapping levels, because these levels do not exist without trapped electrons. The recombination of trapped electrons into the valence band needs preexitation into the conduction band. All four B 12 icosahedra in the unit cell are able to form such traps with one electron captured in one of the six possible levels. From the volume of the unit cell, V ⫽ 2.4616(4) nm3, a maximum density of traps of about 5 ⫻ 10 20 cm⫺3 is possible. According to very far ultraviolet (VUV) measurements of the optical properties, the range of optical fundamental absorption essentially extends to about 9 eV (Fig. 15) (104). From the second derivatives of ⑀ 1 and ⑀ 2, critical points in the energy band structure were determined at 2.6, 3.15, 3.8, 4.5, 5.4, 6.1, 6.6, 7.5, 8.1, 8.53, and 8.95 eV (104). Steps in the photoconductivity spectra after optical excitation confirm the existence of the trapping levels known from absorption and photoabsorption measurements [Fig. 15a (105)]. 3. Electronic Transport Properties of β-Rhombohedral Boron Figure 16 shows the temperature dependence of the DC electrical conductivity of pure and of some selected examples of doped β-rhombohedral boron (see Ref. 2 and references therein). In a large range of temperature the slope meets Mott’s law for variable-range hopping (Fig. 17) (106,107). The striking step between 400 and 500 K is caused by the Fermi level pinned in the trap states (65). The Seebeck coefficient (Fig. 18) (see Ref. 2 and references therein) is positive and indicates p-type conductivity up to the highest temperatures reached. By comparing the temperature dependences of electrical conductivity and Seebeck coefficient according to Bosman and Crevecoeur (108) it was found that the mobility of the holes has an activation energy of 0.18(1) eV (101,106), which corresponds to the distance between the split-off and the lower valence band.

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Figure 15 (a) Second derivatives of the real and the imaginary parts of the dielectric function of βrhombohedral boron in the spectral range of fundamental absorption (104). (b) Photoconductivity of βrhombohedral boron in the low-energy tail of the fundamental absorption. Conditions of measurement: 155 K, sample annealed at 450 K, cooled down to 155 K, 1-h excitation by a xenon arc lamp, quickly cooled down to 90 K, then measured; 320 K, sample annealed at 450 K, cooled down to 320 K, then measured without (unexcited) or after 1-h excitation with a xenon arc lamp. The ionization energies of the electron traps known from absorption and photoabsorption measurements are indicated (105).

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Figure 16 Temperature dependence of the electrical conductivity of pure boron and examples of differently doped β-rhombohedral boron. 1 and 2, High-purity boron; 3, lapped surface; 4, B 6 O surface layer; 5, Mn-doped; 6, Fe-doped, 7, 3% C-doped; 8, FeB 29.5; 9, C-doped (p ⫽ 3 ⫻ 10 20 cm⫺3 ). (See Ref. 2 and references therein.)

The Hall effect indicates p-type behavior as well, and based on classical theory an interband thermal activation of the carriers of 1.52 eV was derived from the slope. This agrees quite well with the gap energy (101). If the energy band structure of β-rhombohedral boron were based on the B 12 icosahedra only, one would expect that the upper valence band is completely free from electrons. In reality this is not the case, which can be seen, e.g., from the interband transitions of electrons into the conduction band by optical absorption. These electrons may come from nonicosahedral structure elements. Hence, in thermal equilibrium the Fermi level is positioned within this upper valence band. Accordingly, different electronic transport mechanisms seem possible in principle: a. Thermal Equilibrium at Low Temperatures Hopping at the Fermi level within the upper valence band Band-type conductivity in the lower valence band

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Figure 17 Electrical conductivity of β-rhombohedral boron plotted against T ⫺1/4 to show the temperature dependence according to Mott’s law for variable-range hopping (106,107).

When the thermal energy is sufficient, free holes are generated by exciting electrons into the upper valence band, which acts in this case like an intrinsic acceptor level. For these free holes the partly occupied upper valence band has a further meaning for the holes in the lower valence band. It acts as a trapping level of high density, hence reducing the relaxation time of the free holes considerably. This explains the p-type behavior at low temperatures. The simultaneously occurring band-type and hopping conduction has been proved in the dynamical conductivity in the far infrared (FIR) spectral range (see Fig. 24) (75,109,110). b. Thermal Equilibrium at High Temperatures At sufficiently high temperatures electrons are thermally excited from the valence into the conduction band. However, because of the high density of electron traps, their contribution to the charge transport is extremely low and p-type behavior prevails irrespective of a probably smaller electron effective mass. c. Thermal Nonequilibrium In particular at lower temperatures, thermal nonequilibrium can be established, for example, by optical interband excitation and subsequent trapping of electrons or by quenching from high temperatures. Compared with equilibrium, the electrical conductivity increases, and this is due to the shift of the quasi-Fermi level toward the lower valence band, which has two effects: The excitation of free holes increases because the activation energy into the upper valence band is reduced, and the trapping probability of the free holes decreases because the number of occupied states in the upper valence band acting as traps for the free holes in the lower valence band becomes smaller. As shown before, the temperature dependence of the electrical conductivity follows Mott’s law in a large temperature range. It seems that two mechanisms can possibly be attributed to

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Figure 18 Seebeck coefficient of β-rhombohedral boron according to the results obtained by different authors (see Ref. 2 and references therein). For interstitially doped boron with negative Seebeck coefficient, see Fig. 21.

this behavior. The first is variable-range hopping excited by phonons in the upper valence band, which doubtless corresponds to the behavior that is the objective of Mott’s theory. For example, the impurity band conduction in p-type silicon exhibits a metal-semiconductor transition for concentrations of about 5 ⫻ 10 18 cm⫺3 statistically distributed acceptors (111) and the density of states of the upper valence band in β-rhombohedral boron generated by 5 ⫻1020 cm⫺3 periodically arranged icosahedra is distinctly higher. However, a second process seems possible as well, and this is multiple trapping of free holes in occupied states of the upper valence band. This process is a type of thermal excitation of carriers as well, and one can imagine that this could also follow a slope similar to Mott’s law. Theoretical calculations for such processes have not yet become available, and therefore the question remains open whether one of these processes or both side by side are responsible for the hopping processes.

4.

Carrier Mobilities

In such complex conductivity processes characterized by a superposition of high-mobility microscopic band-type conduction, low-mobility hopping, and low-mobility drift because of multitrapping, it is very difficult to determine the mobility of the carriers reliably. Obviously, the results depend on the method of measurement. For example, at high frequencies the carriers with bandtype mobility essentially determine the result, whereas at low frequencies hopping prevails.

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Figure 19 Mobility of carriers in β-rhombohedral boron obtained by different methods and different authors. 1, From space-charge limited currents; 2 and 3, µ H; 4, field effect; 6, thermally activated hopping; 䊊, from electrical conductivity and spin density; 䊉, µ H; 䉲, from electrical conductivity and ESR; 䊐; magnetoresistance; ■, from ESR line width; ⫹, band mobility; 䉱, hopping mobility; 䉭, from photoconductivity; 䉮, from high-field conductivity, I, Hall mobility and photoconductivity. (See Ref. 2 and references therein.)

Accordingly, all the results on carrier mobilities in β-rhombohedral boron (Fig. 19) based on the assumption of a single transport mechanism are more or less questionable. A reliable way to determine drift mobilities is based on the transit times of optically excited electrons and holes depending on the drift field (112) Figure 20a–c show the electron, hole, and electron-hole pair densities at different distances from the illuminated surface depending on the space of time after steady-state excitation has been started. Shoulders in the dispersion spectra separate an initial range determined by carriers slowed down by traps, which are in steady exchange with the adjacent band, from the range that is essentially determined by multitrapping in deep trapping levels. Qualitative differences between these transit time spectra are the quenching of hole concentration in the initial range and the considerable delay of the electron saturation compared with the hole saturation at long drift times. The quenched hole conductivity in the initial range is caused by reduction of the electron density in the upper valence band. This range is followed by an enhanced conductivity caused by the decreasing activation energy for free holes in the lower valence band when the Fermi level is lowered. At the beginning, the first electron trap for free electrons and the upper valence band for free holes in the lower valence band have similar effects on the carrier transport, because their reexcitation energies are the same. Accordingly, the shoulders in the dispersion spectra are similar. The delay of the electrons at long times is due to multitrapping in deep traps and to

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Figure 20 (a–c) Drift and diffusion of optically excited carriers in β-rhombohedral boron. Densities of electrons, electron-hole pairs, and holes at different distances from the illuminated surface versus transit time related to the onset of steady-state optical excitation (112). (d) Temperature dependence of the hole drift mobility in β-rhombohedral boron derived from transient photoconduction (113).

the retardation of the recombination because the valence band is largely filled. The transport of electrons and holes is of soliton type. The nonlinearity of the velocity required is evoked by the time-dependent presaturation of the traps by preceding carriers. For details see Ref. 112. Characteristic carrier mobilities determined are for electrons for holes

µ e ⫽ 0.11 cm2 V⫺1 s⫺1 µ h ⫽ 0.076 cm2 V⫺1 s⫺1

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The relations of retrapping to recombination rates are for electrons for holes

R retrapping /R recomb ⫽ 15 R retrapping /R recomb ⫽ 1.2

which means that electrons cover average distances of more than 30 mm before they recombine. This value exceeds those known from classical semiconductors by far.

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The temperature dependence of the hole drift mobility (Fig. 20d) yields a thermal activation energy of 240 meV (113). 5. Interstitial Doping A fundamental prerequisite for the technical application of semiconductors is the possibility of changing their conductivity characteristics by doping. In the case of boron-rich solids, this was realized for the first time by the interstitial accommodation of Fe atoms in the β-rhombohedral boron structure (9). Lateron Ni, Cr, and V (10) have been found to lead to n-type conductivity of β-rhombohedral boron as well (Fig. 21); the highest negative Seebeck coefficient has been obtained with vanadium. According to the band scheme of β-rhombohedral boron (Fig. 14), it is obvious that ntype conductivity requires the unoccupied states in the valence band range and the intrinsic electron trapping levels to be filled by electrons originating from donor levels, which must be positioned above the uppermost trapping level. Two states in the upper valence band originating from the Jahn-Teller effect in the icosahedron at the vertex of the unit cell and four states of intrinsic traps, which are generated by the electron-phonon interaction in the four B 12 icosahedra in the unit cell, i.e., in total six sites, must be saturated by additional electrons to realize n-type behavior. This has been confirmed by Mo¨ssbauer investigations yielding the degree of ionization of Fe atoms accommodated in the interstitial A and D sites of the structure (see Fig. 2) (11). Figure 22 shows the concentrations of Fe 2⫹ and Fe 3⫹ ions. The accordingly calculated electron transfer at the transition from p to n type (Fig. 23) confirms the number of six electrons within the accuracy of measurement.

Figure 21 Seebeck coefficient of β-rhombohedral boron interstitially doped with Ni, Cr, Cu, and V versus metal content (9,10).

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Figure 22 Distribution of Fe 2⫹ and Fe 3⫹⫹ ions in the (a) A sites and (b) D sites of the β-rhombohedral boron structure versus total Fe content. For the D sites the solid lines represent the distribution probabilities for single Fe atoms and pairs, respectively; for A sites they represent the probabilities, whether all neighboring D sites are completely occupied by Fe atoms or not (11).

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Figure 23 Seebeck coefficient of β-rhombohedral boron versus charge transfer from the Fe atoms to the icosahedral boron structure (nominal charge and estimated effective charge) (11).

In n-type B :Fe the DC conductivity was found to meet Mott’s law of variable-range hopping (9). More insight is obtained from the far-infrared reflectivity, which increases toward lower frequencies, thus resembling the plasma edge in semiconductors. A convincing fit to the experimental spectra is possible only when a superposition of hopping and band-type conductivity is assumed. This is demonstrated for the dielectric function of n-type largely vanadiumsaturated VB 32 with the β-rhombohedral boron structure in Fig. 24 (75). The variation depending on the V content is as expected. For Fe doping this holds as well (75). Accordingly, in the case of n-type conduction of β-rhombohedral boron a superposition of band-type conductivity and hopping exists as well. Answering the question of how the hopping processes take place in detail needs further investigation. Several models seem possible in principle: hopping within an impurity band due to the interstitial doping atoms, hopping within a level evoked by the superposition of the uppermost trapping level and the donor level, and multitrapping of electrons thermally excited into the conduction band. 6. Doping by Substitution The substitution of foreign for boron atoms in the structure of β-rhombohedral boron should be possible in principle, if the size of the foreign atoms fits the structure. Up to now, results are available only for carbon atoms. Structural aspects of carbon doping have been discussed in Sec. II.C. With respect to the electronic structure, several influences of the C atoms are indicated in the quotient reflectivity spectrum in Fig. 25 (114). Most important for the transport properties are the effects at and within the band gap. The interband photoconductivity (105) increases, the spin density of trapped electrons increases (see Ref. 58), and the hopping activation energy (see

Boron and Boron-Rich Compounds

619

Figure 24 Real (a) and imaginary (b) parts of the dielectric function of VB 32 in the far-IR spectral range (75,110). For a satisfactory description of the experimental spectra hopping mobility and band-type mobility both must be taken into account.

Ref. 58) decreases with increasing carbon content. From these results, it has been concluded that carbon forms a donor level as expected because of its excess electron. However, the energetic position of this donor level is deep in the band gap and coincides with the split-off valence band, which accordingly the occupied donor states join to. Hence within this band the density and the occupation density both increase with increasing carbon content. 7. Mechanical and Thermal Properties When before free electrons, which polarize their dielectric surrounding, generate traps by electron-phonon interaction, well-defined distortions of the icosahedra result, which depend on the number of pairs of phonons involved. Because of the thermal excitation of phonons required for this interaction, the formation of specific traps is maximum at defined temperatures, when electrons are available, e.g., by optical excitation (65,66,96). In thermal equilibrium the temperature range between about 500 and 600 K is of particular interest because the thermal energy concerned is sufficient to exchange electrons between all the levels in Fig. 14 within rather short relaxation times. With this consideration, Werheit et al. (71) were able to interpret the previously unexplained hysteresis of the thermal expansion coefficient (115) and the maximum of internal friction (116,117) in this temperature range consistently. B.

Boron Carbide

1. Details of the Structure Boron carbide can be synthesized within a large homogeneity range extending from B 4.3C at the carbon-rich limit (118) to about B 12C at the boron-rich limit (119–121). X-ray diffraction

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Figure 25 Quotient spectrum of the reflectivities of two differently carbon-doped β-rhombohedral boron samples (114).

(122–125) and 13C nuclear magnetic resonance (NMR) spectroscopy (126–130) failed to determine the compositions of the structure elements and their variation within the homogeneity range. The same applies to theoretical considerations (131). The problem was solved quantitatively by the decomposition of the IR optical stretching mode of the three-atom chain by model calculations taking the possible compositions and the frequency shift depending on the mass distribution in natural and isotope-enriched boron carbide into account (57). The determined concentrations of B 12 and B 11C icosahedra and CBC and CBB chains are shown in Fig. 26. Other chain compositions can be excluded. Toward the boron-rich limit of the homogeneity range, an increasing number of unit cells without chains arise. Two alternative models are compatible with the optical spectra: completely chain-free unit cells and unit cells in which single B atoms saturate the outer bonds of the equatorial atoms of the adjacent icosahedra. Theoretical calculations of reaction kinetics based on the second version (132) satisfactorily confirm the results in Fig. 26. Obviously, the large interstices in these chainless unit cells are suitable to accommodate foreign atoms. For example, in the ternary BCSi compounds the concentration of Si pairs is exactly equal to the number of chainless unit cells of boron-rich boron carbide of the corresponding composition (133,134). Figure 26 demonstrates that at none of the compositions in the homogeneity range does a completely homogeneous structure exist. This disproves, e.g., the idealized structure model of boron carbide B 6.5 C [structural formula (B 12 )CBC], which is preferably used in theoretical band structure calculations (79,135,136). Obviously, the most homogeneous structure of

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Figure 26 Structure elements in the unit cell of boron carbide. B 12 icosahedra, B 11 C icosahedra, CBC and CBB chains, and chainless unit cells versus carbon content (57).

boron carbide is found at the carbon-rich limit B 4.3 C, and the somewhat deviating composition B 6.5 C exhibits the least homogeneous structure. 2. Interband and Gap-State Related Transitions The high unselected reflection of polished boron carbide surfaces in the visible range of the spectrum makes it immediately clear that the absorption edge is in the IR range, in contrast to all theoretical band structure calculations on boron carbide that have become available (78,79,110,136–138). The densities of states of (B 12 )CBC calculated by Bullett (78,79) and Switendick (135) are shown in Fig. 27. Some optical transmission measurements indicate a minimum band gap of 0.48 eV (139,140), and from the imaginary part of the dielectric function a gap of 1.6 eV was estimated (141) in a somewhat questionable way. Transmission measurements in a more extended spectral range of electronic interband transitions were made by Werheit et al. (142). Figure 28 shows the isotherms of the absorption coefficient of one sample between 80 and 590 K. The very high absorption level down to low photon energies, two strong steps in the absorption at about 1.3 and 3.4 eV, and a strong thermal reallocation of carriers depending on temperature are obvious. Quantitatively, besides a deeplevel to band transition at 0.18 eV, a series of indirect interband transitions starting at 0.48 eV was derived (for details, see Ref. 134). The real and imaginary parts of the dielectric function obtained by ellipsometric measurement with synchrotron radiation indicate several interband transitions at higher energies (Fig. 29) (104). It is noteworthy that these transitions are obviously at energies that do not deviate

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Figure 27 Densities of states of (B 12 )CBC as calculated by Bullett (78,79) and Switendick (135).

Figure 28 Isotherms of the absorption edge of carbon-rich boron carbide (B 4.3 C) (142).

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Figure 29 Real and imaginary parts of the dielectric function of boron carbides of different compositions in the range of interband transitions determined by ellipsometric measurements (104).

essentially from those of β-rhombohedral boron; this is doubtless an indication of similarities of the energy band structures probably due to the icosahedra. This is supported by satisfactory agreement with the density of states distribution of the icosahedron calculated by Shirai and Nakamatsu (72) in Fig. 8, but the energetic differences of the density of states maxima of boron carbide calculated by Bullett (78,79) and Switendick (135) are not confirmed by these experimental results. 3. Electronic Transport Properties Figure 30 shows the electrical conductivity depending on temperature and chemical composition (143,144). At all temperatures the maximum conductivity is related to the maximum concentration of B 12 icosahedra and the minimum concentration of B 11 C icosahedra, refuting the theory of Emin et al. (14–16,145,146), who attribute the conductivity mechanism in boron carbide to bipolaron hopping between B 11 C icosahedra. The temperature dependence of the electrical conductivity (Fig. 31) (16,145–150) shows that even at the highest temperatures reached intrinsic conductivity is not yet realized. The steps are reminiscent of β-rhombohedral boron (see Ref. 68 and above), where the Fermi level is pinnied because of high-density gap states. However, irregularities of the thermal expansion in boron carbide (151) are less well correlated than in boron. At lower temperatures the electrical conductivity is consistent with Mott’s law of variablerange hopping (Fig. 32) (143,144,152,153). The conductivity level seems to depend somewhat on the preparation method, which may influence, e.g., the grain size of the sample. This could

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Figure 30 Electrical conductivity of boron carbide versus composition and temperature (143,144).

Figure 31 Electrical conductivity of boron carbide at high temperatures (16,145–150).

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Figure 32 Electrical conductivity of boron carbide at lower temperatures plotted against T ⫺1/4 according to Mott’s theory of variable-range hopping (143,144,152,153).

also be the reason for the conductivity of some samples reincreasing toward very low temperatures. According to Mo¨bius (154) and Abrahams et al. (155), it can be checked whether a unique conductivity mechanism exists in a system, even if determining parameters of the system such as chemical composition are modified. Figure 33 (140,143) confirms that for boron carbide this is largely the case independent of chemical composition, temperature, and preparation technic. Typical results for the Seebeck coefficient are plotted against temperature in Fig. 34 (147,148,149,153). Boron carbide is the only semiconductor known whose Seebeck coefficient increases monotonously up to such high temperatures. This confirms that up to 2000 K the transport is not intrinsic. Emin (14) attributes this behavior to a phonon-drag effect. However, if the Fermi level is pinned within a kind of impurity band in the band gap of boron carbide, the temperature-dependent broadening of the Fermi edge would explain this behavior at least qualitatively in a more classical way as well (156). The Hall effect of boron carbide is small (Fig. 35a and b). It depends on composition and temperature (14,147–149). Because the calculation of the Hall mobility from the measured Hall constant depends strongly on the electronic transport mechanism, which for boron carbide has not yet been finally solved, the mobilities calculated after classical theories and shown in Fig. 35 are somewhat questionable. Hall effect and magnetoresistance were measured up to 15 T (Figs. 36 and 37) (157). The behavior expected from classical theory was confirmed in a large range, and for B ⬎ 13 T the magnetoresistance seems to indicate beginning Shubnikov–de Haas oscillations. The transport parameters obtained are listed in Table 3. The frequency dependence of the electrical conductivity and the dielectric function of

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Figure 33 Scaling of the electrical conductivity of boron carbide (143).

boron carbide has been measured by several authors (143,150,158). Figure 38 shows the typical behavior, confirming hopping processes as an essential transport mechanism. In cases of sufficiently high conductivities the influence extends up to the optical range. This is the case in boron carbide as well, whose FIR reflectivity spectra increase considerably toward lower frequencies like those of many other icosahedral boron-rich crystals (Fig. 39) (95). For the interpretation of the transport mechanism in boron carbide it is essential that the dielectric function of boron carbide in this frequency range can be fitted neither by hopping processes nor by a classical Drude behaviour of free carriers alone. However, an excellent fit is obtained when a superposition of both mechanisms is assumed (Fig. 40) (75,110). From the plasma frequency obtained from this fit and the carrier density derived in Table 3, the effective mass of holes in boron carbide is estimated to be approximately equal to the free electron mass in vacuum. This is an upper limit, because not the high-mobility part but the total DC conductivity is used to determine the density of high-mobility carriers. These results prove that in boron carbide, as in β-rhombohedral boron, a superposition of both transport mechanisms is present. Depending on frequency, on temperature, or on other experimental conditions, one of both mechanisms may prevail; however, a superposition of both mechanisms must not be excluded. It is well known that excess carbon in boron carbide precipitates as graphite (see, e.g. Refs. 159–162) if the carbon content sufficiently exceeds the carbon-rich limit of the homogeneity range. However, there seems to be a narrow transition region close to the carbon-rich limit of the homogeneity range where carbon is atomically dispersed when the samples are carefully prepared, e.g., by melting. For example, in a sample with the atomic ratio C/(C ⫹ B) ⫽ 0.199 (see Refs. 147 and 148) there is an excess carbon concentration of 0.155 C atoms per unit cell

Boron and Boron-Rich Compounds

627

Figure 34 Typical results for the Seebeck coefficient of boron carbide depending on temperature (147– 149,153).

compared with the carbon-rich limit of the homogeneity range. It can be largely excluded that this low excess carbon concentration is sufficient to form joined graphitic layers forming conducting channels across the macroscopic sample. Nevertheless, this excess carbon content leads to a conductivity behavior that is qualitatively different from that at the carbon-rich limit of the homogeneity range. The activation energy of the conductivity tends to zero toward low temperatures, suggesting the existence of a concentration-dependent metal-semiconductor transition (147,148). Obviously, this effect exists in carefully prepared largely homogeneous samples. 4.

Other Properties Important for Electronic Applications

The thermal conductivity is important for many applications in semiconductor technology, e.g., for thermoelectric devices. In Fig. 41 the thermal conductivity of boron carbide is plotted versus chemical composition (163–165). The strong decrease from B 4.3 C at the carbon-rich limit of the homogeneity range toward more boron-rich compositions can easily be explained by the change of the most homogeneous structure at B 4.3 C to the most distorted one at about B 6.5 C shown in Fig. 26. For temperature dependence, see Ref. 166. C.

Other Representatives of the ␣-Rhombohedral Boron Structure Group

1. α-Rhombohedral Boron The electronic transitions of α-rhombohedral boron derived from the decomposition of the absorption edge and its low-energy tail are listed in Table 4 (167). The third transition agrees with

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Figure 35 Hall mobility of carriers in boron carbide (a) versus reciprocal temperature and (b) versus B/C relation (147–149). Temperature dependence of the mobility as derived from conductivity and Seebeck coefficient for B 6.3 C (14) in (a) for comparison.

Boron and Boron-Rich Compounds

Figure 36 Hall constant of single crystal B 4.3 C in high magnetic fields (157).

Figure 37 Magnetoresistance of single-crystal B 4.3 C in high magnetic fields (157).

629

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Table 3 Transport Parameters of Boron Carbide (Composition Approximately B 4.3 C) Obtained from Measurements in Magnetic Fields up to 15 T Mobility (cm 2 V⫺1 cm⫺1) T(K)

σ (Ω⫺1 cm⫺1)

Hall effect

Magnetoresistance

Carrier density (cm⫺3)

77 293

2.5 ⫻ 10 ⫺4 5 ⫻ 10 ⫺1

37 0.8

20 1

2.1 ⫻ 10 13 3.9 ⫻ 10 17

Source: From Ref. 157.

results in Refs. 2, 168, and 169. With respect to the second transition, two alternatives could not be distinguished without investigating the temperature dependence. The experimentally obtained results are in satisfactory quantitative and partly qualitative agreement with calculations by Bullett (79) yielding a minimum direct transition at 2.3 eV and a minimum indirect transition at 1.7 eV. Density of states calculations of Switendick (170) yield a gap of about 1.5 eV; calculations by Shirai and Nakamatsu (Fig. 8) (72) exhibit a nonzero density of states at the Fermi level in a rather small gap. The rather low effective mass (Table 4) is in qualitative accordance with the carrier mobility of about 100 cm 2 V⫺1s⫺1 derived from transport measurements (171). Information on the electronic properties of α-rhombohedral boron is scarce; nevertheless, it proves that its transport properties differ qualitatively, for example, from those of β-rhombohedral boron and boron carbide. As discussed in Sec. III.B, the reason is the difference in the

Figure 38 Frequency dependence of the electrical conductivity of boron carbide. The solid lines are fits based on Dyre’s model (143,150,158).

Boron and Boron-Rich Compounds

631

Figure 39 Far-IR reflectivity spectra of boron carbide for different chemical compositions versus wavenumber (95).

external bonds of the equatorial atoms of the icosahedra. The high mobility and the direct gap are favorable for some technical applications. 2. Compounds with Pairs of Bonded Atoms on the Main Diagonal of the Unit Cell Si, P, and As atoms form two-atom chains in the α-rhombohedral boron unit cell. Both atoms in these chains are bonded to one another and saturate the external bonds of the equatorial atoms of the icosahedra (17). As can be qualitatively concluded from their transparency in the visible range, these compounds are semiconductors with rather large band gaps when they are pure (172). Quantitative spectroscopic investigations of the interband transitions are scarce. In the case of B 6 P it was shown that, when deposited of Si surfaces, a considerable amount of Si atoms is incorporated in the structure, and probably a ternary compound is formed in which the Si 2 chains in the unit cells are partly substituted for P 2 chains (173). Compared with that of pure B 6 P (174), the absorption edge is considerable shifted toward lower energies (Fig. 42). 3. Compounds with Pairs of Separate Atoms on the Main Diagonal of the Unit Cell Be, O, and S atoms can be accommodated in pairs on the main diagonal of the rhombohedral unit cell without essential bonding forces between them. Investigations of electronic properties are largely missing. Only for B 6 O can some indirect conclusions based on IR-optical investigations be made (57,175). B 6 O is a semiconductor similar to boron carbide—the electrical conductivity is somewhat higher as indicated by the reflectivity—whose increase toward low frequencies is distinctly stronger than that of boron carbide.

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Figure 40 Real and imaginary parts of the dielectric function of boron carbide in the far-IR range (B 6.2 C as example). The theoretical fit demonstrates that both hopping and band-type conductivity must be considered for a satisfactory description (75,110).

D.

Other Representatives of the ␤-Rhombohedral Boron Structure Group

1. SiB 14 [Structural Formula B 84 (B 7 Si 3) 2 Si] Some investigations of the electronic transport properties have been performed by Pistoulet et al. (176–180). The fundamental properties seem to be rather similar to those of β-rhombohedral boron. The material is p type (181), the Hall mobility is small (⬍1 cm 2 V⫺1 s⫺1 ), the Seebeck coefficient is maximum at about 400 K with 470 µ V K⫺1, and there is a dominating trapping level with an activation energy of 0.39 eV (see Ref. 3 and references therein). Ternary compounds with Fe, Co, and Ni, which probably have an SiB 14 structure, exhibit n-type behavior at low temperatures changing to p-type with increasing temperature (182). The transition temperature depends on the kind of metal atom. 2. B 32Al 3 [Structural Formula B 84 (B 6 Al 4) 2Al] No results for the electronic properties of this compound are known. E.

␣-Tetragonal Boron Structure Group

Only a few results for the electronic properties of members of the α-tetragonal boron structure group are available, which are not sufficient for a complete description of one or a comparison of several members of this structure group. The band gaps (Table 5) seem to be comparably large. The dielectric function of C 2Al 3 B 48 between about 0.5 and 40 eV was determined by

Boron and Boron-Rich Compounds

633

Figure 41 Thermal conductivity of the boron-carbon system versus carbon content (163–165).

Peshev et al. (183). Temperature dependences of electric conductivity and Seebeck coefficient are reported by Karlamov anf Loichenko (184).

F.

␤-Tetragonal Boron Structure Group

Very limited investigations of the electronic properties of representatives of this structure group have been performed. Some experimentally determined band gaps are listed in Table 6. Theoretical band structure investigations (79) for α-AlB 12 yield a band gap of about 2.6 eV. The gap Table 4 Electronic Transitions of α-Rhombohedral Boron Determined by the Decomposition of the Absorption Edge No. 1 2a 2b 3

Transition energy (eV) 0.73(2) 1.49(2) or 1.63(2) 2.055(2)

Transition type Deep level to band Deep level to band Direct allowed interband Direct allowed interband

Density of states

Reduced mass 2m r /m e

1.2 ⫻ 10 19 1.25 ⫻ 10 19 0.029 0.034

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Figure 42 Absorption edge of B 12 P 2 deposited on silicon (173), with spectrum of pure B 12 P 2 after Slack et al. (174) for comparison.

Table 5 Transition Energies of Some Representatives of the α-Tetragonal Boron Structure Group Compound β-AlB 12 C 2 Al 3B 48

Gap (eV)

Method

References

2.5 ⬎3

Optical and electrical Estimated from yellowish transparency

(1,12,198) (4)

Table 6 Transition Energies of Some Representatives of the β-Tetragonal Boron Structure Group Compound α-AlB 12

Al 1.44Mg 0.65B 22

Be mAl nB 12

Gap (eV)

Method

References

⬃0.4 1.9 1.96 2.2 1.85 1.92 2.01 2.12 2.1

Urbach tail (optical) Optical Optical Electrical Optical

(12) (185) (186) (187) (188)

Optical Electrical

(169,198)

Boron and Boron-Rich Compounds

635

of β-tetragonal B 192 is almost the same; however, there are two narrow bands of considerable density within the gap. G.

Amorphous Boron

Investigations of the electronic properties of amorphous boron based on icosahedra are scarce. Some results for the absorption edge are available and yield an absorption edge of about 0.7 eV (38,189,190). Investigations of transport properties are missing. The IR and Raman-active phonon spectra exhibit pronounced maxima in the ranges of the intraicosahedral phonons of crystalline icosahedral boron-rich structures and in particular of the covalent intericosahedral BB bonds known from boron-rich solids. This confirms that the external bonds of the icosahedra are largely covalent, similar to those of β-rhombohedral boron. Therefore a certain relationship between the electronic properties seems possible. There are indications that the electronic properties are considerably influenced by the method of preparing the samples (38). H.

Orthorhombic Borides (MgAlB 14 Type)

The gap energy of the orthorhombic borides seems to depend strongly on the composition. Some results are shown in Table 7. Some results for an orthorhombic AlB 10 compound were obtained by Golikova et al. (191). Detailed optical absorption spectra of some of the orthorhombic borides (Fig. 43) show that the interband transition energies of these compounds are not far from those of β-rhombohedral boron (for details, see Ref. 45). This seems to suggest that the energy band structures of both groups of boron-rich solids do not differ essentially, at least as far as they are relevant for the electronic transport. It has been shown that the prevailing carrier type of β-rhombohedral boron can be changed from p to n by interstitial doping. However, the degree of doping is limited by the number of interstices available for the accommodation of suitable atoms or by the number of electrons transferred from the metal atoms to the boron framework, probably because the structure becomes destabilized by higher electron transfer. The maximum concentration does not exceed a few atomic percent, and even for vanadium, with the strongest doping effect, only weak n-type conductivity can be achieved (10,109). The orthorhombic borides may yield a way to extend the metal content of boron-rich structures considerably. If complete occupation of the metal sites is assumed to be achievable, which has been approximately realized in LiAlB 14, the metal content amounts to about 14 at.%,

Table 7 Minimum Interband Transition Energies of Some Orthorhombic Borides Compound LiAlB 14 NaB 15 MgAlB 14 ErAlB 14

Gap (eV)

Method

References

1.55 0.32 0.99 1.55 0.97 1.30

Optical Electrical Optical

(45) (192) (45)

Optical

(45)

For detailed results see also Refs. 2 and 4.

636

Figure 43 Absorption spectra of some orthorhombic borides (45).

Figure 44 Seebeck coefficient of some orthorhombic borides at room temperature (45).

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Boron and Boron-Rich Compounds

637

Figure 45 Electrical conductivity of YB 66 and DyB 66 versus T ⫺1/4 (195). YB 66 (a), twice zone melted; YB 66 (b), once zone melted; YB 66 (c), polycrystalline technical material; DyB 66, polycrystalline, porous.

Figure 46 Seebeck effect of YB 66 (see Fig. 45a) versus temperature (196).

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Figure 47 Hall mobility of YB 66 versus reciprocal temperature (195). For sample characterization see Fig. 45.

and the lower limit, which is obviously necessary to stabilize the structure, seems to be about 7.8 at.%, at least according to the compositions hitherto reported (45). In the case of MgAlB 14 with occupation densities of 78 and 75%, respectively, of the metal sites, a very high negative Seebeck coefficient has been found (Fig. 44) (45). I.

YB 66-Type Structures

There is no doubt that the crystal quality of the YB 66 crystals presently available (47) is very high, as they are suitable for use as monochromator crystals for synchrotron radiation (193). Nevertheless, some essential physical properties of YB 66-type crystals seem to suggest a rather close relationship to amorphous structures. This holds, e.g., for the thermal conductivity, whose temperature dependence reminds one of glassy structures (194); for the electrical conductivity, whose temperature dependence corresponds to Mott’s law of variable-range hopping (Fig. 45) (195); and for the low-energy tail of the absorption edge, exhibiting an exponential dependence of the absorption coefficient seemingly similar to the Urbach tail in amorphous semiconductors (Fig. 46) (196). However, there is some evidence that the electronic band structure of YB 66 is characterized by trapping levels of high density in the band gap similar, e.g., to the case of βrhombohedral boron (196). Although the sign of the Seebeck coefficient of YB 66 proves p-type conduction up to 700 K (Fig. 47), the Hall coefficient changes sign in a certain range, which obviously depends on the structural quality of the sample (Fig. 48) (195). The properties of other compounds belonging to this structure group seem to be qualitatively similar and deviate only quantitatively to some extent (195–198) (for electrical conductiv-

Boron and Boron-Rich Compounds

639

Figure 48 Absorption edge of YB 66 (196).

ity see, e.g., Fig. 45). In this respect the question has remained open of how far these deviations are due to the quality of the structure or to the composition only. The dependence of the electronic properties on the metal content within the homogeneity range seems to be proved: Investigations of GdB 66 show that the conductivity and the Seebeck coefficient both increase with increasing metal content (197,198).

J. Correlation Between Structural Defects and Electronic Properties Recently the immediate correlation between the structural and electronic properties of some icosahedral boron-rich solids has been proved and opened completely new aspects of understanding the basic reasons for their specific properties. The configuration interaction (CI) calculation by Fujimori et al. (201) on the icosahedral B12H12 cluster representing the bonding of B12-icosahedra in β-rhombohedral boron and boron carbide proved that the Jahn-Teller effect, distorting the regular icosahedron to the D3d-Symmetrie, causes a separation between ground and first excited state of about 1.5 eV. As shown, this value is close to the typical band gaps of many icosahedral boron-rich solids, which seem to be accordingly explained; however, it considerably exceeds the energetical distance between the actual valence band and the split-off band in β-rhombohedral boron (see Fig. 14). Hence its attribution to the Jahn-Teller effect could not be maintained and its identification required new considerations. In the former discussions of electronic properties summarized in this chapter the influence

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of structural defects has not been considered; they were assumed to be unsystematic or caused by insufficient preparation methods. However, in reality, careful fine-structure investigations indicate that, apart from α-rhombohedral boron, the structures of the other icosahedral boronrich solids contain appreciable concentrations of well-defined defects in the form of incomplete occupations of specific atomic sites or of antisite defects. At least in many cases, insufficient preparation methods can be excluded as the reason for these defects. This suggests that the defects are fundamental peculiarities of the icosahedral boron-rich structures (202). Examples of such defects are: 1. α-rhombohedral boron structure group (idealized structure formulas B12X 2 or B12X 3 (X ⫽ B or specific non-B atoms in two-atom or three-atom arrangements on the trigonal axis of the rhombohedral unit cell)): incomplete occupied sites in the chains (16,17,22,60,134,203–205). In α-rhombohedral boron the two different atomic sites B(1) and B(2) are completely occupied, and hence the defect concentration is zero. In boron carbide the concentrations of B12 and B11C icosahedra and of CBB and CBC chains vary, and chainless unit cells occur when the composition deviates from the carbon-rich limit B 4.3 C of the homogeneity range (204). According to Kleinman et al. (206,207) B13 C2 with the structure formula B12 (CBC) is the most energetically favorable structure. When it is therefore taken for reference, based on the 42% B12 icosahedra 58% B11C icosahedra, 62% CBC chains, 20% CBB chains and ⬃19% missing chains experimentally determined by Kuhlmann et al. from phonon spectroscopy (53,204), the defect concentration in B13 C2 is about 9.3 at.%. 2. β-rhombohedral boron structure group (idealized structure formula (B12) 4(B 28) 2 B or B 84 (B10) 2 B): The regular B(13) position is occupied by 74.5(6)% (208) and the sites B(16)-B(20) by 27.2%, 8.5%, 6.6%, 6.8% and 3.7% (in total 1.7 B atoms per unit cell), respectively (209). This leads to an intrinsic point defect density of about 4.9 defects per unit cell (⬃4.7 at.%) (10,25,209). 3. α-tetragonal structure group (idealized structure formula (B12) 4 X 2Y2): missing or incomplete occupation of the X, Y sites (210). 4. β-tetragonal structure group (idealized structure formula (B 21⋅2B12) 4 (X mYn)): missing or incomplete occupation of X,Y sites, two missing B sites in B 21 double-icosahedra (B19 in α-AlB12) (210). 5. orthorhombic MgAlB14 type compounds (idealized structure formula (B12) 4 Me(1) 4 Me(2) 4 B 8): incomplete occupation of the Me(1) and Me(2) sites, possibly incomplete occupation of the non-icosahedral B sites (see Ref. 45 and references therein). 6. YB 66 type structures (idealized structure formula Y48⋅((B12)13) 8⋅(B 80) 8): The occupancies of the sites B(10)–B(13) in the nonicosahedral B 80 unit of YB66 are 72, 65, 31 and 22% respectively leading to an actual number of ⬃42 B atoms in this B 80 unit (211). Accordingly, the average defect concentration in the whole structure is 17 at.%. Table 8 shows that, for α-rhombohedral boron, β-rhombohedral boron and boron carbide, the electron deficiencies determined by electronic band structure calculations are correlated with the densities of defects in the structures. Since calculations of the electronic properties of defects in icosahedral boron-rich solids are missing, the following assumptions (202) were made in accordance with general results obtained on defects in semiconductors. 1. Electronic Structure of β-Rhombohedral Boron In the rhombohedral unit cell, there are 1.52 vacancies (partially occupied B(13) sites) and 3.38 interstitial atoms (weakly occupied sites B(16)–B(20)). Bullet (208) calculated for the idealized

Boron and Boron-Rich Compounds

641

Table 8 Calculated Electron Deficiencies for the Valence Bands of Idealized Crystal Structures and Experimentally Determined Point Defect Concentrations in the Real Crystals Idealized crystal structure Valence states [(unit cell)⫺1]

Valence electrons [(unit cell)⫺1]

Electron deficiency [(unit cell)⫺1]

Real crystal structure Electronic character (theoretical)

α-rhombohedral boron 36 [212] 36 0 Semicond. β-rhombohedral boron 320 [208] 315 5 Metal Boron carbide B13 C 2 (idealized structure formula B12 (CBC)) 48 [137] 47 1 Metal B 4,3 C (idealized structure formula: B11C (CBC)) 48 [137] 47 0,17 Metal Hypothetical B 4 C (idealized structure formula: B11C (CBC)) 48 [137] 48 0 Semicond.

Electronic character (experimental)

Intrinsic point defects [per unit cell]

Semicond.

0

[3]

Semicond.

4,92(20)

[209]

Semicond.

0,97(5)

[53,204]

Semicond.

0,19(1)

[53,204]

—

—

—

Source: From Ref. 202.

structure (sites B(1)–B(15) fully occupied, B(16)–B(20) unoccupied) 320 valence band states occupied by 3 ⫻ 105 ⫽ 315 valence electrons. Hence the deficiency is 5 electrons. Based on the properties of point defects, for each B(13) vacancy 3 electronic states and three electrons are separated from the valence band. Moreover, 6 ⫻ 1/2 ⫽ 3 occupied localized electronic states from the surrounding B atoms additionally reduce the number of regular valence states by 3. In total, for each vacancy, 6 electronic states and 6 electrons are removed from the valence band. However, the 3 electrons in the localized states may fall down into the more energetically favorable unoccupied valence band states. Hence, from the 1.52 B(13) vacancies per unit cell, 3 ⫻ 1.52 ⫽ 4.56 unoccupied localized states are generated. Compared with the calculated deficiency of 5 valance electrons this would satisfactorily explain the semiconducting character of β-rhombohedral boron. Taking B(16)–B(20) as interstitial sites, in total there are 3 ⫻ 1.52 ⫹ 3 ⫻ 3.38 ⫽ 14.70 electrons per unit cell available compared with the valence electron deficiency of 5. Assigning an error of only 2% to the site occupation densities determined by X-ray fine structure investigations, the completely occupied valence band leaves 10 electrons per unit cell to be distributed on localized gap states originating from the B(13) vacancies or from interstitial B(16)–B(20) states. If one assumes that the B(13) vacancy generates a gap state, which can be occupied by two paired electrons, similar to the vacancy V⫹⫹ state in silicon (213,214), the number of interstitial B(16)–B(20) atoms exactly corresponds to the number of unoccupied sites in this orbital. If single ionization of the interstitial B atoms is assumed, the valence band and the B(13) vacancy orbitals are exactly filled up. That assumption easily explains the density of paramagnetic centers (about 1015 cm⫺3 (215), which is very low compared with the defect concentration (about 10 20 cm⫺3) and can only be appreciably enhanced by heating or optical excitation (216,217). Moreover, it is consistent with the charge transport in β-rhombohedral boron (see section A.3). 2. Electronic Structure of Boron Carbide The idealized, most energetically favorable structure of boron carbide B13 C 2 (structure formula B12 (CBC)) (206,207) was taken for reference to determine the composition dependent electron deficiency and the concentration of structural defects (202).

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Band structure calculations of B13 C 2 yield 48 electronic states per unit cell in the valence band, while the number of valence electrons depends on the carbon content. For B13 C 2 47 and for B12 C 3 (structure formula B11C(CBC)) 48 valence electrons per unit cell are available (137). The structural defects are antisite defects in the form of B11C icosahedra (donors) and CBB chains (acceptors) and vacancies in the unit cells with missing chains. For chainless unit cells, the following configurations have been taken into consideration: (i) α-rhombohedral boron-like, (i.e. no atom on the trigonal axis); (ii) B䊐B arrangements (䊐, vacancy) on the trigonal axis with two separated B atoms and vacant B(3) site (B(3), central chain site), based on phonon spectroscopy (53,204); (iii) B䊐B arrangements, based on reaction kinetics (132); (iv) vacancy of B(3), no specification of the chain end atoms, derived from neutron diffraction (205). The B䊐B configuration, that was shown to be the most probable one, yields two localized states and two acceptors separated from the valence band. Taking as the only experimental parameter the CBC to CBB relation from phonon spectroscopy (53,204), the CBC, CBB and B䊐B concentration were calculated (Fig. 49). Subsequently the concentrations of B12 and B11C icosahedra (Fig. 50) immediately follow from the stoichiometry of the compound. The calculated B䊐B concentrations agree with the concentrations of B(3) vacancies determined by neutron diffraction. Compared with Fig. 26 (based on absolute oscillator strengths experimentally determined) the results in Fig. 49 and 50 (based on the quotient of oscillator strengths) show remarkable differences in the more boron-rich range only. The results in Figs. 49 and 50 are more reliable because in the quotient, systematic experimental error is largely eliminated (for details see (202)). At B 4.3 C the electron deficiency is exactly compensated by the obviously intrinsic concentration of CBB chains and proves that electronic reasons are responsible for this composition being the carbon rich limit of the homogeneity range that was previously experimentally determined by microprobe investigations (107,218).

Figure 49 Calculated densities of atom arrangements on the trigonal axis of the rhombohedral unit cell of boron carbide (CBC and CBB chains, B䊐B arrangements); solid symbols (202); diamonds, B(3) vacancies (B(3), center of the three-atom chain) determined by neutron scattering (205). Calculated valence electron deficiency for comparison.

Boron and Boron-Rich Compounds

643

Figure 50 Density of B12 and B11C icosahedra calculated from the densities of the atoms on the trigonal axis (Fig. 1) and the stoichiometry of the samples (202).

3.

Electronic Structure of YB66

Unfortunately, there are no calculations of the electronic band structure available. However, the high defect concentration of 17 at.% is at least qualitatively correlated with the very strong tail of the absorption edge (Fig. 48) exceeding that of boron carbide by far. The shown possibility to exactly explain the structural defects of some icosahedral boronrich solids by the electron deficiency considerably raises the estimation of the theoretical band structure calculations, hitherto essentially based on the more or less significant shortage of agreement with experimental results. Calculations of the electronic orbitals of defects are desirable to improve the quantitative understanding of the different defects. It seems that, on one hand, the electron deficiency is the driving force for the generation of structural defects in the icosahedral boron-rich solids in general, and on the other hand, the influence of these defects on the electronic properties is a main reason for their peculiar properties.

V.

CONCLUSION

The boron-rich solids with icosahedral structures are semiconductors with unique electronic properties, which are essentially determined by the icosahedra as general structural elements. This implies an interrelation of their properties, which can be modified within sometimes large homogeneity ranges of chemical compositions by forming ternary compounds, by changing the chemical composition within the specific structure groups, and by going to the different structure groups. Accordingly, the icosahedral boron-rich solids offer an excellent chance to study the electronic properties of complex structures and their modification by slight and considerable changes of composition and structure. Some highlights of these properties with particular interest for fundamental research are the Jahn-Teller effect in the icosahedra; the formation of intrinsic

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traps by electron-phonon interaction; the correlation between electron deficiency and structural defects; the soliton-type transport of electrons and holes; the very long lifetime of electrons under specific, externally controllable conditions; the electronic interaction between foreign atoms and the boron framework; and the high, monotonously (up to very high temperatures) increasing Seebeck coefficient of boron carbide. For technical application, the high melting point, the great hardness, and the strong resistivity to chemical attack are of fundamental importance. The specific electronic structures make the boron-rich solids rather insensitive to influences of foreign atoms at concentrations that already change the semiconductor properties of classical semiconductors decisively. Nevertheless, doping is possible in principle, indeed at higher concentration levels. This makes the material preparation much easier and less expensive than in the case of the classical semiconductors. The only electronic property that is already at the threshold of technical application at present is the high Seebeck coefficient just mentioned for high-efficiency direct thermoelectric energy conversion and measurement of very high temperatures under extreme conditions. Moreover, general application for high-temperature electronic devices and at least in some structure groups for wide-gap semiconductors seems promising. Boron, aluminum, and gallium belong to the same group of the periodic table. Accordingly, they have the same number of valence electrons, and therefore similarities of the crystal structures and of the electronic structures as well should be expected. However, in the case of aluminum and gallium, no elementary crystals with icosahedral structures have become known. Nevertheless, these elements, too, generate icosahedra, namely in quasi-crystalline structures, and Kimura et al. (199) have pointed to the structural similarities to the boron-rich solids. The relation between their electronic properties has been proved by Werheit et al. (200), and hence the aluminum- and gallium-based quasi-crystals may provide a further opportunity to utilize the variation of electronic properties in icosahedral structures.

ACKNOWLEDGMENTS At first I should like to thank the numerous students who have worked during the years in my laboratory at the Gerhard-Mercator University of Duisburg and in particular the graduate scientific coworkers Dr. Richard Franz, Dr. Udo Kuhlmann, Roland Schmechel, and Frank Kummer for their effective cooperation, which was an essential basis for our scientific progress. I am obliged to Prof. T. Lundstro¨m, Uppsala, Dr. I. Higashi, Wako, Dr. K.A. Schwetz, Kempten, Asst.-Prof. Dr. Kimura, Tokyo, Dr. T. Tanaka and Dr. Y. Ishizawa, Tsukuba, Prof. V.N. Gurin and Dr. M.M. Korsukova, Sankt Petersburg, Dr. Y. Paderno, Kiev, Dr. K. Shirai, Osaka, and Prof. Y. Kumashiro, Yokohama, for providing samples, for interdisciplinary cooperation, and for stimulating scientific discussions, which have made a large part of the work summarized in this chapter possible. I acknowledge the provision of samples and material by the Consortium fu¨r Elektrochemische Industrie (Wacker-Chemie) Munich, Elektroschmelzwerk Kempten, and H.C. Starck, Goslar and Laufenburg, and I am grateful to the Deutsche Forschungsgemeinschaft, the Ministry of Research and Technology of the FRG, and the Ministry of Science and Research of the Nordrhein-Westfalen Region for financial support.

REFERENCES 1. OA Golikova. Phys Status Solidi (a) 51:11, 1979. 2. H Werheit. Boron, In: O Madelung, M Schulz, H Weiss, eds. Landoldt-Bo¨rnstein, Numerical Data

Boron and Boron-Rich Compounds

3.

4.

5. 6. 7. 8.

9. 10.

11. 12.

13. 14.

15.

16.

17.

18.

19. 20. 21.

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161. H Werheit, KA Schwetz. Comment on: The role of free carbon in the transport and magnetic properties of boron carbide by A.K. Bandyopadhyay et al. J Phys Chem Solids 46:1331, 1985. 162. M Bougoin, R Fillit, F Thevenot, H Bruyas. Determination of free graphite in textured samples of boron carbide and boron-carbide–silicon carbide composites. J Less Common Met 117:215, 1986. 163. D Gosset, M Guery, B Kryger. Thermal properties of some boron-rich compounds ‘‘Bn C and AlB 12’’. In: D Emin, T Aselage, AC Switendick, B Morosin, CL Beckel, eds. Boron-Rich Solids, AIP Conference Proceedings 231. Albuquerque: AIP, 1990, p 380. 164. H Werheit. Boron-rich solids: A chance for high-efficiency high-temperature thermoelectric energy conversion. Mater Sci Eng B 29:228, 1995. 165. U Kuhlmann, H Werheit. Properties of boron carbide related to the carbon distribution in the unit cell. Proceedings of the 11th International Symposium on Boron, Borides and Related Compounds, Tsukuba, 1993, JJAP Series 10:84, 1994. 166. PRH Tu¨rkes, ET Swartz, RO Pohl. Thermal properties of boron and boron carbides. In: D Emin, T Aselage, CL Beckel, IA Howard, C Wood, eds. Boron-Rich Solids, AIP Conference Proceedings 140. Albuquerque: AIP, 1985, p 346. 167. H Werheit, U Kuhlmann, NE Solov’ev, GP Tsiskarishvili, G Tsagareishvili. Optical properties of α-rhombohedral boron. In: D Emin, T Aselage, AC Switendick, B Morosin, CL Beckel, eds. BoronRich Solids, AIP Conference Proceedings 231. Albuquerque: AIP, 1990, p 350. 168. FH Horn, EA Taft, DW Oliver. In: GK Gaue´, ed. Boron. Vol 2. New York: Plenum, 1964, p 231. 169. OA Golikova, NE Solov’ev, YA Ugai, VA Feigel’man. Sov Phys Semicond 13:245, 1979. 170. AC Switendick. The electronic structure of boron and borides: The evolution from cubic to rhombohedral based structures. In: H Werheit, ed. Proceedings of the 9th International Symposium on Boron, Borides and Related Compounds, Duisburg. University of Duisburg, 1987, p 349. 171. OA Golikova. Electron transport in boron-rich solids. In: D Emin, TL Aselage, C Wood, eds. Novel Refractory Semiconductors. MRS Symposia Proceedings 97:17, 1987. 172. P Yang, TL Aselage. Crystal growth of B 12 P 2. Proceedings of the 11th International Symposium on Boron, Borides and Related Compounds, Tsukuba, 1993. JJAP Series 10:84, 1994. 173. H Werheit, U Kuhlmann, K Shirai, Y Kumashiro. Optical properties of B 12 P 2. J Alloys Compos 233:121, 1996. 174. GA Slack, TF McNelly, EA Taft. J Phys Chem Solids 44:1009, 1983. 175. H Werheit, U Kuhlmann. J Solid State Chem 130:260, 1997. 176. B Pistoulet, JL Robert, JM Dusseau, FM Roche, P Girard. Physics of Semiconductors (Edinburgh Conference), 1978, p 793. 177. B Pistoulet, JL Robert, JM Dusseau, L Ensuque. J Non-Cryst Solids 29:29, 1978. 178. B Pistoulet, JL Robert, JM Dusseau. Physics of Semiconductors (Edinburgh Conference), 1978, p 1009. 179. JM Dusseau, L Ensuque, Im-Sareoun, TP Lepetre. Phys Status Solidi (a) 47:K11, 1978. 180. B Pistoulet, JL Robert, JM Dusseau, FM Roche, P Girard, L Ensuque. J Less Common Met 67: 131, 1979. 181. B Armas, C Combescure, JM Dusseau, TP Lepetre, JL Robert, B Pistoulet. J Less Common Met 47:135, 1976. 182. JM Dusseau, JL Robert, B Armas, C Combescure. J Less Common Met 82:137, 1981. 183. TP Peshev, G Gyorov, M Khristov, VN Gurin, MM Korsukova, FY Solomkin, KK Sidorin. J Less Common Met 117:34, 1986. 184. AI Karlamov, SV Loichenko. Electronic transport properties of hot-pressed boron-rich compounds of the AlBC system. In: D Emin, T Aselage, AC Switendick, B Morosin, CL Beckel, eds. Boron-Rich Solids, AIP Conference Proceedings 231. Albuquerque: AIP, 1990, p 94. 185. OA Golikova, JA Drabkin, VK Zaitsev, MM Kazanin, DN Mirlin, JV Nelvson, EN Tkalenko, T Chomidov. Bor, Poluchenie, structura i svojstva (Proceedings International Symposium Boron, Tbilisi, 1972). Tbilisi: Izd. Mecniereba, 1974, p 44 (in Russian). 186. OA Golikova, NE Solov’ev, YA Ugai, VA Feigel’man. Sov Phys Semicond 13:486, 1979. 187. HJ Becher, R Mattes. Tetragonal boron I and ist derivatives. In: VN Matkovich, ed. Boron and Refractory Borides. Berlin: Springer, 1977, p 107. 188. H Werheit, G Krach, U Kuhlmann, I Higashi, VN Gurin, MM Korsulova. Optical properties of

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192. 193.

194.

195.

196.

197.

198.

199. 200. 201. 202. 203.

204. 205. 206. 207. 208. 209. 210. 211.

Werheit some α-AlB 12 and γ-AlB 12 representatives. Proceedings of the 11th International Symposium on Boron, Borides and Related Compounds, Tsukuba, 1993. JJAP Series 10:96, 1994. K Kimura, T Tada, A Hori, A Furukawa. J Non-Cryst Solids 13:919, 1991. A Hori, M Takeda, H Yamashita, K Kimura. Absorption edge spectra of boron-rich amorphous films with icosahedral cluster. J Phys Soc Jpn 64:3496, 1995. OA Golikova, MM Kazanin, Z Mirzazhonov, T Khomidov, YA Shiyanov. Films of aluminium boride (AlB 10 ). In: D Emin, T Aselage, AC Switendick, B Morosin, CL Beckel, eds. Boron-Rich Solids, AIP Conference Proceedings 231. Albuquerque: AIP, 1990, p 117. R Naslain, J Etourneau, P Hagenmuller. Alkali metal borides. In: VN Matkovich, ed. Boron and Refractory Borides. Berlin: Springer, 1977, p 262. T Tanaka, Y Ishizawa, J Wong, ZU Rek, M Rowen, F Scha¨fers, BR Mu¨ller. Development of a YB66 soft X-ray monochromator for synchrotron radiation. Proceedings of the 11th International Symposium on Boron, Borides and Related Compounds, Tsukuba, 1993. JJAP Series 10:110, 1994. PA Medwick, DG Cahill, AK Raychaudhuri, RO Pohl, F Gompf, N Nu¨cker, T Tanaka. In: D Emin, T Aselage, AC Switendick, B Morosin, CL Beckel, eds. Boron-Rich Solids, AIP Conference Proceedings 231. Albuquerque: AIP, 1990, p 363. H Werheit, U Kuhlmann, T Tanaka. Electronic transport and optical poperties of YB 66, In: D Emin, T Aselage, AC Switendick, B Morosin, CL Beckel, eds. Boron-Rich Solids, AIP Conference Proceedings 231. Albuquerque: AIP, 1990, p 125. U Kuhlmann, H Werheit, J Hassdenteufel, T Tanaka. New aspects of the optical and electronic properties of YB66. Proceedings of the 11th International Symposium on Boron, Borides and Related Compounds, Tsukuba, 1993. JJAP Series 10:82, 1994. OA Golikova, MM Kazanin, Z Mirzazhonov, T Khomidov, YA Shinayov. In: D Emin, T Aselage, AC Switendick, B Morosin, CL Beckel, eds. Boron-Rich Solids, AIP Conference Proceedings 231. Albuquerque: AIP, 1990, p 121. OA Golikova. Boron-rich semiconductors—two types of the disorder. Proceedings of the 11th International Symposium on Boron, Borides and Related Compounds, Tsukuba, 1993. JJAP Series 10: 82, 1994. K Kimura, A Hori, H Yamashita, H Ino. Crystalline structures as an approximant of quasicrystals and distortion of B 12 icosahedron in boron-rich solids. Phase Transitions 44:173, 1993. H Werheit, R Schmechel, K Kimura, R Tamura, T Lundstro¨m. On the electronic properties of icosahedral quasicrystals. Solid State Commun 97:103, 1996. M Fujimori, K Kimura. Ground and excited states of an icosahedral B12 H12 cluster simulating the B12 cluster in beta-rhombohedral boron. J Solid State Chem 133:178, 1997. R Schmechel, H Werheit. Correlation between structural defects and electronic properties of icosahedral boron-rich solids. J Phys: Condensed Matter 11:6803, 1999. B Morosin, AW Mullendore, D Emin, GA Slack. Rhombohedral Crystal Structure of Compounds containing Boron-Rich Icosahedra, in Boron-Rich Solids (AIP Conf Proc 140), Albuquerque, New Mexico 1985, ed D Emin, TL Aselage, CL Beckel, IA Howard, American Institute of Physics: New York, 1986, p 70. U Kuhlmann, H Werheit. Solid State Comm 83:849, 1992. GH Kwei, B Morosin. Structure of the Boron-Rich Boron Carbides from Neutron Powder Diffraction: Implication for the Nature of the Inter-Icosahedral Chains. J Phys Chem 100:8031, 1996. DM Bylander, L Kleinman, S Lee. Self-consistent calculation of the energy bands and bonding properties of B12 C 3, Phys Rev B42, 1394, 1990. DM Bylander, LO Kleinman. Structure of B13 C 2, Phys Rev B43, 1487, 1991. DW Bullett. Structure and bonding in crystalline boron and B12C3, J Phys: Solid State 15:415, 1982. GA Slack, CJ Hejna, MF Garbauskas, JS Kasper. The crystal structure and density of beta-rhombohedral boron, J Solid State Chem 28:489, 1988. I Higashi. Structure and preparation of boron-rich borides, in D Emin, T Aselage, CL Beckel, IA Howard, C Wood, Boron-rich solids, AIP Conf Proc 140:1, 1986. I Higashi, K Kobayashi, T Tanaka, Y Ishizawa. Structure refinement of YB 62 and YB 56 of the YB 66type structure, J Solid State Chem 133:16, 1997 (Proc 12th ISBB’96, Baden, Austria, 1996).

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212. F Perrot. First approach to the band structure of α-rhombohedral boron. Phys Rev B23, 2004, 1981. 213. GD Watkins. The lattice vacancy in silicon in ST Pantelides. Deep centers in semiconductors, Gordon and Breach, New York, 1986, p 147. 214. GD Watkins. Intrinsic point defects in semiconductors. In: W Schro¨ter, ed. Materials science and technology, Vol 4, Electronic structure and properties of semiconductors. VCH Weinheim, 1991, p 105. 215. CD Siems. The Quantitative Evaluation of the Electron Paramagnetic Resonance Anisotropy of beta rhombohedral Boron. J Less-Common Met 67:155, 1979. 216. D Geist. The Mechanism and Quantitative Description of the Photoconductivity and Photo-EPR in beta-Rhombohedral Boron Single Crystals at 77 K, Z. Naturforsch. 28a:953, 1973. 217. A Nadolny. Photo-Induced Electron Spin Resonance (Photo-ESR) in beta-Rhombohedral Boron. Phys Stat Sol (b) 65:801, 1974. 218. KA Schwetz, P Karduck. J Less-common Met 175:1, 1991.

24 Boron Films Katsumitsu Nakamura Nihon University, Setagaya-ku, Tokyo, Japan

I.

INTRODUCTION

A large number of detailed studies of the properties of boron have been done by Werheit as shown in Chapter 23. These studies have been carried out with bulk boron samples (mainly single crystals). However, high-purity bulk samples are hard to obtain and that is an obstruction for studies. In order to solve the problem, studies using film samples, which are easier to obtain than single crystals, are considered. In the application of boron, the film form is more advantageous than the bulk form. Elemental boron is an interesting material because, at the same time, it has low density (d ⫽ 2.35 g cm⫺3 ), is refractory (T m ⫽ 2075°C), has high hardness (H v ⫽ 3000 kg) and is resistant to corrosion. It also has a high mechanical strength and a high capture section for neutrons. Moreover, it is one of the elemental semiconductors. However, the resistivity of boron is several hundred times larger than that of Si and Ge at room temperature. Although many studies (1–3) of the properties of boron have been done, the physical properties reported are not in agreement with each other because it is very difficult to obtain high-purity bulk boron. However, we can obtain pure and uniform boron in film form. In the form of films, boron has many potential applications, such as infusion reactor wall components or semiconductor films. In particular, the first wall and limiter coatings in fusion reactors are very promising candidates (4,5). Many methods have been developed for preparing boron films. Hydrogen reduction of volatile boron halides (such as BBr 3 or BCl 3 ) is a convenient method for producing boron films. This technique has been extensively studied for some time. Preparative methods for boron films have been developed and must be used properly. However, contamination with halogens generated by reduction of the halogenide compound in the case of CVD and with residual gas in the vacuum chamber in the case of evaporation and sputtering prevents the formation of high-purity boron films. A preparative method using diborane and decaborane is superior to the preceding method. In particular, it is easier to prepare high-purity boron films with decaborane than with diborane, which is hard to handle at present. Boron films have been prepared by means of chemical vapor deposition (6–8), vacuum evaporation using electron bombardment of boron (9–11), and sputtering of a boron target. The several methods mentioned are summarized in Table 1. Croft (26) has obtained high-purity boron films by pyrolysis of diborane. However, diborane is a very dangerous gas that requires much care in handling. Pentabo655

Method

Evapo Evapo CVD CVD CVD CVD CVD Evapo. Sputter CVD

Evapo. CVD CVD Sputter CVD CVD CVD CVD

1 2 3 4 6 7 10 11 12

14 15 16 17 18 19 21 23

Boron Boron BCl 3 BCl 3 B2H6 B2H6 B2H6 Boron Boron B2H6 Boron BCl 3 BBr 3 Boron B2H6 BCl 3 B 10 H 1 B2H6

Source

Electro-bombered RF heat MW plasma Magnetron ECR RF heat DC glow RF glow

Electro-bombered Electro-bombered Resistive heat RF heat RF heat DC glow RF heat, RF glow Carbon crucible DC glow RF glow

Activate

777–1227 300–650 room 230–400 827–1227 70–400 300–800

450 930–950 950–1200 400–900 150–350 150–500 260–420

Sub. temp. (°C)

Preparations of Boron Films Developed Until Now

No.

Table 1

Graphite Graphite Quartz, glass Quartz, Si Mo, Ti foil Stainless steel Quartz, Si, sapphire

Fused silica Mo, silica Graphite, iron Graphite Fused silica Graphite Glass, mica

Substrate

Soft X-ray filter Preparation Reduce the prep. temp. Multilayer Characterization Crystallization Fusion reactor Preparation

Electrical properties Characterization Characterization Preparation Fusion reactor Electrical Reduce the prep. temp. Mechanical properties Photoconductivity

Purpose

1970 1975 1976 1976 1979 1980 1981 1982 1984 1985 1985 1990 1990 1900 1991 1993 1994

˚ 1000 A β-rhombohedral Amorphous Amorphous foil Amorphous Amorph., α-rhombo ˚ 700–900 A Polycrystal.

Year

Amorphous Amorphous Amorphous Amorphous α,β-rhombo., tetra. Amorphous Amorphous Amorphous a-B:H

Film

19 20 21 22 23 24 4 25

12 13 8 6 14 15 16 17 18

Ref.

656 Nakamura

Boron Films

657

Figure 1 The purification apparatus used for decaborane.

rane (B 5 H 9 ; ⫺46.5°C melting point, 60°C boiling point) and decaborane (B 10 H 14 ; 99.6°C mp, 213°C bp) can be used as alternative boron hydride sources. Decaborane is safer and more stable than pentaborane and diborane. Furthermore, decaborane has advantages as a source material for boron films because high-purity decaborane is easy to obtain by a sublimation purification process (Fig. 1). Many studies of the electrical (8,14,27,28) and optical (10,11,14,29) properties of boron films prepared by vacuum evaporation (28,29) and chemical vapor deposition (CVD) (7,14) have been reported. However, the properties reported scatter widely (e.g., the values of electrical conductivity and optical gap energy at room temperature). In this chapter, method for preparing high-quality boron films by pyrolysis of decaborane in the molecular flow region at temperatures between 350 and 1200°C is described. The deposition mechanism is discussed in terms of the dependence of the deposition rate on the substrate temperature and the impingement frequency of decaborane molecules onto the substrate surface. The temperature dependences of the electrical conductivity and of the thermoelectric power of boron films deposited on sapphire substrates have been measured. The energy band gap and optical constant (n, k) of boron have been estimated from the results for optical transmittance and reflectance in the visible and infrared spectral regions. In this chapter, preparation of boron films by pyrolysis of decaborane is discussed and properties of the boron films deposited are described,

II. PREPARATION A.

Deposition

A schematic diagram of the apparatus used in this preparation is shown in Fig. 2. The vacuum chamber was evacuated with an oil diffusion pump system, and the ultimate pressure was 2 ⫻ 10⫺6 torr. Sapphire and silicon were used as the substrates. The substrate was fixed on the tungsten sheet heater (0.05 mm thick) and was heated from 600 to 1200°C (Fig. 3). A tantalum sheet was also used as a substrate and was heated between 350 and 700°C by direct resistance heating. The sapphire substrate temperature was estimated from the heater temperature, which was measured with an optical pyrometer. The relation between the substrate and heater tempera-

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Figure 2 Schematic diagram of the apparatus used for deposition of boron films by pyrolysis of decaborane.

Figure 3 Assembly of the substrate and the heater.

Boron Films

659

tures was previously obtained. The tantalum substrate temperature was measured directly with a welded thermocouple. Decaborane (Arfa Product) was sublimated by heating at about 70°C and was introduced into the vacuum chamber through a variable leak valve. Boron films were deposited on the heated substrate by thermal decomposition of the decaborane. The pressure of decaborane was measured as a corresponding nitrogen pressure by a BA-type ionization gauge and was kept between 1 ⫻ 10⫺5 and 2 ⫻ 10⫺4 torr. Deposition time varied from 0.5 to 60 min, depending on the gas pressure and the substrate temperature.

B.

Analysis

The thicknesses of the films on the sapphire substrates were measured with a multiple-beam ˚ . In the case of the films deposited on tantalum, interferometer and ranged from 442 to 4740 A the film thickness could not be measured optically because of the rough surface of the tantalum substrate. The thickness of boron films on tantalum substrates was estimated from the measured X-ray fluorescence of boron deposited using electron probe microanalysis (EPMA) with a 7kV acceleration voltage, a 0.1-µA sample current, and a 100-µm beam diameter. The relation between the X-ray intensity and the film thickness was previously obtained using boron films on a sapphire substrate. The crystal structure of boron films was studied by reflection electron and X-ray diffraction techniques. The electrical conductivity and its temperature dependence were measured by a twoprobe technique at temperatures ranging from 300 to 1000 K in vacuum. A gold film, deposited on the boron films by vacuum evaporation, was used as an electrode. Thermoelectric power of the films was measured by using a Pt-PtRh (10%) thermocouple that was 0.2 mm in diameter. The distance between two thermocouples was 10 mm (Fig. 4). The boron films measured were 5 ⫻ 13 mm2, and the film thicknesses were 1.2 and 1.5 µm. The thermoelectric power could not be measured below 250°C because it was too small in comparison with the electrical noise in this temperature range. Transmission and reflection spectra of the boron films on sapphire were measured over a wavelength range 200–2500 µm using an MPS-50 (Shimazu) spectrophotometer. In the transmission and reflection measurements, an uncoated sapphire and an evaporated aluminum film were used as the references, respectively. Absorption coefficient, refractive index, and extinction coefficient of the boron films were calculated from the measured transmittance and reflectance at normal incidence. Infrared transmittance at normal incidence on boron films deposited on high-resistivity silicon wafers was measured in the wavelength range 2.5–50 µm using a DS-701G (Jasco) infrared spectrophotometer.

III. RESULTS AND DISCUSSION A.

Deposition Rate

The influence of the deposition parameters on the deposition rate is as follows. The deposition ˚ /s), is linearly dependent on the decaborane pressure P (torr), as shown in rate of boron, D (A Fig. 5, and is given by D ⫽ 3.57 ⫻ 10⫺3 P for substrate temperatures of 750 and 1000°C. It is thought that the deposition rate of boron films obtained by pyrolysis of decaborane depends on the impingement frequency of decaborane on the substrate. From gaseous molecular dynamics, the impingement frequency S of decaborane on the substrate surface is given by

660

Figure 4 Electric motive force measurement apparatus.

Nakamura

Boron Films

661

Figure 5 Deposition rate of pyrolytic boron films as a function of B 10 H 14 pressure. The films were deposited at substrate temperatures of T s ⫽ 750°C (䊉) and T s ⫽ 1000°C (䊊).

S ⫽ P (M2π/RT g ) 1/2 ⫽ 5.8 ⫻ 10⫺2P(M/T g ) 1/2 (g/cm2 ⋅ s)

(1)

where R ⫽ 62.36 torr ⋅ l/mol ⋅ deg is the gas constant, P is the decaborane pressure in torr, M is the molecular weight of decaborane, and T g is the gas temperature considered to be at room temperature (i.e., T g ⫽ 300 K). The rate of chemisorption depends on the impingement frequency S of the decaborane molecules on the surface, the condensation coefficient γ, and the fraction of collisions that take place at available sites f (θ), where θ is the fractional surface coverage. The rate of chemisorption, U is given by U ⫽ Sγf (θ) exp (⫺E a /RT s )

(2)

where T s is the substrate temperature and E a is the activation energy for chemisorption. As shown in Fig. 5, the deposition rate is independent of temperature, and the chemisorption is nonactivated; hence, the activation energy E a ⫽ 0. Under the experimental conditions, we suppose that f (θ) ⱌ 1 and γ ⱌ 1; hence, the rate of chemisorption is equal to the impingement frequency S. The theoretical deposition rate D t , in this high temperature range is D t ⫽ 1.66 ⫻ 10⫺2P(cm/s)

(3)

taking into account the ratio of boron weight to decaborane molecular weight (0.9) and the density of boron (2.0 g/cm 3 ). Comparison with the experimental values of Fig. 5 shows that

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Nakamura

D t must be multiplied by a factor of 0.22. This factor is due to either f(θ), γ, or the sensitivity difference of decaborane and nitrogen in the ionization gauge. Figure 6 shows the temperature dependence of the deposition rate of boron films in the temperature range 350–700°C at two decaborane partial pressures, 2 ⫻ 10⫺5 and 8 ⫻ 10⫺5 torr. In each case, the deposition rate increases steeply with an increase in temperature up to 416°C and then saturates. In the low-temperature range at T s ⫽ 416°C, the activation energy is found to be 39 kcal/ mol from the slope, and the deposition rate is given by D ⫽ 7.16 ⫻ 10 9 P exp(⫺39,000/RT s ) (cm/s)

(4)

The saturated deposition rate above 416°C can be explained by Eq. (2). The activation energy of 39 kcal/mol is in agreement with 41.4 kcal/mol (30) and 41.6 ⫾ 0.5 kcal/mol (31), both reported for the activation energy of the decomposition of decaborane at temperatures below 250°C.

Figure 6 Logarithm of the deposition rate divided by the decaborane pressure as a function of reciprocal absolute temperature of the substrate. The films were deposited at decaborane pressures of P ⫽ 2 ⫻ 10 ⫺5 torr (䊉) and P ⫽ 8 ⫻ 10 ⫺5 torr (䊊).

Boron Films

663

Figure 7 X-ray diffraction pattern of a pyrolytic boron film.

B.

Characterization of the Films (Structure, Impurities)

The X-ray diffraction pattern of a boron film deposited on sapphire at a substrate temperature of 700°C and a decaborane pressure of 2 ⫻ 10 ⫺5 torr for 15 min is shown in Fig. 7. The Xray and electron diffraction analysis indicates that the films are amorphous. The electron spectroscopy for chemical analysis (ESCA) spectrum of the boron film deposited at a decaborane pressure of 4.4 ⫻ 10 ⫺5 torr and a substrate temperature of 700°C is shown in Fig. 8. The figure shows the spectrum of the film before and after ion etching. The peaks at

Figure 8 ESCA spectra of a pyrolytic boron film.

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Nakamura

Table 2 ESCA Data for a Boron Film Deposited at a B 10 H 14 Pressure of 4.4 ⫻ 10 ⫺5 torr and a Substrate Temperature of 700°C Intensity (arbitrary units) Sample

Boron

Carbon

Oxygen

C/B

O/B

95 131

28 12

6.1 5.7

0.298 0.092

0.065 0.044

As deposited After argon etching

Table 3 Data for Boron Films Analyzed by EPMA Characteristic x-ray intensity (CPS)

B 10 H 14 pressure (torr)

Deposition rate ˚ /s) (A

Boron

Carbon

C/B

2 ⫻ 10 4 ⫻ 10 ⫺5 1 ⫻ 10 ⫺4

7 14 33

1740 1020 1320

18 6 4

0.0103 0.0059 0.003

⫺5

binding energies of 191, 288, and 512 eV correspond to boron 1s, carbon 1s, and oxygen 1s, respectively. The amounts of carbon and oxygen at the surface were estimated from the observed peak intensities multiplied by the photoionization cross-section factor (B, 0.486; C, 1.00; O, 0.293) and are shown in Table 2. The table shows that oxygen decreased little on ion etching, even though the apparent carbon content decreased to almost one third its original value. These results indicate that it is difficult to remove oxygen from the film surface by ion etching alone. The boron films were analyzed by EPMA because this method was not influenced by surface impurities. The amounts of impurities in three films deposited on sapphire substrates at decaborane pressures of 1.4 ⫻ 10 ⫺5, 3.3 ⫻ 10 ⫺5, and 4 ⫻ 10 ⫺5 torr are shown in Table 3. This table shows that carbon decreases with increasing deposition rate. Oxygen impurities in boron films on sapphire substrates cannot be analyzed by EPMA because the primary electrons penetrate the film and extend into the oxygen-bearing substrate. On the contrary, no oxygen was found in the films on tantalum substrates by EPMA. The EPMA and the ESCA analyses suggest that oxygen impurities localized near the surface are due to the exposing air, while carbon impurities are incorporated in the films from a residual gas. C.

Electrical Properties

The conductivities of boron films as a function of reciprocal absolute temperature are shown in Fig. 9. Conductivity varied from 3 ⫻ 10 ⫺3 S ⋅ cm ⫺1 at room temperature to 30 S ⋅ cm ⫺1 at 1000 K. The conductivity at room temperature is in agreement with that for amorphous boron films deposited by CVD and vacuum evaporation (1 ⫻ 10 ⫺3 S ⋅ cm ⫺1 ) (28) but much larger than that of single crystals (⯐ 10 ⫺6 S ⋅ cm ⫺1 ) (32,33). The conductivity decreases slightly with increasing deposition temperature and is not affected by the carbon impurities. Generally, the conductivity of semiconductors in the intrinsic conduction region is written as

Boron Films

665

Figure 9 Temperature dependence of the conductivity of pyrolytic boron films. The films were deposited at substrate temperatures and B 10 H 14 pressures of T s ⫽ 700°C and P ⫽ 1.4 ⫻ 10 ⫺5 torr (䉱), T s ⫽ 700°C and P ⫽ 2 ⫻ 10 ⫺5 torr (䊉), T s ⫽ 800°C and P ⫽ 3.3 ⫻ 10 ⫺5 torr (■), and T s ⫽ 750°C and P ⫽ 1.5 ⫻ 10 ⫺5 torr (䊊).

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σ ⫽ σ 0 exp(⫺E g /kT )

(5)

where σ 0 is a constant, E g is the band gap energy, k is the Boltzmann constant, and T is the absolute temperature. The E g can be determined from the slope of the straight line in the plot of log σ 0 against 1/T. By applying this method to Fig. 9, we obtained E g ⫽ 1.07 eV. This value is in agreement with values reported for amorphous boron films (1.0–1.16 eV) (14,34,35) but is smaller than those for polycrystalline and single-crystal boron (1.3–1.4 eV) (35–37). On the other hand, because the boron films obtained are amorphous, the electric conduction is considered to be hopping conduction. Mott (38) has derived the equation for hopping conduction, σ ⫽ σ 0 exp(⫺(T 0 /T) 1/4 )

(6)

where σ 0 and T 0 are constants. Plots of log σ of the boron films as a function of T1/4 are shown in Fig. 10. The observed values show a good linear relation between log σ and T1/4, and values of σ 0 ⫽ 3.2 ⫻ 10 11 S ⋅ cm and T 0 ⫽ 3.5 ⫻ 10 ⫺8 K are obtained. According to Mott, T 0 is given as a function of the density of localized states at the Fermi level, N (E F ), T 0 ⫽ 16 ε 3 /kN (E F )

(7)

˚ ) (8), and k is the Boltzmann where ε is the exponential decay factor of localized states (ε⫺1 ⱌ 5 A constant. From the value of T 0 and Eq. (7), N(E F ) ⫽ 3.8 ⫻ 10 18 cm ⫺3 ⋅ eV⫺1 is obtained. This value is in agreement with the value for amorphous boron films, 5 ⫻ 10 17 –10 19 cm 3 ⋅ eV⫺1 (8), and the value for amorphous bulk, ⱌ10 18 cm ⫺3 ⋅ eV⫺1 (39). As already mentioned, the conduction of the boron films can be explained successfully by two conduction mechanisms. We cannot decide which mechanism is valid within our experimental accuracy. Figure 11 shows the temperature dependence of the thermoelectric power of the films with the results obtained up to now. The films obtained in this experiment show p-type conduction. The thermoelectric power increases rapidly from 107 µV deg⫺1 at 230°C to a maximum value of 400 µV deg⫺1 at 427°C; it then decreases gradually to 310 µV deg⫺1 at 730°C. As the positive carrier concentration increases with increasing temperature, the thermoelectric power also increases with increasing temperature. However, at higher temperature, the thermoelectric power decreases with increasing temperature because the hole mobility decreases. Values of the thermoelectric power reported for bulk boron (32,33,43) show a large peak at a lower temperature, compared with those for the boron films we obtained (420 µV at 700 K). These results can be explained by the assumption that the concentration of the impurities or defects in the boron films should be much higher than that in bulk boron. Johnson and Lark-Horonitz (44) have explained the same results for germanium by the higher concentration of aluminum. The figure of merit for thermoelectric materials, Z, is given as Z ⫽ r 2σ/κ(deg⫺1 )

(8)

where r is the thermoelectric power, σ is the electrical conductivity, and κ is the thermal conductivity. The thermal conductivity of boron is assumed to be 0.05 W ⋅ cm ⫺1 ⋅ deg⫺1 (45,46). Figures of merit of the boron films as a function of temperature are shown in Fig. 12. The value Z increases steeply with an increase of temperature. However, the Z values of the boron films are smaller than those reported for the amorphous bulk material (47). A figure of merit higher than 10 ⫺3 deg⫺1 is required for the material of a practical thermoelectric converter. Figure 12 suggests that boron films deposited by pyrolysis of decaborane are useful for thermoelectric devices at over 2000 K.

Boron Films

Figure 10 Dependence of conductivity S on T1/4; symbols correspond to those in Fig. 9.

667

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Nakamura

Figure 11 Temperature dependence of the thermoelectric power. Numbers are listed in Table 4.

D.

Optical Properties

The absorption coefficient of the boron films, α, is shown in Fig. 13 as a function of incident photon energy hν. The absorption coefficient increases rapidly at about 1.3 eV. It is well known that boron is an indirect energy gap type of material. The absorption coefficient α near the absorption edge E g for the indirect allowed transition can be described as a function of the photon energy hν, αhν ⬀ (hν ⫺ E g ) 2

(9)

Table 4 List of Thermoelectric Power Studies for Boron No.a 1 2 3 4 5 6 7 8 9 10 11 12 a

Author

Structure

Form

Year

Ref.

W. C. Shaw R. Uno Sh. Z. Dzhamagidze A. Zareba O. A. Golikova H. Werheit G. Majini A. A. Berezin

Single Poly. Poly. Single Single Single Single Amorphous single

1957 1958 1968 1970 1970 1970 1971 1974

3 40 35 37 41 33 43 39

J. Cueilleron

Poly., 0.1% impu. Poly., 1% impu. Amorphous

Bulk Bulk Bulk Bulk Bulk Bulk Bulk Bulk Bulk Bulk Bulk Film

1978

32

1983

42

K. Nakamura

Number corresponding to Fig. 11.

Boron Films

669

Figure 12 EMF figure of merit Z of pyrolytic boron films as a function of absolute temperature.

Figure 13 Absorption coefficient of pyrolytic boron films as a function of incident photon energy.

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Figure 14 The absorption edge fitted to the indirect allowed transition.

The variation of the square root of the adsorption coefficient multiplied by photon energy (αhν) 1/2 for boron films with incident photon energy is shown in Fig. 14. The figure shows that the boron film is an indirect energy gap type of material. The energy gap E g is estimated to be 1.28 ⫾ 0.08 eV by extrapolation of the linear part to the horizontal axis in Fig. 14. This value is larger than the value obtained by electrical measurement (1.07 eV) and the values reported for amorphous films by Adirovich and Goldshtein (34) and Morita and Yamamoto (13). The refractive index n and the extinction coefficient k of the boron films are shown as a function of wavelength in Figs. 15 and 16, respectively. These results agree well with the values obtained by Murphy (11) and Morita and Yamamoto (13), for amorphous films deposited by vacuum evaporation. The hillock of the refractive index at wavelengths around 1 µm corresponds to the absorption edge. An increase in the extinction coefficient is also shown at wavelengths below 1 µm. Figure 17 shows the infrared transmission spectrum of the boron film deposited on a silicon substrate. As shown in Fig. 17, the absorption of the boron film in the IR spectral region increases at about 8 µm and reaches a maximum at 12.5 µm. Blum et al. (48) studied the effect of impurities such as carbon and hydrogen on the infrared absorption of amorphous boron films and showed that the narrow band at 2560 cm ⫺1 observed in hydrogen-doped samples is due to BH bond vibration. Also, the broad strong band from 1000 to 1200 cm ⫺1, which is

Boron Films

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Figure 15 Refractive index of pyrolytic boron films as a function of wavelength.

correlated strongly with the amount of carbon in the films, is due to an overlapping and broadening of various BC bond vibrations. Therefore, the absorption band from 8 to 12.5 µm observed in our films is not considered to be due to hydrogen and carbon impurities. Although many absorption bands caused by the complex crystal structure of boron have been reported, they are all in the wavelength region shorter than 8 µm (49). Werheit et al. (50,51) have studied the optical properties of β-rhombohedral boron single crystals in detail and have shown that absorption has a peak at 8 µm. According to Decker and Kasper (52), the absorption spectra of α-rhombohedral boron have absorption peaks at 18.2, 10.9, 9.3, and 8.2 µm. These absorption bands are not in agreement with those observed for boron films deposited by pyrolysis of decaborane. On the basis of studies by Golikova et al. (36), it can be considered that the absorption at 12.5 µm is associated with the short-range lattice structure in the boron films.

Figure 16 Extinction coefficient of pyrolytic boron films as a function of wavelength.

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Figure 17 Infrared transmission spectrum of a pyrolytic boron film deposited on a silicon substrate. The solid line and broken line correspond to the results of the author and Blum (48), respectively.

IV. CONCLUSION Amorphous boron films have been deposited by pyrolysis of decaborane in the molecular flow region. On the assumption that the deposition rate of boron films is determined by the impingement frequency of the decaborane molecules onto the substrate surface, we have derived an equation for the deposition rate D at temperatures lower than 416°C. The equation, D ⫽ 7.16 ⫻ 10 9 P exp(⫺39,000 Rt s )(cm/s), explains the experimental results successfully. Electrical conductivity of these boron films is ⱌ 10 3 larger than that of single-crystal boron and is in agreement with that of amorphous films deposited by CVD and vacuum evaporation. The influence of impurities on the conductivity is not clear. The activation energy for conduction of the boron films is estimated to be 1.07 eV in the intrinsic temperature range. The temperature dependence of the electrical conductivity can also be explained by a hopping conduction mechanism of amorphous materials. Plots of log σ against T 1/4 show a good linear relation, and the density of localized states at the Fermi level, N(E F ), is estimated to be 3.8 ⫻ 10 18 cm ⫺3 eV⫺1. However, we cannot decide which mechanism is valid within our experimental accuracy. The thermoelectric power of the boron films obtained shows a small peak at a higher temperature, compared with those for bulk boron. This may be attributed to the fact that the concentration of the acceptors in amorphous boron films is higher than that in boron crystals. From the measurements of optical absorption, it is found that boron films are an indirect band gap type of material and have an energy gap of 1.28–0.08 eV. Refractive indexes and extinction coefficients of the boron films in the wavelength range 0.27–2.5 µm were obtained. In the infrared spectral region, an absorption peak was observed at 12.5 µm, which is considered to be associated with short-range order in the boron lattice. It is well known that boron is a low-Z material and shows its characteristics in a semiconductor. To our regret, these properties of boron have not been applied sufficiently until now. It

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673

is to clear that boron films can be made easily. As an example of application the studies described in Refs. 4 and 5 have been carried out.

REFERENCES 1. 2. 3. 4.

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

H Werheit. Festkoerperprobleme 10:189, 1970. OA Golikova. Phys Status Solidi A 51:11, 1979. WC Shaw. Phys Rev 107:419, 1957. M Saidoh, N Oriwara, M Shimada, T Arai, H Hiratsuka, T Koike, M Shimizu, H Ninomiya, H Nakamura, R Jimbou, J Yagyu, T Sugie, A Sakasai, N Asakura, M Yamage, H Sugai, GL Jackson, Jpn J Appl Phys 32:3276, 1993. M Yamage, H Sugai. Jpn J Appl Phys Ser 10:184, 1994. L Vandenbulke, G Vuillard. J Electrochem Soc 123:278, 1976. JO Carlsson. J Less Common Met 70:69, 1980. M Prudenziati. Thin Solid Films 36:97, 1976. VS Postnikov. J Less Common Met 47:255, 1976. JS Lannin. Solid State Commun 25:363, 1978. AM Murphy. J Opt Soc Am 57:845, 1967. JR Bosnell, VC Voisey. Thin Solid Films 6:161, 1970. N Morita, A Yamamoto. Jpn J Appl Phys 14:825, 1975. HO Pierson, AW Mullendore. Thin Solid Films 63:87, 1979. BL Zalph, IJ Dimmey, H Park, PL Jones, FH Cocks, Phys Stat Solid 62:K185, 1980. HO Pierson and AW Mullendore. Thin Solid Films 83:87, 1981. N Matsuda, S Baba and A Kinbara. Thin Solid Films 89:139, 1982. JP Schaffer, H Park, JH Lind, PL Jones. Phys Stat Solid (a) 81:K51, 1984. S Labov, S Bowyer, G Steele. Appl Optics 24:576, 1985. CS Park, JS Yoo and JS Chun. Thin Solid Films 131:205, 1985. V Cholet, R Herbin and L Vandenbulke. Thin Solid Films 192:235, 1990. DM Makowiecki, AF Jankowski, MA McKernan and RJ Foreman. J Vac Sci Technol A8:3910, 1990. K Shirai and S Gonda. J Appl Phys 67:6286, 1990. U Jansson, M Boman, LC Markert, J-O Carlssson and JE Greene. J Vac Sci Technol A9:266, 1991. K Kamimura, I Ohtake and Y Onuma. Japan J Appl Phys Series 10: 170, 1994. OWJ Croft. Mater Res Bull 5:489, 1970. G Caserta and A Serra. Thin Solid Films 20:91, 1974. C Feldman, HK Charler Jr, FG Statkiewicz, J Bohandy. J Less Common Met 47:141, 1976. K Moorjani, C Feldman. Electron Technol 3:265, 1970. HC Beachell, JF Haugh. J Am Chem Soc 80:2939, 1958. AJ Owen. J Chem Soc 5438, 1961. J Cueilleron, JC Viala, F Thevenot, C Brodhag, JM Dusseal, A Elbiach. J Less Common Met 59: 27, 1978. H Werheit, HG Leis. Phys Status Solidi 41:247, 1970. EI Adirovich, LM Goldshtein. Sov Phys Semicond 3:196, 1969. Sh Z Dzhamagidze, Yu A Maltsev, RR Shvangiradze. Sov Phys Semicond 2:320, 1968. OA Golikova, DN Mirlin, AS Umarov, T Khomidov. Sov Phys Semicond 7:1091, 1974. A Zareba and M Maszkiewicz. Phys Status Solidi A 3, K207 1970. NF Mott, J Non-Cryst. Solids 1: 1 (1968) Philos Mag 19:835, 1969. AA Berezin, OA Golikova, MM Kazanin, T Khomidov, DN Mirlin, AV Petrov, AS Umarov, VK Zaitsev. J Non-Cryst Solids 16:237, 1974. R Uno. J Phys Soc Jpn 13:667, 1958. OA Golikova, A yu Kiskachi, T Khomidov. Sov Phys Semicond 4:683, 1970.

674 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52.

Nakamura K Nakamura. Nihon Kagaku Kaishi 646, 1983. G Majini and M Prudenziati. Phys Status Solidi A 5:K129, 1971. VA Johnson, K Lark-Horonitz. Phys Rev 92:226, 1953. OA Golikova, VK Zaitsev, VM Orlov, LS Stilbans, FS Tkalenko. Phys Status Solidi A 21:405, 1974. GA Slack, DW Oliver, FH Horn. Phys Rev B 4:1714, 1971. OA Golikova, VK Zaitsev, AV Petrov, LS Stilbonds, EN Tkalenko. Sov Phys Semicond 6:1488, 1973. NA Blum, C Feldman, FG Satkiewicz. Phys Status Solidi A 41:48, 1977. OA Golikova. Sov Phys Solid State 11:1341, 1969. J Jaumann, H Werheit. Phys Status Solidi 33:587, 1969. H Werheit, AH Ausen, H Binnenbruck. Phys Status Solidi B 51:115, 1972. BF Decker, JH Kasper. Acta Crvstallogr 13:1030, 1960.

25 Single Crystal of AlN Takeshi Meguro and Katsutoshi Komeya Yokohama National University, Hodogaya-ku, Yokohama, Japan

I.

INTRODUCTION

Aluminum nitride has a hexagonal crystal structure based on the wurtzite-type lattice. It has not been found in nature. Although AlN has been synthesized for a long time, studies of the growth of single crystals or whiskers are relatively new. Studies reported by Taylor and Lenie (1) and Matsumura and Tanabe (2) in the 1960s are considered to be foremost with respect to single crystals. Systematic studies have been performed by Drum (3–5), Pastrnak and Roskovcova (6), and Witzke (7). In particular, the detailed structural analyses by Drum contributed much to the development of single crystals in later years. AlN does not melt at a pressure of 1 atm but does decompose at 2200 to 2450°C. Typical effective methods for synthesizing AlN single crystals depended exclusively on sublimation of AlN. A variety of morphologies of single crystals, such as platelike, needle (prism), and whisker morphologies, were confirmed by the preceding researchers. However, in all cases the details of experiments were obscure, and therefore the formation conditions intrinsic to each crystal morphology were not clarified. In addition, it was well known that impurities play an important role in crystal growth, but the effect of the kinds and the amounts of impurity on AlN crystal growth was not clarified either. These were comprehensively described by Ishii et al. (8–10). In spite of the detailed studies of the crystallography of AlN by Drum and Witzke, the mechanism for determing how various kinds of single crystals grow was insufficient. Drum (3) stated that the assumption requiring the presence of an axial dislocation is doubtful and concluded that inferring the relationship between defects and crystal growth mechanism is not valid. Ishii et al. (10) proved experimentally that whiskers and prisms of AlN grow through the vaporliquid-solid (VLS) mechanism during the sublimation process.

II. MORPHOLOGIES AND CLASSIFICATION OF AlN CRYSTALS Drum (3,4) studied synthesized crystals using a transmission electron microscope and classified the crystals into the following five types: (a) platelets with an (0001) plane, (b) thin bladeshaped whiskers with large surfaces (0001), (c) plates with a (1010) plane, (d) thin blade-shaped filaments with large surfaces (1010), and (e) needles with a hexagonal cross section and 〈0001〉 growth direction. He focused on the shape of a blade with large surfaces (1010) and with growth direction along [c ⫹ 2a] or [2423]. Witzke (7) related the morphologies of the single crystals 675

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Table 1 Comparison of Classifications of the Morphology of AlN Crystals by Several Authors Type of AlN crystals

Author Drum Witzke Pastrnak and Roskovcova Ishi et al.

Tabular crystal with (0001)

Blade-shaped crystal with (0001)

Platy crystal with (10-10)

(1) (IV) Type C

(2) (V) Type C

(3) (III)? Type B

T-type

a-type whisker and crystal

P-type and platelike crystal

Blade-shaped filament with (1010) (4)

Whisker and needle normal to (0001)

Whisker normal to (10-11)

(5) (I)(II) Type A c-type

b-type

to the temperatures of crystal growth and also classified them into five types. A comparison of the classifications by Ishii et al. (10), shown in Table 1, is very helpful for understanding the concrete content including the other researchers’ results. Ishii et al. (10) investigated the conditions of formation single crystals of AlN by the sublimation method and discussed the mechanism of crystal growth in relation to their morphology. The crystals were classified into five types: whiskers of a type, b type, and c type and crystals of p type and T type. These results are also included in Table 1. They conducted experiments using a graphite resistance tube furnace and found that many single crystals, each crowned with a black globe on the top, grew at temperatures between 1700 and 2000°C on the closed graphite crucible wall and sometimes on the inside wall of the furnace. The morphologies of the single crystals thus obtained were classified into the following three types. The first type includes crystals with large (0001) faces elongated perpendicular to (1010) and was called an ‘‘a-type crystal.’’ An example of a blade-shaped crystal is shown in Fig. 1. According to their explanation, this type of crystal corresponds to Drum’s type (2), Witzke’s (V), and Pastrnak and Roskovcova’s type C. The central axis lies in the (0001) plane. A small black globe is

Figure 1 A typical blade-shaped crystal is an a-type crystal with large (0001) and elongated perpendicular to (1010).

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677

observed on the top of the central axis. They confirmed with electron probe microanalysis (EPMA) that iron is distributed along the central axis and in the globe on the top. Moreover, the globes are composed mainly of iron and small amounts of chromium and manganese. An electron micrograph and an X-ray image of iron are shown in Fig. 2a and b. The temperature at which a crystal of this type begins to grow was found to be above 1700°C in an open crucible. The second type consists of whiskers with the growth direction making an angle of 5° with the normal to (1011). Ishii et al. called this product a ‘‘b-type whisker.’’ A typical crystal is shown in Fig. 3. This type of whisker was unlike any in Table 1, so they thought that this was a new type. The whiskers are characterized by being needle-like and having a black globe on the top. Such b-type whiskers were confirmed to have the same components as the a-type crystals. However, there was a major difference between the a-type crystal and b-type whisker in that no iron could be detected along the axes of the b-type whisker. Crystals of this type are said to grow above 1850°C in an open crucible but are not found as frequently as the a-type crystals. The third type consists of whiskers and needle crystals with a growth direction along the

A

B Figure 2 Electron microscopy of an a-type crystal (a) and X-ray image of Fe (b).

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Figure 3 Whisker of a b-type one crystal with the growth direction making an angle of 5° with the normal to (1011).

c-axis. This product was called a ‘‘c-type whisker.’’ This type of whisker was identified as Drum’s type (5), Witzke’s types (I) and (II), and Pastrnak and Roskovcova’s type A. It is reported that this type of whisker begins to grow at 1550°C in an open crucible. They investigated the effect of iron on the crystal growth using the ‘‘L-type furnace’’ described later. The products obtained from commercial AlN and pure AlN powders were compared after heating at 2100°C for 5 h in a nitrogen atmosphere. From pure AlN powder, tabular crystals and prismatic crystals were found to form above 1700°C, whereas the three types of crystals were formed. It was confirmed that adding iron to the pure AlN powder yielded three types of crystals. The tabular crystals, shown in Fig. 4, have large (0001) basal faces. In contrast, the prismatic crystals, shown in Fig. 5, have large (1010) prismatic faces and (0001) faces. Ishii et al. called the former crystals T-type crystals and the latter P-type crystals. Both crystals correspond to the types proposed by Drum, Witzke, and Pastrnak and Roskovcova as shown in Table 1.

Figure 4 Tabular crystal (T-type crystal) with a large (0001) face.

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Figure 5 Prismatic crystal (P-type crystal) with a large (1010) face and (0001) face.

III. METHODS FOR PREPARING AlN SINGLE CRYSTALS AND AlN FILMS A.

Sublimation Method

Because AlN does not melt at atmospheric pressure, the sublimation method has been applied in many cases. Relatively large AlN crystals can be obtained because AlN sublimes rapidly at high temperatures and recrystallizes easily. Several systematic studies (3–7) using single crystals prepared by the sublimation method are noteworthy. Drum has studied the axial imperfections (3), magnitude of the lattice twist, and the Burgers vector of the axial dislocations (4). He synthesized AlN crystals by nitriding aluminum powder in graphite crucibles placed in a vertical induction furnace in a nitrogen atmosphere at temperatures between 1800 and 2200°C with a temperature gradient of 75°C/cm (3). He also reported that basal platelets and whiskers grew at temperatures between 1950 and 2150°C, whereas only whiskers grew at temperatures lower than 1900°C. However, more details of the experimental conditions are not found in his reports, so the crystal growth conditions are unknown. Davies and Evans (11) prepared 18–20-mm-long AlN whiskers by heating AlN powder at 1820°C in order to determine the bend strength. More details of the preparation method are not provided. In this section, an experimental method adopted by Ishii et al. (10), who reported their experimental procedure in detail, will be introduced. They used a graphite resistance tube furnace and a high-frequency induction furnace to investigate the growth of AlN crystals. The graphite

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Figure 6 Schematic diagram of the closed crucible designed by Ishii et al. A, graphite crucible; B, charged powder of AlN; C, space for crystal growth; D, graphite pipe to transport nitrogen gas; E, joint made of graphite; F, outlet for nitrogen gas; G, inlet for nitrogen gas; H, holder (water cooled).

crucible they designed is shown in Fig. 6 and is called a closed crucible. The crucible enabled most of the vapor sublimed from AlN as starting material to remain within the crucible. In addition, a temperature gradient in the graphite crucible was derived by changing the length of the junction between the crucible and water-cooling holder. A graphite crucible without a watercooling holder or lid was also used. In order to change the temperature gradient, two kinds of induction coil for the highfrequency induction furnace were employed. One furnace had a 60-mm-long coil and 160-mmlong susceptor. The molded AlN specimen was placed in the middle of the susceptor, whose ends were closed to enclose the sublimed vapor and to make the temperature gradient gentle. Ishii et al. called this type of furnace an L-type furnace. The other type of furnace was heated by a 6-mm-wide whirlpool-type induction coil. The graphite susceptor was 70 mm long. They called this a W-type furnace. These furnaces were used horizontally as shown in Figs. 7 and 8. At first, Ishii et al. prepared single crystals in the graphite resistance tube furnace using commercial AlN powder. The commercial powder put in the closed crucible was set in the region of the highest temperature in the furnace. The temperature was kept at 2150°C for 5 h in a nitrogen atmosphere. Consequently, they found that blade-shaped crystals and whiskers with a black globe on the top were formed at temperatures between 1700 and 2000°C on the wall of the closed crucible. These crystals were confirmed to be single crystals by optical and X-ray techniques. They confirmed that these crystals could also be formed in the high-frequency induction furnace. The resultant crystals were classified into three types corresponding to the morphologies mentioned earlier. Subsequently, they investigated the effect of iron on the crystal

Figure 7 Schematic diagram of L-type furnace. A, molded sample of AlN; B, graphite susceptor; C, alumina tube; D, carbon felt; E, induction coil; F, graphite disk for thermal shield.

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Figure 8 Schematic diagram of W-type furnace. A, molded sample of AlN; B, graphite susceptor; C, alumina tube; D, carbon felt; E, induction coil.

growth using the L-type furnace. The experiment was performed at a temperature of 2100°C. The results were also explained earlier. Second, the pellet-drop technique devised by Slack and McNelly (12) will be introduced. They assembled a furnace for crystal growth as illustrated in Fig. 9. The main parts of the furnace are composed of the tungsten crucible, flat foil tungsten radiation shields, radio frequency heating coil, fused quartz housing, rolled foil radiation shield, tungsten support tube, and tungsten susceptor tube. They placed about 5 g of AlN in the left-hand end of tungsten crucible C. The sharp tip of the crucible was placed in the center (2250°C) of the furnace at the start of the run. The inside was constructed so that the crucible rotated at about 2 rev/h and passed through the hot zone at about 0.3 mm/h. They reported that the largest single crystal of AlN grown was a conical boule 12 mm long and 4 mm in diameter with a mass of 0.23 g and that the c-axes of the AlN crystals are generally parallel to the long dimension of the tungsten

Figure 9 Tungsten tube furnace for growing AlN crystals devised by Slack and McNelly. A, alumina; C, tungsten crucible; F, flat foil tungsten radiation shields; H, radio frequency heating coil; J, water cooling jacket; Q, fused quartz housing; R, rolled foil radiation shields; S, tungsten support tube; T, tungsten susceptor tube; W, clear fused quartz window; Z, rubber O-ring seal.

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crucible. They mentioned that leaks through the pinhole developed on the tungsten crucible grain boundaries during long runs limited the maximum size of the crystals. Tanaka et al. (13) have investigated AlN single crystal growth by the sublimation method devised by Slack and McNelly (12) in order to produce substrates for GaN-based diodes. They reported that the morphology of AlN crystals depended on the sublimation temperatures.

B.

Chemical Engineering Method

Manufacture of single crystals far larger than the whisker level has not yet been reported. However, expectations for whiskers are growing in industry because whiskers could be important as reinforcing materials. Nevertheless, techniques for mass production have not been established. In this section, a chemical engineering method designed by Hotta et al. (14–16) is introduced, although their process still remains in the experimental stage. They investigated synthesis methods for AlN powder by floating-type fluidized-bed nitridation of aluminum powder. Later, they also reported a process with alumina powder as a raw material. In addition, they tried to produce tranparent AlN whiskers using the same apparatus. The apparatus they designed is shown in Fig. 10. Ultrapure Al powder was used as a raw material. The Al powder was continuously fed in an N 2 stream from the lower end of a reactor made of alumina. A gas mixture of NH 3 and N 2 was introduced in the reactor through another feeding tube. The nitridation temperature was controlled from 1450 to 1550°C. After nitridation, the whiskers deposited on the walls of the reactor and on the feeding tube of the gas mixture were collected. The whiskers were transparent and hexagonal columnar. A typical scanning electron microscopy (SEM) photograph of whiskers is shown in Fig. 11. They reported that the rates of growth of whiskers were 2 µm/s in the length direction and 0.0014 µm/s in the radial direction.

Figure 10 Schematic diagram of experimental fluidized-bed apparatus. A, Source of supply; B, nitriding reactor; C, separator; 1, container; 2, nitrogen gas inlet; 3, Al powder inlet; 4, agitator; 5, alumina tube; 6, heater; 7, separator; 8, nitrogen outlet; 9, silicone tube.

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Figure 11 Typical SEM photograph of whiskers obtained with a floating-type fluidized bed.

The maximum length and diameter were 15 mm and 120 µm. They thought that the mechanism by which the whiskers grow is not VLS, which will be mentioned in Sec. IV, but VS, because the tops of the whiskers did not have special elements such as Fe. It is noteworthy that the oxidation resistance is high. The transparency of the whiskers was confirmed even after oxidation at 900 to 1000°C in air for 4 h.

C.

Physical Vapor Deposition Method

There were only few detailed studies of physical vapor deposition (PVD) of AlN. However, publications on various deposition methods for AlN have increased because of the potential applications in surface acoustic devices (SAWs) and in optical devices in the ultraviolet spectral region. AlN films have important characteristics such as piezoelectricity, high ultrasonic velocity, and high-temperature stability. Although these studies were not always targeted at forming AlN single crystals, some studies will be introduced in this section because the properties and crystalline structure are considered to be very important in relation to crystal formation with orientation. Also, AlN materials may receive much attention in the future as thermal barriers or protective coatings in aggressive environments because AlN is an excellent oxidation-resistant material. Bienk at al. (17) have studied a method for preparing AlN films by reactive sputtering, with a transition region in which the deposited films change their optical characteristics from nontransparent to highly transparent films. The effects of accurate mass flow control of the reactive gas under a constant argon flow on deposition of AlN films with well-defined stoichiometry, crystalline texture, and morphology were examined using an Alcatel RF/DC sputtering unit (SCM 650) with two cathodes of Al. Film depositions were performed in the RF model at 13.56 MHz with 1200 W. They found that the film composition and sputtering rate depend strongly on the deposition conditions and, in particular, on the mass flow and the sputtering pressure. Thus, for films prepared under three sputtering conditions, A, B, and P (P was called the working point), the relation between experimental total pressure and mass flow of the reactive gas was compared. The deposition conditions and Al/N ratio of the resulting films are listed in Table 2.

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Table 2 Deposition Conditions and Al/N Ratio of Films Deposition point A B P A B P A B P

Ar flow (sccm)

N 2 flow (sccm)

Pressure ⫻ 10 ⫺3 (mbar)

Al/N ratio

40.0

3.53 3.53 3.30 3.76 3.76 2.98 3.47 3.52 2.57

19.4 19.9 19.8 4.6 5.7 5.4 2.4 3.6 3.3

1.2 1.1 1.1 1.5 1.1 1.1 1.6 1.1 1.1

8.0

4.0

They reported that the films prepared at points B and P are almost stoichiometric and transparent independent of argon flow, whereas the nonstoichiometric films prepared at point A are nontransparent. The reflected X-ray diffraction patterns of P films showed that the crystalline texture is very dependent on the sputtering pressure. At the lowest sputtering pressure, the characteristic (002) orientation in AlN and (200) in Al were the only peaks observable. However, peaks assigned to AlN(101) and AlN(102) appeared when the pressure increased. For SAW applications, c-axis-oriented (a-axis-oriented) AlN films are required for longitudidal (transverse) waves. Okano et al. (18) have investigated the orientation of AlN films deposited by electron cycloton resonance (ECR) dual ion beam sputtering, using an ECR ion source for irradiation and a Kaufman-type ion source for sputtering. The ECR ion beam sputtering system employs high-density ion beam irradiation, is a low-pressure process, and produces plasma-free deposition. The apparatus they used is shown in Fig. 12. They found that c-axisoriented AlN films could be obtained by controlling the nitrogen ion beam energy and microwave power of ECR and that the upper area of the films with c-axis orientation parallel to the substrate was nearly single crystal. Akiyama et al. (19) confirmed that highly c-axis-oriented AlN thin films can also be formed on polycrystalline substrates such as MoSi 2 , Al 2O 3 , and SiC. They prepared AlN thin

Figure 12 Apparatus of the ECR ion beam sputtering system. A, ECR ion gun; B, target holder; C, rotary pump; D, substrate holder; E, Kaufman ion gun; F, main valve; G, cryo pump.

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Figure 13 Schematic diagram of electron shower apparatus. A, DC bias; B, substrate; C, anode; D, tungsten filament; E, nitrogen inlet; F, Al; G, pump.

films using RF magnetron sputtering equipment and reported that the crystal orientation of the thin films was not influenced by the difference in such substrate materials. However, the orientation on the polycrystalline substrates was worse than that of thin films deposited on singlecrystal substrates. Ishihara et al. (20,21) devised a new type of PVD method called the electron shower. In general, it has been difficult to obtain a-axis-oriented AlN films by sputtering and ion plating. However, they succeeded in preparing a-axis-oriented AlN films by their method. A schematic diagram of the electron shower apparatus is shown in Fig. 13. Thermal electrons emitted from a heated tungsten filament are accelerated by a potential of 500 V between the filament and the ring-shaped anode. Al was evaporated in an Al 2O 3-coated tungsten basket. The Al vapor and N 2 gas were activated by passing through an electron shower, and AlN film was formed on the substrate. They reported that both a-axis-oriented films and c-axis-oriented films could be prepared, and the orientation changed to c-axis orientation when a negative bias of ⫺200 V was applied. D.

Ammonothermal Reaction Method

Peters (22) proposed a new method for preparing AlN single crystals. This method is based on the ammonothermal reaction of Al with ammonia using potassium amide as a transporting agent. He used potassium amide, KNH 2 , as a mineralizer. KNH 2 reacts with Al and NH 3 to form KAl(NH 2 ) 4 . Both compounds, KNH 2 and KAl(NH 2 ) 4 , are very soluble in ammonia. KAl(NH 2 ) 4 decomposes to KNH 2 , NH 3 , and AlN as expressed by the following equation: KAl(NH 2 ) 4 ⇔ KNH 2 ⫹ 2NH 3 ⫹ AlN

(1)

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There exists an equilibrium in this relation. Only KAl(NH 2 ) 4 and AlN were detected at the end of the experiments, although the actual Al transporting compound was not assigned. For this reason, he thought that Eq. (1) was acceptable. He reported that AlN single crystals grown predominantly in the direction of the c-axis were obtained in the temperature range 500 to 600°C at pressures of 1 to 2 kbar.

IV. MECHANISM OF AlN CRYSTALLIZATION BY SUBLIMATION METHOD Judging from the fact that many whiskers are known to be free from dislocations, Drum (3) denied the necessity for the presence of an axial dislocation, which is required for the proposed mechanisms for whisker growth from vapor. He pointed out that AlN whiskers of the 〈c ⫹ 2a〉 type might be unique in that every crystal with this orientation contained an axial imperfection. He discussed the growth mechanism based on the presence of axial dislocation. However, he could not present a consistent explanation and finally concluded that inferring the relationship between defects and the crystal growth mechanism solely on the basis of data on growth directions is not valid. He also did not explain the growth mechanism of the other types of crystals. The report by Witzke (7), who related the morphologies of single crystals to the growth temperature, did not mention the detailed mechanism. Pastrnak and Roskovcova (6) investigated the effect of the degree of supersaturation on the types of crystals and suggested that small amounts of oxygen, carbon monoxide, and carbon might affect the morphology. According to them, a high degree of supersaturation yielded type A crystals, and a lower degree of supersaturation yielded types C and B. Ishii et al. (8,10) investigated the growth mechanism and the growth conditions of single crystals of AlN prepared by the sublimation method. They found that P-type and T-type crystals grow in a system containing no iron impurities. They thought that since {1011} is the least important face among the three F-faces ({0001}, {1010}, and {1011}, crystals grown under near-equilibrium conditions are expected to be bounded by {0001} and {1010} and {1011} is absent. It was shown that T-type crystals were related to CO in an atmosphere without Fe. For a system containing impurities such as iron, they described the VLS mechanism as follows. A crystallite with a large (0001) face forms in a drop of liquid iron determing the size of the crystallite. The Fe on the (0001) face causes the crystal to grow in the form of a whisker perpendicular to (0001). This crystal is called a c-type whisker. The second and the third important faces appear on the crystallite in Fe at high temperatures, resulting in the growth of whiskers perpendicular to (1010) and (1011). The a-type and b-type whiskers grow by such a mechanism. Kato (23) reported that the diameter of whiskers is proportional to the size of the globes consisting mainly of iron.

V.

THERMAL CONDUCTIVITY OF AlN SINGLE CRYSTAL

Slack (24) reported the thermal conductivity, κ, of AlN to be 200 W/m ⋅ K at 300 K using a synthetic single crystal supplied by the company Peciney Compagnie de Produits Chimiques et Electrometallurgiques of Grenoble, France. The crystal was grown by sublimation at about 2100°C. However, the details were not made clear. The only information given was that oxygen, the dominant impurity, was (3 ⫾ 2) ⫻ 10 26 atoms/m 3 in total. He found that the κ of AlN is sensitive to the oxygen content and at 300K varies from about 320 W/m ⋅ K for pure AlN to about 50 W/m ⋅ K for AlN with 2 ⫻ 10 21 atoms/cm 3 of oxygen. He summarized the other values for κ of AlN in the literature. Subsequently, Slack and McNelly (12) reported that a

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single crystal had a value of 250 W/m ⋅ K (run W-154) at 300 K and that a polycrystalline sample had a value of 220 W/m ⋅ K at 300 K. In 1987, Slack et al. (25) studied the intrinsic thermal conductivity of single crystals. They obtained high-purity single crystals by the sublimation method devised by Slack and McNelly (12,26). A single crystal weighing 1.00 g and 1.41 cm long and with an average diameter of 0.54 cm was used for the measurements at temperatures of 0.4 to 300 K. The oligocrystalline samples of sublimed AlN in the form of 1.2-cm-diameter, 0.3-cm-thick flat disks were used for measurements between 370 and 1800 K. The impurity of oxygen was estimated to be 343 ⫾ 17 ppm in weight (from starting powder). The tungsten content was about 50 ppm (from the crucible). The other impurities were analyzed and found to be 10 ppm or less. The results are shown in Fig. 14 and the numerical data are given in Table 3. The value for pure AlN in Table 3 are corrected for the residual oxygen content. In the figure, the solid curve plotted as circles and squares shows the measured thermal conductivity. The circles are for the oligocrystallne sample. They discussed the effect of substitutional impurity oxygen in AlN on phonon scattering. Oxygen replaces nitrogen, and the aluminum deficit produces vacancies in the aluminum sublattice. When the density of AlN is 3.05, the number density, n 0 , of nitrogen atoms in AlN is 4.478 ⫻ 10 22 . Since the AlN they used included 340 ppm, oxygen the number density of the oxygen impurity, ∆n, is 3.902 ⫻ 10 19 . The ratio ε (⫽∆n/n 0 ) is then 8.713 ⫻ 10 ⫺4. Since the thermal resistivity, ∆W 1 , is estimated to be 0.0375, the value of λ pure calculated from the following equation is 319 W/m ⋅ K. λ ⫺ 1 ⫽ λ pure ⫺1 ⫹ ∆W 1 They proved that this is very close to the value predicted by Slack (24) for pure AlN.

Figure 14 Measured thermal conductivity of high-purity AlN (solid curve) (W201 single crystal was used). (䊉) Cornell; (䊐) Slack; (䊊) Tanzilli.

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Table 3 Thermal Conductivity as a Function of Temperature Temperature T (K)

W-201 (W/m ⋅ K)

Pure AlN (W/m ⋅ K)

0.4 0.6 1.0 2.0 4.0 6.0 10.0 15 20 30 45 60 100 150 200 300 400 600 1000 1800

0.38 0.97 3.2 21 108 240 570 1,020 1,500 2,000 2,300 2,200 17,500 1,100 650 285 180 96 48 24

0.38 1.3 5.8 48 380 2,000 5,800 19,500 45,000 70,000 46,000 20,500 4,700 1,570 780 319 195 100 49 24

VI. ELEMENTS THAT ACT AS IMPURITIES IN AlN Knowledge and problems of the elements that act as impurities in AlN are important. Slack and McNelly (26) carefully considered the related substances. In this section, an editorial by Slack will be introduced. He thought that atoms with tetrahedral radii close to those of Al and N would be able to substitute for Al or N. A difference in radii of 0 to 10% indicates high solubility, a 10 to 20% difference indicates moderate to low solubility, and a difference greater than 20% indicates very low solubility. He claimed from these criteria that C and O should have high solubility in the Al sublattice and that Be, Cd, In, Hg, Tl, and Pb should have moderate to low solubility in the Al sublattice. Both C and O are expected to act as highly soluble impurities in AlN by substituting for N because Al 4 C 3 and Al 2 O 3 are stable to a temperature of at least 1500°C. Because only Mg 3 O 4 , Si 3 N 4 , and Be 3 N 2 , of the possible nitrides, exist above 1000°C at 1 atm of N 2 , Si and Be are the possible substituents for Al. Judging from the tetrahedral radii and the stability, he mentioned that Ti and Mn in the first transitional metal series might also substitute for Al. He summarized by stating that Be, C, O, Mg, and Si have high solubilities and that the other impurities such as S, Mn, or the rare earths may have lower maximum solubilities. Contamination from crucibles is always a problem because high temperatures such as 1500°C or above are required to form AlN single crystals. The crucible materials whose melting points are above 2500°C are Mo, Os, Ta, Re, W, and C. Mo is known to produce a low-melting eutectic with Al. Os is toxic, and Ta reacts readily with N to form Ta 2 N and TaN. Therefore, Re, W, C, and TaN are candidates for crucible materials. He confirmed that AlN powder can be heated in sealed W crucibles up to 2275°C without visible attack. The W content of the AlN was reported to be about 50 ppm. With the Re crucible, the Re content of the AlN was found

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to be 60 ppm at 2370°C. Re is therefore not significantly better than W. The main disadvantage of carbon crucible material is the carbon impurity in the crystals.

VII. CONCLUSION In this chapter, single crystals of AlN were described primarily with respect to the preparation method and the morphology. AlN whiskers are an additional important material, especially in the field of composite ceramic materials. AlN is not only a semiconductor material but also a refractory material, which may be considered suitable as a fiber-reinforcing material. In this sense, the development of a mass production process is very desirable. Simultaneously, advances in novel techniques for growing large single crystals are sought. The current studies tend to concentrate on the preparation and the properties of highly oriented thin films. Studies on the preparation and application of AlN films with exellent properties, in fields such as surface acoustic wave devices, should be accelerated in the future.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

KM Taylor, C Lenie. J Electrochem Soc 107:308, 1960. T Matsumura, Y Tanabe. J Phys Soc Jpn 15:203, 1960. CM Drum. J Appl Phys 36:816, 1965. CM Drum. J Appl Phys 36:824, 1965. CM Drum. Phil Mag 25:313, 1965. J Pastrnak, L Roskovcova. Phys Status Solidi 7:331, 1964. HD Witzke. Freiberg Forschungsh C195, 1965. T Ishii, T Sato, M Iwata. Mineral J 6:323, 1971. T Ishii, T Sato, M Iwata. J Miner Soc Jpn 11:127, 1973. T Ishii, T Sato, M Iwata. Mineral J 8:1, 1975. TJ Davies, PE Evans. Nature 207:254, 1965. GA Slack, TF McNelly, J Cryst Growth 42:560, 1977. M Tanaka, S Nakahata, K Sogabe, H Nakata, M Tobioka. Jpn J Appl Phys 36:L1062, 1997. N Hotta, I Isao, M Tanaka. Kagakusochi 2:72–78, 1991. N Hotta. Annu Rep Murata Sci Found 7:184–187, 1993. T Watanabe, N Hotta, K Kotera, K Komeya, T Meguro, T Sasamoto. Proceedings of International Ceram. Conference Austceram 94, Vol 1, 1994, p 184. EJ Bienk, H Jensen, GN Pedersen, G Sorensen. Thin Solid Films 230:121, 1993. H Okano, T Tanaka, K Shibata, S Nakano. Jpn J Appl Phys 31:3017, 1992. M Akiyama, K Nonaka, K Shobu, T Watanabe. J Ceram Soc Jpn 103:1093, 1995. M Ishihara, H Yumoto, T Tsuchiya, K Akashi. J Surf Finish Soc Jpn 47:152, 1996. M Ishihara, H Yumoto, T Tsuchiya, K Akashi. Thin Solid Films 281–282:321, 1996. D Peters. J Cryst Growth 104:411, 1990. A Kato. Denki Kagaku 40:743, 1972. GA Slack. J Phys Chem Solids 34:321, 1973. GA Slack, RA Tanzilli, RO Pohl, JW Vandersande. J Phys Chem Solids 48:641, 1987. GA Slack, TF McNelly. J Cryst Growth 34:263, 1976.

26 AlN Sintered Polycrystal Fumio Ueno Toshiba Corporation, Kawasaki, Japan

I.

INTRODUCTION

Aluminum nitride (AlN) falls under a family of wurtzite structures (2H) and is the only stable compound in the binary system between aluminum and nitrogen. The cell dimensions are a ⫽ 311 pm, c ⫽ 499 pm, and become shorter when oxygen is dissolved in AlN lattice. AlN has received much interest in the electronic industry in recent years because of the need for devices with high power applications (Fig. 1) and the need for smaller and more reliable high speed integrated circuits (Fig. 2). These electronic devices place a number of significant demands upon materials, chief among which is the need to dissipate heat efficiently. The thermal conductivity of pure AlN is predicted to be 319 W/mK (80% of that of pure copper) (1). Aluminum nitride ceramics has a thermal conductivity ranging from 70 W/mK to 270 W/mK, about 5–6 times higher than aluminum oxide (Fig. 3). However, it is not only the high thermal conductivity that makes AlN an excellent candidate for electronic packaging but also properties like its low dielectric constant, low thermal expansion coefficient (close to that of silicon) (Fig. 4), low dielectric loss at high frequencies, high electrical resistivity, high dielectric strength, and nontoxic nature (2–4). Table 1 shows various properties of AlN ceramics and related materials. Research of AlN ceramics started in the late 1950s (5), and was based on numerous properties including corrosion resistance, piezo-electricity nature, thermal conductivity, fluorescence characteristics, chemical inertness toward molten metals, high-temperature stability, optical translucence, high hardness, shock absorption properties, et al. (6). Although pressure sintering and reaction sintering were tried at the beginning, full dense ceramics were only obtained after the 1970s when the sintering additives for AlN were discovered (7). Properties of AlN ceramics improved after the 1980s and since then AlN ceramics has become a practical material. All these properties and their unique combinations make AlN a very worthwhile substance. As a result, AlN ceramic has many different applications. For example, couplers for acoustic surface waves, microwave windows, windows for UV-light and infrared sources, neutron absorbers (in fusion reactors), heat sinks and heat exchangers, molten metal containers and crucibles, heat jigs and refractories, sintering additives for SiC and Si 3 N 4 , fillers for polymers and glass compounds, armor plates, etc. (2).

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Figure 1 AlN direct bond copper substrate for IGBT power device.

Figure 2 AlN package for a high-speed gate ally chip.

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Figure 3 Thermal conductivity of AlN ceramics compared with other materials.

Figure 4 Thermal expansion of substrate materials.

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Table 1 Typical Property Values of AlN and Related Ceramic Materials Property Thermal conductivity Electrical resistivity Dielectric constant Dielectric loss Thermal expansion coefficient Density Bending strength Hardness Young’s modulus

Unit

AlN

Al 2 O 3

SiC

BN

BeO

W/mK Ohm cm 1 MHz 10 ⫺4 (1 MHz) 10-6/K (RT-623K)

70–270 ⭌10 14 8.6 5 4.7

25 ⭌10 14 9.9 4 7.1

70–270 ⭌10 11 40 500 3.8

25 ⭌10 11 4.1 45 0.0

260 ⭌10 14 6.7 4 7.2

G/cm 3 MPa GPa GPa

3.3 280–480 11.8 330

3.89 440 19.6 345

3.21 440 27.5 410

1.9 50 2.7 40

2.85 220 9.8 260

II. MANUFACTURING PROCESS AND PROPERTIES OF AlN POWDER There are several industrial methods of producing AlN powder, but three of them are currently utilized (8–10). Among these, carbothermal reduction of aluminum oxide powder and direct nitridation of aluminum metal are the dominant methods. In the case of carbothermal reduction (Fig. 5), aluminum oxide powder is reduced by carbon and reacts with nitrogen gas to form AlN powder Eq. (1). Reaction temperature is ca. 1550°C. Al 2 O 3 ⫹ 3C ⫹ N 2 → 2AlN ⫹ 3CO

(1)

Excess carbon must be removed after the carbothermal reduction. This process is normally carried out at around 700°C in dried air and residual carbon becomes less than 0.1 mass %. Carbothermal powder typically contains about 1 mass % of oxygen which stays as a surface oxide layer of AlN powder derived from the carbon removal process. Other impurities are mainly driven by the alumina powder source. The morphology of the AlN powder tends to conform to that of starting aluminum oxide powder. In most cases, carbothermal powders are fine, have

Figure 5 Carbothermal reduction furnace (11).

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Figure 6 SEM photographs of AlN powders manufactured by a carbothermal process (left) and a direct nitridation process (right).

equiaxial or spherical shape, and can be easily sintered. Electron microscope photographs of carbothermal and direct nitridation AlN powder are shown in Fig. 6. The direct nitridation method (Fig. 7) uses the nitridation of aluminum metal powder under nitrogen gas Eq. (2). 2Al ⫹ N 2 → 2AlN

(2)

In this case, exothermic self combustion reaction starts at above 800°C and careful treatment is necessary to reach 100% nitridation. After the nitridation process, the crude product requires milling that yields a powder with rough angular particles that exhibit relatively wide size distri-

Figure 7 Direct nitridation process of AlN powder (12).

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Figure 8 Particle size distribution of direct nitridation AlN powder and carbothermal AlN powder.

bution and gives high levels of impurities. Particle size distribution of direct nitridation powder and carbothermal powder is shown in Fig. 8. A surface stabilization process is adopted after milling because a major problem with AlN powders is hydrolysis of the particle surface, resulting in oxidation of the powder that reduces the thermal conductivity of the final product, and may produce ammonia during the storage or prefiring process. Oxygen impurity of direct nitridation powder (more than 1 mass %) comes from starting the aluminum metal and milling process in most cases. Direct nitridation powder has high press density, but is difficult to sinter and the resulting ceramics have relatively lower thermal conductivity. Pyrolysis of organometallic compound is also adopted by a commercial powder process. Chemical vapor deposition of triethylaluminum with ammonia yields a pure and very fine powder (10). The main impurity in the AlN raw powder is oxygen, which is dissolved in AlN lattice during sintering and substituted at the nitrogen site in AlN lattice Eq. (3). Consequently, aluminum vacancy (VAl ) is produced to maintain the charge balance, and the formation of such vacancies promotes sintering of AlN ceramics. On the other hand, thermal conductivity goes down due to the defect generation accompanied by oxygen dissolution. Al 2 O 3 → VAl ⫹ 2Al Al ⫹ 3O N

(3)

When carbon is added to AlN powder, the oxide layer of AlN is removed by a carbothermal reaction (⬃1600°C) during heating before the sintering starts (ca. 1800°C). In this case, grain growth can be observed but shrinkage does not occur even with sintering additives. Existence of oxygen is indispensable for the densification of AlN during sintering. Before the discovery of sintering additives for AlN, more than 3% of oxygen was necessary for the densification even in the case of hot pressing. Recently, grain size, particle size distribution, and the agglomeration nature of AlN powder have greatly improved. As a result, AlN powder with 1 mass % of oxygen can be sintered at 1900°C without sintering additives. Furthermore, pressureless sintering of AlN below 1400°C is also possible with very fine powder prepared by a pyrolysis of

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organometallic compound or plasma nitridation of aluminum metal. However, such a fine powder usually has higher oxygen content and poor durability against moisture.

III. SINTERING OF AlN CERAMICS Like silicon nitride, aluminum nitride is not easy to sinter. The high covalent bonding character (60% covalent–40% ionic (13)) of AlN limits the atomic mobility and prevents complete densification. The condition of the starting materials—purity, particle size, particle-size distribution, oxygen content and specific surface area—influences the sinterability and properties of AlN ceramics (14). There are three solutions proposed to accelerate the densification kinetics of AlN ceramics: 1. Use of hot isostatic pressing or hot pressing that gives an external driving force for densification, 2. Use of pure powders with a high specific surface area (15,16) that promote diffusion at the surface of grains and along grain boundaries, and 3. Use of sintering aids that densify the material by liquid-phase sintering as a liquid is formed between aluminum oxide in the AlN powder and the additives. Figure 9 shows the density and thermal conductivity of AlN ceramics sintered with various compounds. There are three type of additives:

Figure 9 Thermal conductivity and density of AlN ceramics sintered at 1800°C for 2 hours with 3 mass % of additives.

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Figure 10 The phase diagram of Al 2 O 3-Y2 O 3 system (21).

1. Additives that promote the sintering of AlN and increase the thermal conductivity of AlN, 2. Additives that promote the sintering but has no activity to increase the thermal conductivity, and 3. Additives that have no effect on shrinkage nor on thermal conductivity increase. Well known sintering aids in category (1) are alkali-earth oxides or rare-earth oxides such as Y2 O 3 (17,18) and CaO (19,20). These can be added not only as oxide but also as nonoxide compounds such as halide, nitride, carbide, nitrite, or carbonate. Some of the transition elements such as NiO and TiO 2 can be classified as category (2) additives. Rare earth or alkali-earth oxide additive reacts with aluminum oxide of AlN powder (i.e. oxide layer of AlN powder) to form aluminate liquid at a high temperature Eq. (4) and promotes liquid-phase sintering of AlN powder. AlN ⫹ x/2Al 2 O 3 ⫹ y/2Y2 O → AlN ⫹ Al x Yy O 3(x⫹y)/2

(4)

The ratio of aluminum oxide in the powder and added Y2 O 3 gives the grain boundary phase composition in the fired AlN ceramics, according to the phase diagram of the Al 2 O 3-Y2 O3 system (Figs. 10 and 11). The phase diagram (Fig. 10) consists of four different two-phase fields. One of these is the field of Al 2 O 3-Al 5 Y3 O 12 , but AlN ceramics with grain boundary phase consisting of both Al 2 O 3 and Al 5 Y3 O 12 were found in the ceramics sintered with Y2 O 3 . This is because of the dissolution of Al 2 O 3 into AlN lattice, which gives lower thermal conductivity of AlN ceramics.

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Figure 11 Grain boundary phase composition in AlN ceramics sintered with different amounts of Y2 O 3 at 1800°C for 2 hours. Oxygen content of starting AlN powder was 1 mass %.

On the other hand, Y2 O 3 traps Al 2 O 3 and prevents the dissolution into AlN lattice and thermal conductivity increases as Y2 O 3 is added to AlN (Fig. 12). There are some elements such as silica or boron, which improve sinterability when a small amount is added with alkali-earth oxides or rare-earth oxides. Many of the transition elements have almost no influence on sintering and thermal conductivity of AlN (22). Kasori sintered AlN with 0.3 mass % of transition metal oxide (Fe, Ti, Zr, Ta, Nb, W, Cr, Co, Hf, and Mn) and 3 mass % of Y2 O 3 . These oxides became nitride, carbide, metal, or alloy as dispersed particles located inter- and intragranularly in AlN, as shown in Fig. 13. Body color of AlN became black or gray (Fig. 14) but sintering ability, thermal conductivity, and electrostatic properties were almost unchanged. The shading was attributed to optical absorption and multiple reflections by the surface of the electrically conductive fine particles. Effective sintering aids are insoluble in AlN and exhibit a high affinity for Al 2 O 3 . At a suitably high temperature, the oxide coating the AlN grains reacts with the additive to form a eutectic liquid. The liquid wets the grains and allows the material transfer that is essential for densification. During this densification process, oxygen and metal impurities of the AlN grain are incorporated into the grain boundary phase. With prolonged firing the liquid phase migrates through the grain boundaries and either concentrates at grain boundary triple points or migrates to the surface of the sintered AlN body. The role of the sintering aid can be summarized as follows (23,24): 1. 2. 3. 4.

Promotion of particle rearrangement and grain growth through liquid phase sintering, Prevention of oxygen diffusion into AlN grains due to high affinity for Al 2 O 3 , Removal of metal impurities within the grains, and Elimination of the formed secondary phase from the sintered body, after full densification.

This impurity gathering and the removal of the secondary phase by carbothermal reactions,

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Figure 12 The density and the thermal conductivity of AlN ceramics sintered with different amount of Y2 O 3 at 1800°C for 2 hours.

during prolonged firing, drastically increases the thermal conductivity. So even though it is possible to sinter AlN today without a sintering aid, an aid is still required to obtain high thermal conductivity.

IV. THERMAL CONDUCTIVITY OF AlN CERAMICS In AlN there are no free electrons so that the dominant mechanism of heat transportation is phonon (25), i.e. energy quanta are transferred through the crystal body by lattice vibrations. Therefore, it is expected that impurities or other lattice and microstructural defects, such as vacancies, interstitials, dislocations, and grain boundaries, can cause phonon scattering and thus lower the thermal conductivity. Incorporation of oxygen in the AlN, where oxygen substitutes for nitrogen in the wurtzite structure, creates aluminum vacancies to maintain the charge balance (25). With an increasing amount of oxygen (above 0.75 atom %) the topology of the primary defect-type changes from isolated clusters to extended two-dimensional inversion domain boundaries (26–29), with aluminum atoms octahedrally coordinated to oxygen (Fig. 15). This critical oxygen content has also been noted by Slack (25) who observed a contraction of the unit cell followed by a re-expansion at higher oxygen contents. All nonmetals with a known high-thermal conductivity have either diamond-like, boron carbide, or graphite crystal structure. The fundamental characteristics for a crystal to exhibit

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Figure 13 TEM photograph of AlN ceramics prepared by pressureless sintering with WO 3 and Y2 O 3 . W particles are located intragranularly in the AlN ceramics. White bar (at bottom right) indicates 200 nm.

these high values are high purity, strong interatomic bonding, simple crystal structure, low atomic mass, and low anharmonicity (25,30). The thermal conductivity is given by Eq. (5) (31). κ ⫽ 1/3 ⫻ C p ⫻ v ⫻ l

(5)

where C p is the heat capacity, v the phonon velocity, and l the phonon mean free path. At constant temperatures, l is controlled by the phonon–phonon interaction and is much smaller (around 10–30 nm (1)) than the grain size (typically 3 µm). Therefore, phonon scattering at the AlN–AlN grain boundaries has a negligible influence on thermal conductivity compared to lattice defects such as oxygen. Figure 16 shows the oxygen concentration dependency on the thermal conductivity of AlN ceramics and single crystals without second phase. Oxygen concentration dependency can be seen very clearly, and single crystal and polycrystal show the same oxygen concentration dependency. Of course, the mean free path of phonon becomes longer at a low temperature and the thermal conductivity of ceramics becomes lower than that of single crystal shown in Fig. 17. Figure 18 shows the grain size effect for thermal conductivity of pure AlN ceramics without grain boundary phases and with nearly the same oxygen content in AlN lattice. Thermal conductivity is independent from the grain size in this region at room temperature. The existence and removal of the secondary phases is important to reach higher and final values of the thermal conductivity (24,32) because: 1. Up to about 170 W/Km of the main mechanism is considered to be oxygen trap by sintering aids (18), and

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Figure 14 AlN ceramics sintered with 3 mass % of Y2 O 3 (left) and AlN sintered with 0.3 mass % of TiO 2 and 3 mass % of Y2 O 3 (right) at 1800°C. Thermal conductivity is 270 W/mK for translucent AlN (left) and 250 W/mK for black AlN (right).

2. Over 170 W/Km of the mechanism changes from oxygen trapping to elimination of oxygen in AlN grain, along with grain boundary phase elimination from AlN ceramics. Grain boundary phase (second phase) morphology is also important for the thermal conductivity of AlN. Grain boundary phase morphology changes very much. If the cooling rate after sintering is changed, then the interconnection of AlN grain is also changed, thereby changing the thermal conductivity (33). For low additive content, secondary phases are precipitated at triple junctions only, and they do not scatter phonons severely, i.e. there is still contact between the AlN grains. For high additive contents, wetting of the grains occur (even though wettability of Y2 O 3 on AlN is worse than CaO (19)), and aluminates form a continuous layer around the AlN grains. This leads to scattering of phonons at the interfaces and therefore a conductivity decrease. Another reason for the lower values of the thermal conductivity at high additive contents is the fact that they have very low conductivity themselves (Y3 Al 5 O 12 : 11 W/Km (34)). However, it should be pointed out that if the addition is too low there will be a problem removing the oxygen from

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Figure 15 Schematic representation of the oxygen-related defect evolution as a function of oxygen content: (a) region I–isolated aluminum vacancy with associated oxygen, (b) region II–aluminum octahedrally coordinated to oxygen, and (c) extended defect–an inversion domain boundary consisting of aluminum atoms octahedrally coordinated to oxygen at the boundary (26).

Figure 16 Thermal conductivity vs. oxygen concentration of AlN single crystals and ceramics without second phase at room temperature (1).

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Figure 17 Temperature dependency of thermal conductivity for AlN ceramics and single crystal.

Figure 18 The grain size effect for thermal conductivity of pure AlN ceramics without grain boundary phases and with nearly the same oxygen content.

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Figure 19 Reaction of rare-earth additive with AlN powder.

the surface of and inside the grains. Therefore it is important to achieve an optimum addition (35,36). Since most grain boundary phases are concentrated at triple points the AlN will exist as a continuous phase and therefore the thermal conductivity can be expressed as follows (30). κ ⫽ κ AlN ⫻ (1 ⫺ V) ⫹ κ gb

(6)

As the volume fraction of the secondary phase (V ) usually is small and the thermal conductivity of AlN(κ AlN ) is much larger than that of the grain boundary phase, the relation can be further simplified to: κ ⫽ κ AlN ⫻ (1 ⫺ V)

(7)

Also, when one considers the activity of Al 2 O 3 in different parts of the phase diagram (37) of the Al 2 O 3-Y2 O 3 system, one finds some explanation for the variation of the thermal conductivity.

Figure 20 SEM photographs of AlN ceramics sintered at 1700°C (left) and 1800°C (right) with Y2 O 3 .

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The phase diagram (Fig. 10) consists of four different two-phase fields—Al 2 O 3-Al 5 Y3 O 12 , Al 5 Y3 O 12-AlYO 3 , AlYO 3-Al 2 Y4 O 9 and Al 2 Y4 O 9-Y2 O 3 —where the activity of Al 2 O 3 dissolved in AlN is highest in the last phase field above (38,39). Therefore, as long as the volume fraction of secondary phase is low, the thermal conductivity of AlN increases with the amount of Y2 O 3 . As mentioned before, when AlN is sintered with rare earth or alkali-earth oxide, thermal conductivity of ceramics is improved (Fig. 12). This is because such oxides react with aluminum oxide in AlN powder preventing oxygen dissolution into the AlN lattice. The oxides segregate to form rare-earth-aluminum oxide grain boundary phase but defect levels in AlN are minimized. Figure 19 illustrates the reaction scheme of this process. To utilize such oxygen trapping during sintering, we must choose adequate compounds that do not release oxygen at high temperature by decomposition or reduction, but form stable aluminate compounds to trap aluminum oxide. TiO 2 or NiO are also good sintering additives, but become second phase containing TiN or Ni-Al alloy, respectively, during sintering. As a result of a no oxygen trapping effect, thermal conductivity of AlN ceramics with TiO 2 or NiO additives become very low level. There is an optimum amount of addition depending on the oxygen content of AlN powder. Carbonate, nitrites, halide, nitride, or carbide can be also used as sintering additives. The effect is essentially the same but handling of powder improves. In addition, some other benefits, such as improvement of thermal conductivity and lowering of sintering temperature have been reported. After firing at 1200°C with Y2 O 3 for only 10 minutes, Y3 Al 5 O 12 is observed at grain boundary already, but the shrinkage starts at around 1700°C which is below the lowest eutectic temperature in the Al 2 O 3-Y2 O 3 system. On the contrary, shrinkage starts higher than the eutectic point (1360°C) of grain boundary phase, ca. 1500°C in the case of AlN with CaO additive. In both cases, in spite of a large difference in the eutectic temperature, the temperature, which gives the full dense ceramics, is nearly the same. This might not indicate liquid phase sintering. Figure 20 shows the microstructure of AlN sintered with Y2 O 3 at 1700°C and 1800°C. The morphology of ceramics is very different. Recently, partial phase diagram of yttrium aluminate and AlN was reported (40). The eutectic point of the AlN-Y4 Al 2 O 9 system was 1790°C, and the AlN-Y3 Al 5 O 12 system was as low as 1690°C, which indicated the liquid phase sintering of AlN (Fig. 21).

V.

DIFFUSION OF ELEMENTS IN AlN CERAMICS

Diffusion constants of AlN are obtained by high temperature creep phenomena and shrinkage behaviors during hot pressing (41,42). Lattice diffusion constant (D L ) from creep observation is 10⫺12 cm 2 /s at 1700°C and the activation energy is from 530 to 630 kJ/mol, depending on the grain size of the ceramics. The diffusion constants obtained by these experiments are thought to be the diffusion of aluminum due to its large dependence on oxygen concentration because point defect generation at the aluminum site, when the oxygen dissolves in the AlN polycrystal, is well known. Sumino obtained the diffusion coefficient of nitrogen using nitrogen isotope ( 15 N) tracer technique in a very pure AlN polycrystal with only 400 ppm oxygen (43). The lattice diffusion coefficient was 2.6 ⫻ 10⫺13 cm 2 /s at 1930°C and 3.1 ⫻ 10⫺14 cm 2 /s at 1700°C and the activation energy was 370 kJ/mol, as shown in Fig. 22. The grain boundary diffusion parameter δ D b is 1.0 ⫻ 10⫺16 cm 3 /s at 1930°C, where δ means grain boundary width and D b is the grain boundary diffusion coefficient (Fig. 23). The diffusion constants of nitrogen also show oxygen concentration dependency. The diffusion constant calculated from creep or shrinkage during hot pressing for the sample containing % order oxygen, may not be composed of aluminum but, rather, of nitrogen. Muller et al. measured diffusion of oxygen in an Al 2 O 3-AlN diffusion couple to be 6.7 ⫻ 10⫺15 cm 2 /s at 1700°C and

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Figure 21 Three-dimensional view of liquid phase formation temperatures determined by DTA measurements in the system AlN-Y2 O 3-Al 2 O 3 (40).

Figure 22 Logarithmic plot of the intensity of mass number 69 against the depth squared for the sample heat treated at 1930°C for 6 hours.

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Figure 23 The plot of the intensity of mass number 69 following Fisher’s equation for the sample heat treated at 1930°C for 6 hours.

1.9 ⫻ 10⫺14 cm 2 /s at 1900°C (44). Compared to the D L from high temperature creep and hot pressing, Muller concluded that the oxygen atom in AlN ceramics cannot go in and out of the AlN lattice by a solid diffusion process during sintering of AlN. Oxygen dissolution, which causes a decrease of thermal conductivity, is observed by the lattice constant change for the sintered AlN. If the oxygen dissolution during sintering is not due to solid diffusion, this may indicate the diffusion during liquid phase sintering. The diffusion constant of oxygen and aluminum is 10⫺11 cm 2 /s and 10⫺10 cm 2 /s at 1800°C for aluminum oxide (45), which means the diffusion in AlN is about 100 times smaller that in aluminum oxide.

VI. LOW-TEMPERATURE SINTERING OF AlN CERAMICS The sintering temperature of Al 2 O 3 is around 1500°C, while that of AlN is ca. 1800°C. This difference can be understood by the difference of diffusion coefficient mentioned earlier. Several attempts have been carried out to lower the sintering temperature of AlN ceramics for the purpose of keeping processing costs down. If AlN fine powder is used, sintering temperature can be decreased down to 1600°C with Y2 O 3 additive, but in this case, thermal conductivity also decreases as low as 100 W/mK. Fluoride is a promising low temperature sintering additive (46). AlN commercial powder can be sintered with YF 3 at 1550°C, and the combination of AlN fine powder and YF 3 changes the sintering of AlN at 1400°C. The thermal conductivity of YF 3 added to AlN and sintered at 1600°C becomes as high as 245 W/mK. However, the mechanical strength of AlN with YF 3 additive is relatively low. There is no lower eutectic composition in Y2 O 3-CaO-Al 2 O 3 system compared to a simple Al 2 O 3-CaO system, but sintering temperature lowers with the combination of CaO-Y2 O 3 . Sintering additives based on a 1 :1 molar ratio of Y2 O 3 and CaO can be a promis-

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Figure 24 Shrinkage curve for AlN sintered with Y2 O 3 and low temperature firing compositions.

ing sintering additive system with good thermal, mechanical, and electrical properties. Small amounts of boron, or other elements such as boron or lithium, added to the Y2 O 3-CaO system improve the sintering ability of AlN (Fig. 24) (47,48). Fully densified AlN ceramic substrates were obtained with Y2 O 3-CaO-LaB 6-WO 3 by a 1600°C continuous furnace firing. The resulting thermal conductivity was 150 W/mK.

VII. PREPARATION OF PURE AlN POLYCRYSTAL The grain boundary phase can be completely removed by prolonged firing in a carbon reductive atmosphere (23,24). Sintering AlN with 5 mass % Y2 O 3 at 1900°C in a carbon sagger under nitrogen atmosphere for 96 hours produces ceramics with 3.26 g/cm 3 theoretical density of AlN (Fig. 25). This is free of grain boundary phase and with a thermal conductivity of 270 W/mK, so the eliminated yttrium aluminates are found as YN and AlN deposited on the ceramic surface. The elimination reaction of Al 2 O 3 under carbon reductive atmosphere with nitrogen gas occurs above ca. 1500°C (Eqs. (8) and (9)). Al 2 O 3 ⫹ C ⫹ N 2 → 2AlN ⫹ 3CO

(8)

Y2 O 3 ⫹ C ⫹ N 2 → 2YN ⫹ 3CO

(9)

This reaction is the same one used for AlN powder preparation, as mentioned earlier. Although vapor pressure of carbon gas (C n ; n ⫽ 1,2,3, . . .) is very low at 1500°C, it becomes 3 ⫻ 10⫺3 Pa at 1900°C. Free energy change is ⫺40 kJ/mol and ⫹80 kJ/mol for Eq. (8) and Eq. (9), respectively. This heat treatment is carried out under excess carbon gas and nitrogen gas flow to eliminate CO gas. Such a condition expedites the carbothermal reduction of Y2 O 3 to YN at the surface of AlN ceramics (Fig. 26). Of course reaction of Eq. (8) is faster than that of Eq. (9) as grain boundary phase changes from Al rich oxide (i.e. Y3 Al 5 O 12 YAlO 3 ) to Y rich (i.e. Y4 Al 2 O 9 , Y2 O 3 ) (Fig. 25). The overall reaction mechanism of grain boundary phase elimination can be expressed as follows:

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Figure 25 Morphology change of AlN ceramics under high temperature heat treatment in a carbon reductive atmosphere.

Figure 26 AlN grain boundary phase elimination mechanism at high temperature in a carbon reductive atmosphere.

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Figure 27 Grain boundary phase elimination kinetics. Weight loss by grain boundary elimination was observed at 1930°C in different settings under nitrogen gas flow.

xAl 2 O 3 yY2 O 3 ⫹ 3(x ⫹ y)C ⫹ (x ⫹ y)N 2 → 2xAlN ⫹ 2yYN ⫹ 3(x ⫹ y)CO

(10)

CO gas has no chance to produce YN Eq. (11) because the formation of YN is hindered when CO gas is introduced to the furnace (49). This grain boundary phase elimination reaction is not a diffusion controlled process because the rate of it is remarkably sensitive to sample atmosphere (e.g. with different using setter or gas purity) and time dependency of grain boundary phase elimination rate (Fig. 27). xAl 2 O 3 yY2 O 3 ⫹ 3(x ⫹ y)CO ⫹ (x ⫹ y)N 2 → 2xAlN ⫹ 2yYN ⫹ 3(x ⫹ y)CO 2 (11) This process is not limited to the initial stages of sintering, where the porosity is still open (shown by oxygen gradients increasing from the ceramic surface (24) and the well-documented phase associations). YN crystals can be easily removed from the ceramic surface by hydrolysis in boiling water and pure AlN polycrystal can be obtained: YN ⫹ 3H 2 O → Y(OH) 3 ⫹ NH 3

(12)

In summary, the Al 2 O 3 concentration in AlN results from two reactions: (i) a fast internal reaction equilibrating dissolved oxygen content and the yttrium aluminates, and (ii) a slow external reaction tending to equilibrate the ceramic with graphite and furnace atmosphere. Since Y2 O 3 is thermodynamically more stable than Al 2 O 3 the continuous loss of oxygen with sintering time leads to formation of aluminate that is richer in Y2 O 3 . Consequently, it will pump out aluminum oxide inside the AlN lattice to form Y–Al–O grain boundary phase and the AlN lattice is purified during heat treatment. Oxygen content is reduced as low as 400 pmm

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Figure 28 Reduction of yttrium and oxygen content in AlN ceramics under high temperature heat treatment.

(Fig. 28). Hot pressed AlN without yttrium oxide (thermal conductivity is ca. 90 W/mK) cannot be purified by this treatment but AlN sintered with Y3 Al 5 O 12 (thermal conductivity is also as low as ca. 100 W/mK) becomes pure AlN polycrystal with its thermal conductivity of 250 W/mK (23, 24). 3YAlO 3 ⫹ Al 2 O 3 → Y3 Al 5 O 12 Y4 Al 2 O 9 ⫹ Al 2 O 3 → 4YAlO 3 2Y2 O 3 ⫹ Al 2 O 3 → Y4 Al 2 O 9

(13)

The developed oxygen gradient is relaxed by grain boundary migration of the liquid phase as evidenced by an increase in the Y concentration near the surface. Grain boundary phase elimination reaction is also observed in the case of CaO added to AlN (50), but oxygen remains in the AlN lattice and thermal conductivity does not change remarkably because CaO has high vapor pressure and disappears before the elimination of oxygen in the AlN lattice.

CONCLUSION Improvement of processing and properties of AlN powder and ceramics over the last two decades has been remarkable. Although the performance of the AlN ceramics has advanced very much, it is not yet widely used in the industry. Cost reduction processes, designs to make the best use

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of high performance AlN, establishment of evaluation method, and standardization of properties are necessary for a newly developed material such as AlN.

REFERENCES 1. GA Slack, RA Tanzilli, RO Pohl, JW Vandeersande. The intrinsic thermal conductivity of AlN. J Phys Chem Solids 48:641 (1987). 2. LM Sheppard. Aluminum nitride: a versatile but challenging material. Am Ceram Soc Bull 69:1801 (1990). 3. P Garrou, et al. Aluminum Nitride. Advancing Microelectronics 21:6–42 (1994). 4. Y Kurakawa, et al. AlN substrates with high thermal conductivity. IEEE Trans Components Hybrids & Manuf Technol 8:247 (1985). W Werdecker, F Aldinger. Aluminum nitride—an alternative ceramic substrate for high power applications in Microcircuits. IEEE Trans, Components, Hybrids, Manuf Technol CHMT-7:3394 (1984). N Iwase, et al. Thick film and direct bond copper forming technologies for aluminum nitride substrate. IEEE Trans Comp HEMT-8:253 (1985). N Iwase, et al. Development of a high thermal conductive AlN ceramic substrate technology. Int J Hybrid Microelectron 7:49 (1984). 5. KM Taylor, C Lenie. Some properties of aluminum nitride. J Electro Che Soc 107:308 (1960). 6. DD Marcant, TE Nemecek. Aluminum nitride preparation, processing and properties. Adv Ceram 26:19 (1989). 7. K Komeya, et al. Effect of various additives on sintering of aluminum nitride. J Jpn Ceram Soc 89: 58 (1981). 8. W Rafaniello, D Dunmead, M Crosbie. In: AW Weimer, ed. Carbide, Nitride and Boride Materials Synthesis and Processing, Chapman and Hall. pp. 97–104 (1997). 9. N Kuramoto, H Taniguchi. J Mater Sci Lett 3:471 (1984). 10. K Wakimura, A Hiai. FC Report 8:270 (1990). 11. AW Weimer, et al. J Am Ceram Soc 77:3 (1994). 12. Jpn. Kokai Tokkyo Koho, JP 04-108605. (Japanese patent.) 13. L Pauling. The Nature of Chemical Bond. Ithaca, NY: Cornell University Press. pp. 64–107 (1960). 14. N Kuramoto, H Taniguchi, I Aso. Development of translucent aluminum nitride ceramics. Am Ceram Soc Bull 68:883 (1989). 15. K Komeya, H Inoue. Sintering of aluminum nitride: particle size dependence of sintering kinetics. J Mater Sci 4:1045 (1969). 16. GP Vissokov, LB Brakalov. Chemical preparation of ultra-fine aluminum nitride by electric-arc plasma. J Mater Sci 18:2011–2016 (1983). 17. K Komeya, H Inoue, A Tsuge. Role of Y2 O 3 and SiO 2 additions in sintering of AlN. J Am Ceram Soc 54:411–412 (1974). 18. K Anzai, N Iwase, K Shinozaki, A Tsuge. Development of high thermal conductivity aluminum nitride substrate material by pressureless sintering. In: Proceedings of 1st IEEE CHMT Symposium, Tokyo. 10:23–28 (1984). 19. P Sainz de Barada, AK Knudsen, E Ruh. Effect of CaO on the thermal conductivity of aluminum nitride. J Am Ceram Soc 76(7):1751–1760 (1993). 20. K Komeya, A Tsuge, H Inoue, H Ohta. Effect of CaCO 3 addition on the sintering of AlN. J Mater Sci Lett 1:325–326 (1986). 21. T Noguchi, M Mizuno. Kogyo Kagaku Zasshi 70:839 (1967). 22. M Kasori, et al. Effect of transition-metal additions on the properties of AlN. J Am Ceram Soc 77: 1991 (1994). 23. M Kasori, F Ueno. Thermal conductivity improvement of YAG added AlN ceramic in the grain boundary elimination process. J Eur Ceram Soc 15:435 (1995). 24. F Ueno, A Horiguchi. Grain boundary phase elimination and microstructure of aluminum nitride.

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25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.

36.

37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.

50.

Ueno In: G de With, RA Terpstra, R Metselaar, eds. Euro-ceramics. London and New York: Elsevier Applied Science pp. 383–387 (1989). CA Slack. Non metallic crystals with high thermal conductivity. J Phys Chem Solids 34:321–325 (1973). RA Youngman, JH Harris. Luminescence studies of oxygen-related defects in aluminum nitride. J Am Ceram Soc 73(11):3238–3246 (1990). MF Denanot, J Rabier. Extended defects in sintered AlN. J Mat Sci 24:1594 (1989). S Hagege, Y Ishida, S Tanaka. TEM analysis of impurity induced microstructures in sintered aluminum nitride ceramics. J Ceram Soc Jpn Int Edn 96:1093 (1988). AN Pilyankevich, VF Britun, GS Oleynik. Micro-structural studies of polytype formation in oxygen containing aluminum nitride. J Mat Sci 25:3517 (1990). AV Virkar, TB Jackson, RA Cutler. Thermodynamic and kinetic effects of oxygen removal on the thermal conductivity of aluminum nitride. J Am Soc 72(11):2031–2042 (1989). C Kittel. Introduction to Solid-State Physics, 3rd ed. New York: Wiley, 1967. N Iwase, T Yanazawa, M Nakahashi, K Shinozaki, A Tsuge. Aluminum nitride multi-layer pin grid array packages. 37th Electronic Components Conference, IEEE CHMT, 384–391 (1987). W Kim, et al. Morphological effect of second phase on the thermal conductivity of AlN ceramics. J Am Ceram Soc 79:1066 (1996). PH Klein, WJ Croft. Thermal conductivity, diffusivity and expansion of Y2 O 3 , Y3 Al 5 O 12 and LaF 3 in the range of 77-300 K. J Appl Phys 38:1603–1607 (1967). F Miyashiro, N Iwase, A Tsuge, F Ueno, M Nakahashi, T Takahashi. High thermal conductivity aluminum nitride ceramic substrates and packages. IEEE Trans Components, Hybrids, Manuf Technol 13(2):313–319 (1990). WE Lee, SK Chiang, DW Readey, R Donn, PTB Shaffer. Relation between thermal conductivity, sintering mechanism and microstructure of AlN with yttrium aluminate grain boundary phase. J Mater Sci Mater Electronics 3:93–101 (1992). NA Toropov, IA Bonder, FY Galahov, XS Nikogosyan, NV Vinogradova. Izu.Akad.Nauk SSSR, Ser. Khin, No 7, 1167 (1964). Y Kurokawa, K Utsumi, H Takamizawa. Development and characterization of high thermal conductivity ceramics. J Am Ceram Soc 71:588 (1988). H Buhr, G Mu¨ller, H Wiggers, F Aldinger, P Foley, A Roosen. Phase composition, oxygen content and thermal conductivity of AlN (Y2 O 3 ) ceramics. J Am Ceram Soc 74(4):718–723 (1991). K Shinozaki, et al. Liquid phase formation and its migration in aluminum nitride ceramics. Ceramic Trans 71:307 (1996). T Sakai, M Iwata. J Mater Sci 12:1659 (1977). ZC Jou, AV Virkar. J Am Ceram Soc 73:1928 (1990). H Sumino, F Ueno. Diffusion of elements in AlN ceramics. Proceedings of the International Symposium on Aluminum Nitride Ceramics, Tokyo, 1998. M Sternitzke, G Muller. J Am Ceram Soc 77:737 (1994). AE Paladino, WD Kingery. J Chem Phys 37:957 (1962). M Kasori, et al. Mechanical and thermal properties of low temperature sintered AIN. Ceram Trans 83:485 (1998). K Watari, et al. Low-temperature sintering and high thermal conductivity of YliO2-doped AlN ceramics. J Am Ceram Soc 79:1979 (1996). F Ueno, et al. Low temperature sintering of high thermal conductivity aluminum nitride. Proceedings of the International Symposium on Aluminum Nitride Ceramics, Tokyo, 1998. K Oh-ishi, et al. The carbo reductive reaction for the improvement of the thermal conductivity of AlN ceramics. Proceedings of the International Symposium on Aluminum Nitride Ceramics, Tokyo, 1998. N Kuramoto, et al. J Jpn Ceram Soc 93:517 (1985).

27 GaN-AlN-InN Blue Light–Emitting Devices Shuji Nakamura University of California, Santa Barbara, California

I.

INTRODUCTION

GaN and related materials such as AlGaInN are III-V nitride compound semiconductors with the wurtzite crystal structure and energy band structures of direct interband transition, which is suitable for light-emitting devices. The band gap energy of AlGaInN varies between 6.2 and 1.95 eV depending on its composition at room temperature (Fig. 1). Therefore, these III-V semiconductors are useful for light-emitting devices especially in the short wavelength regions. In the AlGaInN system, GaN has been most intensively studied. GaN has an band gap energy of 3.4 eV at room temperature. On the other hand, much research has been done on high-brightness blue light–emitting diodes (LEDs) and laser diodes (LDs) for use in full-color displays, full-color indicators, and light sources for lamps with the characteristics of high efficiency, high reliability, and high speed. For these purposes, II-VI materials such as ZnSe (1–3), SiC (4,5), and III-V nitride semiconductors (6) have been investigated intensively for a long time. However, it was impossible to obtain high-brightness blue LEDs with brightness over 1 cd and reliable LDs. Research on III-V nitrides has paved the way for the realization of high-quality crystals of GaN, AlGaN, and GalnN and of p-type conduction in GaN and AlGaN (7,8). The mechanism of the acceptor compensation that prevents obtaining low-resistivity p-type GaN and AlGaN has been elucidated (9–13). In Mg-doped p-type GaN, Mg acceptors are deactivated by atomic hydrogen, which is produced from NH 3 gas used for the N source during GaN growth. After the growth, thermal annealing in an N 2 ambient can reactivate the Mg acceptors by removing the atomic hydrogen from the Mg-hydrogen complexes. High-brightness blue LEDs have been fabricated on the basis of these results, and luminous intensities over 1 cd have been achieved. These LEDs are now commercially available (14–17). Studies of (Al, Ga, In)N compound semiconductors are described.

II. UNDOPED GaN GaN films are grown on a sapphire substrate with (0001) orientation (c face) at temperatures around 1000°C by metalorganic chemical vapor deposition (MOCVD) as one of the growth methods. The lattice constants along the a-axis of the sapphire and GaN are 4.758 and 3.189 Aº, respectively. Therefore, the lattice mismatch between the sapphire and the GaN is very 715

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Figure 1 Lattice constant of III-V nitrides as a function of their band gap energy.

˚ , which is relatively close to large. The lattice constant along the a-axis of 6H-SiC is 3.08 A that of GaN (Fig. 1). However, an SiC substrate is extraordinarily expensive to use for the practical growth of GaN. Therefore, at present, there are no alternative substrates except for sapphire, considering the price of substrates and the high growth temperature, although the lattice mismatch is large. The grown GaN layers usually show n-type conduction without any intentional doping. The donors are probably native defects or residual impurities such as nitrogen vacancies or residual oxygen. The surface morphology of the GaN films was markedly improved when an AlN buffer layer was initially deposited on the sapphire, as shown first by Yoshida et al. (18). Amano et al. (19,20) and Akasaki et al. (21) have obtained high-quality GaN films using this AlN buffer layer by means of the MOCVD method. They showed that the uniformity, crystalline quality, luminescence, and electrical properties of the GaN films were markedly improved. The carrier concentration and Hall mobility, whose values were (2–5) ⫻ 10 17 /cm 3 and 350–430 cm 2 /V ⋅ s at room temperature, were obtained by the prior deposition of a thin AlN layer as a buffer layer before the growth of the GaN film (22). Those values became about 5 ⫻ 10 16 /cm 3 and 500 cm 2 / V ⋅ s at 77 K. Also, high-quality GaN films were obtained using GaN buffer layers instead of AlN buffer layers on a sapphire substrate by Nakamura (23). He developed a novel two-flow MOCVD reactor for the GaN growth (Fig. 2). It has two different gas flows. One is the main flow, which carries the reactant gas parallel to the substrate with a high velocity through the quartz nozzle. Another flow is the subflow, which transports the inactive gas perpendicular to the substrate for the purpose of changing the direction of the main flow to bring the reactant gas into contact with the substrate (Fig. 3). Sapphire with (0001) orientation (C face) was used as a substrate. Trimethylgallium (TMG) and ammonia (NH 3 ) were used as Ga and N sources, respectively. First, the substrate was heated to 1050°C in a stream of hydrogen. Then the substrate temperature was lowered to about 550°C to grow the GaN buffer layer. Next, the substrate temperature was elevated to about 1000°C to grow the GaN film. The total thickness of the GaN film was about 4µm. Hall measurements were performed on GaN films grown with a GaN buffer layer as a ˚ GaN function of the thickness of the GaN buffer layer. For the GaN film grown with a 200-A buffer layer, the carrier concentration and Hall mobility were 4 ⫻ 10 16 /cm 3 and 600 cm 2 /V ⋅ s, respectively, at room temperature. The values became 8 ⫻ 10 15 /cm 3 and 1500 cm 2 /V ⋅ s at 77 K, respectively (see Fig. 4). The carrier concentration and Hall mobility of GaN films grown with GaN buffer layers

GaN-AlN-InN Blue Light–Emitting Devices

Figure 2 Schematic diagram of novel two-flow MOCVD reactor for GaN growth.

Figure 3 Schematic principles of two-flow MOCVD.

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Figure 4 The Hall mobility measured at 77 and 300 K as a function of the thickness of the GaN buffer layer.

are shown as a function of the temperature in Fig. 5 (24). The GaN films were grown with an ˚ -thick GaN buffer layer. The total thickness is about 4 µm. The Hall mobilapproximately 200-A ity is 700 cm 2 /V ⋅ s at room temperature. The crystal quality of this GaN film was characterized by the double-crystal X-ray rocking curve (XRC) method. The full width at half-maximum (FWHM) for (0002) diffraction from this GaN film was 4 min. Therefore, the value of the FWHM is not directly related to the Hall mobility because the Hall mobility becomes smaller than 600 cm 2 /V and the value of FWHM becomes smaller than 4 min as the buffer layer thick˚ (23). The Hall mobility gradually increases as the temperature ness is decreased below 200 A decreases from room temperature (see Fig. 5). The Hall mobility is about 3000 cm 2 /V ⋅ s at 70 K. According to Amano et al. (19,20,22) and Akasaki et al. (21), maximum Hall mobility (about 900 cm 2 /V ⋅ s) was obtained at around 150 K using AlN buffer layers. On the other hand, GaN film grown with GaN buffer layers has a maximum value at around 70 K. Therefore, the contribution of ionized impurity scattering in a GaN film grown with GaN buffer layers is much smaller than that in a GaN film grown with AlN buffer layers. The Hall mobility varies roughly following µ ⫽ µ0 T ⫺1 between 70 and 300 K, where µ is the Hall mobility, µ0 a constant practically independent of temperature, and T absolute temperature. Thus, in this temperature range, the Hall mobility is mainly determined by the contribution of polar phonon scattering.

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Figure 5 Carrier concentration and Hall mobility of GaN films grown with GaN buffer layers as a function of the temperature.

Below 70 K, ionized impurity scattering dominates and Hall mobility decreases. The carrier concentration decreases drastically below 100 K and varies slightly between 100 and 300 K. Therefore, it seems that a different donor level contributes to the generation of the carrier corresponding to the two different temperature ranges. To consider these two different donor levels, the carrier concentration as a function of the reciprocal of the temperature was plotted, as shown in Fig. 6. The thermal activation energy of the electron from the donor level to the conduction band can be obtained from the gradient of linear regions in Fig. 6, assuming that the carrier concentration varies following the formula N ⫽ N 0 exp(⫺E/2kT ), where N is the carrier concentration, N 0 a constant practically independent of temperature, E a thermal activation energy, k the Boltzmann constant, and T the absolute temperature. A thermal activation energy of 34 meV was obtained between 100 and 42 K and of 5 meV between 300 and 100 K.

III. n-TYPE GaN Figure 7 shows the carrier concentration of Si-doped GaN films as a function of the flow rate of SiH 4 . The carrier concentration varies between 1 ⫻ 10 17 and 2 ⫻ 10 19 /cm 3 (25). Good linearity

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Figure 6 Carrier concentration as a function of the reciprocal of the temperature.

Figure 7 Carrier concentrations of Si-doped GaN films as a function of the flow rate of SiH 4 .

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Figure 8 Photoluminescence spectra of Si-doped GaN films grown with GaN buffer layers under the same growth conditions except for the flow rate of SiH 4 . The flow rates of SiH 4 were (a) 2 nmol/min and (b) 10 nmol/min. The carrier concentrations were (a) 4 ⫻ 10 18 /cm 3 and (b) 2 ⫻ 10 19 /cm 3 .

is observed between the carrier concentration and the flow rate of SiH 4 . Therefore, Si is considered to be a good donor impurity for GaN in order to control the carrier concentration. Photoluminescence (PL) measurements were performed at room temperature. The excitation source was a 10-mW He-Cd laser. Figure 8 shows the PL spectra of Si-doped GaN films whose carrier concentrations are 4 ⫻ 10 18 and 2 ⫻ 10 19 /cm 3, respectively. In spectra, relatively strong deep-level (DL) emission is observed around 560 nm. The ultraviolet (UV) emission, which is a band edge (BE) emission of GaN, is observed around 380 nm. The intensity of DL emissions is always stronger than that of BE emissions in this range of the flow rate of SiH 4 . Undoped GaN also shows strong DL emissions and weak BE emissions at room temperature. The origin of these strong DL emissions has not been elucidated.

IV. p-TYPE GaN It was impossible to obtain p-type GaN films for a long time. Unavailability of p-type GaN films has prevented III-V nitrides from being used for light-emitting devices, such as blue LEDs and LDs. In 1989, Amano et al. (26) succeeded in obtaining p-type GaN films using Mg doping and post low-energy electron beam irradiation (LEEBI) treatment by means of MOCVD. After the growth, LEEBI treatment was performed for Mg-doped GaN films to obtain a low-resistivity p-type GaN film. The hole concentration and lowest resistivity were 10 17 /cm 3 and 12 Ω ⋅ cm, respectively. These values were still insufficient for fabricating blue LDs and high-power blue LEDs. The effect of the LEEBI treatment was considered to be Mg displacement by the energy of electron beam irradiation. At the first stage of as-grown Mg-doped GaN, the Mg atoms lie in sites different from Ga sites, where they act as acceptors. With LEEBI treatment, the Mg atoms move to the exact Ga sites. In 1992, low-resistivity Mg-doped p-type GaN films were obtained by N 2-ambient thermal

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Figure 9 Resistivity of Mg-doped GaN films as a function of annealing temperature.

annealing at temperatures above 700°C by Nakamura et al. (27). Before thermal annealing, the resistivity of Mg-doped GaN films was approximately 1 ⫻ 10 6 Ω ⋅ cm. After thermal annealing at temperatures above 700°C, the resistivity, hole carrier concentration, and hole mobility became 2 Ω ⋅ cm, 3 ⫻ 10 17 /cm 3, and 10 cm 2 /V ⋅ s, respectively, as shown in Fig. 9. In PL measurements, the intensity of 750-nm deep-level emissions (DL emissions) sharply decreased upon thermal annealing at temperatures above 700°C, as did the change in resistivity, and 450-nm blue emissions showed maximum intensity with thermal annealing at approximately 700°C, as shown in Fig. 10.

Figure 10 Photoluminescence of Mg-doped GaN films that were annealed at different temperatures: (a) room temperature, (b) 700°C, and (c) 800°C.

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Soon, Nakamura et al. (9) proposed a hydrogenation process whereby acceptor-H neutral complexes are formed in p-type GaN films as a compensation mechanism. Low-resistivity ptype GaN films, which were obtained by N 2-ambient thermal annealing or LEEBI treatment, showed a resistivity as high as 1 ⫻ 10 6 Ω ⋅ cm after NH 3-ambient thermal annealing at temperatures above 600°C. In the case of N 2-ambient thermal annealing at temperatures between room temperature and 1000°C, the low-resistivity p-type GaN films showed no change in resistivity, which was almost constant between 2 and 8 Ω ⋅ cm, as shown in Fig. 11. Figure 12a shows the PL spectrum of 800°C N 2 ambient thermal-annealed GaN film, Fig. 12b shows the film after NH 3-ambient thermal annealing at 800°C for the sample in Fig. 12a, and Fig. 12c shows the film after N 2-ambient thermal annealing at 800°C for the sample in Fig. 12b. Before NH 3-ambient thermal annealing, the intensity of blue emissions is strong, and broad DL emissions are not observed around 750 nm (see Fig. 12a). After NH 3-ambient thermal annealing at 800°C for the sample in Fig. 12a, the intensity of blue emissions becomes weaker, and DL emissions around 750 nm appear (see Fig. 12b). The PL spectrum recovers after N 2-ambient thermal annealing at 800°C. These changes in PL spectra were found to be reversible with change in the annealing ambient gas from NH 3 to N 2, as is the case with the resistivity change. These results indicate that atomic hydrogen produced by NH 3 dissociation at temperatures above 400°C is related to the acceptor compensation mechanism. A hydrogenation process whereby acceptor-H neutral complexes are formed in p-type GaN films was proposed. The formation of acceptor-H neutral complexes causes acceptor compensation and deep-level and weak blue emissions in photoluminescence. At temperatures above 400°C, dissociation of NH 3 into hydrogen atoms occurs at the surface of GaN films because dangling bonds exist mainly at the surface, and the atomic hydrogen easily diffuses into the GaN films because the number of hydrogen atoms is too great at the surface and the hydrogen atoms are very small. First, the atomic hydrogen, produced by dissociation of NH 3 at temperatures above 400°C, diffuses into p-type GaN films. Second, the formation of acceptor-H neutral complexes, i.e., Mg-H complexes in GaN films, occurs. As a result, the formation of Mg-H complexes causes hole compensation, and the resistivity of Mg-doped GaN films reaches a maximum of 1 ⫻ 10 6 Ω ⋅ cm (see Fig. 11). For PL measurements, it is assumed that DL emissions are caused by related levels of Mg-H complexes, and blue emissions are caused by Mg-related levels. When these proposals

Figure 11 Resistivity change in N 2-ambient thermal-annealed low-resistivity Mg-doped GaN films as a function of annealing temperature. The ambient gases NH 3 and N 2 were used for thermal annealing.

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Figure 12 PL spectra of Mg-doped GaN films that were continuously annealed under different conditions: (a) GaN film after 800°C N 2-ambient thermal annealing of the Mg-doped GaN film; (b) GaN film after 800°C NH 3-ambient thermal annealing of the GaN film in (a); (c) GaN film after 800°C N 2-ambient thermal annealing of the GaN film in (b).

are applied to the results of the PL measurements in Figs. 10 and 12, the results are quite well explained. The change in the PL spectra of Fig. 10 is easily explained using these models. When the N 2-ambient thermal annealing temperature exceeds 400°C, removal of atomic hydrogen from Mg-H complexes begins, the number of blue emission centers that are Mg-related radiative recombination centers begins to increase, and the intensity of blue emissions of the PL spectrum gradually increases. However, when the temperature reaches approximately 700°C, the effects of N vacancies produced by the dissociation of GaN films (mainly near the surface) begin to exceed those of the increased number of Mg-related radiative recombination centers. As a result, the intensity of blue emissions shows a maximum around 700°C in N 2-ambient thermal annealing of as-grown GaN films (see Fig. 10). In the NH 3-ambient thermal annealing of Figs. 11 and 12, Mg-H complexes are not formed below 400°C, but Mg-H complexes are formed above 400°C in Mg-doped GaN films because the amount of atomic hydrogen diffused into the bulk of the GaN films is not great until the temperature exceeds 400°C. As a result, the resistivity of NH 3-ambient thermal-annealed GaN films above 400°C becomes higher (almost insulating) in Fig. 11, and the intensity of blue emissions of NH 3-ambient thermal-annealed GaN films at 800°C becomes weaker than that of N 2-ambient thermal-annealed GaN films at 800°C because the number of Mg-related levels is reduced by formation of Mg-H complexes under NH 3-ambient thermal annealing (see Fig. 12). With NH 3-ambient thermal annealing at 800°C, DL emissions can be observed because Mg-H complexes are formed. With N 2-ambient thermal annealing at 800°C, DL emissions cannot be observed because atomic hydrogens are removed from Mg-H complexes and the number of Mg-H complexes is reduced dramatically (see Fig. 12). Usually, NH 3 is used as the N source for GaN growth in MOCVD. Therefore, an in situ

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hydrogenation process in which Mg-H complexes are formed during MOCVD growth naturally occurs, and the resistivity of as-grown Mg-doped GaN films becomes high (almost insulating). After the growth, N 2-ambient thermal annealing can reactivate the acceptors by removing atomic hydrogen from the acceptor-H neutral complexes in p-type GaN films. As a result, the resistivity of p-type GaN films becomes lower and the intensity of blue emissions becomes stronger. This hydrogenation process is now accepted as the acceptor compensation mechanism of p-type IIIV nitride by many researchers (9–13).

V.

GaN p-n JUNCTION BLUE LEDS

High-quality GaN films were grown using GaN or AlN buffer layers as Hall mobility value of undoped GaN films grown with GaN buffer layers was 600 cm 2 /V ⋅ s at room temperature (23). The carrier concentration of n-type GaN films was controlled between 1 ⫻ 10 17 and 2 ⫻ 10 19 / cm 3 by Si doping of GaN (25). The hole concentrations of p-type Mg-doped GaN films grown with GaN buffer layers were of the order of 1 ⫻ 10 18 /cm 3 (28). Because of these results, there is great interest in fabricating emitting devices using GaN films grown with buffer layers. Using these techniques, Nakamura et al. (29) fabricated GaN p-n junction blue LEDs in 1991. Here, GaN p-n junction blue LEDs are described. The structure of a GaN p-n junction LED is shown in Fig. 13 (29). The carrier concentration of the n-type GaN layer was 5 ⫻ 10 18 /cm 3 and that of the p-type GaN layer was about 8 ⫻ 10 18 /cm 3. Si was doped into the n-type GaN layer as a donor impurity. Mg was doped into the p-type GaN layer as an acceptor impurity. After the growth, thermal annealing or LEEBI treatment was performed in order to obtain a low-resistivity p-type GaN layer. Electroluminescence (EL) of the LED is shown in Fig. 14. The peak wavelength and the FWHM of the EL are 430 nm and 55 nm, respectively, at 10 mA. According to Amano et al. (26) and Amano and Akasaki (22), the EL of GaN LEDs showed two peaks, one at 370 nm (UV EL) and the other at 430 nm (blue EL), when the forward current was lower than 30 mA. In the present LEDs, however, there was a strong blue EL and no UV EL when the forward current was lower than 30 mA. Also, there were weak deep-level emissions whose peak wave-

Figure 13 Structure of the GaN p-n junction LED.

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Figure 14 Emission spectra of the GaN p-n junction LED at different forward currents. Hole concentration of the p-type GaN of the LED was 8 ⫻ 10 18 /cm 3.

length was 550 nm. At 50 mA, a weak UV EL whose peak wavelength was 390 nm was observed (see Fig. 14). This peak wavelength (390 nm) of UV EL is longer than that of previously reported LEDs (370 nm) (22,26). The forward current density of LEDs is almost the same as that of previously reported LEDs because the chip size of the present LEDs (0.6 ⫻ 0.5 mm) is almost the same as that of LEDs with AlN buffer layers (22,26). Therefore, it is difficult to conclude that the difference in the current density caused these EL differences. Amano et al. (26) and Amano and Akasaki (22) attributed the origin of the blue EL to the emission in the p-type GaN layer: electrons were injected from the n-type GaN layer to the p-type GaN layer, and blue emission occurred through recombination. Therefore, it is considered that the number of radiative recombination centers of blue emission in the p-type GaN layer is much larger than that in the previous LEDs because the intensity of the blue EL is much stronger than that of UV EL in GaN LEDs with GaN buffer layers (see Fig. 14), assuming that the intensity of UV EL is almost the same in the present LEDs and previously reported LEDs. Considering that the hole concentration of the p-type GaN layer with GaN buffer layers (about 8 ⫻ 10 18 /cm 3 ) is much higher than that with AlN buffer layers (typical value is of the order of 10 16 /cm 3 ), such a proposal is probably correct, because blue emission centers are related to the energy level introduced by Mg doping in the energy gap of GaN, and the intensity of the blue emission in PL measurement of the p-GaN layer becomes strong when the hole concentration becomes high (26–28). Therefore, in the present LEDs, UV EL was not observed below than 30 mA, and the UV EL intensity was very weak above 30 mA in comparison with those of previously reported LEDs. The peak wavelength of

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UV EL of the present LEDs (390 nm) is longer than that of the LEDs of Amano et al. (370 nm) (26). Amano et al. (26) and Amano and Akasaki (22) used an undoped GaN layer as the n-type GaN layer for their LEDs, and the peak wavelength of UV EL was 370 nm. Considering this result, the longer peak wavelength of UV EL (390 nm) may be caused by Si doping of the n-type GaN layer, because the UV EL was caused by hole injection from the p-type GaN layer to the n-type GaN layer, and UV emission occurred in the n-type GaN layer through radiative recombination. A relatively strong UV EL against the blue EL was observed in the present GaN LEDs when the crystal quality of the GaN film was poor and the hole concentration of the ptype GaN layer was as low as 1 ⫻ 10 17 /cm 3. This is shown in Fig. 15. The shape of the EL and the hole concentration of this LED were almost the same as those of the LEDs previously reported by Amano et al. (26). Considering that the hole concentration is as low as 1 ⫻ 10 17 / cm 3, this weak blue EL is related to the small number of radiative recombination centers in the p-type GaN layer that contributes to the blue EL, and UV EL becomes dominant. The output power of this LED, which had a low hole concentration (1 ⫻ 10 17 /cm 3 ), was very low (about one fourth) in comparison with that of LEDs that had a high hole concentration (8 ⫻ 10 18 / cm 3 ). This LED was easily broken over 50 mA. On the other hand, LEDs that had a high hole concentration (8 ⫻ 10 18 /cm 3 ) were not broken even at 100 mA. The 550-nm deep-level emissions may be caused by hole injection from the p-type GaN layer to the n-type GaN layer, similarly to the UV EL, because the intensity of deep-level emissions becomes strong when the UV EL becomes strong (see Figs. 14 and 15) and the PL measurement of the n-type GaN layer shows deep-level emissions.

Figure 15 Emission spectra of the GaN p-n junction LED at different forward currents. Hole concentration of the p-type GaN of the LED was 1 ⫻ 10 17 /cm 3.

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Figure 16 Output power (P) of the GaN p-n junction LED and the conventional 8-mcd SiC LED as a function of the forward current (I F ). m is an exponent of I F when it is assumed that P is proportional to I mF .

The output power is shown as a function of the forward current in Fig. 16. Commercially available SiC LEDs whose brightness is 8 mcd and peak wavelength is 480 nm are also shown for comparison with GaN LEDs. The output power of GaN LEDs is almost 10 times stronger than that of SiC LEDs in the range of forward current between 1 and 4 mA. At 4 mA, the output power of GaN LEDs is 20 µW and that of SiC LEDs 2 µW. At 20 mA, the output power of GaN LEDs is 42 µW and that of SiC LEDs 7 µW. Generally in LEDs, the output power (P) is proportional to I mF (I F is forward current). If the recombination current is dominant, m becomes 2; if the diffusion current is dominant, m becomes 1. In the range of DC current between 0.2 and 0.8 mA (low current range) in GaN LEDs, m is almost equal to 2.23. Between 1 and 4 mA (intermediate current range), it is 1.15. Over 6 mA (high current range), it is 0.41. Therefore, the recombination current is dominant in the low current range and the diffusion current becomes dominant in an intermediate current range. Generation of heat may have caused the low output power in the high current range. In SiC LEDs, m was almost equal to 0.73 between 0.2 and 30 mA. The highest external quantum efficiency, 0.18%, was obtained in an intermediate current range for GaN LEDs and 0.02% was obtained for SiC LEDs. Blue EL was dominant below 50 mA (see Fig. 14). Therefore, these changes in output power are caused by the change in the intensity of the blue EL. High-power GaN p-n junction blue LEDs were fabricated using GaN films grown with GaN buffer layers. The external quantum efficiency was as high as 0.18%. The output power was almost 10 times higher than that of conventional 8-mcd SiC blue LEDs. The forward voltage was 4 V at 20 mA. The recombination current was dominant below 1 mA. Therefore, further

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improvement of the crystal quality is required to obtain high-power GaN p-n junction blue LEDs.

VI. InGaN Utilizing an (In,Ga,Al)N system, a band gap energy from 1.95 to 6.2 eV can be chosen. For high-performance optical devices, a double-heterostructure is indispensable. This material enables double-heterostructure construction. In this system, the ternary III-V semiconductor compound InGaN is one candidate as the active layer for the blue and green emissions because its band gap varies from 1.95 to 3.4 eV depending on the indium mole fraction. If the InGaN semiconductor compound is used as an active layer in the double heterostructure, a InGaN/ AlGaN double heterostructure can be considered for blue-emitting devices because p-type conduction has been obtained for AlGaN in the (In,Ga,Al)N system. Up to now, only a little research has been performed on InGaN growth (30–32). InGaN crystal growth was originally performed at low temperatures (about 500°C), to prevent InN dissociation during growth, by means of MOCVD (30,31). Later, relatively high-quality InGaN films were obtained on a (0001) sapphire substrate by Yoshimoto et al. (32) using a high growth temperature (800°C) and a high indium mole fraction flow rate. They reported that deep-level emissions were dominant in PL measurements of the InGaN film at room temperature and that the FWHM of the double-crystal XRC for (0002) diffraction from the InGaN films was about 30 min. Nakamura and Mukai (33) also grew InGaN films on GaN films with a high indium source flow rate and high growth temperatures between 780 and 830°C. They observed strong and sharp band edge (BE) emissions of InGaN between 400 and 445 nm in PL at room temperature. Figure 17 shows the double-crystal XRC for the (0002) diffraction of InGaN films grown on the GaN films. Curve (a) represents InGaN films grown at a temperature of 830°C (sample A) and curve (b) those grown at a temperature of 780°C (sample B). Both curves clearly show two peaks. One is the (0002) peak of the X-ray diffraction of GaN, and the other is that of InGaN. The indium mole fraction of the InGaN films was estimated by calculating the difference between the positions of the InGaN and GaN peaks assuming that the (0002) peak of the Xray diffraction of GaN is constant at 2θ ⫽ 34.53° and Vegard’s law is valid. These calculated values of the indium mole fraction of the InGaN films of 0.14 for sample A and 0.24 for sample B, shown in Fig. 17. Therefore, the incorporation rate of indium in the InGaN film during growth is increased when the growth temperature is decreased. The FWHM of the double-crystal XRC for the (0002) diffraction from the InGaN film was about 8 min and that from the GaN film was 6 min for sample A. The FWHM of the XRC for the (0002) diffraction from the InGaN film was about 9 min and that from the GaN film was 7 min for sample B. The values of FWHM of InGaN films are almost the same as those of the GaN films that are used as substrates. Figure 18 shows the results of PL measurements at room temperature. The excitation source was a 10-mW He-Cd laser. Curve (a) represents sample A and curve (b) sample B. Sample A shows a strong sharp peak at 400 nm and sample B at 438 nm. These emissions are considered to be the BE emissions of InGaN films because they have a very narrow FWHM (about 70 meV for sample A and 110 meV for sample B). The broad deep-level emissions, which were considered to originate from defects such as nitrogen vacancies in InGaN films and were dominant in the PL measurements of Yoshimoto et al. (32), were barely observed in this study. These results of PL measurements also indicate that the crystal quality of InGaN films grown on the GaN films is very good, as is also shown by the XRC measurements.

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Figure 17 The XRC for (0002) diffraction from InGaN films grown on GaN films under the same conditions except for the InGaN growth temperature. The growth temperatures of InGaN were (a) 830°C and (b) 780°C.

Nakamura (34) also grew InGaN films with an indium mole fraction X up to X ⫽ 0.33 at temperatures between 720 and 850°C. The growth rate of InGaN films had to be decreased sharply to obtain high-quality InGaN films when the growth temperature was decreased. Band gap energies between 2.67 and 3.40 eV obtained by room-temperature PL measurements fit quite well to parabolic forms on the indium mole fraction X assuming that the band gap energies for GaN and InN are 3.40 and 1.95 eV, respectively, as shown in Fig. 19. Figure 19 shows the band gap energy of grown InGaN films as a function of the indium mole fraction X (34). The bandgap energy was obtained by room-temperature PL measurements assuming that the narrow sharp emissions in the violet and blue regions are BE emissions. The indium mole fraction of the InGaN films was determined by measurements of X-ray diffraction peaks. Osamura et al. (35) had already shown that E g in ternary alloys In X Ga (1⫺X)N obeys parabolic forms on the molar fraction X: E g (X) ⫽ X)E g,InN ⫹ (1 ⫺ X)E g,GaN ⫺ bX(1 ⫺ X)

(1)

where E g (X ) represents the band gap energy of In XGa (1⫺X)N; E g,InN and E g,GaN represent the band gap energy of compounds InN and GaN, respectively; and b is the bowing parameter. In that calculation, E g,InN was 1.95 eV, E g,GaN was 3.40 eV, and b was 1.00 eV. These values calculated from Eq. (1) are shown by the solid curve in Fig. 19. The solid curve fits the experimental data quite well between indium mole fractions X ⫽ 0.07 and X ⫽ 0.33.

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Figure 18 Room-temperature PL spectra of InGaN films grown on GaN films under the same growth conditions except for the InGaN growth temperature. The growth temperatures of InGaN were (a) 830°C and (b) 780°C.

VII. IMPURITY DOPING OF InGaN Si-doped InGaN films were grown on GaN films by Nakamura et al. (36). Figure 20 shows typical results of PL measurements of an Si-doped InGaN film that was grown at a temperature of 830°C and a SiH 4 flow rate of 1.5 nmol/min. The PL measurements were performed at room temperature. Very strong and sharp violet emission at 400 nm was observed, but deep-level emissions were not observed in this spectrum, shown in Fig. 20. This violet emission is considered to be a BE emission of Si-doped InGaN because the FWHM of violet emission is very small (about 140 meV). Nakamura and Mukai (33) also reported on undoped InGaN films that were grown under the same growth conditions as in this study without SiH 4 gas flow. Comparing the Si-doped InGaN with undoped InGaN, the peak position of 400 nm of the BE emissions at an indium mole fraction (X) of 0.14 is not changed by Si doping, but the intensity of BE emissions of Si-doped InGaN films becomes much stronger than that of undoped InGaN films. This is shown in Fig. 21. Figure 21 shows the relative intensity of BE emissions of PL measurements of Si-doped and undoped InGaN films as a function of the SiH 4 flow rate. These InGaN films were grown at a temperature of 830°C under the same conditions except for the SiH 4 flow rates. The peak wavelength of BE emissions of these InGaN films was 400 nm and the indium mole fraction determined by measurements of the X-ray diffraction peaks was 0.14. At an SiH 4 flow rate of 0.22 nmol/min, the intensity of BE emissions became 20 times stronger than that of undoped InGaN films. At an SiH 4 flow rate of 1.50 nmol/min, the intensity of BE emissions became 36 times stronger than that of undoped InGaN films. However, at an SiH 4 flow rate of 4.46 nmol/ min, the intensity of BE emissions became weak. Therefore, it is considered that the optimal SiH 4 flow rate is around 1.50 nmol/min, judging from the intensity of the BE emissions under these growth conditions.

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Figure 19 Band gap energy of In X Ga (1⫺X) N films as a function of the indium mole fraction X. The indium mole fraction X was determined by measurements of the X-ray diffraction peaks. The solid curve represents values that were obtained from Eq. (1) as discussed in the text, assuming that the band gap energies for GaN and InN are 3.40 and 1.95 eV, respectively.

Figure 20 Room-temperature PL spectrum of Si-doped InGaN film grown at an SiH 4 flow rate of 1.5 nmol/min and a growth temperature of 830°C.

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Figure 21 Relative PL intensity of the band edge emissions of Si-doped InGaN films as a function of the SiH 4 flow rate. The growth temperature of the Si-doped InGaN films was 830°C.

This Si doping of InGaN films may form shallow donor levels in InGaN, as does Si doping of GaN films (25). The carrier concentrations of InGaN increased from 10 17 to 10 19 /cm 3 with Si doping at an SiH 4 flow rate of 1.50 nmol/min. This may explain why the intensity of the BE emissions of Si-doped InGaN films becomes stronger. Nakamura (37) performed Zn doping of InGaN for the purpose of obtaining blue emission centers. Figure 22 shows typical results of room-temperature PL measurements of the Zn-doped InGaN films. Spectrum (a) represents a Zn-doped InGaN film that was grown at a temperature of 800°C and a diethylzinc (DEZ) flow rate of 8.0 nmol/min (sample A). Spectrum (b) represents a Zn-doped InGaN film that was grown under the same conditions as sample A except for the growth temperature and DEZ flow rate, which were changed to 810°C and 2.7 nmol/min (sample B). Both spectra clearly show two peaks. Spectrum (a) shows peak emissions at 410 nm (3.02 eV) and 494 nm (2.52 eV). Spectrum (b) shows peak emissions at 398 nm (3.12 eV) and 462 nm (2.68 eV). The shorter wavelength peak is the BE emission of InGaN, and the longer wavelength peak is Zn-related emission with a large value of FWHM (about 66 nm). The difference in peak emission energy between the BE and Zn-related emissions is 0.50 eV for spectrum (a) and 0.44 eV for spectrum (b). Figure 23 shows the Zn-related emission energy as a function of the indium mole fraction X of In X Ga (1⫺X )N. Curve (a) shows the band gap energy of In X Ga (1⫺X )N, which was calculated using Eq. (1). Curves (b) and (c) show the energy levels that are 0.4 and 0.5 eV below the band gap energy of In X Ga (1⫺X )N, respectively. From this figure, it is noted that 2.51 eV (494 nm) to 2.83 eV (438 nm) between X ⫽ 0.16 and X ⫽ 0.07 can be obtained as Zn-related emission energy in Zn-doped InGaN. Also, the Zn-related emission energy is always between 0.4 and 0.5 eV lower than the BE emission energy of InGaN in this Zn doping range. Zn doping of GaN has been performed by many researchers in order to obtain blue emissions for application to blue LEDs (38,39). Peak energy shifts from blue emission at a low Zn concentration to red

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Figure 22 Room-temperature PL spectra of Zn-doped InGaN films grown under the same conditions except for the InGaN growth temperatures and DEZ flow rates. The growth temperatures of InGaN were (a) 800°C and (b) 810°C. The flow rates of DEZ were (a) 8.0 nmol/min and (b) 2.7 nmol/min.

Figure 23 Zn-related emission energy as a function of the indium mole fraction X of In X Ga 1⫺X N. Curve (a) shows the band gap energy of In X Ga 1⫺X N calculated using Eq. (1). Curves (b) and (c) show energy levels 0.4 and 0.5 eV below the band gap energy of In X Ga 1⫺X N, respectively.

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Figure 24 Room-temperature PL spectra of Si-and Zn-doped InGaN films. Spectrum (a) represents typical Si-doped InGaN films grown at an SiH 4 flow rate of 1.5 nmol/min and a temperature of 800°C. Spectrum (b) represents a Zn-doped InGaN film that was grown under the same conditions as in Fig. 22a. The indium mole fraction X was 0.16 for both films.

at a high Zn concentration have been observed. Therefore, Zn doping of GaN forms many deeper Zn-related levels above the valence band, depending on the Zn concentration in GaN. On the other hand, Zn doping of InGaN results in values between 0.4 and 0.5 eV lower than the BE emission energy of In X Ga (1⫺X )N as a Zn-related emission energy under these growth conditions. Figure 24 shows PL spectra of Si- and Zn-doped InGaN films. Spectrum (b) represents a Zn-doped InGaN film that was grown under the same conditions as in Fig. 22a at a DEZ flow rate of 8.0 nmol/min. Spectrum (a) represents typical Si-doped InGaN films grown at an SiH 4 flow rate of 1.50 nmol/min and a temperature of 800°C. The indium mole fraction X was 0.16 for both spectra (a) and (b). Spectrum (b) shows strong blue emission at 492 nm with a broad FWHM (66 nm) and weak BE emission at 410 nm, and spectrum (a) shows strong violet emission at 410 nm with a narrow FWHM (20 nm). The intensity of the blue emission of spectrum (b) is almost the same as that of the violet emission of spectrum (a). Therefore, Zn-doped InGaN films have potential for use as the active layer of InGaN/AlGaN DH-structure blue LEDs with bright blue emissions.

VIII.

InGaN/AlGaN DH LED

Figure 25 shows the structure of InGaN/AlGaN DH LEDs (14–17). As a buffer layer, GaN was used instead of AlN. For cladding layers of DH structure, Al 0.15Ga 0.75N was used. As an active layer, an InGaN layer codoped with Si and Zn was used to enhance blue emissions. When

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Figure 25 Structure of the InGaN/AlGaN DH LEDs.

Si and Zn were codoped into an InGaN active layer, the intensity of blue emission became maximum around the electron carrier concentration of 1 ⫻ 10 19 cm ⫺3. This codoping suggests that the high-efficiency of this InGaN/AlGaN DH LED is the result of impurity-assisted recombination, such as free carrier–acceptor (FA) recombination. A p-type GaN layer was used as a contact layer for a p-type electrode in order to improve the ohmic contact. After the growth, N 2ambient thermal annealing was performed to obtain a highly p-type GaN layer at a temperature of 700°C. Fabrication of LED chips was accomplished as follows: the surface of the p-type GaN layer was partially etched until the n-type GaN layer was exposed. Next, an Ni/Au contact was evaporated onto the p-type GaN layer and a Ti/Al contact onto the n-type GaN layer. The wafer was cut into a rectangular shape (350 ⫻ 350 µm). These chips were set on a lead frame and were then molded. The characteristics of LEDs were measured under DC-biased conditions at room temperature. Figure 26 shows electroluminescence (EL) spectra of InGaN/AlGaN DH blue LEDs at forward currents of 0.1, 1, and 20 mA. The carrier concentration of the InGaN active layer in this LED was 1 ⫻ 10 19 cm ⫺3. A typical peak wavelength and FWHM of the EL were 450 nm and 70 nm, respectively, at 20 mA. The peak wavelength shifts to shorter wavelengths with increasing forward current. The peak wavelength is 460 nm at 0.1 mA, 449 nm at 1 mA, and 447 nm at 20 mA. At 20 mA, a narrower, higher energy peak emerges around 385 nm, as shown in Fig. 26. This peak is due to band-to-band recombination in the InGaN active layer. This peak becomes resolved at injection levels at which the impurity-related recombination is saturated. The output power of the InGaN/AlGaN DH blue LEDs is 1.5 mW at 10 mA, 3 mW at 20 mA, and 4.8 mW at 40 mA. The external quantum efficiency is 5.4% at 20 mA. The typical on-axis luminous intensity of InGaN/AlGaN LEDs with 15° conical viewing angle is 2.5 cd at 20 mA. The forward voltage was 3.6 V at 20 mA. Blue-green LEDs were fabricated for application to traffic lights by increasing the indium mole fraction of the InGaN active layer from 0.06 to 0.19 in the blue LEDs (16,17). Figure 27 shows the EL spectra of the blue-green InGaN/AlGaN DH LEDs at forward currents of 0.5, 1, and 20 mA. A typical peak wavelength and FWHM of the EL were 500 nm and 80 nm, respectively, at 20 mA. The peak wavelength shifts to shorter wavelengths with increasing forward

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Figure 26 EL spectra of InGaN/AlGaN DH blue LEDs with different forward currents.

current. The peak wavelength is 537 nm at 0.5 mA, 525 nm at 1 mA, and 500 nm at 20mA. The output power of the InGaN/AlGaN DH blue-green LEDs is 1.0 mW at 20 mA. The external quantum efficiency is 2.1% at 20 mA. A typical on-axis luminous intensity of InGaN/AlGaN blue-green LEDs with 15° conical viewing angle is 2 cd at 20 mA. This luminous intensity is sufficiently bright for outdoor applications, such as traffic lights and displays. The forward voltage was 3.5 V at 20 mA. Figure 28 shows the EL spectrum of the InGaN/AlGaN DH violet LEDs at forward currents of 1 and 20 mA (34). These violet LEDs were grown under the same conditions as blue and blue-green LEDs, except for the InGaN active layer. During InGaN growth, only Si was doped without Zn. The typical output power was 1.5 mW and the external quantum efficiency was as high as 2.3% at a forward current of 20 mA at room temperature. The peak wavelength and the FWHM of the EL were 385 nm and 10 nm, respectively. These InGaN/AlGaN DH violet LEDs will be very useful for the realization of violet LDs in the near future because the emission is very sharp and strong. Figure 29 shows the external quantum efficiencies as a function of the peak wavelength of various commercially available LEDs. Judging from this figure, there are no LED materials except for InGaN that have high efficiencies over 1% below the peak wavelength of 550 nm. Therefore, InGaN is one of the most promising materials for LEDs and LDs with peak wavelengths between 550 and 360 nm. Among II-VI materials, a ZnSe/ZnTeSe DH green LED has been reported (1–3). The output power, external quantum efficiency, and peak wavelength of those II-VI LEDs are 1.3 mW, 5.3%, and 512 nm at a forward current of 10 mA. A ZnSe/ZnCdSe

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Figure 27 EL spectra of InGaN/AlGaN DH blue-green LEDs with different forward currents.

Figure 28 EL spectra of InGaN/AlGaN DH violet LEDs with different forward currents.

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Figure 29 External quantum efficiencies as a function of the peak wavelength of various commercially available LEDs.

DH blue LED also had an output power, external quantum efficiency, and peak wavelength of 0.3 mW, 1.3%, and 489 nm at a forward current of 10 mA. However, a lifetime of these II-VI LEDs is only a few hundred hours at room-temperature operation. Because of this poor reliability, II-VI LEDs and LDs have never been commercialized. Therefore, II-VI LEDs are not shown in Fig. 29. Table 1 shows a comparison of commercially available red, green, and blue LEDs in terms of luminous intensity, output power, and external quantum efficiencies. From this table, the peak wavelength of green and blue III-V nitride LEDs is much shorter than that of conventional green GaP and blue SiC LEDs. Also, the output power and the external quantum efficiencies of III-V nitride LEDs are much higher than those of conventional green and blue LEDs. Table 1 Comparison of Commercially Available Red, Green, and Blue LEDS

LED

Material

Peak wavelength (nm)

Red Green

GaAlAs GaP InGaN SiC InGaN

660 555 500 470 450

Blue

Luminous intensity (mcd)

Output power (µW)

External quantum efficiency (%)

1790 63 2000 9 2500

4855 30 1000 11 3000

12.83 0.07 2.01 0.02 5.45

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IX. QUANTUM WELL STRUCTURES Nakamura et al. (40) grew two kinds of In 0.22Ga 0.78 N/In 0.06Ga 0.94 N multi-quantum-well (MQW) structures on GaN films. One was MQW-100, in which the thicknesses of both barrier (L B ) and ˚ (L B ⫽ L W ⫽ 100 A ˚ ) and the number of periods was 10. The other well layers (L W ) were 100 A ˚ (L B ⫽ L W ⫽ 30 was MQW-30, in which the thicknesses of barrier and well layers were 30 A ˚ A) and the number of periods was 20. Figure 30 shows the XRC for (0002) diffraction from In xGa (1⫺X) N/In yGa (1⫺y) N MQW structures grown on GaN films. Curve (a) represents MQW-100 and curve (b) MQW-30. Both curves clearly show three peaks, which are the (0002) peak of the X-ray diffraction of GaN, a zeroth-order peak marked ‘‘0,’’ and satellite peak marked ‘‘⫺1’’ associated with the MQW structures. The FWHMs of the zeroth-order peak and GaN underlayer peak were 7.1 and 5.4 min for MQW-100, and 6.3 and 4.3 min for MQW-30. The In x Ga (1⫺x) N/In yGa(1⫺y) N MQW period (L B ⫹ L W ) can be accurately determined using the equation (2 sin Θ n ⫺ 2 sin Θ SL ) ⫽ ⫾ nλ/(L B ⫹ L B ), where λ is the X-ray wavelength, n is the order of satellite peaks, Θ n is their diffraction angle, and Θ SL is the Bragg angle of the ˚ as the period (L B zeroth-order peak. Using this equation, Nakamura et al. (40) estimated 194 A ˚ ˚ for ⫹ L W ) for MQW-100 and 64 A for MQW-30. These values were almost equal to 200 A ˚ MQW-100 and 60 A for MQW-30, which were determined by the GaN growth rate and the gallium source flow rate. Figure 31 shows the results of room-temperature PL measurements of an In 0.22Ga 0.78 N/ In 0.06Ga 0.94 N MQW structure. Curve (a) represents MQW-100 and curve (b) MQW-30. MQW100 shows a strong sharp peak at 420 nm (2.952 eV) and MQW-30 exhibits one at 412 nm (3.010 eV). Both curves show no deep-level emissions. The intensities of these peak emissions

Figure 30 The XRC for (0002) diffraction from In X Ga (1⫺X)N/In yGa (1⫺y)N MQW structures grown on GaN films under the same growth conditions except for the period (L B ⫹ L W ). The periods were (a) 200 ˚ and (b) 60 A ˚. A

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Figure 31 Room-temperature PL spectra of In xGa (1⫺X) N/In yGa (1⫺y) N MQW structures grown on GaN ˚ and films under the same growth conditions except for the period (L B ⫹ L W ). The periods were (a) 200 A ˚. (b) 60 A

were about twice as strong as that of BE emission of bulk InGaN, and the FWHMs were 26 and 22 nm for samples A and B. These emissions are considered to be due to radiative transitions between quantum energy levels in the MQW structures. High-quality In 0.22Ga 0.78 N/In 0.06Ga 0.94 N MQW structures were grown on GaN films with ˚ . Double-crystal XRC measurements showed satellite peaks that indiperiods of 60 and 200 A cated the existence of the In 0.22Ga 0.78 N/In 0.06Ga 0.94 N MQW structure. The quantum effects were observed through room-temperature PL measurements. These high-quality MQW structures can be used for an active layer of blue LEDs and LDs.

X.

InGaN LEDs WITH QUANTUM WELL STRUCTURES

High-brightness blue and blue-green InGaN/AlGaN DH LEDs with a luminous intensity of 2 cd have been fabricated and are now commercially available, (14–17). In order to obtain blue and blue-green emission centers in these InGaN/AlGaN DH LEDs, Zn doping of the InGaN active layer was performed. Although these InGaN/AlGaN DH LEDs produced a high-power light output in the blue and blue-green region with a broad emission spectrum (FWHM ⫽ 70 nm), green or yellow LEDs that have a peak wavelength longer than 500 nm have not been fabricated. The longest peak wavelength of the electroluminescence of InGaN/AlGaN DH LEDs achieved thus far is 500 nm (blue-green) because the crystal quality of the InGaN active layer of DH LEDs becomes poor when the indium mole fraction is increased in order to obtain a green band-edge emission. On the other hand, in conventional green GaP LEDs the external quantum efficiency is only 0.1% because of the indirect transition band gap material and the peak wavelength is 555 nm (yellowish green) (41). As another material for green emission devices, AlInGaP has been used. The present performance of green AlInGaP LEDs is an emission wavelength of 570 nm (yellowish green) and maximum external quantum efficiency of 1% (41,42). When the emission

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wavelength is reduced to the green region, the external quantum efficiency drops sharply because the band structure of AlInGaP becomes close to an indirect transition band structure. Therefore, high-brightness pure green LEDs, which have a high efficiency of above 1% at a peak wavelength between 510 and 530 nm with a narrow FWHM, have not yet been commercialized. Among II-VI materials, ZnSSe- and ZnCdSe-based materials have been intensively studied for use in green light–emitting devices, and much progress has been made. The performance of II-VI green LEDs is an output power of 1.3 mW, external quantum efficiency of 5.3% at 10 mA, and peak wavelength of 512 nm (1–3). However, the lifetime of II-VI–based devices is still short, which prevents their commercialization at present. Nakamura (34) reported violet InGaN/AlGaN DH LEDs with a narrow spectrum (FWHM ⫽ 10 nm) at a peak wavelength of 400 nm originating from the band-to-band emission of InGaN. However, the output power and the external quantum efficiency of the violet InGaN/AlGaN DH LEDs were only 1 mW and 1.6%, respectively, probably because of the formation of misfit ˚ ) caused by the stress introduced in dislocations in the thick InGaN active layer (about 1000 A the InGaN active layer by lattice mismatch and the difference in thermal expansion coefficients between the InGaN active layer and AlGaN cladding layers. When the InGaN active layer becomes thin, the elastic strain is not relieved by the formation of misfit dislocations and the crystal quality of the InGaN active layer improves. A high-quality InGaN MQW structure with ˚ well and 30-A ˚ barrier layers has been described (40). Here, quantum-well (QW) structure 30-A ˚ ) in order to obtain high-power emission LEDs that have a thin InGaN active layer (about 20 A in the region from blue to yellow with a narrow emission spectrum are described. ˚ GaN buffer layer grown The green LED device structures (Fig. 32) consist of a 300-A ˚ -thick layer of at a low temperature (550°C), a 4-µm-thick layer of n-type GaN: Si, a 1000-A ˚ ˚ n-type Al 0.1Ga 0.9 N: Si, a 500-A-thick layer of n-type In 0.05Ga 0.95 N :Si, a 20-A-thick active layer ˚ -thick layer of p-type Al 0.1Ga 0.9 N: Mg, and a 0.5-µm-thick of undoped In 0.43Ga 0.57 N, a 1000-A layer of p-type GaN: Mg. The active region forms a single-quantum-well (SQW) structure con˚ In 0.43Ga 0.57 N well layer sandwiched between 500-A ˚ n-type In 0.05Ga 0.95 N and sisting of a 20-A ˚ 1000-A p-type Al 0.1Ga 0.9 N barrier layers. The indium mole fraction of the InGaN active layer was varied between 0.2 and 0.7 in order to change the peak wavelength of the InGaN SQW LEDs from blue to yellow.

Figure 32 The structure of a green SQW LED.

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Figure 33 Electroluminescence of (a) blue, (b) green, and (c) yellow SQW LEDs at a forward current of 20 mA.

Figure 33 shows typical EL of the blue, green, and yellow SQW LEDs with different indium mole fractions in the InGaN well layer at a forward current of 20 mA. The longest emission wavelength is 590 nm (yellow). The peak wavelength and the FWHM of typical blue SQW LEDs are 450 nm and 20 nm, respectively; of green SQW LEDs 525 nm and 45 nm, respectively; and of yellow SQW LEDs 590 nm and 90 nm, respectively. When the peak wavelength becomes longer, the FWHM of the EL spectra increases, probably due to the strain between well and barrier layers of the SQW, which is caused by mismatch of the lattice and thermal expansion coefficients between well and barrier layers. In the green SQW, the indium mole fraction of the InGaN active layer is 0.43, corresponding to the band edge emission wavelength of In 0.43Ga 0.57 N of 490 nm under stress-free conditions (34). On the other hand, the emission wavelength of green SQW LEDs is 525 nm. The energy difference between the peak wavelength of the EL and the stress-free band gap energy is approximately 170 meV. In order to explain this band gap narrowing of InGaN in the SQW, quantum size effects, exciton effects (electron-hole pairs correlated by Coulomb effects) of the active layer, and mismatch of the lattice and thermal expansion coefficients between well and barrier layers must be considered. Among these effects, the exciton effects and the tensile stress caused by the difference in thermal expansion coefficients between well and barrier layers may be primarily responsible for the band gap narrowing of the InGaN in the SQW structure. The output power of the SQW LEDs is shown as a function of the forward current in Fig. 34. The output power of the blue SQW LEDs slightly increases sublinearly up to 40 mA as a function of the forward current. Above 60 mA, the output power almost saturates, probably because of the generation of heat. At 20 mA, the output power and the external quantum efficiency of blue SQW LEDs are 4 mW and 7.3%, respectively, which are much higher than those of InGaN/AlGaN DH LEDs (1.5 mW and 2.7%). Those of the green SQW LEDs are 1 mW and 2.1%, respectively, and those of yellow SQW LEDs are 0.5 mW and 1.2%, respectively. The output power of green and yellow SQW LEDs is relatively small in comparison with that of blue SQW LEDs, probably because of poor crystal quality of the InGaN well layer, which has large lattice mismatch and difference in thermal expansion coefficients between well and

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Figure 34 Output power of (a) blue, (b) green, and (c) yellow SQW LEDs as a function of the forward current.

barrier layers. A typical on-axis luminous intensity of Green SQW LEDs with 10° cone viewing angle is 4 cd at 20 mA. The output power decreases when the peak wavelength becomes longer, probably because of the large strain between well and barrier layers. The output power of green and yellow LEDs is 1 mW (at 525 nm) and 0.5 mW (at 590 nm), respectively. The conventional green GaP LED with a peak wavelength of 555 nm has an output power of 0.04 mW (41). Also, the output power of green AlInGaP LEDs with a peak wavelength of 570 nm is 0.4 mW (41,42). Therefore, the output power of green InGaN SQW LEDs is much higher than that of conventional yellowish green LEDs. Also, the luminous intensity of InGaN green SQW LEDs (4 cd) is about 40 times higher than that of conventional green GaP LEDs (0.1 cd), and the color of InGaN SQW LEDs is greener than those of conventional GaP and AlInGaP LEDs. A typical example of the I-V characteristics of the green SQW LEDs shows that the forward voltage is 3.6 V at 20 mA.

XI. SUMMARY Highly efficient InGaN/AlGaN DH blue LEDs with an external quantum efficiency of 5.4% were fabricated by codoping Zn and Si into the InGaN active layer. The output power was as high as 3 mW at a forward current of 20 mA. The peak wavelength and the FWHM of the EL of blue LEDs were 450 nm and 70 nm, respectively. Blue-green LEDs with a brightness of 2 cd were fabricated by increasing the indium mole fraction of the InGaN active layer. High-brightness blue LEDs with a luminous intensity over 1 cd will pave the way toward realization of full-color LED displays, especially for outdoor use. Total power consumption by traffic lights reaches the gigawatt range in Japan. InGaN/AlGaN blue-green LED traffic lights, with an electrical power consumption 12% that of present incandescent bulb traffic lights, prom-

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ise to save vast amounts of energy. They have an extremely long lifetime of several tens of thousands of hours, so the replacement of burned-out traffic light bulbs will be dramatically reduced. Using these high-brightness blue-green LEDs, safe and energy-efficient roadway and railway signals will be achieved in the near future. High-brightness InGaN green SQW LEDs were fabricated. The luminous intensity was 4 cd and the external quantum efficiency was as high as 2.1% at a forward current of 20 mA at room temperature. The peak wavelength and the FWHM of the green LEDs were 525 nm and 45 nm, respectively, and those of yellow LEDs were 590 nm and 90 nm, respectively. The color of green InGaN SQW LEDs was greener than those of conventional GaP and AlInGaP LEDs. Fabrication of practical visible LEDs in the range from blue to yellow is possible at present using III-V nitride materials. In the near future, III-V nitride blue, violet, or UV LDs with high reliability will be realized because high-quality III-V nitride films are already available and high-power blue LEDs with quantum well structures are also available.

REFERENCES 1. W Xie, DC Grillo, RL Gunshor, M Kobayashi, H Jeon, J Ding, AV Nurmikko, GC Hua, N Otsuka. Room temperature blue light emitting p-n diodes from Zn(S,Se)-based multiple quantum well structures. Appl Phys Lett 60:1999, 1992. 2. H Okuyama, A Ishibashi. Growth of ZnMgSSe and a blue-laser diode. Microelec J 25:643, 1994. 3. DE Eason, Z Yu, WC Hughes, WH Roland, C Boney, JW Cook Jr, JF Schetzina, G Cantwell, WC Harasch. High-brightness blue and green light–emitting diodes. Appl Phys Lett 66:115, 1995. 4. K Koga, T Yamaguchi. Single crystals of SiC and their applications to blue LEDs. Prog Cryst Growth Charact 23:127, 1991. 5. J Edmond, H Kong, V Dmitrieve. Blue/uv emitters from SiC and its alloys. Inst Phys Conf Ser 137: 515, 1994. 6. JI Pankove, EA Miller, JE Berkeyheiser. GaN electroluminescent diodes. RCA Rev 32:283, 1971. 7. S Strite, H Morkoc¸. GaN, AlN and InN: A review. J Vac Sci Technol B10:1237, 1992. 8. H Morkoc¸, S Strite, GB Gao, ME Lin, B Sverdlov, M Burns. Large-band-gap SiC, III-V nitride and II-VI ZnSe-based semiconductor device technologies. J Appl Phys 76:1363, 1994. 9. S Nakamura, N Iwasa, M Senoh, T Mukai. Hole compensation mechanism of p-type GaN films. Jpn J Appl Phys 31:1258, 1992. 10. JA Van Vechten, JD Zook, RD Horning, B Goldenberg. Defeating compensation in wide gap semiconductors by growing in H that is removed by low temperature de-ionizing radiation. Jpn J Appl Phys 31:3662, 1992. 11. M Rubin, N Newman, JS Chan, TC Fu, JT Ross. p-type gallium nitride by reactive ion-beam molecular beam epitaxy with ion implantation, diffusion or coevaporation of Mg. Appl Phys Lett 64:64, 1994. 12. MS Brandt, NM Johnson, RJ Molnar, R Singh, TD Moustakas. Hydrogenation of p-type gallium nitride. Appl Phys Lett 64:2264, 1994. 13. JM Zavada, RG Wilson, CR Abernathy, SJ Pearton. Hydrogenation of GaN AlN and InN. Appl Phys Lett 64:2724, 1994. 14. S Nakamura. Nichia’s 1cd blue LED paves way for full-color display. Nikkei Electronics Asia 6: 65, 1994. 15. S Nakamura, T Mukai, M Senoh. Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes. Appl Phys Lett 64:1687, 1994. 16. S Nakamura, T Mukai, M Senoh. High-brightness InGaN/AlGaN double-heterostructure blue-greenlight-emitting diodes. J Appl Phys 76:8189, 1994. 17. S Nakamura. InGaN/AlGaN blue-light-emitting diodes. J Vac Sci Technol A13:705, 1995.

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18. S Yoshida, S Misawa, S Gonda. Improvements on the electrical and luminescent properties of reactive molecular beam epitaxially grown GaN films by using AlN-coated sapphire substrates. Appl Phys Lett 42:427, 1983. 19. H Amano, N Sawaki, I Akasaki, Y Toyoda. Metalorganic vapor phase epitaxial growth of a high quality GaN film using an AlN buffer layer. Appl Phys Lett 48:353, 1986. 20. H Amano, I Akasaki, K Hiramatsu, N Koide. Effects of the buffer layer in metalorganic vapor phase epitaxy of GaN on sapphire substrate. Thin Solid Films 163:415, 1988. 21. I Akasaki, H Amano, Y Koide, K Hiramatsu, N Sawaki. Effects of AlN buffer layer on crystallographic structure and on electrical and optical properties of GaN and GaAlN films grown on sapphire substrate by MOVPE. J Cryst Growth 98:209, 1989. 22. H Amano, I Akasaki. GaN blue and uv light emitting diodes with a pn-junction. Oyo Buturi 60:163, 1991. 23. S Nakamura. GaN growth using GaN buffer layer. Jpn J Appl Phys 30:L1705, 1991. 24. S Nakamura, T Mukai, M Senoh. In situ monitoring and Hall measurements of GaN grown with GaN buffer layers. J Appl Phys 71:5543, 1992. 25. S Nakamura, T Mukai, M Senoh. Si- and Ge-doped GaN films grown with GaN buffer layers. Jpn J Appl Phys 31:2883, 1992. 26. H Amano, M Kito, K Hiramatsu, I Akasaki. p-type conduction in Mg-doped GaN treated with lowenergy electron beam irradiation (LEEBI). Jpn J Appl Phys 28:L2112, 1989. 27. S Nakamura, T Mukai, M Senoh, N Iwasa. Thermal annealing effects on p-type Mg-doped GaN films. Jpn J Appl Phys 31:L139, 1992. 28. S Nakamura, M Senoh, T Mukai. Highly p-type Mg-doped GaN films grown with GaN buffer layers. Jpn J Appl Phys 30:L1708, 1991. 29. S Nakamura, T Mukai, M Senoh. High-power GaN p-n junction blue-light-emitting diodes. Jpn J Appl Phys 30:L1998, 1991. 30. T Matsuoka, H Tanaka, T Sasaki, A Katsui. Wide-gap semiconductor (In,Ga)N. Inst Phys Conf Ser 106:141, 1989. 31. T Nagatomo, T Kuboyama, H Minamino, O Omoto. Properties of GaInN films prepared by MOVPE. Jpn J Appl Phys 28:L1334, 1989. 32. N Yoshimoto, T Matsuoka, T Sasaki, A Katsui. Photoluminescence of InGaN films grown at high temperature by metalorganic vapor phase epitaxy. Appl Phys Lett 59:2251, 1991. 33. S Nakamura, T Mukai. High-quality InGaN films grown on GaN films. Jpn J Appl Phys 31:L1457, 1992. 34. S Nakamura. Growth of InGaN compound semiconductors and high-power InGaN/AlGaN double heterostructure violet-light-emitting diodes. Microelec J 25:651, 1994. 35. K Osamura, S Naka, Y Murakami. Preparation and optical properties of GaInN thin films. J Appl Phys 46:3432, 1975. 36. S Nakamura, T Mukai, M Senoh. Si-doped InGaN films grown on GaN films. Jpn J Appl Phys 32: L16, 1993. 37. S Nakamura. Zn-doped InGaN growth and InGaN/AlGaN double-heterostructure blue-light-emitting diodes. J Cryst Growth 145:911, 1994. 38. JI Pankove, JA Hutchby. Photoluminescence of ion-implanted GaN. J Appl Phys 47:5387, 1976. 39. P Bergman, G Ying, B Monemar, PO Holz. Time-resolved spectroscopy of Zn-and Cd-doped GaN. J Appl Phys 61:4589, 1987. 40. S Nakamura, T Mukai, M Senoh, S Nagahama, N Iwasa. In xGa (1⫺x) N/In yGa (1⫺y) N superlattices grown on GaN films. J Appl Phys 74:3911, 1993. 41. MG Craford. LEDs challenge the incandescents. Circuits Devices September:24, 1992. 42. H Sugawara, K Itaya, G Hatakoshi. Emission properties of InGaAlP visible light–emitting diodes employing a multiquantum-well active layer. Jpn J Appl Phys 33:5784, 1994.

INDEX

Ab initio self-consistent pseudopotential calculation, BP, 559 Absorption diamond, 375–376, 378–381 SiC, 451 Absorber TiC, TiC x Ny , ZrC, ZrC x N y, ZrC 6, 314 Absorption edge, 603 a-B, 635, 666–667, 670 B 4C, 621 B 12P2, 631 β-B, 605 diamond, 375–376 ACCU field effect transistor (FET), SiC, 487– 488 Acoustic surface wave (see also Surface acoustic wave), AlN, 691 Activated reactive evaporation (ARE), 322 c-BN, 73 Active diamond electronics, 365 electronic device, 369, 382–383 heterojunction device, 400 high-temperature operation, 394, 396, 398, 403 industrial application, 405 power device, 385, 387, 403 Activity (coefficient) C and Nb in NbC, 192 C and V in VC, 193 C and Zr in ZrC, 194 Si in SiC, 414 Zr in ZrN, 195 AlGaInN, 715–718 Aluminum nitride (AlN), 292, 294 Aluminum oxide (AlO x ), 289, 292, 299 Al In GaP light emitted diode (LED), 742 Alkali metal adsorption on TMC, 241 amorphous (a) a-B, 595, 635 a-BN, 499–500, 510

[amorphous (a)] a-BP, 264, 566 a-Si, 265, 289, 292 a-SiC, 482 angle-resolved photoemission spectroscopy (ARPES), 84–85, 234, 239 NbC, 228–230 TMC, 226, 228, 231–232, 236, 241 antiphase boundary (APB) SiC, 443, 445 VC, 36–37 antiphase domain c-BN, 543 SiC, 357–358 antisite defect boron-rich solid, 640 SiC, 416 Baliga’s figure of merit (BFOM), 358, 387, 478–479 Baliga’s high frequency (BHFOM), 385, 387 Baliga’s pair, 488 SiC, 490–491 Band gap, 228, 246, 312, 666 B, 656, 666, 670 B4C, 621 BP, 567–568, 571, 584 β-B, 605 boron-rich solid, 603 c-BN, 495, 509–510, 523, 545, 548 diamond, 393 GaN, 715 In xGa 1-x N, 730 SiC, 447, 459 Band gap engineering, diamond, 395, 403 Band structure, 83, 120 α-B, 602 B 4C, 620–621 BP, 558 β-B, 603 747

748 [Band structure] c-BN, 509, 545 diamond, 385 δ-TaN, 113 HfC, 112 HfN, 112 MC x (x⬍1), 123–124 MN, 85 MN x (x⬍1), 123–124 NbN, 88 TaC, 112 TaN, 112 TiC, 82 TiN, 82 TMC, 85 Si/BP, 583 of surface state on TMC, 236 WC, 118 ZrC, 90 ZrN, 90, 258 B 11C icosahedra, 591–592, 599–600, 606–607, 620, 623, 640, 642 Bias voltage (potential), 322 c-BN, 537 TiC, 59, 333–334, 343 TiB 2, 328 B 12 icosahedra, 590–592, 595–596, 598–600, 602, 606, 610, 620, 623, 639–640, 642 Bipolaron (hopping), B 4C, 591–592, 623 Blister, TiC, 333–334, 344 Bloch-Gru¨neisen (BG) formula, 174–177, 186 BN phase, 496–499 c-BN, 495–556 h-BN, 497–498 r-BN, 497–498 t-BN, 499–500 w-BN, 496–499 Bonding mechanism, 113 MC-MN, 95 MX x (x⬍1), 132 TiC, 105 TiN, 105 VN, 105 Bond type TiC, TiN, 102 Boron (B), 589 α-rhomb.B, 590–592, 602, 627, 630, 640– 641 α-tetra.B, 593–594, 632, 634, 640 β-rhomb.B, 590, 592, 594–595, 599, 602– 607, 608–612, 616–618, 623, 635, 639– 641 β-tetra.B, 595–596, 633–635, 640

Index Boron-rich compound, 589, 591, 593, 632, 634– 636, 643 Bowing parameter b, In xGa 1-x N, 730 Brillouin (light) scattering BP, 559, 567 MN superlattice, 14 TiN, 12 Brillouin zone (BZ), 85 δ-TaN, 113 SiC, 446 TiC, 123 WC, 117 Buffer layer AlN, 716, 725 GaN, 718, 742 Bulk modulus (moduli) B, 153, 155–157, 171 BP, 558–559 TiC, TiN, VC, VN, 121 Carrier removal rate, SiC, 464 Carbothermal (carbothermic) reduction (powder) AlN, 693–696, 700 NbB 2, 23 TiB 2, 19 TiC, 23 Channeling (ion channeling), 119, 248 Characterization, 1, 3, 4 a-Si, 265 B, 662 diamond, 354 Charge distribution, 95 Charge transfer, 96–97, 99, 113 Chemical vapor deposition (CVD), 19–20, 30, 46, 55–57, 68, 75, 78, 219, 312, 322 AlN, 696 BN, 500, 537, 542 BP, 263, 562–564, 566, 581–582 diamond, 347–351, 354, 357–360, 365–366, 370, 374–375, 377–378, 380–382, 389, 391 NbN, 290 SiO 2, 295 TiB 2, TiC phase diagram, 32 TiC, 32, 63, 70 TiN, 32, 77 Chemical vapor transport (CVT), 46 BP, 562 TiB 2, 32 Cluster method, 83, 120 Cohesive energy, 121, 165–168 Composite material, 1, 14, 29 c-BN/TiC, TiN, Al 2O 3, Si 3N 4, WC, 534

Index [Composite material] C/C, 336, 341–342 Ti/TiB 2, 184 TiB 2 /Al, 217 TiB 2 /TiC 0.5N 0.5, 30 Computational method, 83 Conversion efficiency (CE), 310, 317 Critical supersaturation σ cr, SiC, 430 Czochralski technique (growth), 43 TaC, 34 Debye (characteristic) temperature, 10, 153– 154, 158–159, 162, 169, 174, 176, 185 BP, 573–574 c-BN, 514, 519 h-BN, 519 SiC, 417, 463 TiB 2, 201 TiC, 164–165 TMC, 157 VN, 203 w-BN, 519 Debye model, 153, 161, 165, 175 Debye-Waller (D-W) factor, 119, 161, 247 ZrC, 203 Defect, 178, 188, 264 AlN, 686, 696, 701–702 BP, 248, 266, 564 c-BN, 522–525 diamond, 354, 358–359, 378, 381 MB 2, 34 NbC, 248 SiC, 419, 429, 448, 468 w-BN, 499 Density of state (DOS), 107, 123 B 12 icosahedron, 602 β-B, 603 c-BN, 509 HfC, HfN, 112 MB 2, 142–144 M 2X, 138–139 MN, 88, 130, 132–133, 135, 242 NbC, 227 TaC, 112 TiC, 121, 125–126 TiN, 121 TMC, 88, 130, 132–133, 135, 242 ZrC, ZrN, 90 Deposition rate, 63 B, 659, 662 Ti 1-xB x, 326 TiC, 332–333

749 Diamond, 347–366, 369–383, 385, 388–399, 403 Diamond single crystal, 354–355, 360–361, 364, 374, 399 Dielectric function B 4C, 621, 625–626 BP, 560 c-BN, 509 C 2Al 3B 48, 632 VB 32, 618 Diffusion coefficient (constant) AlN, 706–707 SiC, 422–425, 444 TMC, 197 Diffusion profile, SiC, 422, 425 Diffusion rate, SiC, 423, 425, 433 Direct current (DC) magnetron sputtering, 63 Ti-B-C, 74 DC-superconducting quantum interference device (SQUID), 300 DC plasma CVD, c-BN, 537 Direct nitridation, AlN, 679, 693–695 Direct sputtering, 55, 62–63 Donor-acceptor (D-A) pair BP, 562 SiC, 454–455 Donor in SiC, 424–425 Doping (dopant) by substitution, β-B, 618 Al in 3C-SiC, 455, 462 B in diamond, 370, 372–373, 375, 377, 379– 382, 389, 396–397 of c-BN, 546 Be in c-BN, 523–525, 534 codoped InGaN, 735–736 columm III element for 6H- and 4H-SiC, 461 diamond, 359 Ti in SiC, 456 V in 6H-SiC, 456, 462 impurity a-B, 595 AlN, 359, 688 B in diamond, 370, 374–375, 377–398 c-BN, 525, 532, 546 nitrogen in 3C-SiC, 454, 463 nitrogen in diamond, 351, 370, 375–377, 381–382 nitrogen in 6H-SiC, 454, 461 nitrogen or Al in SiC, 433, 461 S in c-BN, 548 SiC, 434 Si in c-BN, 523, 526 Si in GaN, 719–721

750 [nitrogen in 6H-SiC] Si in InGaN, 731–732 Zn in InGaN, 733–735 Drude behavior, B 4C, 626 Ductile-brittle (D-B) transition TiC, 214, 218 (Ti,Mo)C, 215 TMC, 210 Edge termination, 482 in SiC, 481 Effective mass B 4C, 626 c-BN, 509 diamond, 371, 375 SiC, 459 Elastic constant (modulus), 12, 153, 155, 169, 171, 339 BP, 558–559, 567 c-BN, 510, 512, 514 TiB 2, 158 Electrical conductivity (see also Resistivity), 5, 173–174, 180 α-B, 633 B, 658, 663, 665, 671 B 4C, 623, 625 BP, 570–571 β-B, 608, 613 YB 66, 638 Electron cycloton resonance (ECR) ion beam sputtering, AlN, 684 ECR assisted etching, diamond, 395 ECR plasma CVD, c-BN, 537 Electron deficiency B, B 4C, 640–641, 644 boron-rich solid, 601, 644 YB 66, 643 Electronic structure, 81, 83 MB 2, 142 MC, 82, 85, 112, 119–120 MC-MN, 135 MN, 82, 85, 112, 119–120 M 2X, 138 WC, 117–119 Electron-phonon interaction (scattering), 10, 154, 174, 179, 185, 619 β-B, 605–606, 616 boron-rich solid, 644 Electron spin resonance (ESR) boron-rich solid, 591–592 β-B, 607 c-BN, 523 SiC, 429, 449, 462–463, 466–467

Index Emission (emissivity), 191 diamond, 376 TaC, 233 TMC, 192 ZrC, 195, 201 Emission current stabilization, 283 Emission spectra TaC, 232, 234 TiC, 237 Emittance, 192, 308, 310 Empirical pseudopotential method (EPM), BP, 566 Entropy, 159, 162 NbC, 192–193 SiC, 414, 416 Etching B, 663 c-BN, 505–506, 508, 537 diamond, 349, 363, 395 Exchange-correlation potential, 84 Excitation, diamond, 376–378, 382 Excitation coefficient, B, 659, 670 Exciton energy gap, SiC, 451 Exciton diamond, 376–388, 382 SiC, 453–454 Far infrared (FIR) reflectivity B 4C, 626 β-B, 618 Fiber-reinforced material (FRM), 1 AlN, 689 TiB 2, 217 TiC, 45 Field effect transistor (FET) diamond, 390–392 SiC, 480 Field emission (FE), 269 Field emission current, TMC, 272, 280 Field emission pattern, TMC, 270, 277, 280 Field ion microscopy (FIM) HfC, 30 TiC, 271 Figure of merit of morphology (FOMM), 57 First-order (phase) transition (transformation) BN, 500 VC, 202, 209 V 2C, 194 First wall, 321, 337 Floating-type fluidized-bed nitridation, AlN, 682 Flux method BP, 562, 584 MB 2, TMC, 33

Index Force constant, 10, 166 c-BN, 512 TMC, MN, 169 Four-junction logic (4JL), NbN, 295–296 Fowler-Nordheim (F-N) plot, TMC, 281–282 Fracture strength (toughness), 14, 341 TiB 2, 216–217 Free carrier-acceptor (FA) recombination, InGaN/AlGaN DHLED, 736 Full width at half-maximum (FWHM) diamond, 354, 364 GaN, 718 InGaN, 729, 731, 735 InGaN/AlGaN, 736, 742 SQW, 743 TiC, 61 Fusion reactor, 321, 336–337 GaN, 715–718 GaN diode, 682 GaP LED, 382, 456, 741 Grain boundary, 36 AlN, 701–703, 705–707, 709, 711 diamond, 364 NbB 2, TiN, ZrB 2, 28 TiB 2, 29, 200–211, 214 TiC, 29, 198 Growth sectors, diamond, 352–353, 358, 363, 380–381 Gru¨neisen parameter, TiB 2, 201 GW approximation BP, 559–560 c-BN, 509 Hall coefficient HfC, TaC, VC, ZrC, 186 TiC, 186, 199 YB 66, 638 Hall measurement (effect) B 4C, 625 BP, 567 β-B, 610 c-BN, 525 diamond, 359, 371, 375, 377 SiC, 449, 456 Hardness (see Micro-Vickers hardness and Knoop hardness), 169 Hashin-Shtrikman bounds, 156, 183–184 Heat capacity (see also Specific heat capacity), 165, 181 AlN, 702 c-BN, 522 NbC, 193

751 [Heat capacity] TaC, 177 TiC, TiN, 207 Heat sink AlN, 691 BP, 574 c-BN, 546 diamond, 347 Heteroepitaxy diamond, 360, 365, 395, 399, 400, 495 SiC, 444 Heterojunction (heterostructure) BP/Si, 557, 576–577, 582–584 diamond/c-BN, 395, 400–401, 495, 543 Si/BP/Si, 577 Heteropolytype, SiC, 433 Hexagonality, SiC, 418, 452 High pressure/high temperature (HP/HT) synthesis BN, 495 c-BN, 528 diamond, 347, 349, 355, 361 High pressure synthesis catalyst method, a-BN, 529–532 c-BN, 528–535 High-resolution (transmission) electron microscopy [HR(T)EM] BP, 546 c-BN, 543 diamond, 365 NbC, 36 SiC, 446 VC, 38 High strain rate superplasticity (HSRS), 217 High-temperature device, c-BN, 547 Hollow cathode-discharge (HCD) ion plating, 59 TiN, 61 Homoepitaxy diamond, 355, 391 SiC, 442 Homogeneity range B 4C, 619–620 boron-rich boride, 590 MB 2, 39 Hopping conduction a-B, 665, 671 B 4C, 226 B(:Fe), 618 boron-rich solid, 591 β-B, 610–612 diamond, 372–373 Hot electron bolometer (HEB), NbN, 300 Hot implantation, SiC, 461

752 Hot isostatic pressing (HIP) technique, 20, 28 AlN, 697 BP, 561 TiB 2, TiC, 29 Hydrogenation GaN, 723, 725 diamond, 375 GaN, 723 MN, TMC, 15 Hydrogen atom GaN, 723 diamond, 375 Hot electron bolometers (HEB), 300 Ideal solar absorber, 309 Indentation hardness (see also Micro-Vickers hardness and Knoop hardness) MB 2, 211 TiN, ZrC, 11 TMC, 209–210 Impact-collision ion scattering spectroscopy (ICISS) TiC, 240 TMC, 224–225 Impurity, 178 AlN, 675, 687–688, 694, 696 B, 672 c-BN, 523–524 SiC, 449 InGaN, 729–731 Infrared (IR) spectrum B, 657, 670 BN, 500, 516, 518, 537 BP, 569 boron-rich solid, 591 InGaN, 729–731 Integrated circuit (IC), 77 diamond, 396, 401 NbN, 291, 293, 300 SiC, 477 Interband transition B 4C, 621 β-B, 605 Internal stress, 61 SiC, 448–449 TiC, 324 Interstitial accommodation (site), 590, 600 compound, 7, 82 doping, β-B, 616 Intervalley scattering, SiC, 459–461 Inversion layer mobility, SiC, 485, 487 Ion beam bombardment, c-BN, 537

Index Ion beam deposition, a-BN, 500 Ion beam-induced crystallization (IBIEC), BP, 246, 262, 265, 585 Ion beam-induced reaction, BP, 261 Ion beam irradiation BP, 259 MN, 253–255 VN, ZrN, 312 Ion implantation diamond, 389 SiC, 424, 461, 464, 482 MN, 253–257 Ion plating, 55 TiC, 330 Irradiation, 245 BP, 259 NbC, 247 Isoelectronic trap, SiC, 456 Jahn-Teller (J-T) effect B 4C, 639 β-B, 605, 616 boron-rich solid, 600–602, 644 Johnson’s figure of merit (JFOM), 385 Key’s FOM (KFOM), 385, 387 Knoop hardness (see also Micro-Vickers hardness) B 4C, c-BN, diamond, SiC, 513 NbB 2, 211 TiN/AlN, 74 Kondo effect, TiB 2, 186 Laser diagnostic, ZrC, 198, 218 Laser-ablated deposition, c-BN, 541 Laser-assisted CVD, diamond, 351 Laser-assisted plasma CVD, c-BN, 537 Laser diode (LD), 715 GaN, 721 InGaN/AlGaN, 737 Lattice parameter (constant), 121, 203, 255 AlN, 691, 707 BN, 496 BP, 562, 567, 574 diamond, 385, 393 HfN, 253–255 GaN, 716 MB 2, 205–206 MC, MC-MN, MN, 204 MN, 204 NbC, 246–247, 250–253, 255, 278 SiC, 409, 416, 429, 433–434 (SiC) x (AlN) 1-x, 625

Index [Lattice parameter] TiB 2, 328 TiC, 207, 332 TiN, 204, 207 ZrN, 253–257 Lattice vibration, 10, 153, 159 AlN, 701 c-BN, 514, 516, 518 LCAO-coherent potential approximation (CPA), NbC, 245 LCAO partial l-like density of statue (DOS), 95 MXx (x⬍1), 125 TiC, TiN, VC, VN, 91 Light-emitting diode (LED), 715, 737, 739 AlInGaP, 741, 744 blue, red, 739 c-BN, 547–548 GaN, 721, 725–727 GaP, InGaN, 741, 744 green, 739–742 InGaN/AlGaN, 736, 741, 744 SiC, 728 Liquid-phase epitaxy (LPE), SiC, 437–438, 462 Liquid-phase sintering, 20 AlN, 697–698, 700 Local density approximation (LDA), 83 BP, 558, 560 c-BN, 509 Ti 2N, 141 Local partial l-like DOS, 90, 104 MX x, 125 TaC, 112 TiC, 121 Ti 2N, 138 Lorentz number, 180 Low-energy electron diffraction (LEED) diamond, 356 graphite, 277 NbC, 277–279 SiC, 441 TMC, 223, 225, 277 Low-pressure synthesis, c-BN, 536–543 Low-Z material, 321–322 B, 672 C, 336 Luminescence c-BN, 523 diamond, 375–378, 381–382 SiC, 447, 453–454, 463 Magnesium oxide (MgO), 290, 292–296, 298– 300 Magnetic effect, TiB 2, 186

753 Magnetic penetration depth, NbN, 291 Magnetron sputtering, 63 TiB 2, 324, 334 TiC, 323–324, 331 Mass transfer, SiC, 427–431, 433 Matthiessen’s rule, 178–179 SiC, 460 VC, 202 Mean free path, 179 of phonon, 181 Mechanical alloying, 45 MB 2, TMC, 22–23 Melting point (temperature), 165, 291, 322, 336, 343 boron-rich solid, 589–590, 644 c-BN, 503, 536 diamond, SiC, 385 graphite, 322 C/C, 336 TiB 2, 322 TiC, 164, 322 TiC-TiB 2, 337 TiN, 21 TMC, MN, 168 Metal diffusion (diffusivity), 197 NbC, 198 Metal organo CVD, 56 GaN, 715–716, 721, 724 Metal-oxide semiconductor (MOS)FET, 77 diamond, 390, 392, 400, 403 SiC, 444, 470, 484, 488, 490, 493 Metal semiconductor (MES) FET, 390 diamond, 392, 397–399, 402–403, 444 SiC, 444, 470, 488, 490, 493 Microhardness anisotropy, 10 BP, 567 NbC, 36 Micro-Vickers hardness (see also Knoop hardness), 171 BN, 73–74 BP, 567 c-BN, 513 MN, 11–12 NbB 2, TaB 2, 9 NbC, 36 SiC, 418 TiB 2, 28 Ti 1-x B x, 328 TiC, 57, 59 Ti-C-B, 29 TiN/AlN, 74 TiN/VN, TiN/(V 0.6Nb 0.4)N, ZrC-ZrB 2, 14 TMC, 70, 169, 209–210

754 Microwave plasma CVD, c-BN, 537 Mobility B 4C, 625 BP, 567, 570–571, 578, 585 β-B, 608, 612 diamond, 354, 364, 369–371, 374–375, 382 GaN, 715, 718–719, 725 SiB 14, 632 SiC, 457, 459, 466, 479–480 TiC, 199 Modified variable threshold logic (MVTL), NbN, 295 Molecular orbital (MO), 102, 106 B 12 icosahedra, 600 MB 2, 142 Monolayer graphite (MLG), 276–277 Morphology AlN, 675, 686 c-BN, 505, 543 diamond, 352, 363–364 NbN, 292 TiC, 333 TiC/MO, 338 Mott-Schottky (M-S) plot, BP, 582–584 Mott’s law (formula) B 4C, 623 β-B, 608, 618 diamond, 373, 375 YB 66, 638 Muffin tin potential, 84 Multi-quantum well (QMW), InGaN, 740–741 Nanocrystalline (nanosized) powder, 19–20, 45 MC, MB 2, 23 TiN, 28 Nanorod, 45 NbC, 32 TiC, 31 Nb, 289–290, 294–296, 299–300 Niobium carbide (NbC) tip, 276, 280–284 Nb(CN), 300 NbN, 289–300 Niobium oxide (NbO x), 292, 297–298, 300 Nonstoichiometric compound (nonstoichiometry), 186 AlN, 684 c-BN, 523 HfC, HfN, 132 MN, 119, 123, 135 TiC, 125–126, 132 TiN, 128–129, 132–134 TMC, 7, 119, 123, 135, 178, 209 VC, 129–130

Index n-type diamond, 375 B 14Si, 632 β-B, 616 Nucleation c-BN, 532, 534 diamond, 361–364, 366 Ohmic contact (electrode), 403 c-BN, 526–527, 548 diamond, 392–394 GaN, 736 Ohmic metal, 393 diamond/Ti/Mo/Au, 394, 403 Optical absorption AlN, 700 β-B, 607, 610 SiC, 454 Ordered compound (phase), 130 NbC, 36 TiC, 125 TiN, 125, 128 VC, 129 Order-disorder transformation TMC, MN, 119 VC, 202, 209 V2C, 194 Oriented growth, diamond, 362, 364 Oxygen adsorption, TiC, 237 Partial l-like density of state (DOS), 90, 102, 105 Phase diagram, 191 AlN, 698 BN, 500–504, 535 BP, 561 carbon, 350, 503 carbon-boron, 337 SiC, 411 TiC, 32 Phonon (abnormality) anomaly, 10 NbC, 253 Phonon density of state (DOS), 159, 165 c-BN, 517 TiC, 163 Phonon (dispersion) curve c-BN, 517 NbC, 278–279 SiC, 446 Phonon drag, B 4C, 625 Phonon replica diamond, 376–377 SiC, 453 BP, 562

Index Phonon (scattering), 178 AlN, 687, 701, 703 β-B, 619 BP, 558–559, 573 diamond, 354, 371, 376–379 SiC, 456–457, 459, 461 Phonon (spectrum), 161, 165, 169, 177, 181 AlN, 701, 703 c-BN, 516, 518 SiC, 448, 454 TiC, 163 VN, 176 Phonon velocity (speed), 522, 702 Photoconductivity, β-B, 607–608, 618 Photoelectrochemical (PEC) cell, BP, 580–581 Photoluminescence (PL) spectra BP, 562 GaN, 721–723, 726–727 InGaN, 729, 731 SiC, 447, 453–455, 468–469 Physical vapor deposition (PVD), 3, 19, 55–57, 68 AlN, 483, 685 BN, 537 carbide, nitride, 70 c-BN, 538 Piezoelectricity AlN, 683, 691 c-BN, 514 Plasma-arc heating MN, 20 TiB 2, 28 TMC, 20, 42 Plasma disruption, 338 Plasma (enhanced) CVD, 67 BP, 585 diamond, 348, 365 TiC, TiC-TiN, TiN, 73 Plasma-facing material (component), 321 C/C, 344 TiB 2, TiC, 336, 343 TiC-TiB 2-C, 337 Plasma frequency, B 4C, 626 Plasma impurity, 321 Plasma oxidation, NbN, 292 Plasma zone melting, 192 Plastic deformation, 191 c-BN, 534 TiC, 215 ZrB 2, 211 p-n junction BP, 558, 578 c-BN, 523, 525, 532–533, 547–548

755 [p-n junction] GaN, 725, 728 SiC, 417, 464, 481 Poisson’s number, 156–157, 171 Polar surface (polarity) c-BN, 504–505 TMC, 225, 230 Polycrystalline material, 55–78, 155, 184 insulator (excluding diamond), 339, 534, 543, 682, 687, 691–712 metallic ceramics, 28–30, 35, 182–195, 200, 204–207, 214–218 semiconductor (excluding diamond), 259– 263, 526, 561, 567, 571, 573–574, 581, 589–644 Polytypes in SiC, 409–410, 416–418, 423, 427, 429–430, 433–434, 446–447, 451, 453, 456–457, 463, 470, 479 Porosity, 158, 171 AlN, 709 NbB 2, 28 Porous material, 183 DyB 66, 638 Positron annihilation, SiC, 467 Power device, diamond, 387 Preferential growth BN, 502 TiN, 21 Pseudopotential calculation, 84 BP, 559 p-type GaN, 721–723, 725–727 Pyrogenic oxidation, SiC, 470 Radial charge density, 97, 113 Radiation damage, SiC, 464 Radiation detector, BP, 580 Radio frequency (RF) RF floating zone MB 2, 20 TiN, ZrN, 38 TMC, 20, 35 RF ion plating, 61 RF magnetron sputtering AlN, 77, 685 TiB 2, 324, 334 TiC, 323–324, 331, 343 RF plasma CVD, c-BN, 537 RF reactive ion plating, 322 TiC, 336 RF sputtering, 61, 313 AlN, 683 c-BN, 537 h-BN, 540

756 [Radio frequency (RF)] HfN, 254 NbC, 246 NbN, 291, 294 ZrN, 254, 256 Raman spectra a-B, 635 BN, 500 BP, 569–570 c-BN, 516–518 diamond, 352, 354 SiC, 446 Random phase approximation (RPA), BP, 560 Ratherford back scattering spectrometry (RBS) BP, 259–261, 263, 585 c-BN, 505 NbC, 248–249 SiC, 448 Reactive evaporation, 55, 58 Reactive ion etching (RIE) NbN, 294–295 SiC, 464 Reactive ion plating, 55, 58 TiC, TiC-TiN, 70 TiN, 70, 78 Reactive sputtering, 55, 62–63 AlN, 683 Reflectance (spectra), 316 B, 657, 659 c-BN, 509–510 TiC-TiN, 8 TiN, 75 Reflection high energy electron diffraction (RHEED), BP, 564, 566–567 diamond, 356, 364 SiC, 444, 466 Reflection (reflectivity) spectrum, BP, 560 TiN, 75 Refractive index, B, 659, 670–672 BP, 568–569 c-BN, 517–518 SiC, 452 Relativistic effect, 84, 87, 112, 118 Residual resistivity VC, 9, 201 ZrN, 255 Residual resistivity ratio (RRR) HfN, ZrN, 255 NbC, 250, 252 VC, 41

Index Resistivity (see also Electrical conductivity) AlN, 691 BP, 562, 564, 566–567 c-BN, 525–526, 533, 548 diamond, 372–373 NbC x, 178 MN, ZrB 2, 186 TiB 2, 186, 200 TiC, 178, 199 TMC, 9, 174, 178, 186 VC x, 178, 202 ZrC, 201 ZrN, 258 Resistivity saturation, TMC, 178 Resonant photoemission spectroscopy TaC, 232 TiC, NbC, 233 Rippled reconstruction HfC, TaC, 223 Scanning tunneling microscopy (STM) diamond, 356–357 SiC, 441 VC, 225 Seebeck coefficient (see also Thermoelectric power) B 4C, 625, 644 boron-rich solid, 590 β-B, 608, 616 C 2 Al 3 B 48, 633 SiB 14, 632 YB 66, 638 Selective growth, diamond, 395 Self-consistency, 83 Self-diffusion coefficient, 219 NbC, 197 SiC, 420–424 TiC, VC, 197 Self-diffusion (diffusivity), 191 NbC, 252 SiC, 420, 431 TMC, 197–198, 211 Self-propagation high temperature synthesis (SHS), 19, 219 NbC, 23, 42 TiB 2, 27 TiB 2 /Ti(CN), 30 TiC, 41 TiC-Ni-Al, TiC-TiB 2, 29 ZrB 2, 28 Semiconducting c-BN, 525–526 diamond, 369–372, 375, 377, 378, 381–382, 399, 402

Index Shear modulus (G), 153, 155–156, 171, 215 BP, 558 SiC, 512 TiN, 12 TMC, 157 Shock-induced reaction, 19, 29 Shock wave compression c-BN, 503 w-BN, 499 Shottky barrier height BP, 578, 580 diamond, 390–391 SiC, 492 Shottky barrier rectifier, SiC, 482, 490–492 Shottky diodes, BP, 579 diamond, 359, 365, 382, 403 SiC, 290, 715 SiC LED, 382, 728 SiC polytype 3C-, 409, 411, 416, 418, 426, 430, 434, 437, 439, 442, 444, 446–448, 451, 454– 456, 459, 461–464, 466, 468–470, 479 4H-, 411, 416, 432, 434, 438–439, 442, 447, 451, 456, 461, 479 6H-, 411, 413, 416, 418–419, 434–435, 438– 439, 442, 446–447, 454, 456–457, 459, 461, 464, 479 8H-, 416, 446 10H-, 416 15R-, 411, 416, 438, 442, 446, 451, 456, 459, 461 27R-, 416 Single crystal insulator, 256, 290, 361, 395, 400, 525, 532– 534, 675–689, 702 metal, 361 metallic ceramics, 10–12, 20, 30–45, 178, 182, 186, 192, 197–199, 201–202, 209– 211, 214–215, 223–242, 248–249, 269– 285, 291 Semiconductor (excluding diamond), 290, 363–364, 409–435, 426–470, 525–526, 562–564, 567, 570–574, 716 Si 3N 4, 77, 399 Sintering additive, 20 AlN, 691, 705–706, 708–709 NbB 2, TiB 2, TiC, TiN, 28 SiO, 294–295, 391–392 Solar absorptance, 317 Solid state epitaxial (SPE), BP, 263 Sound velocity, 154, 174, 181 c-BN, 514

757 Specific heat capacity (see also Heat capacity), 153–154, 159, 162, 181, 522 BN, 519 BP, 573–574 TaC, 177 TiC, TiN, 207 Specific on-resistance, SiC, 479–480, 484, 487– 488, 490 Spectral absorptance, 309 Spectral emittance, 191 TMC, 192 Spectral reflectance, 311, 316 TiN x, ZrN x, 314 Spectral selectivity, 307, 316 Spin fluctuation, VN, 10, 186 Sputtering, 55, 62 B, 655 dielectric film, 312 NbN, 295 SiO 2, 295 TiN, 77 Stagnation temperature, 309–310 ZrN x, 317 Step flow growth, diamond, 355, 357 Step growth mode, SiC, 444 Stoichiometric compound (composition), 122, 219 AlN, 683 HfN, 254 MN, 27, 85, 112 TiB 2, 41–42, 328, 343 TiC, 126, 343 TiN, 23 TMC, 7, 85, 112 ZrN, 254 Stoichiometry AlN, 683 BN, 528 BP, 564 MN, 8 NbC, 36 SiC, 416 VC, 193 Structural defect, 644 boron-rich solid, 639–640 Structural disorder, 245 NbC, TaC, 249 Subcarbide, 138–141 Sublimation method AlN, 675, 679, 682, 686 SiC, 426–427, 429, 431, 462, 476, 486 Substitutional impurity, AlN, 687 Superconducting transition temperature (T c), 9, 81, 185, 245

758 [Superconducting transition temperature] HfN, 255 NbC, 22, 250–253 NbC xN 1-x, 135 NbN, 35, 291, 299 ZrN, 255–256, 258 Superconductivity (superconducting), 10, 78, 81, 185 NbC, 183, 203 NbC xN 1-x, 9 VN, 195 ZrN, 27 Superlattice film TiN/AlN, 74 TiN/VN, TiN/(V 0.6Nb 0.4)N, 14 Supersaturation AlN, 686 c-BN, 529, 532 SiC, 430 Surface acoustic (wave) (SAW) device, 77 AlN, 683–684, 689 Surface atomic structure, TMC, 223 Surface Brillouin zone (SBZ), 234 TaC, 235 Surface conducting layer, diamond, 398 Surface reactivity, TMC, 236 Surface reconstruction, SiC, 441 Surface relaxation, 225 Surface state, 228–231 TMC, 225 Surface state density, diamond, 392 Tamm surface state, TMC, 228, 230 Thermal annealing, GaN, 721–725, 736 Thermal conductivity, 81, 173, 180–181, 184, 341 AlN, 686–687, 691, 695–698, 700–703, 706–709, 711 B, 666 B 4C, 627 BP, 574, 580, 585 c-BN, 73, 514, 522 C/C, 336 diamond, 347, 354, 369, 385, 387 HfB 2, 207 NbC, 183 SiC, 418, 463, 522 Ti/TiB 2, 184 TiB 2, 183, 186, 207, 336 TiC, 182, 186, 336 VC, 186 YB 66, 638 ZrC, 186 ZrB 2, 207

Index Thermal CVD, 56, 63, 67 diamond, 351 TiC, 71, 73 TiC-TiN, TiN, 73 Thermal emittance, 308–309 TiN, ZrC 6, ZrC xN y, ZrN, 317 Thermal expansion coefficient, 191, 203, 341, 521 AlN, 691 boron-rich solid, 590 BP, 574, 567, 576 β-B, 619 c-BN, 512, 520, 522, 546 h-BN, 520 MC-MN, 204–206 SiC, 416, 445, 448, 463–464 (SiC) x (AlN) 1-x, 425 TiB 2, 201 w-BN, 520 Thermal neutron irradiation, BP, 571–572 Thermal oxidation rate, SiC, 417 Thermal shock resistance, 337 TiB 2, 339, 343 TiC, 342, 344 Thermal stability, 317 c-BN,73, 526 TiC, 330–331, 336, 343 Thermodynamics, 191, 219 MB 2, 218 TiC, 32 TiN, 21 ZrC, 195 Thermoelectric device, BP, 558, 580 Thermoelectric FOM B, 666 BP, 580–581 Thermoelectric power (see also Seebeck effect) B, 657, 666, 672 BP, 572–573 c-BN, 525 TiC, 199 Thin film (including single crystalline and excluding diamond specimens), 55–78, 251 insulator, 292–294, 312, 536–543, 683–685 metal, 295 metallic ceramics, 12, 14, 246–248, 250–259, 290–300, 313–318, 322–344 semiconductor, 259–265, 312, 317, 437–470, 477–492, 566, 569–570, 576–584, 655– 671, 715–745 Titanium carbide (TiC) tip, 207–274, 276, 283– 284

Index Transconductance diamond, 400, 403 SiC, 470 Transition metal carbide (TMC), 2, 4, 10, 12, 20, 24, 29–30, 33, 35–36, 39, 85–88, 90–91, 95–105, 119–123, 125–126, 157, 162, 166, 168–169, 178, 185–186, 192, 195, 197, 207, 209–210, 223–232, 234–242, 269–270, 276, 280–281, 285 Transition metal diboride (MB 2), 2, 6, 12, 20, 23–24, 30, 33, 41–42, 142–144, 166, 186, 205–207, 211 Transition metal nitride (MN), 2, 4, 11–12, 14, 20, 22–24, 30, 36, 38, 43, 46, 85–88, 90–91, 95–105, 119–123, 125–126, 166, 168, 185–186, 198, 204, 207 Transmission electron microscopy (TEM) BP, 564 diamond, 352, 361 SiC, 444–445, 448 TiC, 31 Transmittance, B, 659 Transparent AlN film, 683 AlN whisker, 682 c-BN, 534 Trapping (trap), β-B, 605, 611–613, 616, 619 Travelling solvent float zone (TSFZ) technique, TMC, 39–40 Two-flow MOCVD, GaN, 716–727 Two-step growth (method) BP, 566 SiC, 445 Tungsten monocarbide (WC), 117–119

759

UMOSFET, SiC, 484–485, 487 Unipolar FET, diamond, 402 Urbach tail, 603 YB 66, 638 UV electroluminescence (EL), GaN, 726–727

[Vacancy] VN, 203 ZrN, 259 Vacancy state (band), 122 TiC, 123, 132 TiN, 132–133 VC, 129–130 Vacuum evaporation, 55 B, 655, 659 Valence electron density (VED), 107 MX, 102 TiC, 99–104, 108, 110, 121 TiN, 99, 103–104, 109–110, 121, 133–135, 138 Ti 2N, 139–141 TMC, TMN, 111 VN, 99–102, 110 Vapor-bulk crystal, SiC, 433 Vapor-growth surface, SiC, 433 Vaporization, 191–192, 194 C/C, 341 MC, 194 ZrC, 195 Vapor-liquid-solid (VLS) mechanism, 30 AlN, 675, 682, 686 BP, 563 SiC, 429, 431 TiC, 46 Vapor-phase (crystal) growth, SiC, 424, 426 Vapor-solid (VS) mechanism AlN, 482 HfC, NbB 2, ZrC, 30 SiC, 431 Variable-range hopping B 4C, 623 β-B, 608, 612, 618 diamond, 373 YB 66, 638 Vibrational displacement, 160 Vickers hardness (see Micro-Vickers hardness)

Vacancy, 178, 265 AlN, 687–688, 701 c-BN, 523 diamond, 359 HfC, HfN, 138 MN, 119–122, 130, 135 NbC, 252–253 SiC, 420, 422–424 TiC, 36, 125–126 TiN, 125, 133 TMC, 35, 119–122, 130 VC, 201–202

Whisker, 19, 45, 217 AlN, 675–679, 682, 686, 689 BP, 563 HfC, HfN, NbB 2, TiC, TiN, ZrC, 30 SiC, 419, 426 Wide gap emitter transistor, BP, 576–577 solar cell, BP, 557, 576–577 Wide-gap semiconductor, 4, 482 boron-rich solid, 644 diamond, 369 GaN, SiC, 6

760 Widmansta¨ttaen-type precipitation MB 2, 38 ZrB 2, 211 Wiedemann–Franz law, 9, 180, 182 NbC, 183 TiC, 182 Work function metal, 390, 580 TMC, 282 Work hardening (TiMo)C, 216 ZrB 2, 211 ZrC, 214 Work softening, (TiMo)C, 215 X α method BP, 558 NbC x, TiN, 120 TiC, 135 TMC, MN, 123 X-ray detector, 299 diffraction (diffractometry), 110, 119, 265 AlN, 684 B, 659, 663 BN, 498–500, 504 BP, 562 diamond, 354, 359, 364 GaN, 729

Index [X-ray] NbC, 245–246 SiC, 446, 448 TiC, TiN, 207 TiB 2, 328 rocking curve (XRC) InGaN, 729 InGaN/GaN, 740 InGaN/InGaN, 741 GaN, 718 topography c-BN, 534 HfC, TaC, ZrC, 46 TiC, 30 VB 2, 39 Yellow single-quantum-well (SQW), 742–745 Yield drop (point) TiC, 214 (TiMo)C, 215 ZrB 2, 211 Yield stress, TiB 2, 211 Young’s modulus (E), 153, 156–157, 171, 341 BP, 558 SiC, 429, 512 TiC, 209 ZnSe, 715 Zone folding, SiC, 446, 456