Diamond Films Handbook

ISBN: 0-8247-9577-6 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 䉷 2002 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

It has been known for over two centuries that diamond is a particular form of carbon. Since we live in a world where carbon in general is omnipresent but carbon in the form of diamond is extremely rare, there has been longstanding interest in the development of ways to convert ordinary forms of carbon to diamond. A distinctive method of diamond synthesis at low pressures, in which diamond is metastable with respect to graphite, is often referred to as the ‘‘new diamond technology’’ to distinguish it from highpressure diamond synthesis, in which diamond is the stable form of carbon. Over two decades of intensive science and engineering have gone into developing and understanding low-pressure diamond deposition. Diamond Films Handbook is a comprehensive source of information for readers interested in the details of how low-pressure diamond synthesis is achieved as well as how the diamond may be used for practical applications. In low-pressure diamond synthesis, common sources of carbon, such as methane, are transformed by chemical vapor deposition to diamond at atmospheric or subatmospheric pressures and at temperatures that are common to materials processing. We are fortunate to include in this book a chapter on the history of this amazing achievement, written by John C. Angus, a pioneer in the field. An important practical result of this synthesis approach is the ability to deposit diamond in layers, or films, over substrates of dimensions not previously possible. Currently, the capability exists to synthesize layers of diamond over surface areas as great as several hundred square centimeters. A host of applications are based on this diamond deposition capability combined with the exceptional physical properties of diiii

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Preface

amond. The latter include extreme hardness, high thermal conductivity, low coefficient of friction, high degree of chemical inertness, low electron work function, low infrared and microwave absorption, and wide bandgap semiconductivity. In fact, there are competing methods of achieving low-pressure diamond deposition. The three that have received the most attention in the literature are the arc jet method, the hot-filament method, and the microwave plasma method. However, other methods also show significant promise, including optical assisted deposition and combustion synthesis. This book devotes a chapter to each of these methods, describing them in significant detail. Thus, the reader may compare apparatus requirements, processing conditions, and deposition results. To provide a better understanding of the various deposition methods, a chapter that provides the basic physics and chemistry of diamond film technology, as well as a chapter that describes diamond film quality characterization techniques, precede the deposition chapters. As for applications of diamond formed by low-pressure deposition, the scientific and engineering literature has addressed far too many potential applications for each to be considered in detail in one book. As is often the case in new technologies, the path of applications development has deviated significantly from early projections. Speaking broadly, the technical and marketing difficulties in developing applications-based products have been more difficult than initially envisioned. This book includes four chapters addressing applications that provide useful information on the types of issues generally important in product development. Two chapters discuss applications for which products based on low-pressure diamond deposition are available in a broad market sense: cutting tools and thermal management. Two additional chapters discuss applications for which low-pressure diamond products are primarily in the development stage: optical applications and electrical applications. We have been working jointly on diamond deposition since 1987. Our knowledge of microwave plasma source design and plasma-aided deposition led to an invitation from the Norton Company’s Diamond Film Division to participate in the field of diamond synthesis. Over the past 15 years, it has been remarkable to participate in and observe the evolution of the new diamond technology. Progress in the field, starting with initial efforts to deposit an exotic and useful material at low rates and in small areas to the current capability to deposit films with thickness up to 1 mm and over large areas, has been dramatic. For us it has been an exciting and invigorating experience, and interesting personal relationships have been established in the process that have contributed to many lasting memories.

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Phenomenal advances in the field have resulted from methodical worldwide collaborations among those in industry, academia, and government laboratories. What is the future going to bring? People across the world are working on this technology, and we expect it will continue its rapid pace and development and that applications will appear in areas not yet envisioned. Thus, it is our hope that this book will provide those currently working in this area, and those contemplating entering the area, with a useful source of information, reference, and education. Diamond Films Handbook is intended to serve as a valuable source of information for readers interested in low-pressure deposition of diamond films and their applications. This is made possible by virtue of the chapter authors who have contributed their time and their unique expertise. We thank them for their contributions to this book, as well as to the field in general. We also express our gratitude to the publisher Marcel Dekker, Inc., and for the editing skills of Rita Lazazzaro and Ann Pulido, who made this book possible. Professor Asmussen thanks his wife Colleen for her years of patience, support, and tolerance of his cluttered offices. Professor Reinhard thanks his family, Sharon, Sarah, Daniel, and David for their long-standing support and much valued encouragement along the way. Both editors are grateful to the students with whom it has been their good fortune to work. Jes Asmussen D. K. Reinhard

Contents

Preface Contributors

iii ix

1.

Introduction Jes Asmussen and D. K. Reinhard

2.

A Short History of Diamond Synthesis John C. Angus

3.

Film Characterization Methods: Structure and Composition Ludwig Josef Balk and Ralf Heiderhoff

27

Deposition Chemistry: Deposition Pathways, Nucleation, and Growth David S. Dandy and Michael E. Coltrin

55

4.

5.

6.

Thermally Assisted (Hot-Filament) Deposition of Diamond Joseph E. Yehoda Plasma Torch Diamond Deposition Joachim V. R. Heberlein and Naoto Ohtake

1

17

119

141 vii

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Contents

7.

Microwave Plasma-Assisted Diamond Film Deposition Timothy A. Grotjohn and Jes Asmussen

211

8.

Combustion Synthesis of Diamond Colin A. Wolden

303

9.

Laser-Assisted and Optical Pumping Techniques for Diamond Synthesis Vish V. Subramaniam and Shashi M. Aithal

325

CVD Diamond Solutions for Machining and Other Mechanical Applications Brian L. Cline and James M. Olson

425

10.

11.

Diamond Heat Spreaders and Thermal Management Ajay P. Malshe and W. D. Brown

511

12.

Diamond Active Electronic Devices Hiromu Shiomi

579

13.

Diamond Film Optics D. K. Reinhard

607

Index

665

Contributors

Shashi M. Aithal* Center for Advanced Plasma Engineering and NonEquilibrium Thermodynamics Laboratories, Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio John C. Angus Department of Chemical Engineering, Case Western Reserve University, Cleveland, Ohio Jes Asmussen Electrical and Computer Engineering Department, Michigan State University, East Lansing, Michigan Ludwig Josef Balk Department of Electronics, University of Wuppertal, Wuppertal, Germany W. D. Brown High Density Electronics Center and Department of Electrical Engineering, University of Arkansas, Fayetteville, Arkansas Brian L. Cline

Cline Innovations, LLC, Sterling, Massachusetts

Michael E. Coltrin Chemical Processing Sciences Department, Sandia National Laboratories, Albuquerque, New Mexico *Current affiliation: Novellus Systems, Inc., San Jose, California.

ix

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Contributors

David S. Dandy Department of Chemical Engineering, Colorado State University, Fort Collins, Colorado Timothy A. Grotjohn Electrical and Computer Engineering Department, Michigan State University, East Lansing, Michigan Joachim V. R. Heberlein Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota Ralf Heiderhoff Department of Electronics, University of Wuppertal, Wuppertal, Germany Ajay P. Malshe High Density Electronics Center and Department of Mechanical Engineering, University of Arkansas, Fayetteville, Arkansas Naoto Ohtake Department of Mechanical Sciences and Engineering, Tokyo Institute of Technology, Tokyo, Japan James M. Olson Process Technology Development, Fairchild Semiconductor, South Portland, Maine D. K. Reinhard Electrical and Computer Engineering Department, Michigan State University, East Lansing, Michigan Hiromu Shiomi

Sumitomo Electric Industries Ltd., Itami, Japan

Vish V. Subramaniam Center for Advanced Plasma Engineering and NonEquilibrium Thermodynamics Laboratories, Department of Mechanical Engineering and Chemical Physics Program, The Ohio State University, Columbus, Ohio Colin A. Wolden Department of Chemical Engineering, Colorado School of Mines, Golden, Colorado Joseph E. Yehoda

Diamonex, Inc., Allentown, Pennsylvania

1 Introduction Jes Asmussen and D. K. Reinhard Michigan State University, East Lansing, Michigan

I.

DIAMOND FILM TECHNOLOGY—AN OVERVIEW

Advances in diamond science and technology represent a remarkable achievement in materials research and development. Diamond is, of course, not a new material. Many of the unique properties of naturally occurring diamond have been appreciated since time immemorial. Neither is the synthesis of diamond particularly new: reliable methods of forming diamond from carbon-containing compounds were reported in the middle of the twentieth century. What is remarkable is the current capability of synthesizing diamond structures and layers of dimensions not previously possible, with deposition areas up to several hundred square centimeters and direct deposition on a wide variety of substrates. This achievement has been made possible both by an improved scientific understanding of how diamond is formed and by a significant engineering development of chemical vapor deposition (CVD) systems designed specifically for the deposition of diamond. During recent years, it has become widely recognized that polycrystalline and homoepitaxial diamond can be deposited using a variety of CVD techniques. These new and relatively simple synthesis methods led to a worldwide research effort devoted to improved synthesis, to understanding the properties of the CVD films, and to applications of diamond. Figure 1 shows a simplified phase diagram of carbon. From this it may be seen that diamond is the minimum energy state, and therefore the stable form, of carbon at high pressures and temperatures, that is, at pressures of thousands of atmospheres and temperatures of thousands of degrees Celsius. Graphite, however, is the stable form of carbon under ordinary temperature 1

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Figure 1 Phase diagram for carbon. This simplified phase diagram for carbon shows that at sufficiently high temperatures and pressures diamond is the stable, or minimum energy state, of carbon atoms. At lower temperatures and pressures, graphite is the stable form. Under ordinary conditions for temperature and pressure, near 1 atm and room temperature, diamond may be considered a metastable form of carbon. Even though it is not the minimum energy state, it does not spontaneously convert to graphite.

and pressure conditions. One method of synthesizing diamond is to subject graphite to conditions of approximately 55,000 atmospheres and temperatures of about 2000⬚C. The first group to report diamond synthesis under these conditions publicly was the General Electric group including Bundy, Hall, Strong, and Wentorf in 1955 [1]. Since then, a variety of technical

Introduction

3

approaches to achieve diamond growth under such conditions have been reported, and they are known collectively as high-temperature, high-pressure diamond synthesis. High-temperature, high pressure processes have been proved to be commercially successful in terms of producing diamond powder and grit useful in various industrial applications.* However, these processes are not amenable to direct deposition of diamond on substrates or to large-area deposition and are not the subject of this book. Instead, the focus of the book is on diamond formed under conditions of pressures generally less than an atmosphere and temperatures less than 1000⬚C. This approach to diamond synthesis is sometimes known as the new diamond technology. At ordinary temperatures and pressures, although diamond is not the minimum energy state of carbon, it is also not an unstable stage of carbon. In other words, once carbon atoms are in the diamond lattice spatial arrangement, the solid does not spontaneously convert to graphite under low-temperature, low-pressure conditions. Such nonminimum energy arrangements are known as metastable states. Formation of diamond from nascent carboncontaining species under metastable conditions is both thermodynamically allowed and readily achieved under proper deposition conditions. It is the lower temperatures and pressures associated with this method of diamond synthesis that have offered the capability of direct deposition of diamond on a variety of substrates and have opened the possibility of new applications of diamond. For many such applications, the diamond thickness need be only on the order of micrometers; hence the structures are referred to as diamond films. The applications interests in diamond are based on the exceptional properties of diamond including extreme hardness, high thermal conductivity, high electrical resistivity, low coefficient of friction, high degree of chemical inertness, low electron work function, large energy gap, low infrared absorption, and high breakdown voltage. In many cases, the properties of diamond are superlative. For example, it is reported to have the highest hardness of any material, the highest thermal conductivity, and the lowest compressibility. In other cases, the diamond material property is not necessarily the best, but diamond is still highly competitive with other materials. For example, the coefficient of friction is comparable to that of Teflon. In any case, diamond is properly considered to be a unique material because it exhibits an unusual constellation of highly attractive properties of interest for many applications.

*High-temperature, high-pressure methods have also produced gem quality diamond, apparently not under commercially viable conditions.

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II.

Asmussen and Reinhard

METHODS OF DIAMOND FILM DEPOSITION UNDER METASTABLE CONDITIONS

A history of the development of diamond deposition methods under metastable conditions is provided by Angus in Chap. 2, and a detailed description of the key chemical and physics concepts is presented by Dandy and Coltrin in Chap. 4. The appropriate conditions for achieving low-pressure diamond synthesis can be obtained by a variety of methods. Generally, as shown in Fig. 2, these methods have certain things in common, including gaseous feedstock, a means of providing energy (thermal, electrical, combustion, or optical) that causes the gas components to dissociate, and a substrate on which the deposition takes place [2]. The gas feedstock includes at least one source of carbon-containing species. Most commonly, this is methane; however, a variety of other carbon-containing gas sources have been used. The energy provided to the system breaks down the input gas into a variety of subspecies such as, in the case of methane, CH3 and other molecules and atoms. It is the carboncontaining subspecies that are involved in donating a carbon atom to the growing diamond film on the substrate. In addition to the carbon-containing gas, most methods use hydrogen gas as a feedstock input. Often, for example, methane is diluted to between 0.5 and 5% in hydrogen. The energy provided to the system also breaks down the hydrogen gas, producing large amounts of atomic hydrogen. Atomic hydrogen plays an important role in that it helps maintain the diamond tetrahedral sp3 atomic configuration in the growing film as opposed to the sp2 configuration, which leads to graphite.

Figure 2 Generic deposition system for metastable synthesis of diamond. There are many types of diamond deposition systems that are capable of diamond synthesis under metastable conditions; however, they share generic features. All require a feedstock that contains carbon. The feedstock is usually gaseous and generally contains hydrogen as well as the carbon source. Energy is provided to the system in order to dissociate the molecules of the input gases. A variety of energy sources have been used, including thermal, electrical, optical, and combustion. A substrate is provided on which the deposition takes place.

Introduction

5

A variety of means have been developed to provide energy to the deposition system sufficient to break down the input gases. One of the most straightforward is the hot-filament method. In this method, the gases flow through a reactor that contains a wire or mesh filament apparatus typically made of tungsten, which is heated to a temperature sufficient to decompose significant fractions of the hydrogen and methane gases. Yehoda in Chap. 5 describes the hot-filament method in detail. Alternatively, a variety of approaches use electrical energy inputs to the deposition system in the form of dc, rf, or microwaves. Among the more successful of these are the arcjet method, described by Heberlein and Ohtake in Chap. 6, and microwave plasma–assisted CVD described by Grotjohn and Asmussen in Chap. 7. Combustion processes can also be used to provide the necessary species. Originally this approach used essentially a welding torch apparatus; however, the concept has also been applied to more sophisticated systems as described in Chap. 8 by Wolden. Finally, optical energy may be used, and Subramaniam and Aithal describe laser-assisted and optically pumped methods in Chap. 9. All of these methods have proved to be effective at depositing diamond under metastable conditions, although each has advantages and disadvantages as discussed in more detail in the cited chapters. The cost per carat of producing CVD diamond has decreased in recent years with improved system development. However, the capital cost associated with a production-scale deposition system is still a serious concern for all the various approaches. The associated economic considerations can present a barrier for the introduction of CVD diamond products. Therefore, deposition system development and improvement is a vital aspect of the future of CVD diamond applications.

III.

MATERIAL PROPERTIES OF DIAMOND

A.

General Properties

Pure diamond is composed only of the element carbon. The carbon atoms are arranged in the crystal structure known as the diamond lattice, in which each carbon atom has four nearest neighbors in the tetrahedral arrangement associated with sp3 chemical bonds. The nearest neighbor distance is 1.54 ˚ and the unit cell dimension is 3.567 A ˚ at 298 K. There are 8 atoms per A unit cell and 1.77 ⫻ 1023 atoms/cm3, which is the highest atomic density of any terrestrial material. The density at 298 K is 3.515 g/cm3. Diamond quantity is often expressed in carats, where one carat is equal to 200 mg, or about 57 mm3. The quality of diamond specimens varies considerably because both natural and synthetic diamond may contain impurities and defects. Natural diamond is classified into type I and type II, with the former

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Asmussen and Reinhard

containing nitrogen as an impurity and the latter being essentially nitrogen free. Further information about diamond classification is contained in Chap. 13. As previously discussed, diamond is a metastable form of carbon at ordinary temperatures and pressures, whereas graphite is the stable phase. With sufficient perturbation, the metastable phase gives way to the stable phase. For example, if diamonds are heated in an inert atmosphere, the onset of graphitization is detected at 1800 K. The rate of graphitization increases such that at 2400 K a 0.1 carat diamond is completely reduced to graphite in less than 3 min [3]. Diamond is highly inert chemically, except for two situations. It is susceptible to oxidizing agents at high temperatures. For example, if diamond is heated in the presence of oxygen, oxidation begins at around 900 K. Also, diamond is subject to chemical attack by certain metals at high temperatures. These include carbide formers such as tungsten, tantalum, titanium, and zirconium as well as solvents for carbon such as iron, cobalt, manganese, nickel, chromium, and platinum. Thorough reviews of diamond properties are contained in the literature [4,5]. Several single-crystal diamond properties of particular interest for applications are briefly reviewed in the following sections. Later chapters cover many of these properties in more detail and relate them to deposition conditions and to particular applications. B.

Mechanical Properties

Diamond is the hardest known substance. Diamond also has the lowest compressibility, the highest elastic modulus, and the highest isotropic speed of sound (18,000 m/sec) of any known material. The degree of hardness is quantified in terms of both resistance to indentation and abrasion (or scratch) resistance. One indentation method uses a Vickers indenter with a square pyramidal diamond point. Another hardness test uses a Knoop indenter in which a pyramidal point with long and short axes in the ratio of 7:1 is used. Depending on the crystallographic orientation of the sample, Knoop indentation hardness values are reported to be in the range of 5700–10,400 kg/ mm2 where the values are determined on the basis of the indenter load and the dimensions of the indentation. As a comparison, the value for casehardened steel is approximately 400 kg/mm2. When applying the hardness concept in terms of scratch and abrasion resistance, the scratch hardness Mohs hardness value is 10, the largest of any material. Cline and Olson describe tests related to abrasion resistance of diamond under various conditions in detail in Chap. 10. In terms of compressibility, the ratio of tensile stress to linear strain, or Young’s modulus, is 1050 GPa, a value approximately five times higher

Introduction

7

than that of steel. Because of its brittle nature, diamond is not particularly strong; however, the cleavage strength of diamond is reported to be at least as great as the tensile strength of tungsten wire, approximately 400 kg/ mm2 [4]. C.

Thermal Properties

The thermal conductivity of pure diamond exceeds that of all solids in the range of 90 to 1200 K and is to an extent limited by isotropic purity because the naturally occurring 13C isotope acts as a phonon scatterer. At room temperature, the experimental value for the thermal conductivity of high-purity, natural single crystalline diamond is approximately 20 W/cm-K, which is about five times higher than the thermal conductivity of copper. Diamond’s thermal conductivity increases with decreasing temperature, reaching a maximum of 42 W/cm-K near 80 K, below which the thermal conductivity decreases. Impurities, such as nitrogen, reduce the thermal conductivity. Type I diamonds with 0.1% nitrogen have room temperature thermal conductivity values approximately 50% that of type II diamonds, which have a negligible nitrogen concentration. Isotropic purity increases the thermal conductivity. Synthetic diamond crystals grown with pure carbon-12 have thermal conductivities 50% higher than those of natural diamond for which the atomic weight is 12.01 because the material contains 1.1% carbon-13. Malshe and Brown discuss various practical issues associated with diamond’s thermal conductivity in Chap. 11. Diamond has the lowest specific heat of any solid in the temperature range between 0 and 800 K. At 300 K the value is 6.195 J/mol-K. The thermal expansion of diamond is also low. In the range of 300 to 1200 K, it increases from 0.8 ⫻ 10⫺6 to 4.8 ⫻ 10⫺6 with increasing temperature. D.

Electrical Properties

The electrical conductivity of diamond is even more sensitive to impurities than the thermal conductivity. The energy band structure of diamond exhibits an indirect energy gap with a value of 5.47 eV at 300 K. This is sufficiently large that at temperatures near room temperature the intrinsic carrier concentration is negligible and the material is an insulator with a dielectric constant of approximately 5.7. In practice, the resistivity of highly pure diamond is in the range of 1014 –1016 ⍀-cm. However, it is also possible to dope diamond substitutionally with boron. This introduces holes in the valence band such that the electrical conductivity drops dramatically with increasing boron concentration. Resistivities as low as 0.1 ⍀-cm can be achieved by boron doping. Consequently, diamond can also take the form

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Asmussen and Reinhard

of a p-type semiconductor. The Hall mobility associated with holes in diamond is 1600 cm2/v-sec, a value that is considerably higher than the hole mobility of either silicon or gallium arsenide. The literature also contains reports of n-type doping of diamond; however, the consistent achievement of n-type diamond appears at this time to be highly problematic. Shiomi gives further information about diamond electronic properties in Chap. 12. E.

Optical Properties

It has been argued that pure diamond has the largest optical transmission bandwidth of any solid material. It extends from an ultraviolet (UV) cutoff of approximately 225 nm (corresponding to band-to-band excitation) through the far infrared and into the microwave range and beyond. There is slight absorption between 2.5 and 6 ␮m due to phonon excitation, with the absorption coefficient value peaking at about 12 cm⫺1. Throughout the entire visible region, pure diamond has essentially no optical absorption and is clear. Impurities can appreciably alter the optical transmission, however. As described by Reinhard in Chap. 13, impurities of various types can impart a wide range of colors to diamond and can even cause diamond to be opaque. Diamond has a large refractive index for a transparent material, approximately 2.4, and therefore a large reflection coefficient and a small angle for total internal reflection. Diamond is also photoconductive. There is a strong photoconductive peak at 225 nm due to excitation of electrons across the band gap in pure diamond, and in boron-doped diamond there are also peaks from 1.4 to 3.5 ␮m due to excitation of the deep-lying acceptor levels. F.

Polycrystalline Considerations

When CVD diamond is deposited on nondiamond substrates, the resulting film is polycrystalline. The question arises as to how similar the properties of polycrystalline CVD diamond are to those of single-crystal diamond. The answer is that for the most part, with some notable exceptions, it is possible to grow polycrystalline diamond with properties essentially identical to those associated with single-crystal diamond. One significant exception is that of fracture strength, which may be measured by loading diamond plates to the point of failure. Freestanding plates of CVD polycrystalline diamond are reported to have a fracture strength about an order of magnitude less than that of single-crystal diamond of the same thickness. The fracture paths in CVD diamond samples appear to be a mixture of transgranular and intergranular with no preferred direction, suggesting that the grain boundaries are not inherently weak [6]. The fracture origins appear to be at flaws [7]. A second significant difference between even the best polycrystalline dia-

Introduction

9

mond and single-crystal diamond is that of carrier mobility. Hall effect hole mobilities in p-type CVD diamond are an order of magnitude or more less than single-crystal values. Finally, polycrystalline CVD diamond samples do not show the well-defined cleavage planes of single-crystal diamond and so are not useful for traditional gem applications. Most other material properties of CVD polycrystalline diamond can be quite similar to those of single-crystal diamond—provided care is taken to achieve the desired effect. As a case in point, consider optical transmission. Raytheon, for example, has reported 350-␮m-thick CVD polycrystalline samples with optical transmission essentially identical to that of ideal diamond [6]. That is, except for the onset of band gap absorption at 225 nm and multiphonon absorption in the infrared, the sample is optically clear. However, the same cannot be said for most CVD diamond samples, which often show appreciable optical absorption and scattering, to the point of appearing to the eye to be gray or even black. The difference lies in deposition variables such as the chemical composition of the feed gases, system purity, and also, in this particular case, postprocessing. The sample surface was polished to reduce optical scattering effects. In terms of thermal conductivity, the best CVD diamond is reported to have the same value as single-crystal diamond. However, if CVD diamond is grown with more emphasis on growth rate than quality, such high values are not to be expected. Many nonoptimized CVD diamond samples have thermal conductivities that are one quarter to one half the value of single-crystal diamond. Even so, the thermal conductivity is still significantly higher than that of other high-thermal-conductivity electrical insulators such as aluminum nitride or beryllium oxide. In terms of mechanical properties, experimental studies of Young’s modulus for CVD polycrystalline diamond have resulted in values close to that of single-crystal diamond, that is, about 1000 GPa. In summary, for many (but not all) applications the properties of polycrystalline CVD diamond are sufficiently close to those of single-crystal diamond. However, not all CVD diamond is of the same quality. Therefore it is important to assess diamond quality. There are a variety of means of doing this, as reviewed by Balk and Heiderhoff in Chap. 3.

IV.

CVD DIAMOND APPLICATIONS

A.

Applications Overview

Diamond’s combination of attractive material properties makes it of interest for a large number of applications. Some of these are listed as follows. Cutting tool inserts Coated cutting and drilling tools

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Asmussen and Reinhard

Rotating seals and wear surfaces Laser heat sinks Electronic packaging Electronic passivation layers Optical windows Optical coatings X-ray lithography Gyrotron windows Cold cathode electron emitters Photon emitters Acoustic speakers Active electronic devices Thermistors Pressure sensors Surface acoustic wave devices Nuclear particle detectors UV detectors Lasers Electrodes for electrochemistry Several of these applications are considered in detail in Chaps. 10, 11, 12, and 13, namely applications related to cutting tools, thermal management, electronics, and optics. The purpose of this section is to provide a brief overview of the broad spectrum of present and potential applications. B.

Cutting Tools

Among the early successful CVD polycrystalline diamond products have been those involved in cutting tools of various sorts [8]. One approach is to grow relatively thick layers of CVD diamond from which separate freestanding pieces are obtained. These pieces are then brazed onto a cutting tool. Alternatively, the diamond may be deposited directly onto the cutting tool. Both approaches have proved to be effective in cutting most nonferrous materials including aluminum, brass, bronze, ceramics, graphite, and glass fiber–reinforced structures. Diamond end mill, drill, and router products are available. A thorough treatment of this application may be found in Chap. 10. C.

Wear Surfaces

The abrasion resistance of diamond combined with the low coefficient of friction makes diamond of interest for wear surfaces such as bearings and

Introduction

11

seals. For this application, the diamond surface should be smooth. Generally, polycrystalline diamond film surfaces are not smooth in the as-grown state. Potential solutions are postprocessing, in the form of polishing; growth with highly oriented grains such that a relatively smooth surface results; and growth with extremely small crystallites, sometimes referred to as nanocrystalline films. This is a potentially significant market for which product development is still needed. D.

Thermal Management

The high thermal conductivity of diamond, combined in some cases with its chemical inertness and high electrical resistivity, makes it of interest for a variety of thermal management applications. Laser diamond heat sinks and other thermal management substrates formed from CVD polycrystalline diamond are examples of available products. Because diamond combines exceptionally high thermal conductivity with exceptionally low electrical conductivity, it is of considerable interest in electrical packaging applications. It provides efficient paths for heat flow without compromising the electrical isolation of individual components. This application area is covered in depth in Chap. 11. E.

Transmission Applications

Diamond is of interest for several applications in which it provides a window with high transmittance for various portions of the electromagnetic spectrum. In the x-ray portion of the spectrum, diamond is of interest for x-ray lithography masks. The low atomic number of diamond results in low x-ray absorption. Another example is in high-power gyrotrons such as are used in fusion research. This application requires the transmission of very large powers (megawatts) at microwave frequencies (170 GHz) as well as the ability to dissipate heat rapidly. The ability to transmit high powers in the optical portion of the spectrum is of interest to laser designers because the design of high-power lasers is power limited by damage limits to laser optics rather than limitations of the laser medium or pumping mechanisms. The scratch resistance and chemical inertness make diamond of interest as an optical coating material as well. Optical applications of diamond are covered in Chap. 13. F.

Electron and Photon Sources

Diamond exhibits a low, and sometimes negative, electron affinity. A negative electron affinity indicates that the conduction band minimum lies above

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Asmussen and Reinhard

that of the vacuum level at the surface. Any electrons accumulating in the conduction band are thus readily available for emission into the vacuum. Therefore, diamond is of interest as an electron source and particularly as a cold-cathode electron emitter. Such field emitters are important for the development of field emission flat panel displays and vacuum microelectronic devices. Diamond has also been reported to be a photon source and, in fact, laser action has been reported based on optically active color centers [9]. Also, diamond-based diodes have demonstrated light emission upon forward bias. Further information about diamond-based photon sources is contained in Chap. 13.

G.

Acoustic Applications

High-quality loudspeakers coated with CVD diamond are marketed that show significantly improved performance at high frequencies. One version of the product consists of two layers of aluminum separated by a honeycomb structure. One of the aluminum layers is coated with diamond, giving the unit greater rigidity, which translates into improved high-frequency response. Surface acoustic wave (SAW) devices rely on interdigitated electrodes to launch elastic waves within a solid with frequencies in the MHz to GHz range. Such devices are used in the broadcast industry. Careful choice of the electrode periodicity and the material properties allows band-pass filters to be made. High-frequency operation requires very fine electrode spacing. Because acoustic waves traveling in diamond exhibit extremely high velocities, diamond offers the prospect of high-frequency (>2 GHz) operation without the need for technologically challenging electrode spacing [10].

H.

Detectors and Sensors

Diamond-based devices are also of interest for detecting a variety of radiation types as well as sensing various physical parameters such as temperature and pressure. For example, diamond thermistors have been proposed for temperature measurement in hostile environments such as chemical processing, gearbox oil, and cryogenics [11]. The piezoresistive effect of diamond has been used to sense pressure, and p-type CVD polycrystalline diamond is reported to have a large piezoresistive gauge factor [12]. Diamond is extremely radiation hard, with a 55-eV displacement energy for a carbon atom in the diamond lattice. It also acts as an ionizing radiation detector and is therefore of interest for radiation measurements where exposure to large doses is required. The large band gap of diamond make it of interest as a UV detector, based on photoconductivity, that is blind to visible light.

Introduction

I.

13

Diamond Electronics

Diamond diodes and diamond transistors have been fabricated on polycrystalline CVD diamond. In principle, diamond offers intriguing possibilities for such devices. Diamond has a large electron saturation velocity and a high breakdown field in comparison with both silicon and gallium arsenide. At electric fields above approximately 105 V/cm, the velocity of conduction band electrons in both silicon and gallium arsenide saturates at about 107 cm/sec. The saturation velocity in single-crystal diamond is over twice this high. Higher carrier velocities translate to faster switching speeds and higher operating frequencies. Also, the large band gap of diamond means that even at elevated temperatures, the intrinsic carrier concentration is negligible. In addition, the large thermal conductivity of diamond means heat generated by electronic devices fabricated in and on a diamond substrate would be rapidly dissipated. Together, these properties indicate a potential for diamond in high-speed, high-temperature, high-power, high-voltage applications. In fact, impressive results have been reported for polycrystalline diamond electronic devices with diodes operating at temperatures of 1000⬚C [13] and field effect transistors with a breakdown voltage above 200 V [14]. However the full potential of diamond electronics has not been realized because of the polycrystalline nature of the films. Therefore a significant challenge related to this area is the growth of single-crystal films on nondiamond substrates with significant areas. Chapter 12 discusses the area of active diamond electronics in detail. J.

Electrochemical Applications

The electrochemical behavior of boron-doped CVD diamond has proved to be of interest for electrochemistry applications. Compared with platinum electrodes, diamond electrodes give a much wider potential range over which no significant water decomposition occurs. Therefore, diamond electrodes are suitable substrates for reactions spanning a wide potential range in aqueous solutions [15]. They also have the advantage of chemical stability, even in highly aggressive environments.

V.

SUMMARY

The ability to deposit diamond directly over large areas on a variety of substrates has resulted in a variety of interesting current and potential applications. In most, but not all, cases, the quality of the diamond is sufficient for the intended application. However, market development has been slower

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Asmussen and Reinhard

than many participants had expected. In many cases this is based on economic considerations. Customers for a new product are not easily convinced to commit to significant purchases unless the economic advantages are clear and significant. Therefore, continued reduction in the cost of CVD diamond production is important to the future of the field. In other cases, such as electronic and optical applications, additional product quality improvement is needed. Thus, improvements in deposition methodology and film quality also remain a critical area for future work.

REFERENCES 1. 2. 3. 4. 5. 6.

7.

8.

9. 10.

11.

12. 13.

FP Bundy, HT Hall, HM Strong, RH Wentorf. Nature 176:51–55, 1955. BV Derjaguin, DB Fedoseev. The synthesis of diamond at low pressure. Sci Am 233:102–109, 1975. Properties of Diamond. De Beers Industrial Diamond Division. RM Chrenko, HM Strong. Physical Properties of Diamond. General Electric Technical Information Series, Report No. 75CRD089, October 1975. ER Berman. Physical Properties of Diamond. Oxford: Clarendon Press, 1965. TJ Valentine, AJ Whitehead, RS Sussmann, CJH Wort, GA Scarsbrook. Mechanical properties of bulk polycrystalline CVD diamond. Diamond Relat Mater 3:1168–1172, 1994. DC Harris. Development of Chemical-Vapor Deposited Diamond for Infrared Optical Applications. Status Report and Summary of Properties. Naval Air Warfare Center Weapons Division, China Lake, CA, Report NAWCWPNS TP 8210, 1994. K Bigelow. Progress in the commercialization of CVD diamond. In: M Yoshikawa, M Murakaw, Y Tzeng, WA Yarbrough, eds. Second International Conference on the Applications of Diamond Films and Related Materials, MYU, Tokyo, 1993, pp 5–12. S Rand, L Deshazer. Visible color-center laser in diamond. Opt Lett 10:481– 483, 1985. MD Whitfield, B Audic, CM Flannery, LP Kehoe, GM Crean, C Johnston, PR Chalker, RB Jackman. Polycrystalline diamond films for acoustic wave devices. Diamond Relat Mater 7:533–539, 1998. BL Jones. Novel and electronic applications of diamond materials. In: M Yoshikawa, M Murakawa, Y Tzeng, WA Yarbrough, eds. Second International Conference on the Applications of Diamond Films and Related Materials, MYU, Tokyo, 1993, pp 21–28. M Aslam, I Taher, A Masood, MA Tamor, TJ Potter. Piezoresistivity in vapor deposited diamond films. Appl Phys Lett 60:2923–2925, 1992. A Vescan, I Daumiller, P Gluche, W Ebert, E Kohn. Very high temperature operation of diamond Schottky diode. IEEE Electron Device Lett 18:536–538, 1997.

Introduction 14.

15.

15

P Gluche, A Aleksov, A Vescan, W Ebert, E Kohn. Diamond surface-channel FET structure with 200 V breakdown voltage. IEEE Electron Device Lett 18: 547–549, 1997. H Martin, A Argoitia, JC Angus, AB Anderson, U Landau. Boron-doped diamond electrodes for electrochemical applications. In: A Feldman, Y Tzeng, WA Yarbrough, M Yoshikawa, M Murakawa, eds. Applications of Diamond films and Related Materials, 3rd International Conference, 1995, pp 91–94.

2 A Short History of Diamond Synthesis John C. Angus Case Western Reserve University, Cleveland, Ohio

I.

INTRODUCTION

In this chapter a brief discussion of the events leading to the successful synthesis of diamond at high pressures is given, followed by a somewhat more detailed description of the development of methods of growing diamond by chemical vapor deposition. An excellent source of information on many aspects of diamond has been given by Davies [1]. An important review is by Hazen [2]. Bundy [3], a member of the original General Electric diamond group, has presented an extremely informative account of the highpressure, high-temperature reactions of carbon to form diamond. DeVries [4] and Angus [5] have summarized developments in the low-pressure, chemical vapor deposition of diamond; Amato [6] has given an interesting popular account of the field.

II.

SCIENTIFIC UNDERSTANDING OF DIAMOND

Two fundamental facts about diamond had to be understood before serious attempts at diamond synthesis could be undertaken. The first was to prove that diamond was composed entirely of the element carbon. The second was to determine that diamond was denser than common forms of carbon, such as charcoal. These two empirical facts led to numerous attempts to convert less dense forms of carbon into diamond by compression at high pressures. Foremost among these early workers were Hannay, Moissan, and Parsons. It is now believed that none of these attempts was successful. 17

18

Angus

The very first scientific study of diamond appears to have been done by two Italian scientists, Averani and Targioni [7], at the Accademio del Cimento in Florence. They studied diamond combustion in 1694, but they did not trap or identify the product gases. In 1772, Lavosier showed that the combustion products obtained from diamond and charcoal were similar. In 1797, Tennant did further combustion experiments and concluded that diamond ‘‘consists entirely of charcoal, differing from the usual state of that substance only by its crystallized form.’’ Because diamond was known to be denser than charcoal, compression appeared to be a reasonable route to achieve diamond synthesis. It was not, however, until an understanding of chemical thermodynamics was achieved that high-pressure synthesis was approached from a truly scientific viewpoint. The first accurate determination of a point on the diamond-graphite equilibrium line was made by the American chemists Lewis and Randall [8]. They showed that, at room temperature, diamond and graphite are in equilibrium at approximately 10,000 atmospheres (⬃1 GPa). Subsequent calculations of the diamond-graphite equilibrium curve up to approximately 2000 K were performed by Simon [9], Liepunski [10], Rossini and Jessup [11], and others. A sketch of the phase diagram of carbon is shown in Figure 1. III.

HIGH-PRESSURE SYNTHESIS

The thermodynamic calculation of the diamond-graphite stability line meant that serious, scientifically based efforts to achieve diamond synthesis at high pressures could now be made. Professor Percy Bridgman at Harvard University was a pioneer in these efforts. However, the first high-pressure synthesis of diamond was achieved by Liljeblad and Lundblad at the Swedish firm Allemanna Svenska Elektrisia Aktiebolaget (ASEA). They inexplicably did not announce their success, and the first public announcement of successful diamond synthesis was made by the General Electric Corporation in 1955. Synthesis was achieved by dissolving graphite, or other nondiamond carbons, in molten transition metals and precipitating the carbon out as diamond. This was done in the diamond-stable region of the phase diagram at temperatures in the range 1700 to 2000 K and pressures from 7 to 10 GPa. The history of these developments has been ably documented by others [1–3]. IV.

DIAMOND SYNTHESIS AT METASTABLE CONDITIONS

A.

Earliest Work

Diamond synthesis at low pressures, where diamond is metastable with respect to graphite, received serious attention, even after the diamond-graphite

Short History of Diamond Synthesis

19

Figure 1 Sketch of carbon phase diagram. Regions of metastability of diamond and graphite are bounded by (dashed line) extensions of the melting curves of diamond and graphite, respectively. Approximate regions for high-pressure, high-temperature (HPHT) and chemical vapor deposition (CVD) synthesis of diamond are shown.

equilibrium line was established. The region of diamond metastability is most easily envisioned by extension of the diamond melting curve into the graphite-stable region (see Fig. 1). This extension defines a region where diamond will not transform into liquid carbon. In principle, diamond can be synthesized anywhere within this region of metastability if graphite formation can be suppressed. It is of great interest that only a small fraction of this region has been explored, even though many different approaches have been attempted. The following account of diamond synthesis in the region of diamond metastability is abstracted from Ref. 5. The earliest relevant report appears to be that of Meincke [12]. He reported a series of experiments with carbon arcs in which diamond was formed. Surprisingly, this work, which was reported in the open technical literature, received little attention, either at the time of publication or in recent years. It is also remarkable that Meincke sent some of his samples to William Eversole for identification [13]. William G. Eversole, at the Linde Division of the Union Carbide Corporation in the United States, presented the first documented report of dia-

20

Angus

mond growth at low pressures that was subsequently confirmed by others. Eversole first proposed growing diamond at low pressures in a series of corporate memoranda dated September 9, 1949, October 6, 1949, and October 20, 1949 [14]. In these memoranda he proposed that carbon monoxide be used as a source gas to precipitate diamond on a diamond seed crystal. Growth of diamond seed crystals was achieved in the period November 26, 1952 to January 7, 1953 [14]. Conclusive proof and repetition of the experiments took place from February 17, 1953 to October 15, 1953. This predates the successful diamond synthesis at high pressure by the General Electric Company, which was accomplished in December 1954 and announced publicly in 1955 [15]. It just predates February 15, 1953, indicated by Liander as the date for the first synthesis of diamond at ASEA in Sweden [16]. The record indicates that Eversole was the first to create new diamond by any method. It should be noted, however, that Eversole grew new diamond on preexisting diamond seeds; the General Electric and ASEA synthesis started with nondiamond carbons. The General Electric Company mounted a serious effort to grow diamond at low pressures from 1951 through 1956. This work did not result in successful diamond growth, despite the exploration of numerous methods. These experiments are summarized in an internal General Electric report [17]. The General Electric Group tried several methods for depositing diamond on diamond seed crystals, including deposition from solid iron-carbon alloys, deposition from a column of liquid metal whose carbon supersaturation was controlled by an imposed temperature gradient, electrodeposition from high-temperature carbon-containing electrolytes, and vapor deposition from carbon vapor and from CO, CH4, CCl4, and CBr4. During this era there was much doubt that diamond could be grown at all under metastable conditions. Neuhas [18], for example, used theoretical arguments to show that diamond would not nucleate under metastable conditions. It was accepted without question by many that diamond could be grown only at high pressures where it is the thermodynamically stable phase. A notable exception was Bridgman [19], who said We know from the thermodynamic potential that graphite is ordinarily the preferred form, but this does not enable us to say that the actual precipitate will be graphite and not diamond. As a matter of fact there are many known instances in which an element’s unstable form, corresponding to diamond, separates from a solidifying liquid or solution in preference to the stable form.

In other words, metastable phases can form from precursors with high free energy if the activation barriers to more stable phases are sufficiently high. As the precursors fall in energy they can be trapped in a metastable

Short History of Diamond Synthesis

21

configuration. Formation of a metastable phase depends on selecting conditions under which rates of competing processes to undesired products are low. The processes competing with diamond growth are spontaneous graphitization of the diamond surface and nucleation and growth of graphitic deposits. The critical role of hydrogen in permitting metastable diamond growth was recognized by some early workers. The low-energy electron diffraction (LEED) study at the Bell Laboratories by Lander and Morrison [20] is the most significant. It was shown that a (111) diamond surface saturated with hydrogen gave an unreconstructed (1 ⫻ 1) LEED pattern. The dangling bonds normal to the surface are terminated with hydrogen atoms, which maintain the bulk-terminated diamond lattice to the outermost surface layer of carbon atoms. When hydrogen is absent, the surface reconstructs into more complex structures. Lander and Morrison [20] also noted that there was a kinetic barrier to graphitization of a hydrogen-covered diamond surface and that there was significant mobility of carbon atoms (or vacancies) in the same temperature range. They pointed out that these conditions should permit epitaxial growth of diamond. They stated Epitaxial growth of diamond on diamond is possible despite the large instability with respect to graphite. It is simply necessary to inhibit the nucleation of graphite while adding carbon atoms to the surface. Presumably this restricts the process to temperatures below about 1400⬚C and to low addition rates. . . . Apparently diamond provides a spectacular example of the theorem that extension by epitaxial growth of an unstable phase is possible if the barriers to nucleation of all more stable phases are higher.

Several early U.S. patents also described the beneficial effects of hydrogen. Hibshman [21] synthesized diamond from CO with 5% H2 in the presence of a platinum catalyst. He speculated that the catalyst promoted the formation of atomic hydrogen. Vickery [22] used gas mixtures containing 95% H2 and 5% hydrocarbon to suppress the formation of graphitic carbons. Angus and Gardner [23] discussed the use of hydrogen in a 1972 patent. The detailed molecular mechanism responsible for diamond growth has been a subject of speculation since the earliest successful studies. Angus and his coworkers in 1968 [24] suggested that Thermodynamic computations indicate the partial pressure of free carbon atoms in the vapor phase is exceedingly low, so low, in fact, that free carbon atoms in the vapor probably are not a major source of carbon for diamond growth. A more likely mechanism involves reaction

22

Angus of CH4 or some other hydrocarbon fragment with the diamond surface resulting in the deposition of a carbon atom.

Based on growth rate data, which showed a first-order dependence on [CH4] and half-order with [C2H4], the Angus group proposed a three-step mechanism: formation of mobile surface species containing a single carbon atom, surface diffusion of the species, and subsequent addition to a vacant surface site. The surface sites were proposed to be ‘‘two-bonded’’ sites, that is, kink sites on 具110典 steps on {111} surfaces or sites on {100} surfaces [25]. Critical reviews published during this era accepted the conclusion that diamond could be grown at low pressures [26,27]. There was, however, considerable skepticism that the growth rates could ever be made high enough to support commercially viable technologies. B.

Work at Case Western Reserve University, Cleveland, Ohio

Angus concluded, after reviewing the earlier work and meeting with some of the principals, in particular, Eversole, Lander, and Hibshman, that chemical vapor deposition from hydrocarbons was the method most likely to succeed. To renew the field it would be necessary to obtain absolutely convincing experimental proof of low-pressure diamond growth. Support for this effort, as a ‘‘blue sky’’ project, was obtained from Richard F. Cornelissen of the Air Force Cambridge Research Laboratories. The first goal of reproducing Eversole’s work was achieved by the mid-1960s [24]. To further prove that new diamond was being grown, diborane was added to the gas phase. P-type, semiconducting blue diamond was obtained during diamond growth; no conductivity was achieved by annealing under diborane when growth was not taking place [28,29]. The role of hydrogen in diamond growth was a major focus of the research. This was strongly motivated by the work of Lander and Morrison, who showed that a hydrogen-rich environment should suppress the nucleation and growth of unsaturated, graphitic structures. Initial experimental results clearly showed that hydrogen played a critical role in the diamond growth process [25,30]. The presence of molecular hydrogen dramatically slowed down the spontaneous nucleation and codeposition of graphite. However, molecular hydrogen by itself was not enough to suppress graphite growth completely. Eventually, graphitic carbon nucleated on the surface and suppressed further diamond growth. It was then necessary to remove the graphitic deposits, using atomic hydrogen, and to repeat the sequence. Atomic hydrogen was first used at the suggestion of Nelson C. Gardner, who had studied the decomposition of H2 and desorption of H from

Short History of Diamond Synthesis

23

tungsten surfaces while a graduate student at Iowa State University. Hot tungsten filaments were used for generating atomic hydrogen, which was used to remove graphitic deposits from the diamond after growth. The atomic hydrogen also rationalized and prepared the diamond surface for the next growth cycle. However, atomic hydrogen was not used during the growth part of the cycle. Results from the experiments done at Case Western Reserve University were presented in Kiev in September 1971 at the ‘‘InterDiamond’’ meeting. The work appeared in the scientific literature only in Russian translation [28]. C.

Work at the Physical Chemistry Institute, Moscow, Russia

Research on low-pressure diamond synthesis started at the Physical Chemistry Institute in Moscow in 1956 [31]. The Soviet work prior to 1977 has been reviewed by Badzian and DeVries [4,32]. Their earliest report was an idea of Boris Spitsyn for deposition on diamond using CBr4 or CI4 at temperatures from 800 to 1000⬚C and pressures of about 3 ⫻ 10⫺6 mm of mercury [33]. This method was described in an unpublished author’s certificate filed July 10, 1956; the patent itself did not appear until 1980. The earliest published paper from the Soviet group appeared in 1968 and described growth of diamond filaments by a vapor-liquid-solid technique using molten iron as the liquid catalytic agent [34]. Subsequently, the Soviet group explored direct chemical vapor deposition from hydrocarbons and in 1969 at a meeting in Novosibirsk presented an independent confirmation of Eversole’s results [35]. Pure methane, at pressures from 0.1 to 0.3 torr and temperatures from 950 to 1050⬚C, was used for deposition on diamond seed crystals. Much higher rates were reported than those of Eversole. A major achievement of the Soviet group was the use of atomic hydrogen during growth. This gave much higher growth rates and also permitted nucleation of new diamond crystallites on nondiamond substrates. This development apparently came about as the result of a suggestion of Valentin Varnin (A. Badzian, personal communication, 1991). He had learned of the results from Case Western Reserve University on atomic hydrogen from Dmitri Fedoseev, who had attended the 1971 Kiev meeting where the work was presented. Varnin suggested using atomic hydrogen during the growth process; the first experiments were performed by Polchanskiya. The date of these experiments is not known, but the use of atomic hydrogen is not mentioned in a 1975 Scientific American article by Deryagin [36]. Prior to the use of atomic hydrogen, the Russian group used atomic oxygen to remove graphitic codeposits in a cyclic process [37].

24

Angus

Formation of diamond crystals on nondiamond substrates was first revealed by Deryagin and others in 1976 [38]. The crystals ‘‘were produced in a chemical transport reaction occurring in a closed system at a pressure below atmospheric and a substrate temperature of the order of 1000⬚C.’’ The use of atomic hydrogen was not mentioned. Fedoseev et al. [39] described the effect of molecular hydrogen on diamond nucleation, also in 1976. In a later paper Fedoseev et al. [40] described the effect expected from the use of atomic hydrogen during the growth step.

D.

Work at NIRIM, Tsukuba, Japan

Descriptions of methods for rapid growth of diamond at low pressures were first given by a group of Japanese researchers at the National Institute for Research in Inorganic Materials (NIRIM) in Tsukuba, Japan. The leader of the NIRIM program was Nobuo Setaka; key researchers included Yoichiro Sato, Seichiro Matsumoto, and Mutsukazu Kamo. A project on metastable diamond growth was initiated at NIRIM in 1974. Successful diamond synthesis was first achieved using a hot filament to activate CH4-H2 gas mixtures and reported in December 1981 at a fall meeting of the Carbon Society of Japan. Shortly thereafter, a remarkable series of papers was presented by the NIRIM group in which techniques for vapor growth of diamond at rates of several micrometers per hour were described [41–44]. The Japanese group revealed enough to permit confirmation of their results. The hot-filament and microwave-assisted deposition processes, still very popular, were developed at NIRIM. The current worldwide interest in the new diamond technology follows directly from the NIRIM effort.

V.

SUMMARY

Diamond synthesis at low pressure by chemical vapor deposition has been the result of a number of discoveries by research groups in the United States, the Soviet Union, and Japan. Extension of existing diamond seed crystals by chemical vapor deposition was first achieved in the early 1950s by William Eversole and predates diamond synthesis at high pressures. Understanding the role of molecular and atomic hydrogen in the nucleation and growth process led to higher growth rates, suppression of nucleation of graphitic carbons, and finally the de novo nucleation of diamond crystals on nondiamond substrates. One striking feature of the history was the reluctance by many to accept the possibility of diamond synthesis outside its range of thermodynamic stability.

Short History of Diamond Synthesis

25

ACKNOWLEDGMENTS Paul Mohr made available the report describing Eversole’s work at Union Carbide Corporation. Robert DeVries provided the author with the early internal General Electric report and with many delightful hours of conversation about early diamond work at General Electric and elsewhere. Andrzej Badzian, Valentin Varnin, Boris Spitsyn, and Dmitri Fedoseev provided insights into the relationship between the early American and Russian work. A modified version of this article appeared in Il Nuovo Cimento, The Proceedings of the 1996 Enrico Fermi Summer School on the Physics of Diamond. Permission to reprint it from the Societa Italiana di Fisica is gratefully acknowledged. REFERENCES 1. 2. 3. 4. 5.

6. 7. 8. 9. 10. 11. 12. 13. 14.

15. 16. 17. 18. 19. 20. 21. 22.

G Davies. Diamond. Bristol: Adam Hilger, 1984. RM Hazen. The New Alchemists: Breaking Through the Barriers of High Pressure. New York: Times Books, Random House, 1993. FP Bundy. Mater Res Soc Symp Proc 383:3–20, 1995. RC DeVries. Annu Rev Mater Sci 17:161, 1987. JC Angus. In: KE Spear, JP Dismukes, eds. Synthetic Diamond: Emerging CVD Science and Technology. New York: John Wiley & Sons, 1994, pp 21– 39. I Amato. Stuff: The Materials the World Is Made Of. New York: Basic Books, 1997. G Averani, CA Targioni. G Litt Ital 8:221, 1711. GN Lewis, M Randall. J Am Chem Soc 37:458, 1915. F Simon. Handb Phys 10:350, 1926. OI Liepunski. Usp Khim 8:1519, 1939. FD Rossini, RS Jessup. J Res Natl Bur Stand 21:491, 1938. H Meincke. Schweiz Arch Angew Wiss Tech 23:85, 1957. H Meincke. Gemmologist 26:46, 1957. AD Kiffer. Report, Tonowanda Laboratories, Linde Air Products Co, Synthesis of Diamond from Carbon Monoxide, June 6, 1956; WG Eversole, US Patents 3,060,187 and 3,060,188, 1962. FP Bundy, HT Hall, HM Strong, RH Wentorf. Nature 176:51, 1955. H Liander, E Lundblad. Ark Kemi 16:139, 1960. RA Oriani, WA Rocco. General Electric Research Laboratory Memo No MA 36, August 1957. A Neuhas, Angew Chem 66:525, 1954. PW Bridgman. Sci Am 193:42, 1955. JJ Lander, J Morrison. Surf Sci 4:241, 1966. HJ Hibshman. US Patent 3,371,996, March 5, 1968. EC Vickery. US Patent 3,714,334, January 30, 1973.

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23. 24. 25. 26.

JC Angus, NC Gardner. US Patent 3,661,526, May 9, 1972. JC Angus, HA Will, WS Stanko. J Appl Phys 39:2915, 1968. SP Chauhan, JC Angus, NC Gardner. J Appl Phys 47:4746, 1976. JR Wedlake. In: JE Field, ed. The Properties of Diamond. London: Academic Press, 1979, pp 501–535. FP Bundy, HM Strong, RH Wentorf Jr. In: Chemistry and Physics of Carbon, Vol 10, Methods and Mechanisms of Synthetic Diamond Growth. New York, Marcel Dekker, 1973, pp 213–263. JC Angus, NC Gardner, DJ Poferl, SP Chauhan, TJ Dyble, P Sung. Sin Almazy 3:38, 1971; presented at the International Conference on Applications of Synthetic Diamonds in Industry, Kiev, 1971. DJ Poferl, NC Gardner, JC Angus. J Appl Phys 44:1418, 1973. SP Chauhan, JC Angus, NC Gardner. J Vac Sci Technol 11(1):423, 1974. BV Deryagin, DV Fedoseev. Russ Chem Rev 39:783, 1970. AR Badzian, RC DeVries. Mater Res Bull 23:385, 1988. BV Spitsyn, BV Deryagin. Author’s certificate dated July 10, 1956; USSR Patent 339,134, May 5, 1980. BV Deryagin, DV Fedoseev, BV Spitsyn, DV Lukyanovich, AV Lavrentev. J Cryst Growth 2:380, 1968. BV Deryagin, VA Ryabov, DV Fedoseev, BV Spitsyn, BM Lukyanovich, KS Uspenskaya. Second All-Union Symposium on Processes for Nucleation and Growth of Crystals and Films of Semiconducting Compounds, Novosibirsk, May 12–16, 1969. BV Deryagin, DV Fedoseev. Sci Am 233:102, 1975. BV Deryagin, DV Fedoseev. Proceedings of International Conference on Applications of Synthetic Diamonds in Industry, Kiev, September 14–18, 1971. Kiev: Naukova Dumka, 1974. BV Deryagin, BV Spitsyn, LL Builov, AA Klochkov, AE Gorodetski, AV Smolyaninov. Dokl Akad Nauk SSSR 231:333, 1976. DV Fedoseev, SP Vnukov, BV Deryagin. Zh Fiz Khim 50:2751, 1976. DV Fedoseev, KS Uspenskaya, VP Varnin, SP Vnukov. Izv Akad Nauk SSSR Ser Khim 6:1252, 1978. S Matsumoto, Y Sato, M Kamo, N Setaka. Jpn J Appl Phys Part 2 21:L183, 1982. S Matsumoto, Y Sato, M Tsutsumi, N Setaka. J Mater Sci 17:3106, 1982. M Kamo, Y Sato, S Matsumoto, S Setaka. J Cryst Growth 62:642, 1983. Y Matsui, S Matsumoto, N Setaka. J Mater Sci Lett 2:532, 1983.

27.

28.

29. 30. 31. 32. 33. 34. 35.

36. 37.

38. 39. 40. 41. 42. 43. 44.

3 Film Characterization Methods: Structure and Composition Ludwig Josef Balk and Ralf Heiderhoff University of Wuppertal, Wuppertal, Germany

I.

INTRODUCTION

Diamond thin films produced by chemical vapor deposition (CVD) are projected to have many future applications because of the unique properties of diamond [1]. The applications of diamond are often considered on the basis of the properties of natural diamond crystals. Natural diamond is known to be exceedingly hard and wear resistant, have high thermal conductivity and melting point, be optically transparent from the far infrared to the ultraviolet (5.5 eV), and have unique semiconducting properties. Common applications of diamond based on these properties are cutting tools, wear-resistant parts, medical coatings, heat sinks, acoustic response systems, inert optical coatings, and electronic and electro-optic devices. For this potential to be realized, the nucleation, growth, and resulting structure of diamond films need to be more thoroughly understood and controlled. Numerous techniques are useful in the characterization of diamond, too many to review in this chapter. In fact, even this review is limited to the techniques that have been used in the recent past to analyze CVD diamond. Carbon film deposition or growth has been carried out using different methods. Before the development of chemical vapor deposition methods, the films exhibited an sp2 bonding character, whereas the formation of sp2 bonding is suppressed or removed via an etching process at present. With respect to the critical areas of carbon phase identification, a definition was published in 1987 by Messier et al. [2] for the first time to distinguish diamond films 27

28

Balk and Heiderhoff

from other amorphous carbonaceous materials and hydrogen-rich diamondlike structures: Crystalline morphology can be observed by electron microscopy [scanning electron microscopy (SEM), and transmission electron microscopy (TEM)]. Monocrystallinity is observable by electron or x-ray diffraction. A small Raman peak is present at 1332 cm⫺1. This definition tolerates small impurities, such as nitrogen, hydrogen, silicon, or metals, that are also present in natural diamond. The two techniques that have become the standard methods of assessing the percentage of CVD diamond and the surface morphology are Raman scattering and SEM. The application of SEM is almost qualitative, but the Raman scattering results can be quantitative in some cases.

II.

RAMAN SPECTROSCOPY

Raman spectroscopy has emerged as the most frequently used tool to characterize diamond films prepared by various chemical vapor deposition methods because of the spectroscopic signature [3–13] (see Fig. 1). This technique provides well-known spectra for different carbonaceous compounds, such as graphite, glassy carbon, or amorphous diamond-like carbon, and is also used to determine the phase purity and crystalline perfection by analyzing the peak positions and peak width. The Raman spectra of different forms of sp2- and sp3-bonded carbon are illustrated in Figure 2. The spectra of diamond exhibit a sharp peak that is centered at a Raman shift from 1331 to 1335 cm⫺1 (at room temperature) with a bandwidth Du1/2 at half-intensity less than 2 cm⫺1, whereas graphite exhibits a broad band centered from 1565 to 1585 cm⫺1 (see Fig. 3). The peak frequency is known to downshift with temperature and to upshift when compressive internal stresses are present.

Figure 1

Schematical setup of a Raman experiment.

Film Characterization Methods

Figure 2

Raman spectra of different forms of sp 2- and sp 3-bonded carbon.

29

30

Balk and Heiderhoff

Figure 3

Raman-active normal modes in graphite.

The band broadening is related to internal stresses, thermoelastic stresses, pure thermal effects, and the density of defects in the crystal as well as the crystallite size. For microcrystalline graphite a strong feature appears at 1350 cm⫺1, and the 1580 cm⫺1 feature shifts to lower wave numbers with decreasing crystalline size. The feature at 1350 cm⫺1 has been identified as a vibrational mode that occurs at the boundary of the Brillouin zone.

III.

ELECTRON MICROSCOPY

In the early phase of the development of diamond technology, SEM micrographs captured the attention of researchers throughout the world. SEM is an excellent tool for the examination of the surface morphology of CVD diamond and of growth features such as steps and islands on the diamond surfaces (see Figs. 4 and 5). It has been recognized that CVD diamond films have a wide range of surface morphologies that are highly dependent upon the experimental conditions. These surfaces correlate with other techniques such as Raman spectroscopy. For example, if growth parameters were not optimized, the morphology could become sub-microcrystalline and then cauliflower-like. This correlated with a deterioration of the diamond peak and an increase in the graphitic peak in the Raman spectrum. A review of several reports on surface morphologies of diamond films that have related the morphological development to various deposition parameters is given by Zhu et al. [14]. At present, high-resolution transmission electron microscopes mainly work with acceleration voltages of 200 to 400 kV and can be combined with electron diffraction, x-ray microanalysis, and electron energy loss spectroscopy (EELS) modes (see Fig. 6). In the Bragg contrast mode, the objective diaphragm selects the primary beam for bright-field imaging and

Film Characterization Methods

Figure 4

31

SEM micrograph of a CVD diamond surface. (Courtesy of Zeiss.)

Figure 5 Unprocessed electron beam patterns from 100 nm2 areas of an uncoated polycrystalline diamond layer. (Courtesy of Zeiss.)

32

Figure 6

Balk and Heiderhoff

Schematical setup of a transmission electron microscope.

Bragg reflected beams for dark-field imaging (see Fig. 7). When using small electron probes, information about crystal symmetry, specimen thickness, and lattice distortion can be obtained by the convergent-beam electron diffraction methods (see Fig. 8). The possibility to use higher scattering angles in the diffraction mode makes it possible to record higher order Laue zone (HOLZ) diffraction patterns. Structural determination of the diamond crystalline morphology can be accomplished using transmission electron microscopy [15–19]. Further, TEM studies have shown that a large number of defects, which cannot be detected by other techniques, are present in the layers [20–24]. There are two methods of observing the thin films [25]. One

Film Characterization Methods

Figure 7

33

Bright-field image of a CVD diamond film. (From Ref. 18.)

method is the observation of a film that is thinned in the direction of a cross section or surface plane. This method can be used with any thick sample. But it takes a long time to prepare thin films. The other method is observing the side surface and does not require any thinning of the film or substrate. EELS and especially high-resolution electron energy loss spectroscopy (HREELS) obtained in the transmission mode in a TEM can also be utilized to examine the bonding character of a carbon film (see Fig. 9). Energy losses due to K-shell ionization and the fine structure due to interband transitions and plasmon losses that appears at higher energies can be used to identify different phases of carbon because the spectrum is strongly dependent on the type of bonding present. The fine features of these growth defects can be clearly observed and studied by high-resolution electron microscopy (HREM), which provides, in addition to detailed atomic resolution images, crystallographic information on the defects and their boundaries. Several studies obtained a view of the nature of stacking faults, twins and twinning configurations, as well as the interface between the substrate and the diamond film (see Fig. 10).

34

Balk and Heiderhoff

Figure 8

Diffraction pattern corresponding to Fig. 7. (From Ref. 18.)

Figure 9

EELS of bulk diamond and polycrystalline graphite.

Film Characterization Methods

35

Figure 10 HERM (high-resolution electron microscopy) of twins ending at a virtually amorphous inclusion. T, twin lamellae; I, inclusion; L, lattice image confusion. (From Ref. 19.)

IV.

DIFFRACTION

Low-energy electron diffraction (LEED) is well suited to study the structure of the outermost layers of diamond films. It is possible to combine LEED with Auger electron spectroscopy (AES) to establish the chemical surface situation if the depth of the scattered electrons is small and does not exceed one or two atomic layers. In order to carry out such studies, one must first obtain an unequivocally clean film surface. But it is very difficult to bombard the surface with, for example, argon ions that are sufficiently energetic to remove adsorbed or combined surface layers. The outermost surface layer can become graphitic [26–37] and cannot be annealed out, as a reconstruction of the diamond surface can occur if the impurities are removed by heat treatments [38–45] (see Figs. 11 and 12). LEED studies have shown that hydrogen plays an important role in the reconstruction of diamond surfaces [40,43]. Thermal desorption studies have indicated that hydrogen and oxygen are adsorbed on diamond surfaces [38,44]. Figure 12 illustrates the structural model for the (100) diamond surface: (a) 2 ⫻ 1 and (b) 1 ⫻ 2 reconstruction. Although AES provides valuable compositional information, it does not yield any information about trace impurities because of the sensitivity limitation of the technique. Conventional techniques such as secondary ion mass spectrometry (SIMS) or laser microscope mass analysis spectroscopy

36

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Figure 11 Carbon 1s photoelectron spectra from (111) diamond. (a) Terminated surface polished and heated to 1100 K. (b) Clean surface heated to 1250 K. (c) Clean surface hydrogenated by atomic hydrogen. (From Ref. 32.)

(LAMMA) are much more sensitive than AES, and when electronic devices were realized, such chemical analysis became more important. Several alternative techniques such as Rutherford backscattering have been utilized for detecting hydrogen in diamond films. SIMS can detect hydrogen, but quantification is difficult because of the presence of background hydrogen in the vacuum system. Synchrotron radiation laboratories around the world are using x-ray diffraction (XRD) for the structural determination of diamond. These range from the nondestructive slicing of large diamonds by synchrotron x-ray sec-

Film Characterization Methods

37

Figure 12 Surface model for (a) 2 ⫻ 1 diamond (100) and (b) 1 ⫻ 1 diamond (100). (䡩) H atom; (●) C atom. (From Ref. 59.)

tion topography [46,47] to high-resolution studies of the spike diffuse reflections from platelet crystal topography (see Fig. 13). Mai et al. [48] pointed out the intrinsic suitability of diamond for xray beam conditioning, for example, due to its strong x-ray reflectivity and low x-ray absorption. A detailed comparison of natural and synthesized diamond for these applications was given by Lang [49]. A typical scattering geometry used for x-ray measurements is illustrated in Figure 14. In recent years, several authors have reported on the growth of textured diamond films. X-ray diffraction was used most often to determine the growth orientation and texture of these films [50–55] (see Figs. 15 and 16). The detailed analysis of the texture and surface morphology of polycrystalline diamond films utilized the fact that growth starts from randomly oriented nuclei on Si (100) and Si (111). The texture develops with increasing film thickness because of the competition of differently oriented grains (see Fig. 17). Twinning during the nucleation stage of the film appears to stabilize preferential growth along the (100) or (111) direction. The growth

38

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Figure 13 (a) X-ray projection topography of type a natural diamond shaped as shown in b. (b) Perspective sketch of the part of the polished parallelepiped specimen that contains a large stacking fault. (From Ref. 49.)

parameter ␣ = V100 /(兹3V111), where V100 and V111 are the growth rates on {100} and {111} faces, can be varied by controlling the process parameters. In addition, other techniques such as extended x-ray absorption fine structure (EXAFS) or extended electron energy loss fine structure (EEELFS) are beginning to be utilized for bonding analysis. Several authors reported the x-ray absorption spectra of diamond films (see, for example, Ref. 56), especially to observe the Si-diamond interface [57–60].

V.

LUMINESCENCE

The luminescence from diamond has been studied for more than 50 years and is an established tool to investigate chemical and structural defects in

Film Characterization Methods

Figure 14 62.)

39

Typical scattering geometry used for x-ray measurements. (From Ref.

diamond films. The spectral range covered by the luminescence extends from 5.3 eV in the ultraviolet (‘‘edge emission’’ corresponding to the indirect energy gap [63]) to around 1.2 eV in the near infrared (‘‘H2’’ vibronic band [64]). Approximately 120 optical centers that have been documented for diamond are listed by Clark et al. [65]. The major spectra associated with edge emission, vibronic band, and ‘‘band A’’ emission are discussed in Ref. 66. Figure 18 illustrates a block diagram of an integral, spectral, and timeresolved CL experiment [69]. Cathodoluminescence has proved to be very useful in the characterization of the film because of the high spatial resolution and with respect to the wide energy gap of diamond (Eg = 5.5 eV) (see Fig. 19). The generation rate of a 50-kV beam at a current density of 0.01 A/cm2 is about 2 ⫻ 1023 electron-hole pairs per cm3 per second [67] and the penetration depth is comparable to that with GaAs. The electron beam generates simultaneously a wide variety of intrinsic and extrinsic processes. Cathodoluminescence spectroscopy is therefore less selective than photoluminescence spectroscopy, where the energies of the incident photons are less than the band gap. Diamond is an indirect semiconductor, and the edge emission may be observed only from films that are relatively free from defects. For indirect transitions a phonon must be created, with its energy បw being taken from the stored energy in the exciton. The energy emitted in the photon is given by hu = Eg ⫺ Ex ⫺ បw, where Ex is the exciton binding energy. Free excitons with the emission of transverse acoustic, transverse optic, and longitudinal optic phonons of wave vectors ⫾ k having values between 87 and 163 meV

40

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Figure 15 SEM image and XRD pole figure of a highly oriented (100)-textured diamond film [exhibiting an 8⬚ full width at half-maximum of the (200) peaks] on a (100) Si substrate. (From Ref. 54.)

Film Characterization Methods

41

Figure 16 (a) Experimental XRD intensity map of the C 1S emission of a diamond (111) surface. (b) Calculation for a diamond cluster of 200 C atoms in 10 layers. (From Ref. 61.)

have been found. In contrast, the luminescence from a bound excition can proceed without creating phonons. Qualitatively, this reflects the localization of the hole on an acceptor center. The edge recombination radiation spectrum from a natural p-type semiconducting diamond is illustrated in Figure 20. Regarding donor-acceptor pair spectra, the donor captures an electron and the acceptor captures a hole when electron-hole pairs are generated by the electron beam. This mechanism was used for a long time to explain the broad band A luminescence that is observable in all types of natural, synthetic, and CVD diamond and extends from about 2 up to 3.5 eV. The energy is given by E(r) = Eg ⫺ EA ⫺ ED ⫹

e2 ea 2 ⫺ 4␲␧ r 4␲␧ r 6

where EA and ED are the acceptor and donor binding energies, ␧ is the static dielectric constant, r is the distance between the donor and acceptor, and a is an adjustable parameter in the polarization term [68]. Today, however, one believes that it is better to use the description band A than donor-acceptor pair recombination because at present there is no theory that describes all the phenomena that are observable, for example, in time-resolved and temperature-dependent measurements (see Fig. 21). Investigations have suggested that band A is due to dislocations or vacancy clusters acting as recombination centers for electron-hole pairs [71].

42

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Figure 17 XRD patterns of one given diamond film for different film thicknesses. (From Ref. 62.)

Finally, one has to note that among band A and radiation damages, nitrogen is by far the most common impurity in diamond with many forms. Many sharp lines are correlated with the different nitrogen impurities. The 575-nm system, for example, is most intense in cathodoluminescence spectra in nitrogen-doped thermal CVD diamond. It turns out that the system is due to a single nitrogen atom and a vacancy [72]. Collins and Robertson [73] showed that the zero-phonon line responds relatively rapidly to random stress S and proposed that S can be estimated from the line width ⌬␭ using the expression ⌬␭ = S ⫻ 10 meV/GPA.

Film Characterization Methods

43

Figure 18 Block diagram of an integral, spectral, and time-resolved CL experiment. (From Ref. 69.)

VI.

THERMAL CONDUCTIVITY

It is well known that diamond crystals have the highest known thermal conductivity. The thermal conductivity ␬ of type IIa natural diamond at room temperature (␬ = 2200 W m⫺1 K⫺1) is a factor of 5 greater than that of pure

Figure 19

SEM and Cl micrographs of a CVD diamond film. (From Ref. 69.)

44

Balk and Heiderhoff

Figure 20 Cl spectrum of the edge recombination from natural p-type diamond. (From Ref. 63.)

Figure 21

Time-resolved Cl spectra of a natural diamond. (From Ref. 69.)

Film Characterization Methods

45

Table 1 Thermal Properties of Diamond and Other Materials at Room Temperature

Material Diamond (natural IIa) Copper AlN Si

Thermal conductivity (W m⫺1 K⫺1)

Thermal diffusivity (cm2 sec⫺1)

Linear thermal expansion (10⫺6 K⫺1)

2200 400 200 140

12 1.2 0.8 0.8

1 16 4 3

copper and over a factor of 10 higher than that of commonly used semiconductors (see Table 1). Many researchers have observed a large range of thermal conductivities in films and even in single crystals due to impurities or defects. Polycrystalline diamond films, because of their crystalline boundaries and graphitic contaminations, are not expected to have the same high thermal conductivity as single crystals. Today the highest values 2000 W m⫺1 K⫺1 to 2200 W m⫺1 K⫺1 were found for MWCVD films [70,74,75]. Anthony et al. [76] examined high-quality diamond crystals having different isotopic distributions of carbon. Experimentally, they found an increase of 50% in the diffusivity (thermal diffusivity ␣ related to the thermal conductivity ␬ by ␣ = ␬/c␳, where c is the thermal capacity and ␳ is the density of the material) of isotopically decreased diamond crystals (see Table 2), whereas they had expected only 5% for the isotopically purest specimen. Today there is no theory that is able to give a definite prediction of the measured enhancement in conductivity achieved by reducing the isotope concentration [77,78].

Table 2 Thermal Conductivity of High-Conductive Diamonds Depending on the Isotope Concentration Material 0.07% 13C diamond 0.5% 13C diamond 1.0% 13C diamond (natural abundance) Source: Ref. 76.

Thermal diffusivity (cm2 sec⫺1)

Thermal conductivity (W m⫺1 K⫺1)

18.5 14.5 12.4

3300 2600 2200

46

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In the case of CVD diamond, the thermal conductivity is difficult to measure accurately because of the extremely high values. The difficulty is further increased by the anisotropic nature and the geometry of the samples. Even when comparing measurement techniques that measure bulk, in-plane thermal conductivity, results differ significantly. For instance, a sample that was measured at a large number of laboratories around the world was found to have a thermal conductivity of 1400 to 1550 W m⫺1 K⫺1 by the AC calorimetry method and the converging wave method and found to have a thermal conductivity of 2500 W m⫺1 K⫺1 according to a modified Angstrom method [79]. The measuring methods vary considerably in requirements for operating skills and sample preparation, and they can be divided into contact and noncontact, steady-state or dynamic methods. A review of the different methods is given by Fournier and Plamann [80]. A brief description of two standard methods is given as follows. A.

Conventional Method

In this method, the sample is shaped into a rectangular bar. Two thin-film heaters are evaporated directly onto the sample surface, one near each end (see Fig. 22). The heat flux through the sample is obtained by knowing the electrical power input to the heaters after all the revenues of heat loss have been quantified. Normally, the measurements are performed with the sample in vacuum, surrounded by a heated shield at a known temperature, the temperature of the thermal ground, to minimize unwanted heat transfer through radiation. A row of very fine thermocouples, so that they do not have a thermal gradient of their own, are then attached to the sample bar at a known distance from each other. The measured gradient dT/dx can be corrected for radiative loss and used to calculate ␬. An alternative is to use sinusoidal

Figure 22 Illustration of the two-heater heated-bar technique of measuring the thermal conductivity.

Film Characterization Methods

47

heat flows. Then the thermal waves would be detected and the change in either amplitude or phase of the waves used to determine the diffusivity. Further, it is possible to apply the heat pulse to one side of the sample from a flash lamp or laser and to monitor the temperature with an optical detector on the opposite side of the sample. For films that are transparent, an opaque layer must be evaporated onto the surface. B.

Mirage Effect Method

This thermo-optical method is based on the sensitive detection of thermal gradients in the gas layer adjacent to heated sample surfaces [81]. The experimental setup is shown in Figure 23. The light of a focused modulated laser beam is used as the source of heat and launches a thermal wave in the sample. Detection is through the mirage effect, which utilizes a second laser beam to traverse the heated air above the heated sample. The periodic deflection of the probe beam is monitored by the use of a position-sensitive or angular detector.

VII.

SCANNING PROBE TECHNIQUES

Some papers have shown the feasibility of the scanning tunneling [82,88] and scanning force techniques [89–92] to study the morphologies of CVD diamond films, especially nucleation and growth. Scanning tunneling microscopy (STM) and scanning force microscopy (SFM) routinely achieved atomic resolution on many substrates and are suited to the determination of the nanometer-scale structure of diamond films. STM is a useful characterization technique especially because it provides a direct method for observing surfaces and local electronic structures. STM has very high three-dimensional resolution and does not require special sample preparation, in contrast to, for example, TEM. The graphite form of

Figure 23

Experimental setup of the mirage effect method.

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Balk and Heiderhoff

carbon has proved the standard for demonstration of atomic resolution in air and the technique has been used in the examination of other forms of bonded carbon. As the surface of CVD diamond is stable, STM images can be obtained even in air. It is generally recognized that this stability is due to the termination of freestanding bonds by hydrogen. It is very difficult to achieve high resolution because undoped diamond is normally an insulator and boron doping has been shown to change the surface morphology of diamond films. Therefore SFM, which has no such requirement, would seem to be a more generally applicable tool. Topography and microfriction can be determined simultaneously by SFM by measuring the normal and lateral deflections (torsion of the lever) of the cantilever by means of a laser beam. Since scanning probe microscopy was invented, many different applications have been developed to image various specimen features with high spatial resolution [93,94]. The efficiencies of STM-EBIC (EBIC: electron beam–induced current) and conventional SEM-EBIC measurements on diamond films were compared for the first time by Koschinski et al. [95]. EBIC investigations make it possible to characterize the electrical properties (carrier concentration, electrical potential) of the specimen under test on a microscopic scale [96] (see Fig. 24). Excess carriers are generated in a small volume of the sample

Figure 24

Schematical diagram of the STM-EBIC setup. (From Ref. 95.)

Film Characterization Methods

49

by the electron beam and induce a detectable current that depends on the structure of the sample, the position of the electron beam, and the electrical field inside the sample. This can be used to analyze inhomogeneities and local electrical properties of CVD diamond films (see Fig. 25). The determination of the electrical conductivity with respect to the localization of defects is a problem that is difficult to solve, especially when reaching a nanometer scale. Based on SFM, so-called scanning resistance microscopy (SRM) [97,98] and contact current measurements (CCMs) [99] are able to obtain two-dimensional profiles. In addition, CCM allows simultaneous measurement of the current signal and the topography. CCM determines the variation of the electronic properties of the sample by analyzing the current characteristics. For this purpose, a metallized SFM tip is scanned in contact mode over the sample surface and a potential is applied between the tip and a second fixed electrode. The current signal and the topography are obtained simultaneously and thereby can be easily correlated. It is useful to determine the thermal conductivity in the nanometer region by using an SThM (scanning thermal microscope) [100]. The probe consists of a filament that is resistively heated (see Fig. 26). Being the thermal element of the probe, this filament is part of a Wheastone bridge. High-thermal-conductivity areas of the sample cause the thermal feedback loop to increase the applied voltage to keep the temperature of the tip constant. The applied voltage, therefore, correlates directly with the thermal conductivity (see Fig. 27). A comparison of the determination of the electrical and thermal conductivity in the nanometer region is given by Maywald et al. [101].

Figure 25 Illustration of defects in natural diamond by the EBIC method: (a) SE and (b) EBIC images.

50

Balk and Heiderhoff

Figure 26

VIII.

Schematical drawing of the probe of an SThM. (From Ref. 95.)

SUMMARY

No other material system has been analyzed in such a way as diamond films around the world in recent years. Many applications of diamond related to the large spectrum of properties make it necessary to investigate the samples with many different characterization systems.

Figure 27 101.)

Topography and thermal images of an Si-diamond interface. (From Ref.

Film Characterization Methods

51

In this chapter we presented an overview of the analyzing systems as well as their problems with respect to these outstanding properties. Technological advances in film growth and characterization methods are occurring constantly and theories are beginning to evolve. In some areas such as heat sinks, x-ray windows, and wear-resistant coatings on cutting tools, diamond is already commercial available. However, CVD diamond growth technology is still far from realizing all of the further attractive potential applications. Some of those will certainly be available in the near future, whereas other will require continued research or may even prove impossible.

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.

JE Field. The Properties of Natural and Synthetic Diamond. London: Academic Press, 1992. R Messier, AR Badzian, T Badzian, KE Spear, P Bachmann, R Roy. Thin Solid Films 153:1, 1987. RO Dillon, JA Woolam, V Katkanant. Phys Rev B 29:3482, 1984. SK Sharma, HK Mao, PM Bell, JA Xu. J Raman Spectrosc 16:350, 1985. A Richter, HJ Scheibe, W Pompe, K-W Brzezinka, I Mu¨hling. J Noncryst Solids 88:131, 1986. RJ Nemanich, JT Glass, G Lucovsky, RE Schroder. J Vac Sci Technol A 6: 1783, 1988. DS Knight, WB White. J Mater Res 4:385, 1989. LH Robins, EN Farabaugh, A Feldman. J Mater Res 5:2456, 1990. RE Shroder, RJ Nemanich, JT Glass. Phys Rev B 41:3738, 1990. DW Kweon, J-Y Lee. J Appl Phys 69:8329, 1991. PV Huong. Mater Sci Eng B11:235, 1992. JE Graebner, JA Mucha, L Seibles, GW Kammlott. J Appl Phys 71:3143, 1992. PK Bachmann, DU Wiechert. Diamond Relat Mater 1:422, 1992. W Zhu, BR Stoner, BE Williams, JT Glass. Proc IEEE 79:621, 1991. Y Goto, K Kurihara, Y Sawamoto, T Kitakohji. Appl Phys Lett 60:172, 1992. PJ Fallon, LM Brown. Diamond Relat Mater 2:1004, 1993. H Sjo¨stro¨m, L Hultmann, JE Sundgren. Diamond Relat Mater 2:562, 1992. P Wurzinger, M Joksch, P Pongratz. Inst Phys Conf Ser 134:157, 1994. M Joksch, P Wurzinger, P Pongratz, R Haubner, B Lux. Diamond Relat Mater 3:681, 1994. BE Williams, JT Glass. J Mater Res 4:373, 1989. W Zhu, AR Badzian, R Messier. J Mater Res 4:659, 1989. JL Kaae, PK Gantzel, J Chin, WP West. J Mater Res 5:1480, 1990. J Narayan. J Mater Res 5:2414, 1990. K Suzuki, M Ichihara, S Takeuchi, N Ohtake, M Yoshikawa, K Hirabayashi, N Kurihara. Philos Mag 65:657, 1992.

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Balk and Heiderhoff LD Marks, DJ Smith. Nature 303:316, 1989. S Evans, JM Thomas. Proc R Soc Lond A353:103, 1977. PG Lurie, JM Wilson. Surf Sci 65:453, 1977. TE Derry, RW Fearick, JP Sellschop. Nucl Instrum Methods 170:407, 1980. G Braunstein, R Kalish. Appl Phys Lett 38:416, 1981. TJ Whetton, AA Armstead, TA Grzybowski, AL Ruoff. J Vac Sci Technol A2: 477, 1984. JF Prins, TE Derry, JPF Sellschop. Phys Rev B 34:8870, 1986. S Evans. The Properties of Natural and Synthetic Diamond. London: Academic Press, 1992. R Kalish. Diamond Relat Mater 2:621, 1993. A Boudina, E Fitzer, G Wahl, H Estrom. Diamond Relat Mater 2:678, 1993. PK Bachmann, D Leers, DU Wiechert. Diamond Relat Mater 2:683, 1993. J Ullmann, A Weber, B Mainz, J Stiegler, T Schuhrke. Diamond Relat Mater 3:663, 1994. VS Varichenko, AM Zaitzev, MS Rusetskij, VF Stelmakh, K de Weldige, T Fries, K Wandelt, AJ Didyk, VA Laptev. Diamond Relat Mater 3:711, 1994. S Matsumoto, Y Sato, N Setaka. Carbon 19:323, 1981. WS Yang, J Sokolov, F Jona, PM Marcus. Solid State Commun 41:191, 1982. BB Pate, Surf Sci 165:83, 1986. TE Derry, L Smit, JF Van der Veen. Surf Sci 167:502, 1986. E Sowa, GD Kubiak, RH Stulen, MA Van Hove. J Vac Sci Technol A6:832, 1988. JJ Lander, J Morrison. Surf Sci 4:913, 1988. RE Thomas, RA Rudder, RJ Markunas. J Vac Sci Technol A10:2451, 1992. T Ando, T Aizawa, K Yamamoto, Y Sato, M Kamo. Diamond Relat Mater 3: 975, 1994. AR Lang. Diamond Relat Mater 2:106, 1993. M Moore, R Wagget, W Wierzchowski. Diamond Relat Mater 2:115, 1993. ZH Mai, S Mardix, AR Lang. J Appl Crystallogr 13:180, 1980. AR Lang, M Moore, JC Walmsley. The Properties of Natural and Synthetic Diamond. London: Academic Press, 1992. X Jiang, CP Klages, R Zachai, M Hartweg, PJ Ellis. J Mater Res 8:3438, 1993. A Badzian, T Badzian. Diamond Relat Mater 2:147, 1993. C Wild, P Koidl, W Mu¨ller-Sebert, H Walcher, R Kohl, N Herres, R Locher, R Samlenski, R Brenn. Diamond Relat Mater 2:158, 1993. M Schreck, R Hesssmer, S Geier, B Rauschenbach, B Stritzker. Diamond Relat Mater 3:510, 1994. BA Fox, BR Stoner, DM Malta, PJ Ellis. Diamond Relat Mater 3:382, 1994. C Wild, R Kohl, N Herres, W Mu¨ller-Sebert, P Koidl. Diamond Relat Mater 3:373, 1994. TW Capehart, TA Perry, CB Beetz, DN Belton, GB Fisher, CE Beall, BN Yates, JW Taylor. Appl Phys Lett 55:957, 1989. R Meilunas, MS Wang, KC Sheng, RPH Chang, RP Van Duyne. Appl Phys Lett 54:2204, 1989.

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67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84.

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FX Lu, GS Jiang, BX Yang, J Chen, JJ Wang, Y Yuan. Diamond Relat Mater 2:575, 1993. T Ando, T Aizawa, K Yamomoto, Y Sato, M Kamo. Diamond Relat Mater 3:975, 1994. MC Polo, J Cifre, J Esteve. Diamond Relat Mater 3:492, 1994. OM Kuettel, J Osterwalder, L Schlapbach, R Agostino. Diamond Relat Mater 2:548, 1993. C Wild, N Herres, P Koidl. J Appl Phys 68:973, 1990. PJ Dean, EC Lightowlers, DR Wight. Phys Rev 140:A352, 1965. SC Lawson, AT Collins, S Satoh, H Kanda. Proceedings 2nd International Conference on New Diamond Science and Technology, 1991, p 709. CD Clark, AT Collins, GS Woods. The Properties of Natural and Synthetic Diamond. London: Academic Press, 1992. R Heiderhoff, LJ Balk. Presented at the Thirteenth Pfefferkorn Conference on Luminescence, Niagara Falls, Canada, May 13–18, 1994; submitted to Scanning Microsc Int, 1994. G Davies. The Properties of Natural and Synthetic Diamond. London: Academic Press, 1979. PJ Dean. Phys Rev A 139:588, 1965. R Heiderhoff, R Spitzl, M Maywald, V Raiko, J Engemann, LJ Balk. Proc SPIE 2151:59, 1994. R Heiderhoff, P Koschinski, M Maywald, LJ Balk, PK Bachmann. Diamond Relat Mater, in press. RJ Graham, F Shaapur, Y Kato, BR Stoner. Appl. Phys. Lett 65:292, 1994. AT Collins, SC Lawson. J Phys Condens Matter 1:6929, 1989. AT Collins, SH Robertson. J Mater Sci Lett 4:681, 1985. OW Ka¨ding, M Ro¨sler, R Zachai, HJ Fu¨ßer, E Matthias. Diamond Relat Mater 3:1178, 1994. PK Bachmann, H-J Hagemann, H Lade, D Leers, DU Wiechert, H Wilson, D Fournier, K Plamann. Diamond Relat Mater, in press. TR Anthony, WF Banholzer, JF Fleischer, L Wei, PK Kuo, RL Thomas, RW Pryor. Phys Rev B 42:1104, 1990. JR Olson, RO Pohl, JW Vandersande, A Zoltan, TR Anthony, WF Banholzer. Phys Rev B 47:14859, 1993. L Wei, PK Kuo, RL Thomas, TR Anthony, WF Banholzer. Phys Rev Lett 70: 3764, 1993. G Lu, A Feldmann, J Graebner, O Ka¨ding, PK Kuo, A Maesano, RP Miller, D Pickrell, S Preston, D Slutz. Diamond Relat Mater, in press. D Fournier, K Plamann. Diamond Relat Mater, in press. AC Boccara, D Fournier, J Baoz. Appl Phys Lett 36:130, 1980. KF Tuner, BR Stoner, L Bergmann, JT Glass, RJ Nemanich. J Appl Phys 69: 6400, 1991. MP Everson, MA Tamor. J Vac Sci Technol B9:1570, 1991. H-G Busmann, H Sprang, IV Hertel, W Zimmermann-Edling, H-J Gu¨ntherrodt. Appl Phys Lett 59, 1991.

54 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101.

Balk and Heiderhoff ME Welland, AW McKinnon, S O’Shea, GAJ Amaratunga. Diamond Relat Mater 1:529, 1992. H Sasaki, H Kawarada. Jpn J Appl Phys 32:L1771, 1993. VS Varichenko, AM Zaitsev, MS Rusetskii, VF Stelmakh, K de Weldige, T Fries, K Wandelt, AJ Didyk, VA Laptev. Diamond Relat Mater 3:711, 1994. L Vazques, O Sanchez, F Messeguer, JM Albella. Diamond Relat Mater 3: 715, 1994. LF Sutcu, MS Thompson, CJ Chu, RH Hauge, JL Margrave, MP D’Evelyn. Appl. Phys Lett 60:1685, 1992. LF Sutcu, CJ Chu, MS Thomson, RH Hauge, JL Margrave, MP D’Evelyn. J Appl Phys 71:5930, 1992. U Bo¨gli, A Blatter, A Ba¨chli, R Lu¨thi, E Meyer. Diamond Relat Mater 2:924, 1993. K Schiffmann, X Jiang. Appl Phys A 59:17, 1994. H-J Gu¨ntherodt, R Wiesendanger. Scanning Tunneling Microscopy 1–3. Berlin: Springer-Verlag, 1992. D Sarid. Scanning Force Microscopy. Oxford: Oxford University Press, 1991. P Koschinski, K Kaufmann, LJ Balk. Electron Microsc 2b:1121, 1994. HJ Leam. J Appl Phys 53:R51, 1982. Y Huang, CC Williams. J Vac Sci Technol B12:369, 1994. C Shafai, DJ Thomson, M Simard-Normandin. J Vac Sci Technol B12:378, 1994. LJ Balk, M Maywald. Mater Sci Eng B24:203, 1994. RB Dinwiddie, R Pylkki, PE West. Therm Conduct 22:668, 1994. M Maywald, RJ Pylkki, LJ Balk. J Scan Microsc 2:181, 1994.

4 Deposition Chemistry: Deposition Pathways, Nucleation, and Growth David S. Dandy Colorado State University, Fort Collins, Colorado

Michael E. Coltrin Sandia National Laboratories, Albuquerque, New Mexico

I.

INTRODUCTION

The unique properties of diamond, such as hardness and high thermal conductivity, make it an important new material in a wide range of applications, for example, protective coatings and thermal management. However, the high cost of material production has limited the commercial use of diamond thin films to a few, very specialized applications. In chemical vapor deposition (CVD) of diamond, the factors driving cost include low reagent utilization, low deposition rates, high energy consumption, large thermal management loads at the substrate, and capital equipment costs. For these reasons, there has been much research on the CVD diamond process, including both work on empirical process optimization and work on understanding the fundamental steps in the process. The latter, more basic research is done in the expectation that knowledge of the underlying chemistry, physics, transport, and materials issues will enable optimization (and cost reduction) through model-based process design. In this chapter a review is presented of the current understanding of diamond CVD growth mechanisms. Because diamond deposition depends on different chemical and transport processes occurring in the gas phase and on the surface, discussion of these mechanisms is separated into sections that focus on gas-phase processes, surface chemistry, and nucleation phe55

56

Dandy and Coltrin

nomena. Discussion has also been included on experimental and theoretical studies of diamond deposition to illustrate the insight gained from macroscopic measurements and predictions. Absent from this chapter is a discussion of alternative chemistries in diamond CVD. For example, the addition of oxygen in noncombustion systems to enhance growth rate and film quality and the use of fluorinated hydrocarbons to achieve deposition at lower substrate temperatures are both important areas of study, but these do not change the basic mechanisms controlling the growth of diamond by CVD.

II.

GAS-PHASE PROCESSES IN CVD DIAMOND

All diamond CVD processes have in common a highly energetic activation stage in the gas phase. This stage typically serves two purposes, to dissociate the hydrocarbon precursor molecule into fragments that react more readily at the deposition surface and to dissociate molecular hydrogen to create a superequilibrium concentration of gas-phase hydrogen atoms. Four commonly used diamond CVD reactors to achieve the activation are hot-filament reactors, microwave plasma reactors, dc arcjet reactors, and combustionsynthesis reactors. Although these deposition systems vary greatly in many engineering aspects, they have many important features in common, which is why each is able to produce high-quality diamond films. A large amount of energy, in the form of electrical or chemical free energy, is input to achieve dissociation of molecular hydrogen and the hydrocarbon feedstock. Moderately low pressures (in the range 10 torr to 1 atm) are used to prevent three-body recombination of H to form molecular hydrogen. High gas-phase temperatures, greater than 1700⬚C, are produced in the activation zone, and passive or active cooling is employed to maintain a substrate temperature in the neighborhood of 925⬚C. However, transport processes are quite different among the four reactor types. Hot-filament and microwave plasma reactors are diffusion dominated; typically, there is no thermal, velocity, or concentration boundary layer. Thus, one often finds linear gradients in temperature, velocity, or species concentration between the excitation region (hot filament or plasma ball) and the deposition surface in these reactors. Growth rates and other observables are a weak function of input flow rate (or velocity). On the other hand, arcjet and combustion CVD reactors are characterized by high velocities, for example, greater than 105 cm/sec, and are thus convection dominated. Thin boundary layers in temperature, velocity, and concentration are formed near the growth surface.

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57

Gas-Phase Chemical Kinetics

The gas-phase chemistry occurring in CVD diamond synthesis involves reactions of small hydrocarbons and their dissociation fragments. The chemical kinetics of C, H, and O species has been the subject of decades of experimental, theoretical, and modeling research in the combustion community [1]. Thus, the gas-phase chemistry aspects of diamond growth are probably better understood than for any other CVD system, with perhaps the exception of the CVD of Si from SiH4. Temperature- and pressure-dependent rate constants for a great number of the elementary gas-phase reactions have been measured experimentally and provide the direct input to CVD diamond kinetic models. However, in some cases rate constants for relevant reactions are not available. Sometimes use of a measured rate constant in a calculation, for example, gives a wrong prediction of flame speed or temperature. This may be because the measured rate constant itself is in error or may be due to other unknown sources of error in the simulation. The combustion research community has developed a number of reaction mechanism sets that have been tested and compared with experiment [2–8]. Usually some individual rate constants in a mechanism set have been adjusted such that the overall mechanism as a whole gives optimal predictions for certain types of flames. Hence, it can be dangerous to extract individual reactions from one mechanism and incorporate them into another without a thorough understanding of the limitations and validity of the particular numbers. Therefore, in searching for gas-phase reaction kinetics to use in a simulation of a CVD diamond experiment, it is best to consider published reaction sets ‘‘as a whole’’ and not mix and match information from different mechanism sets. The reaction mechanism of Miller and Bowman [4] was developed to describe nonsooting, oxygen-acetylene flames. It contains about 150 reactions of 51 hydrocarbons up to C2 species and is adequate for many diamond CVD applications in which the gas is rich in H atoms, and thus formation of higher hydrocarbon species is not very important [9]. A near-sooting mechanism was created by Miller and Melius [6] that contains approximately 220 reactions among 49 chemical species. The mechanism includes reactions and species leading to the formation of benzene; it is commonly assumed that benzene is a key precursor in the formation of polyaromatic hydrocarbons and soot. The Miller-Melius mechanism may be appropriate for modeling a combustion-synthesis diamond CVD experiment under fuelrich conditions; however, extremely fuel-rich conditions usually lead to diamond films of poor quality and as such are of less practical importance. A very large reaction mechanism (853 reactions among 190 chemical species)

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including hydrocarbons up to C8H18 was developed by Westbrook and Pitz [3,7]. Recently, a consortium of researchers from several different institutions has joined to produce validated combustion reaction mechanisms under the sponsorship of the Gas Research Institute. At the time of this writing, the latest version of the reaction set [8], GRI-Mech 2.11, contained 276 reactions of 49 species containing the elements C, H, O, and N. Wolden et al. [10] presented a brute-force sensitivity analysis of two different gas-phase reaction mechanisms, the 89-reaction mechanism of Frenklach and Wang [11] and the 24-reaction mechanism of Harris et al. [12,13], to develop a reduced gas-phase reaction mechanism. Wolden et al. used a zero-dimensional model to integrate the kinetics at a temperature of 2000 K and 20 torr for 0.1 sec; these particular conditions were chosen to mimic the conditions encountered by the gas mixture flowing past a hot filament [14,15]. Both of the starting reaction mechanisms reduced to the same set of nine (reversible) gas-phase reactions, which did a good job matching the time evolution of the C2H2, CH3, and H concentrations predicted by the longer reaction mechanisms. These reactions fall into three broad groups: (1) the three-body recombination of atomic H, (2) interconversion reactions between CH4 and CH3, and (3) methyl-methyl recombination reactions, followed by hydrogen-stripping reactions to form acetylene. A key role of hydrogen in the gas-phase chemistry of diamond CVD is to suppress formation of aromatic species [9]. Minimizing production of aromatics is assumed to inhibit formation and growth of graphitic phases on the deposition surface and thus improve diamond film quality.

B.

Reactions at a Hot Filament

Langmuir [16–18] first discovered the catalytic dissociation of hydrogen on a hot tungsten filament, and such a hot filament has proved to be an easily constructed, efficient H-atom source. Matsumoto et al. [19,20] first proposed use of hot filaments for diamond CVD. The majority of basic research has been done on hot-filament reactors because they can be assembled rather inexpensively on the laboratory scale, yet can produce good-quality diamond films. A thorough investigation of H2 dissociation at a hot filament was conducted by Jansen et al. [21], who used the difference in power consumption by the filament in a vacuum and in hydrogen as a measure of the hydrogen dissociation rate. The dissociation rate was shown to depend on the geometry of the heater element. Relatively high dissociation rates, normalized per heater area, were obtained for small-diameter wires, and it was argued that this indicates a nonequilibrium dissociation process. A mathematical analysis

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of the H production rate was presented that depended upon parameters such as the diffusion coefficients, wire diameter, and dissociation rate constant. Meier et al. [22] used two-photon laser-induced fluorescence (LIF) to determine H-atom concentrations relative to a hot filament. In this experiment there was no substrate, and thus no diamond growth was occurring. They measured [H] as a function of total pressure, distance from the filament, filament temperature, filament diameter, filament material, and CH4 mole fraction. They found little effect on [H] due to addition of up to 5% CH4. However, in other studies, tungsten filaments have been found to carburize during diamond CVD upon high exposure to hydrocarbon feedstock [23]. Such carburization degrades the catalytic activity for hydrogen dissociation, and gas-phase H-atom concentrations have been found to drop by at least an order of magnitude when the methane concentration is increased between a factor of 3 and 10 [15,24–27]. As discussed in Sec. VI.A, Dandy and Coltrin [28] found that inclusion of filament poisoning effects was necessary to model the gas-phase chemistry in a hot-filament reactor because the H-atom concentration controls the kinetics to such a large degree. C.

Plasma Activation of the Gas Phase

Direct-current (dc) arcjet-assisted diamond CVD can attain very high growth rates [29–31] because of the high arcjet powers and material flow rates possible in these systems. Within the arcjet, electrical energy is converted to chemical free energy through dissociation of hydrogen. The degree of hydrogen dissociation is typically high, 20% or greater, but not known precisely. Detailed physical models of arcjet operation have not been included in diamond CVD models, although Dandy and Coltrin [32] gave a simple thermodynamic model of an arcjet that predicts the hydrogen dissociation fraction for a specified input power and operational temperature, as illustrated in Fig. 1. Temperatures at the exit of the arcjet can be in the range 1000–4000 K [33–35]. The combination of high temperature and large concentration of atomic H produces high reaction rates of the reactant gases in the free stream below the arcjet. Hydrocarbon feedstock is usually injected downstream from the exit of the arcjet. When methane is the reactant gas, the C1 species, i.e., CHx (x = 0–4) equilibrate very rapidly [36,37], and thus the concentration of methane is very low in the free stream. After equilibration (within a few cm of the exit of the arcjet) the C1 manifold of species remains essentially frozen in the convective free stream until the boundary layer is encountered near the substrate. In contrast, acetylene is much more stable than methane, and when acetylene is used as the reactant gas it undergoes significantly less gas-phase decomposition. Figure 2 shows the time evolution of species con-

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Figure 1 Predicted H-atom mole fraction exiting the arcjet and power required as a function of the arcjet operating temperature. (From Ref. 32.)

centrations from homogeneous chemical kinetics calculations [37] under conditions typical of the free stream beneath the exit of an arcjet, that is, 5000 K, 3 torr, 33% dissociated H2. One sees significant decomposition of methane within a few ␮sec in Fig. 2a, whereas there is much less decomposition when acetylene is the reactant in Fig. 2b. In a microwave plasma system, energy from the microwave electric field ionizes the gas, which is primarily H2 with small amounts of hydrocarbon. Energy is subsequently transferred from the electrons to vibrational levels in H2; then this vibrational energy serves to heat the gas through vibration-to-translation energy transfer to atomic H and vibration-to-vibration or vibration-to-translation energy transfer to other H2 molecules [38]. Ion chemistry is important in these systems as an electron-loss source. Electrons can dissociate H2 and eventually lead to a concentration of H⫹ ions, which can subsequently undergo charge exchange with hydrocarbon and

> Figure 2 Kinetics simulation of gas-phase chemistry under dc arcjet conditions for (a) 0.5% methane and (b) 0.5% acetylene as the hydrocarbon reactant. (From Ref. 37.)

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oxygen-containing species. Neutral chemistry in the gas phase is also initiated by electron-impact dissociation of H2, O2, and hydrocarbons [38].

III.

SURFACE CHEMISTRY IN CVD DIAMOND

A.

Calculation of Diamond Surface Structures and Energetics

Modern theoretical chemistry techniques are well suited to study the bonding and surface structures relevant to diamond CVD because the structures mainly consist of relatively light elements and thus few electrons, i.e., carbon and hydrogen, and because bonding is generally short range and covalent, so relatively small ‘‘slabs’’ can be used to model the lattice. A wide array of theoretical papers have appeared that report stabilities of proposed surface structures, relative bond strengths among competing adsorbate species, reaction barriers, and the like. Mehandru and Anderson [39] used atom-superposition and electrondelocalized molecular orbitals (ASED-MOs) to study adsorption energetics and bonding of CH3, CH2, CH, C2H, and C2H2 on clean and hydrogenated {111} diamond faces. On either the clean or hydrogenated surface, the adsorption bond dissociation energy (BDE) varied as C2H > CH ⬵ CH2 > CH3. The 1:1 (complete monolayer) coverage of CH3 was concluded to be very unstable due to steric repulsions (⫺2.3 eV BDE); the 1:1 coverages of CH2, CH, and C2H were all predicted to be stable. The favored bonding site for C2H2 on a clean {111} surface was di-␴ bridging. Bonding to the surface via a single ␴ bond was found to be very weak (1.2 eV) compared with the di-␴ bond (3.5 eV). Mehandru et al. [40] also used this technique to study hydrogen diffusion within the bulk diamond lattice. They found that a bond-centered (BC) site, that is, a C — H — C structure, was more stable than other interstitial sites (but still about 1.7 eV less stable than a gas-phase H atom plus the cluster). A minimum barrier to H migration (1.9 eV) was found for moving from one BC site to a neighboring one, moving in the {110} plane. They also examined the stability of from one to four H atoms bound to a lattice vacancy. Up to four H atoms could be bound in the vacancy, with the calculated BDE energies decreasing monotonically (5.3, 4.4, 3.6, 2.5 eV) as the number of H atoms increases. Alfonso et al. [41] used a combined density-functional/molecular dynamics simulation to calculate adsorption energies and minimum energy configurations for various hydrocarbons on flat {100}, flat {111}, and stepped {100} surfaces. For onefold adsorption sites, the bonding energies were ordered as follows: C2H > CH2 > CH3 > C2H2; stable twofold adsorp-

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tion sites were found for C2H2 on terrace sites and near steps on the {100} surface. Bonding to {111} surfaces was weaker than to the other two surfaces studied. Alfonso et al. [42] studied the adsorption of various hydrocarbons on a diamond {100}-(2⫻1) surface. They used molecular dynamics and a dynamical quenching technique [43] to calculate stable adsorption binding configurations based on the many-body potential energy function of Brenner [44]. Bonding was studied on a number of different types of sites: at the end of a dimer (having removed an H from the dimer), bridging across the two carbons in a broken dimer (bridge sites), and bridging between the two ends of adjacent dimer pairs (troughs). For the flat {100}-(2⫻1) surface they calculated BDEs CH2 (4.67 eV) > C2H (4.34) > CH3 (4.18). Acetylene was bound considerably tighter at troughs (6.54 eV) than at bridge sites (3.62 eV), but the authors concluded that trough sites are much less abundant than bridge sites under steady-state conditions. The stability of hydrocarbon fragments near step edges was concluded to be very near the values calculated on flat terraces because of the strong covalent (and short-range) nature of the bonding. Angus and coworkers [45] studied nucleation of the diamond {111} plane upon the {0001} plane of graphite using energy minimization of a semiclassical Tersoff potential [46,47]. They found very favorable energetics for an interface matching three diamond {111} planes for every two graphite {0001} planes. A mechanism was proposed that starts with graphitic or aromatic structures, which are then hydrogenated to provide nucleation sites for diamond growth. Molecular mechanics MM2 [48] and MM3 [49] calculations were used by Harris and Goodwin [50] to calculate the free energy change in each step of their detailed reaction mechanism on the reconstructed {100}-(2⫻1):H surface, which in turn was used to calculate the reaction equilibrium constant and reverse rate constant. Yang and D’Evelyn [51] used MM3 to examine the relative stabilities of the {100}-(2⫻1) reconstructed surface with varying degrees of hydrogenation. The monohydride phase was found to be the most stable and was concluded to be the dominant surface phase under CVD conditions. MM3 was also used to examine the energetics of each step in a proposed growth mechanism on the {100}-(2⫻1) surface [52]. Huang and Frenklach [53] used MNDO [54] to calculate reaction energetics on the {100}-(2⫻1) reconstruction. They found a barrier of 37 kcal for H2 elimination from a surface dihydride to form the monohydride and that the dihydride is approximately 80 kcal/mol higher in energy than the monohydride plus H2(g). An alternative mechanism involving H-atom abstraction from the dihydride forming a dihydride surface radical, then H elimination and C — C bond formation, had a barrier of 49 kcal/mol, i.e., 12

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kcal/mol higher than the other channel. They calculated a barrier of 80 kcal/ mol for addition of CH3 to a surface dihydride radical; carbon atoms were found to add to a monohydride radical site with less than a 20 kcal barrier, and acetylene addition to a radical site proceeded with a barrier of 41 kcal/ mol. Brenner [44] developed a potential energy surface for diamond and studied adsorption of hydrocarbon fragments on the {111} surface. The potential uses many-body terms based on Tersoff bond-order expressions [55]. Alfonso and Ulloa [56] performed molecular dynamics calculations employing the Brenner [44] intermolecular potential to study the adsorption of methyl radicals on the diamond {100} surface. The adsorption probability was found to increase with CH3 incident kinetic energy and for normal incidence. Methyl radical did not react with a fully hydrogenated surface. Thus, a surface radical site was required for CH3 chemisorption. The same intermolecular potential was used by Garrison et al. [57], who discovered a low-energy reaction pathway for dimer-bond breaking and addition of CHx (x < 3) on the {100}-(2⫻1):H surface from analysis of their molecular dynamics simulations. B.

H-Abstraction/Radical Termination Reactions

Reactions of atomic hydrogen are a dominant factor in the surface chemistry of diamond CVD. They not only control the gas-phase chemistry, and thus the nature of the reactive species reaching the growth surface, but also determine the availability of reactive sites upon the surface. In addition, the recombination of hydrogen on the surface is an important source of heat in the system and must be accounted for in substrate thermal management. During deposition the diamond surface is usually hydrogen terminated. Growth is initiated by abstraction of an H from the surface, creating a reactive radical site H(g) ⫹ CH(s) ⇔ H2(g) ⫹ C*(s)

(1)

This reaction is accompanied by the radical-termination reaction H(g) ⫹ C*(s) ⇔ CH(s)

(2)

The net of these two reactions is heterogeneous recombination of atomic hydrogen to form H2. Although reactions (1) and (2) are written as reversible, for all practical purposes the reverse reaction rates are negligible. The abstraction reaction (1) is fast but does not occur with unit probability. The rate constants for gas-surface reactions in diamond CVD mechanisms are usually estimated by analogy with gas-phase reactions. This, in essence, assumes that the diamond surface behaves like a giant hydrocarbon

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[58]. The gas-phase rate constant for abstraction of a tertiary hydrogen from an alkane is (in cm3 mol⫺1 sec⫺1) k1 = 1.3 ⫻ 1014 exp(⫺3674/T)

(3)

with the activation energy in K. The rate constant can be converted to a reaction probability ␥ using k=

␥ ⌫

冑

RT 2␲W

(4)

where ⌫ is the surface site density (taken here to be 3 ⫻ 10⫺9 mol cm⫺3) and W is the atomic weight of H; for reactions of H atoms,

␥ = 8.25 ⫻ 10⫺13

k

兹T

(5)

Thus, the rate constant in Eq. (3) corresponds to a reaction probability of 0.14 at a typical growth temperature of 1200 K. Kinetic modeling studies of diamond CVD have used values of ␥1 spanning the range 0.22 [59] down to 0.0037 [11]. Molecular dynamics calculations of Brenner et al. [60] yield an abstraction reaction probability of 0.04 at 1200 K. A reasonable analogue of reaction (2) would be the gas-phase reaction of H with the isopropyl radical, with a rate constant in the high-pressure limit of 2 ⫻ 1013 cm3 mol⫺1 sec⫺1 [2]. This rate constant corresponds to a probability of 0.48 at 1200 K. Previous models have used values of ␥2 ranging from essentially unity [59] to 0.016 [11]. Brenner et al. [60] calculated a value of 0.43 for ␥2 at 1200 K. Although there is quite a range in the probabilities that modeling studies have employed for reactions (1) and (2), there has been a good consensus among such models that the ratio ␥2/ ␥1 should be in the range of 3 to 4 [11,59,61]. This ratio was predicted to be approximately 11 via molecular dynamics [60]. A steady-state analysis [62] shows that the probabilities for reactions (1) and (2) can be combined to yield an effective probability, ␥H, for H-H recombination, 1 1 = ␥H 2

冉

冊

1 1 ⫹ ␥1 ␥2

(6)

Using the probabilities deduced from the gas-phase analogues in Eq. (6) yields an effective recombination probability ␥H = 0.22. Krasnoperov et al. [63] measured an effective H-atom recombination probability of 0.16; Harris and Weiner [64] measured a slightly smaller value, ␥H = 0.12, with about a factor of 2 uncertainty. Thus, we conclude that the rate constants (or equivalently) probabilities for H-atom abstraction and termination reactions de-

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rived from their gas-phase analogues are reasonable but perhaps are as much as a factor of 2 too large. C.

Growth Chemistry

The surface chemical reaction mechanism leading to diamond growth has been the subject of much research, debate, and controversy. It was widely assumed that the ‘‘correct’’ reaction mechanism could be found because diamond is a relatively simple material system: it is dominated by shortrange covalent bonds, chemically related to well-known hydrocarbon chemistry, and is amenable to theoretical or first-principles calculation of energetics and reaction rates. However, a universally accepted diamond growth reaction mechanism has still not yet been found. As an example, much controversy has reigned about the identification of the dominant precursor species leading to growth. In a hot-filament reactor environment, the most abundant gas-phase hydrocarbon species are C2H2 and CH3, and attention focused on these two candidates as the dominant growth species. Many conflicting experiments have concluded that one species or another could or could not account for diamond growth. It is unlikely that there is a single, simple diamond growth mechanism that applies to all deposition conditions. For example, the gas-phase environment present in a dc arcjet reactor is very different from that in a hotfilament reactor; there is no a priori reason to expect that the same growth mechanism will be operative under such different conditions. The first proposal of C2H2 as a growth species was by Frenklach and Spear [58]. A detailed kinetic reaction mechanism for diamond growth was proposed by Frenklach and Wang [11]. Their model was applied primarily to a hot-filament environment and included acetylene as the dominant growth species. However, shortcomings of the acetylene addition mechanisms were discovered [65]. Addition of acetylene go a monoradical surface site is thermodynamically unstable: the adduct formed has too short a lifetime to allow incorporation into the diamond lattice. Addition of acetylene to a biradical site on the {111} or {110} surface forms a thermodynamically stable molecule. However, the admolecule quickly desorbs after reaction with a gas-phase H atom, followed by a ␤-scission cleavage of its surface C — C bond [66]. Alternative reaction schemes for acetylene on the dimerized {110} surface have been proposed that do not suffer from the foregoing deficiencies [65,66]. Cappelli and Loh [67] conducted experiments in an arcjet reactor with C2H2 feed gas and reported high-quality diamond growth. Under these conditions, the concentration of C1 species was too low to account for the observed growth. They concluded that C2H2 was the dominant growth spe-

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cies in this experiment. In a different growth environment, the opposite conclusion was drawn. Chu et al. [68,69] used a mixture of 13C-labeled methane and 12C acetylene for growth rate experiments in a hot-filament reactor. They measured homoepitaxial growth rates on different crystal faces of 0.4 ␮m/hr on the {100} face, 0.5 ␮m/hr on the {111} face, and 1.3 ␮m/ hr on the {110} face. The 13C fraction in the deposited film matched that of the gas-phase methyl radical (as deduced from mass spectrometry probe sampling) and differed significantly from the 13C fraction in the acetylene. From this observation they concluded that CH3 was the dominant growth species in the hot-filament experiment. A number of other experimental papers also concluded that C2H2 is not a viable growth species [69–73]. There has not been a well-accepted mechanism proposed for growth on {111} planes [74,75]. Steric repulsion appears to rule out complete coverage of the {111} plane by methyl radicals [39]. There is only moderate repulsion between just a pair of adjacent surface CH3 groups on the {111} plane [39,76,77], and such a configuration has been examined as a growth route. Atomic hydrogen abstraction from a single one of the adjacent methyls followed by bridging reactions is limited by a high activation barrier, approximately 50 kcal/mol [77]. Abstraction of an H from both adjacent methyls would be followed by rapid formation a C — C bond and thus a surface species such as — CH2 — CH2 — . However, subsequent abstraction of an H from this species will be followed quickly by ␤-hydride elimination of H and desorption of the — CH — —CH2 group [74]. Such a series of reactions has made drafting of a complete growth mechanism on the {111} and {110} planes difficult to date. Frenklach et al. [74] have proposed an atomistic model for step-flow growth upon a {100} facet between two {111} planes. The model is based on bridging methylene, CH2, as the mobile species. However, instead of migrating via surface diffusion, CH2 moves through a sequence of covalent bond breaking and formation. Butler and Woodin [78] propose a detailed reaction sequence for growth of diamond from CH3 (used as a ‘‘generic’’ growth species) on the {110} crystal face. In particular, their mechanism focuses upon reactions among chemisorbed species. Kinetic rate constants for the individual steps in the mechanism were not given, and thus it has not been further incorporated into numerical kinetic or reactor-scale models. Harris [59] proposed a widely used mechanism for growth on the unreconstructed {100} plane with CH3 as the growth species. Rate constants for the 12 reactions in the mechanism were mainly deduced from gas-phase analogues. Thermochemistry for each reaction, i.e., ⌬G, and thus the equilibrium constants and reverse rate constants, was estimated using the bicyclo[3.3.1] nonane molecule as a model of the diamond surface. Steps in this

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mechanism are illustrated in Fig. 3. Methyl radical (denoted by ‘‘M’’ in the figure) was assumed to adsorb on a surface radical site, followed by H abstraction from both the adsorbed methyl (‘‘M*’’) and an adjacent surface H and rapid formation of a C — C bond (‘‘biradical pairing’’). The Harris mechanism was used quite widely to simulate CVD diamond growth in a broad range of growth conditions, including hot filaments, oxygen-acetylene flame, dc arcjet, and rf torch reactors; see Ref. 50 for a summary. Steric crowding makes it very unlikely that the methyl radical can actually bond to the unreconstructed {100} surface [53], and so the original mechanism as proposed by Harris is probably not correct in all of its detail. In fact, it is unlikely that the unreconstructed {100} surface exists at all under growth conditions, due to steric repulsion between adjacent H atoms. The {100}-(2⫻1) reconstruction has been observed experimentally [79– 82], and the stability of this surface has been examined theoretically [51].

Figure 3 Steps in the methyl-addition growth mechanism of Harris [59], which uses the bicyclo [3.3.1] nonane molecule as a model of the unreconstructed {100} surface.

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Harris and Goodwin [50] proposed a growth mechanism on the {100}(2⫻1):H (hydrogen-covered reconstruction) surface, illustrated in Fig. 4. The mechanism consists of two main parts: insertion into dimer bonds according to the route proposed by Garrison et al. [57], shown in Fig. 4b and c, and bridging across the trough between the ends of two dimers, as in Fig. 4f. The latter part of this mechanism basically follows the steps in Harris’ original methyl addition mechanism [59]. Harris and Goodwin give rate constants for each step in their mechanism and the corresponding thermochemistry, calculated via the molecular mechanics code MM3 [49]. Kinetic simulations showed that the trough portion of the mechanism was rate limiting because that portion required more H abstraction steps than the dimer

Figure 4 Steps in the mechanism proposed by Harris and Goodwin [50] for growth on the {100}-(2⫻1):H surface. In parts (a), (c), and (e), the letters A–D represent either an H or a surface radical site at which reaction can take place.

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addition portion. This mechanism was used by Harris and Weiner [83] in simulating the pressure and temperature dependence of diamond growth. There is experimental evidence that surface diffusion is operative on the diamond surface at high temperatures [84–87]. Theoretical analysis of surface diffusion of H atoms, hydrocarbon species, and radical sites found these processes to be very facile [88]. Surface diffusion will be enhanced at higher temperatures, potentially leading to smoother films. However, higher temperatures also lead to increased desorption from the surface and etching. The surface diffusion mechanism was also found to be unstable; the system was found to switch suddenly from a regime of smooth growth to formation of pits. D.

Reduced Reaction Mechanisms

The fine details of diamond growth mechanisms are very complex, still under debate, and dependent upon crystallographic plane and growth condition. However, many general aspects of diamond growth surface chemistry appear to be generic to the process and are widely agreed upon. As a result, a number of simplified models of diamond growth have been developed [32,62,67,78,89]. Although not intended to be mechanistically rigorous in detail, these models attempt to explain some of the overall behavior of the diamond CVD system, e.g., scaling of growth rate, surface coverage, defect formation, energy consumption, in terms of generic reactions taking place. Such models are typified by the discussion given by Butler and Woodin [78], whose simple analysis included reactions for H-atom abstraction and radical termination, incorporation of chemisorbed hydrocarbon species into the lattice, diamond growth, and parasitic growth of defects. This model is perhaps distinguished from some of the others in discussing the surface temperature dependence of these processes. One of the quantities predicted by the model is quality, which was defined as the ratio of the rate at which adsorbed carbons completed their lattice bonds before being overgrown to the total rate of carbon adsorption. Figure 5 illustrates the dependence of quality on substrate temperature for two different reactor types. Case (a) is representative of a dc arcjet system, for which the atomic hydrogen mole fraction at the surface was assumed to be 0.1 and the mole fractions of hydrocarbons were assumed to total 10⫺4. Case (b) represents conditions in a hot-filament reactor, with a near-substrate H mole fraction of 0.01 and CxHy mole fractions of 10⫺5. Goodwin [62] presented a simplified surface reaction mechanism that includes many of the important features present in more detailed kinetic schemes, including H-atom abstraction and termination reactions, addition of CH3 to a surface radical site, and a biradical pairing reaction to form a

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Figure 5 Calculated quality (lattice incorporation/carbon addition) as a function of substrate temperature for conditions characteristic of (a) dc arcjet and (b) hot filament. (From the model of Butler and Woodin [78].)

surface C — C bond. The mechanism also included an alternative reaction path for formation of a buried defect, for example, hydrogen or sp 2 species trapped in the lattice. The simplified reaction scheme can be solved analytically, yielding expressions for deposition rate and lattice-defect fraction as a function of CH3 and H concentrations at the surface. The deposition rate expression containing two adjusted constants reproduces measured diamond growth rates from a wide range of experiments spanning growth rates from 0.1 to more than 7000 ␮m/hr and is G = 1.8 ⫻ 1011

[CH3][H] 5 ⫻ 10⫺9 ⫹ [H]

(7)

where G is the growth rate in ␮m/hr, and the concentrations are in mol/cm3. Assumptions in the analysis lead to the conclusion that the mole fraction of defects in the grown film, Xdef , will scale as Xdef ⬀

G [H]2

(8)

The form of Eq. (8) is especially important in trying to optimize diamond growth conditions. It illustrates the fundamental trade-off between achievable growth rate and film quality; i.e., defect density increases linearly with growth rate. Equation (8) predicts that growth rates can be increased quad-

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ratically with H-atom concentration for a fixed defect density. (This is achieved by simultaneously increasing the hydrocarbon fraction.) Goodwin points out that the scaling of defect fraction with H-atom concentration is uncertain and depends upon the form of the (unknown) defect formation reaction. He gives a more general scaling relationship for defect fraction as Xdef ⬀

G [H]n

(9)

Dandy and Coltrin [32] discussed diamond growth in terms of a simplified growth mechanism that extended the one given by Goodwin [62] to account for growth from atomic C atoms, which were quite abundant in the dc arcjet environment being modeled [36]. They also included a kinetic pathway for formation of lattice point defects due to overgrowth of surface hydrogen species and thus incorporation of hydrogen into the lattice as a defect. As shown in Fig. 6, the scaling of defect fraction was found to follow (very nearly) a linearly scaling with [H], that is,

Figure 6 Predicted growth rate as a function of gas-phase H mole fraction at the surface for a fixed diamond quality (defect concentration). Solid curve is for a defectformation reaction that is first order in surface reactant species; dashed curve is for a defect-formation reaction that is bimolecular in surface species. (From Ref. 32.)

Deposition Chemistry

Xdef ⬀

G [H]

73

(10)

when the defect formation reaction was first order with respect to surface species as reactants. When the reaction responsible for defect formation was assumed to be bimolecular with respect to surface species, a quadratic scaling as in Eq. (8) was obtained, which is also illustrated in Fig. 6. The difference in scaling laws for defect formation has important implications for scaling a CVD diamond reactor to higher arcjet power, for example. If defect formation decreases approximately linearly with [H], as in Eq. (10), higher power and thus increased H-atom production would allow a linear increase in attainable growth rate (holding diamond quality fixed). However, if defect formation scales as in Eq. (8), any increase in [H] is rewarded with a quadratic increase in the attainable growth rate (again, for fixed quality). Angus and Evans [89] present a simple reduced reaction set to describe many aspects of CVD diamond growth. Their model includes growth of diamond from graphitic nucleation sites [45], conversion of sp 2 sites to sp 3 hybridization, and gassification of hydrogenated surface species by atomic hydrogen. The reaction scheme can be solved analytically at steady state to predict growth rates of both diamond and sp 2 impurities as a function of the concentration of a growth precursor, [CHx], and atomic hydrogen, [H]. The model predicts that the impurity concentration will increase with [CHx] and thus with increasing growth rate, and it will decrease more than linearly with [H].

IV.

NUCLEATION PHENOMENA

It has become clear in research on diamond film growth that control of the fundamental phenomena associated with diamond nucleation and the early stages of growth is essential for applications in which material properties are sensitive to, or depend directly upon, the morphology of the polycrystalline film. Film anisotropy, grain size, and nano-, micro-, and macroscopic voids all strongly affect material properties such as thermal conductivity and optical transmissivity. Indeed, if diamond is ever to be used in semiconductor applications, it will be necessary to synthesize large-area, thick, single-crystal films. An increase in surface nucleation density may reduce morphological instabilities and surface roughness and, further, may improve the homogeneity of films and reduce formation of voids at the substrate or coating interface, leading to better diamond-substrate adhesion. Most early studies of the low-pressure CVD of polycrystalline diamond have focused on studying different deposition techniques and correlating

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these techniques with the material properties of the resulting films. These efforts have been successful in gaining a qualitative and semiquantitative understanding of how diamond is deposited from the gas phase. Another result of such studies has been an increasing awareness of the extreme variability in film morphology and crystallinity that could be produced with seemingly minor changes in the growth environment. Because of this observation, increasing attention has been paid to the nucleation and early growth stages of diamond; these nucleation studies have significantly contributed to understanding of diamond nucleation mechanisms in CVD. In this section possible mechanisms for diamond nucleation will be discussed, and the effect of surface conditions and the growth environment on epitaxy, morphology evolution, and texture will be considered.

A.

Nucleation Mechanisms

1.

Homogeneous Nucleation

The emphasis of most studies on nucleation and growth of diamond has been the heterogeneous formation of diamond particles and the crystallization and deposition of diamond films on substrate surfaces. Only limited work has been done to examine the possibility of achieving homogeneous nucleation in the gas phase at subatmospheric pressures. However, there is evidence that, at least in some cases, diamond may be nucleated homogeneously in the gas phase [90–93]. The primary reason that homogeneous nucleation of diamond has not been pursued more aggressively is that using a CVD process to produce diamond powder via homogeneous nucleation does not appear commercially competitive with other techniques because of the low nucleation rate; and conditions conducive to homogeneous nucleation are not favorable for film growth, so it may not even be practical to use the homogeneous nucleation phenomenon as a seeding technique. Classical nucleation theory indicates that homogeneous nucleation of diamond is possible [94], and a number of suggestions have been made regarding possible hydrocarbon cage molecules (such as adamantane) that may serve as gas-phase precursors for the diamond nuclei [95]. The adamantane molecule represents the smallest combination of carbon atoms that possesses the diamond unit structure, that is, three six-membered rings in a chair structure. However, chemical equilibrium calculations reveal that proposed precursors such as adamantane, tetracyclododecane, and hexacyclopentadecane are unstable at the temperatures and pressures typical of CVD diamond growth. Instead, Angus et al. [96,97] suggested that fully hydrogenated ring compounds structurally related to the boat-boat conformer of bicyclodecane are more plausible nucleation seeds due to their greater abun-

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dance in CVD systems, thermodynamic stability, and higher reactivity with hydrocarbon radicals leading to atom addition. While dilute concentrations of 50–200 nm diamond crystals have been successfully produced via homogeneous nucleation using a number of reactant gas mixtures and reactor types [90,92,98], it has been found that higher nucleation densities may be achieved when impurities such as halogens, silane, or diborane are present in the system [99]. It has been suggested that, because of the higher rates of thermal dissociation of these impurities, the decomposition fragments quickly nucleate a relatively large number of small clusters. These clusters then serve as seeds for the subsequent addition of carbon. 2.

Heterogeneous Nucleation

It is possible to grow diamond homoepitaxially on a single-crystal diamond surface using methods such as hot-filament CVD [69,100] and microwave plasma–assisted CVD [101,102] using a variety of hydrocarbon sources. Diamond readily nucleates on cubic boron nitride (cBN) because the two materials have identical crystal structure, a lattice mismatch that is only 1.4%, and similar thermal expansivity [103,104]. However, in almost all other diamond CVD processes where diamond is grown on nondiamond substrates, the initial nucleation stage is extremely slow and nucleation density is very low unless some form of active substrate pretreatment takes place. Conventional growth of polycrystalline diamond generally consists of up to five distinguishable stages: (1) the incubation period, (2) three-dimensional nucleation of individual crystallites on the substrate surface, (3) termination of surface nucleation and subsequent three-dimensional growth of individual crystallites, (4) faceting and merging with neighboring crystallites, and (5) growth of the continuous film. These different stages are illustrated by the micrographs shown in Fig. 7. Before nucleation begins, the system undergoes an incubation period that may last from several minutes up to hours [13,105], depending upon substrate material, surface pretreatment, and deposition conditions. The lone nanocrystals formed during the nucleation stage often exhibit roughly spherical geometry. Nucleation density increases with time up to values that, again, depend upon the substrate and pretreatment method, after which surface nucleation ceases to occur at a measurable rate. The isolated crystallites grow and develop faceting due to the relatively high rate of surface carbon diffusion from the surrounding substrate surface. Once the crystals grow large enough to impinge upon one another, they form grain boundaries and then continue growing as a continuous film, as indicated by the highly textured morphology shown in Fig. 7f.

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Figure 7 Diamond growth on a nondiamond substrate occurs by sequential steps: (a) nucleation of individual crystallites; (b and c) termination of nucleation followed by growth of individual crystallites; (d) faceting and coalescence of crystallites; (e and f ) competition between growing crystallites and eventual overgrowth to form continuous film. (From Ref. 203.)

Under certain growth conditions the competitive growth process of the individual crystallites governs the subsequent growth of the continuous film. In these cases, the grains exhibit fastest growth in the direction perpendicular to the substrate, overshadowing any slower growing neighbors and forming a continuous film with a very distinct columnar structure [105]. This mode of film growth, where crystallites successfully overshadow their neighbors, has been observed in many vapor-deposited materials and is described as evolutionary selection [106]. Surface nucleation processes can be described with two quantities: the surface nucleation density, Nd (cm⫺2), and surface nucleation rate, Nr (cm⫺2 hr⫺1). The nucleation density is the number of nuclei grown per unit area, and the rate is the number grown per unit area per unit time. The density depends upon the number of activated nucleation sites available; thus, nucleation on the substrate will cease when all active sites have been occupied or when the discrete crystallites grow together and completely cover the surface. The nucleation density determines the ultimate thickness, average crystal size, homogeneity, substrate adhesion, texture, and roughness of the resulting film. Generally, the higher the nucleation density, the smoother the surface of the continuous film [107]. On an atomic scale, the surface nucleation process may include the following events: 1.

Atoms from the gas collide with the deposition surface and are adsorbed.

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3.

4.

5.

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The adatoms may desorb back into the gas phase or diffuse along the surface; they may also diffuse into the substrate or form bonds with other surface species. As time increases, the concentration of surface adatoms also increases and clusters begin to form as the adatoms bond with one another. The clusters grow or decay in size, depending upon their thermodynamic stability, rate of atom addition from the gas phase, and surface diffusion from the surrounding substrate. Once the clusters reach a critical size, they become thermodynamically stable and will continue to grow as new atoms are adsorbed.

This model for nucleation is necessarily simplistic because it presumes an ideal substrate with no defects or existing impurities. In practical systems where pretreatment occurs, as discussed in Sec. IV.C, nucleation may take place on existing particles, at defects induced on the substrate surface, or at intermediate carbide layers of varying chemical composition. However, the general steps just outlined are adequate to describe the principal features of diamond nucleation. It was recognized fairly early in diamond CVD research that the surface nucleation process of diamond was a controlling factor in the formation and subsequent growth of continuous films [108,109]. Experiments were performed to nucleate diamond on nondiamond substrates, including singleand polycrystalline Au, Cu, Si, Mo, and W. From those studies, a number of general trends emerged regarding diamond nucleation on nondiamond substrates: 1.

2.

3.

4.

5.

Diamond nucleation rates on nondiamond substrates range from 103 to 108 cm⫺2 hr⫺1, depending upon the surface preparation method and deposition conditions. Nucleation of the diamond crystals is observed primarily on substrate defects (scratches, grain boundaries, dislocations), indicating that diamond nucleation is, indeed, occurring via a heterogeneous mechanism. Diamond nucleation rates are lower on single-crystal substrates than on polycrystalline substrates of the same material after identical surface pretreatment. Diamond nucleation rates on carbide-forming substrates (Si, Mo, W) are one to two orders of magnitude higher than on non–carbide-forming materials (Cu, Au). Nucleation rates on nondiamond substrates decrease as both substrate coverage and crystal size increase.

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A large number of experimental observations employing transmission electron microscopy, scanning electron microscopy, x-ray diffraction, x-ray photoelectron spectroscopy, low-energy electron diffraction, Rutherford backscattering spectrometry, electron energy loss spectroscopy, and Auger electron spectroscopy, to name but several techniques (for example, [110– 117]), validate the observations of Spitzyn et al. [108,109]. Together, the experimental studies of diamond nucleation and growth reveal that, in most cases, diamond does not actually nucleate directly on a nondiamond substrate surface but instead forms on an intermediate layer that develops at the interface of the substrate during the incubation period prior to actual diamond nucleation. The intermediate layer, formed due to chemical reactions between activated gas species and the substrate material, may consist of a combination of diamond-like amorphous carbon, metal carbides, or graphite, depending upon substrate pretreatment, the substrate material, and deposition conditions. It is generally agreed that the intermediate layer provides nucleation sites for diamond crystal growth and thus increases Nd on nondiamond substrates. Knowledge of the details of formation of the intermediate layers may provide a means of controlling the morphology and texture of the resulting diamond films. Diamond is often grown on materials that form refractory carbides, such as silicon, molybdenum, tantalum, and tungsten, in part because of the availability of these materials and their thermal properties (they can withstand the high temperatures and energy loads associated with diamond deposition) and in part because it was discovered that diamond would nucleate and grow on these materials with little or no pretreatment. It is now generally accepted that the reason for the ease of growth on these materials is the initial formation of a carbide layer that in turn acts as a medium for diamond nucleation. These intermediate layers are thin, often in the range of tens of nanometers, and do not strongly affect the material properties of the grown film. From observation and thermodynamic calculation [118,119], it has been suggested that diamond nucleation on Si must be preceded by the formation of a ␤-SiC buffer layer and that diamond actually nucleates on the surface of the carbide layer. This is supported by a large number of experiments in which particles or films of diamond were grown on silicon substrates. Systematic studies of diamond growth on other carbide-forming materials have also been carried out [120], and the same observation was made, namely that diamond nucleation was preceded by formation of a thin carbide layer. It has been postulated [121] that diamond growth on carbide-forming substrates is initiated by the dissolution of carbon into the substrate material, forming the stable carbide. Diamond nucleation on the carbide then occurs when the surface becomes saturated with adsorbed carbon. In this model, the diffusion of carbon into substrate and on the surface both play key roles

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in the rate of diamond nucleation. It was found that qualitative features of the model agreed with experimental observation: materials with high carbon diffusivities had the longest incubation period because they required the most time to achieve a carbide layer thick enough for the surface to become saturated with carbon. However, enough experimental data exist to conclude that, although the formation of carbide interlayers is an important factor for diamond nucleation on carbide-forming substrates, it is probably not the sole mechanism by which nucleation occurs [122]. Intermediate layers of a-C:H or a-C were found to form on Si and Mo substrates, for example. Graphite interlayers have also been observed on carbide-forming substrates. What can be said is that, in general, formation of interlayers is a necessary step in the spontaneous nucleation processes of diamond on nondiamond substrates, but this alone is not sufficient for nucleation to occur. Two criteria must be satisfied for nonepitaxial surface nucleation when an interlayer is present: (1) carbon saturation of the substrate surface and (2) presence of high-energy surface sites (unsatisfied valences). Distinctly different interlayers may form on different substrate materials at different rates, and different reactant gas mixtures or different substrate temperatures may produce different intermediate layers on the same substrate. Low C:H ratios and/or high substrate temperature may favor the formation of carbides, while high C:H ratios and/ or low substrate temperature may lead to the formation of a-C or diamondlike carbon (DLC), or even direct nucleation of diamond on the bare substrate surface.

B.

Diamond Epitaxy and Morphology Evolution

1.

Epitaxy

Diamond films epitaxially deposited on both diamond and cBN single-crystal substrates demonstrate that, under typical low-pressure processing conditions, single-crystal diamond deposition is possible [109,123]. However, deposition of single-crystal diamond films on substrates other than diamond and cBN is desirable due to the difficulty in obtaining large-area single crystals of either of these two materials. Methods for obtaining large-area single crystals, or at least highly oriented films, must be developed for largescale electronic applications. Heteroepitaxial growth of diamond has been and will continue to be a major research objective. The primary difficulty associated with diamond epitaxy is the small number of materials available with suitable crystal structures and lattice constants. Some transition metals and ceramics, such as Ni, Cu, Fe, and cBN, constitute the few isostructural materials with sufficiently similar lat-

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tice constants (mismatch < 5%). Further, the extremely high surface energies of diamond, ranging from 5.3 to 9.2 J m⫺2 for the principal low-index planes, and the presence of interfacial misfit and strain all present major obstacles in forming oriented, two-dimensional diamond nuclei [124]. Early attempts to grow heteroepitaxial diamond on transition metals were unsuccessful, possibly due to the high solubility and mobility of carbon on these materials and the formation of intermediate layers, as discussed in Sec. IV.A. More recently, however, there have been a number of successes in obtaining heteroepitaxial growth on Ni, Cu, and cBN [104,124–126]. 2.

Oriented Growth

The crystal habit of diamond is, in general, determined by the relative growth velocities of the {100} and {111} planes, denoted as v100 /v111, and the appearance or disappearance of crystallographic planes in diamond films depends upon the growth velocities of the corresponding planes. The facets that appear on a crystal are those for which the normal growth velocity is the slowest. Based on the Wulff criterion for crystal habit [127], it is predicted that the most stable growth planes in diamond are the octahedral {111} planes, followed by cubic {100} planes and the {110} planes. At low substrate temperature, when v100 /v111 > 兹3, the crystal habit of diamond is octahedral, and at high substrate temperature, v100 /v111 ⱕ 兹3/3, it is cubic, and in between it is cubo-octahedral. Increasing the hydrocarbon concentration in the gas phase has the same effect as increasing the substrate temperature, specifically, that the morphology of polycrystalline diamond films evolves from octahedral, to cubo-octahedral, to cubic. Success in growing highly oriented, textured diamond on silicon represents a novel approach for obtaining near-single-crystal morphology over large areas [128,129]. In initial experiments no texture formed, in part because of the creation of a-SiC interlayers, which led to the growth of randomly oriented diamond particles. Subsequent attempts resulted in the growth of highly oriented, textured films on single-crystal Si{100} substrates. In the latter experiments, a two-step procedure was applied. First, diamond was nucleated using a CH4 /H2 gas mixture, and it is believed that in situ carburization occurred during this stage, converting the Si surface to an epitaxial ␤-SiC layer. Nucleation of diamond produced partially oriented nuclei. Then, during the growth stage CO was added to the CH4 /H2 mixture, resulting in textured growth. The ability to obtain highly oriented, textured films has led to the investigation of the dependence of film texture and morphology on deposition conditions [130]. Oriented films are categorized according to whether they are (1) strongly fiber textured, (2) epitaxially textured films grown on

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{100} Si, or (3) homoepitaxial films grown on {100} diamond. The {100} faceted surfaces were selected because CVD diamond grown on {100} is known to contain significantly fewer structural defects than that grown on {111}. The data for the experiments of Wild et al. [130] were correlated by a growth parameter, ␣ = 兹3(v100 /v111), and it was concluded that the microstructure (texture and orientation) and morphology of diamond films could be controlled through manipulation of this parameter, which in turn can be controlled by altering the growth environment. For fiber-texture films, low CH4 concentrations or high substrate temperatures (corresponding to ␣ < 1.5) result in films with a pronounced 具110典 texture; at intermediate CH4 concentrations and substrate temperatures (1.5 ⱕ ␣ ⱕ 3), a transition of the fiber axis from 具110典 to 具100典 occurs; further increases in CH4 concentration or lower substrate temperature (␣ > 3) leads to a complete deterioration of the film morphology, such that the films lose their 具100典 texture, become very fine grained, and do not show any distinct faceting. The evolution of crystal shape as a function of ␣ is illustrated in Fig. 8. In that figure, the arrows indicate the direction of fastest growth. In the case of homoepitaxial or heteroepitaxially textured films of {100} orientation, the microstructure and morphology of the films are strongly affected by twin formation, which may lead to complete deterioration of the epitaxial orientation. Deposition conditions corresponding to values of the growth parameter ␣ ⬇ 2.5 tend to suppress twin formation, and the subsequent film growth improves epitaxial alignment of the crystals. In contrast, small values of the growth parameter (␣ ⬇ 1.5) usually indicate that the film orientation and morphology will deteriorate due to twinning. The fact that film texture and morphology can be correlated to this one parameter (␣) is a strong indication that these two properties depend most strongly on substrate temperature and the gas composition near the deposition surface. By investigating different combinations of Ts and reactant composition, it may therefore be possible to control film texture, surface morphology, and stability with respect to twin formation and, in particular, to grow 具100典 textured diamond films with {100} faceted surfaces.

Figure 8 Transition of crystal shape from cubic to octahedral as the growth parameter, ␣, is increased. The arrows indicate the direction of fastest growth.

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Morphology Evolution

Regarding the size distribution and grain evolution during film growth, a number of experiments indicate that, for nucleation and growth on Si{100}, the crystal size and size spectrum both grow with increasing deposition time. During the early stages of growth, crystals are small and relatively uniform in size; as the films grow, the average size increases and, simultaneously, the size distribution broadens. The great disparity in crystal sizes and pronounced surface roughness in high-growth-rate systems led to a detailed set of experiments to study possible morphological instabilities during diamond growth [85]. Indeed, it was observed that in low-pressure, high-growth-rate systems (plasma arcjet and combustion), the lack of surface diffusion and reevaporation at diamond film surfaces during growth accelerated any stochastic interface perturbations, leading to fast growth of some crystals relative to others. The instabilities are then magnified during sustained growth as a result of competitive shadowing and reactant depletion by the taller crystals. This phenomenon is usually observed only in high-growth-rate systems and only for films thicker than 20 ␮m. The possible morphological instabilities inherent to diamond film growth not only result in extreme variations in the sizes of the crystallites but also lead to the incorporation of voids and noncrystalline phases in the films. As growth proceeds, smaller crystals are often found to be coated with DLC, which may be attributed to reactant starvation and lower temperature experienced by these smaller grains. Several possibilities exist for surmounting these instabilities in high-growth-rate systems. The first is to increase the nucleation density of diamond on the substrate, so that the inevitable onset of instability is delayed. The second is to grow the films in a cyclical manner, so that the growth phase is interrupted regularly with a renucleation phase. C.

Effects of Surface Conditions

It has long been recognized in film deposition that the substrate material and surface pretreatment both strongly affect the properties of the resulting film. As mentioned earlier, two key issues in diamond deposition are the surface nucleation density and rate, and a number of nucleation enhancement techniques have been developed to maximize both of these quantities. Nucleation density has been increased from less than 105 cm⫺2 on untreated substrates up to 1011 cm⫺2 on scratched or biased surfaces. The effects of surface conditions on nucleation processes have been investigated to provide guidelines for selection of optimal surface pretreatment methods. Methods of substrate surface pretreatment that have been tested include

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(1) scratching with abrasives; (2) seeding with diamond grit and other ceramic powders; (3) electrical bias; (4) covering the substrate with graphite films or fibers; (5) coating the substrate with thin metal films, a-C, C70, cBN, SiC, WC, or hydrocarbon oil; (6) ion implantation; (7) pulsed-laser irradiation; (8) carburization; and (9) chemical etching. These different methods make it possible to control diamond nucleation density over many orders of magnitude. The reverse problem, that is, preventing diamond from growing on specific portions of a deposition substrate, is important for selective or patterned growth, a technique of particular importance in electronics applications. A number of surface pretreatment methods have been proposed for preventing diamond nucleation on foreign surfaces, including oxidation, sputtering, reactive ion etching, excimer laser irradiation, and surface melting with lasers. It is generally accepted that native oxides (SiO2) are the most effective at impeding diamond nucleation [131,132]. Chemical etching in HNO3, HF, and HCl; plasma etching in NF3 and Cl2; and sputtering in N2 have shown success in introducing surface roughness on selected regions of the surface but have not resulted in increased nucleation density and have, in fact, had the opposite effect. Scratching is the most widely used technique for enhancing diamond nucleation, although this pretreatment method is not easily applied to surfaces of complex shape and is not generally attempted when growing films that require extremely smooth surfaces. Often in this technique, the surface is scratched, abraded, or blasted with diamond particles or paste, but other abrasives are also used; these include borides, carbides, nitrides, silicides, oxides, and graphite. Diamond nucleation densities after scratching pretreatment typically range from 106 to 1010 cm⫺2. Scratching may also be accomplished using ultrasonic vibration with an abrasive paste suspended in methanol or acetone. It has been observed that an ultrasonically damaged surface has more uniformly distributed defects, and this leads to slightly higher nucleation densities (107 –1011 cm⫺2) and more reproducible effects [99,122]. A number of explanations have been put forth for the enhancement of nucleation density and rate caused by scratching. The first of these is the seeding effect: diamond, DLC, or other carbonaceous residues from the scratching process are left behind, either adhering to or imbedded in the substrate, and these nano- and microparticles may act as nucleation sites [133]. Because other abrasive materials yield a similar yet less pronounced effect, it is likely that this is not the only operative mechanism in diamond nucleation on scratched surfaces. A second possible mechanism for nucleation is that the highly disordered surface materials or microscopic crater edge sites on the polished surface create high-energy sites. Diamond nucle-

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ates preferentially at these sites because (1) there is a resultant minimization of interfacial energy from the formation of diamond nuclei on the sharp convex surfaces, (2) the microscopic craters and trenches formed by scratching may leave dangling bonds, and (3) carbon saturation will occur most rapidly at sharp edges. Topography patterning analyses lend credence to the second postulate [134]. It was observed that, although residual abrasive powder may enhance nucleation, the nucleation event is promoted by topological features alone, and the presence of residual abrasive is not a necessary condition for nucleation. A third possible mechanism for nucleation is that the scratching process produces nonvolatile graphitic particles through local pyrolysis; the graphitic particles are subsequently hydrogenated in the growth environment. Scratching and seeding cause substrate surface damage and contamination, as mentioned earlier. Therefore, these pretreatment methods are incompatible with many applications requiring extremely smooth, clean surfaces, such as diamond films for electronic devices, optical window materials, and smooth, wear-resistant coatings. Alternative pretreatment methods that yield high nucleation densities without substrate damage are of particular importance. Biasing pretreatment of substrates has been increasingly employed to enhance surface nucleation of diamond [129,135, 136]. Using a potential bias to obtain large nucleation densities on unscratched substrates provides an opportunity to control nucleation densities through variation of the applied voltage and current, while reducing surface damage. Most investigations of bias-enhanced nucleation have focused on mirror-polished Si substrates, and possible explanations for the nucleation enhancement have emerged. For negative biasing of an Si substrate, the role of biasing is to (1) increase the flux of carbon-containing cations (C⫹, ⫹ CH⫹ x , CxHy ) to the surface, expediting the local carbon saturation on the surface and leading to a thin layer of amorphous carbon on the SiC interlayer to form small clusters for diamond nucleation; (2) transfer more energy to the surface through ion bombardment, resulting in increased surface mobility of adsorbed species; (3) reduce and suppress surface oxide formation and remove native oxides; and (4) accelerate gas-phase reactions because of the increased ion-neutral collisions and higher energy of the sheath region, leading to higher concentrations of reactive hydrocarbon radical species. It is believed that nucleation enhancement on positively biased substrates is due to a high electron density, which in turn results in a high electron kinetic energy. Such a high-speed electron impingement process may increase the rate of decomposition of adsorbed hydrocarbons through hydrogen desorption.

Deposition Chemistry

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85

Effects of Deposition Conditions

Deposition conditions, such as substrate temperature, reactor pressure, and reactant composition, critically influence diamond nucleation rate and density, but conditions optimal for growth may not be ideal for nucleation. Experiments on bias-enhanced nucleation revealed that negative biasing greatly increases diamond nucleation, but poor-quality films are produced when biasing continues during growth [137]. Similarly, optimal values of temperature and pressure for growth may not be the same as those for nucleation. 1.

Substrate Temperature

Experiments carried out in different reactor systems present a consistent physical picture of the dependence of nucleation density on substrate temperature [138–140]. In these studies it was found that, for growth on silicon substrates, nucleation density falls off sharply for substrate temperatures below 820–850⬚C; for temperatures greater than 850⬚C, the nucleation density gradually decreases but remains on the order of 1010 cm⫺2 up to the highest temperatures studied (950⬚C). It is speculated that this overall dependence of nucleation density on substrate temperature is due to the change in adsorption state and surface diffusion length of growth precursors. At temperatures below approximately 900⬚C, the nucleation precursors are adsorbed primarily by physical adsorption (physisorption), whereas chemical adsorption (chemisorption) is dominant at higher temperatures. This change in the adsorption state causes an abrupt change in the diffusion length of the precursors as the temperature is increased above 900⬚C. As a result, the capture efficiency of precursors on the substrate surface and thus the nucleation rate and density dramatically increase when the temperature approaches 900⬚C. 2.

Reactor Pressure

Investigations indicate that there is an inverse relationship between pressure and nucleation density and rate, at least for diamond growth on silicon [111,141]. However, the effect does not appear to be nearly as strong as substrate temperature, resulting in a factor of 3–4 decrease when the pressure is increased from 2 to 50 torr. For silicon substrates, it is possible that the inverse dependence on pressure is due to a competition effect between ␤-SiC formation (which increases diamond nucleation density) and atomic hydrogen etching of material, which decreases the number of nucleation sites. Because of these observations it has been suggested that the nucleation phase be carried out at lower pressure (2–5 torr) and subsequent growth be carried out at higher pressure (20–40 torr).

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The effect of pressure has also been examined for nucleation on Mo substrates [142]. It was found that good nucleation density was achieved for high gas-phase hydrocarbon fractions at low pressure due to the promotion of carburization of the substrate surface and increased surface C concentration. Growth was then carried out at lower hydrocarbon concentrations and higher pressure to preserve diamond film quality. Films grown in this manner have been shown to be dense, homogeneous, and well crystallized. 3.

Reactant Composition

In nucleation on carbide-forming substrates, it has been observed that diamond nucleation density increases as the inlet CH4 mole fraction is increased. The gas composition influences not only the nucleation density but also the nucleation behavior and the resultant crystal morphology. At lower CH4 mole fractions (<0.5%), diamond nucleation may actually cease while a significant area of the substrate remains unnucleated, and the subsequent growth leads to good-quality, well-faceted, isolated diamond crystals. At higher CH4 concentrations (1–2%), isolated crystals may grow large enough to occlude one another before nucleation terminates [143]. A side effect of higher hydrocarbon concentrations is formation of appreciable nondiamond components. The addition of small amounts of oxygen has been generally found to reduce the incubation period and to increase nucleation density. For growth on silicon, it has been postulated that the role of oxygen is to participate in reactions leading to preferential formation of SiOx on the surface rather than SiC; the SiOx layer may impede Si diffusion from the bulk to the substrate surface, allowing the adsorbing carbon species to saturate the surface more quickly and then nucleate [144]. Further, the presence of oxygen allows lower substrate temperatures during nucleation due to the lower binding energy of OH to C (3.68 eV) compared with that of CH to C (4.63 eV); OH is more readily abstracted by atomic hydrogen, creating reactive sites for hydrocarbon adsorption. However, for growth on Ni and Pt substrates, oxygen may have an adverse effect. In experiments using these substrate materials it was observed that, although the addition of oxygen did not suppress growth of existing diamond and resulted in sharply faceted crystals, it degraded diamond nucleation by eliminating nucleation sites [114]. For high oxygen concentrations (O:H = 1), Ni and Pt surfaces are etched clean; oxygen must be decreased by a factor of 2 or more (O:H ⱕ 0.5) before nucleation sites last long enough for growth to occur. Once growth does occur, oxygen does not act as an inhibitor, and, in fact, the reason that large, well-faceted crystals form is the preferential etching of potential nucleation sites on the crystals, thereby suppressing secondary nucleation.

Deposition Chemistry

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87

IN SITU DIAGNOSTICS

The rate of growth of a diamond film and its uniformity, morphology, texture, and thermal and mechanical properties all critically depend upon the state of the gas phase adjacent to the deposition surface, that is, the composition, temperature, and flow field. The gas properties at the surface, in turn, depend upon the upstream conditions in the reactor. As discussed in Sec. VI, one- and two-dimensional physical models have been used, with varying degrees of success, to predict the flow field and temperature and species profiles within different types of diamond CVD reactors. Such models are a powerful tool for exploring issues related to diamond growth and may help provide links between operating conditions and film growth rate, morphology, and quality. However, the models cannot stand alone: to gain a true understanding of the mechanisms underlying diamond growth it is necessary to couple predictions with experimental measurement. In situ measurements of the gas phase and the deposition surface during diamond growth provide data that may be used both as input to the detailed models and as a means of validating such models. Diagnostic technique may be used, for example, to measure concentrations of postulated growth precursors such as CH3 or the species crucial for diamond growth, atomic hydrogen. Because the mechanisms describing the gas-phase chemistry are relatively well understood, it may only be necessary to measure several key species in order to have quantitative knowledge of the overall species distribution. A strong need also exists for on-line process monitoring in diamond CVD because this material is extremely expensive to synthesize, and many reliability issues remain to be addressed. Diagnostics well suited for fundamental studies are not necessarily appropriate as process monitors. Currently, most process measurement and control techniques in diamond reactors focus on average substrate temperature, reactor pressure, reactant flow rate, and power. These are important parameters, but they do not give enough explicit information to determine the state of the gas phase uniquely. For example, if laboratory measurements of gas-phase composition and temperature reveal a strong correlation between specific measurable quantities and film growth rate and/or properties, there may be an opportunity to exploit this information through the development of an on-line process sensor. Such a sensor could be tightly coupled to an overall process control strategy. Discussion of the diagnostic methods in this section is segregated according to the reactor type in which the measurement was made: hot-filament, plasma-assisted, and combustion. This section will not constitute a thorough review of diagnostic techniques employed in diamond CVD but is instead intended to indicate how measurements made by extraction, physical

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probes, and optical probes advance understanding of the growth process. A complete review of gas-phase diagnostic techniques in diamond CVD has been presented by Thorsheim and Butler [145].

A.

Hot-Filament Deposition

The hot-filament reactor is the most studied of the various diamond reactor types. Diagnostics in hot-filament systems have addressed three specific issues: (1) identification of diamond growth precursors, (2) determination of the role of other species in the growth process, and (3) quantification of the effect of operating conditions on gas-phase composition and spatial distribution. One of the first measurements of the gas-phase environment in diamond CVD was made by Kawato and Kondo [146] using gas chromatography (GC) to sample residual gas from a reactor. They observed detectable quantities of CH4, C2H4, C2H2, H2, and CO from a feed gas mixture of CH4, H2, O2, and Ar and found that most of the inlet CH4 was converted to C2H2. As more oxygen was added to the system, the amount of CO increased at the expense of C2H2. Because this was a sampling of the downstream stable gas species, the relationship between the measured concentrations and the conditions at the growth surface is not clear. Celii et al. [24] used infrared diode laser absorption spectroscopy for the in situ measurement of gas species in the region between the filament and the substrate. Using this method, C2H2, CH3, C2H4, and CH4 were detected. In contrast to the measurements of Kawato and Kondo, CH4 was found to be the predominant species (⬇8 ⫻ 1014 cm⫺3), with a concentration approximately four times greater than that of C2H2 and a factor of 10 greater than CH3. The fact that the measured CH4 concentration was over 40% of its inlet value indicates that a significant fraction of the inlet gas may completely bypass the filament, never undergoing thermal or heterogeneous dissociation. Using a combination of ex situ mass spectroscopy and x-ray photoelectron spectroscopy (XPS), Harris et al. [147] investigated diamond growth on platinum. By sampling at discrete points between the filament and the substrate, they observed that only CH4 showed a significant change with position, with its concentration growing by a factor of 5 at 30 mm from the filament. The concentrations of C2H2 and C2H4 remained flat in this region. Wu et al. [148] also used gas chromatography and quartz microprobe sampling through a temperature-controlled probe to measure gas-phase concentrations. They found that, while the CH4 concentration also increases with distance from the filament, the increase was a factor of 3 rather than the factor of 5 reported by Harris et al. [147]; the C2H2 mole fraction was seen

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to decrease by a factor of 2. The discrepancies between the results may be explained by differences in deposition conditions and reactor geometry. Atomic hydrogen has also been measured in hot-filament reactors using laser-induced fluorescence (LIF) [22,149], and its concentration was inferred from crossed beam coherent anti-Stokes Raman spectroscopy (BOXCARS) measurements of H2 concentrations [150]. The LIF measurements indicated that, with no substrate present, H concentrations decreased by only a factor of 3 (relative to the value at the filament) at a distance of 30 mm from the filament. This result is expected because the low pressures used in the experiments (20 torr) greatly reduce the rate at which H recombines to form H2. The known high reactivity between H and heated surfaces (such as a substrate) would undoubtedly cause a more significant drop in H concentration with distance from the filament if a surface were present. The atomic hydrogen concentrations derived from the BOXCARS measurements [150] were an order or magnitude greater than those obtained from the LIF measurements. The differences between the two measurements were explained by filament temperature variation and other experimental factors. Molecular beam mass spectrometry (MBMS) measurements of predominant gas phase species were made within 0.1 mm of the substrate [15], and it was found that the absolute H concentrations were uniformly lower than those measured by either LIF or BOXCARS. As shown in Fig. 9, the MBMS measurements revealed that, as the inlet CH4 concentration was varied between 0.4 and 7%, a transition occurred in the predominant hydrocarbon species present near the substrate: C2H2 was dominant for CH4 feed fractions less than ⬇1%, while CH4 was dominant for feed fractions greater than this value. It was postulated that CH4 became the dominant species near the substrate because the filament became coated with carbonaceous material for high inlet carbon concentrations, and this poisoning resulted in lower atomic hydrogen concentrations and hence lower conversion of CH4. This was corroborated by a subsequent theoretical study using a stagnation flow model in which a primitive filament poisoning model was included [28], as described in Sec. VI.A. It was also observed in the MBMS study that, at the surface, CH3 closely tracked CH4, and its concentration was approximately 10% that of CH4, a result consistent with the infrared diode laser measurements of Celii et al. [24]. A possible diamond growth precursor, CH3, has a much stronger concentration dependence on distance from the substrate than do other measured stable hydrocarbon species such as CH4, C2H2, or C2H4, and it is expected that this larger spatial gradient is due to the higher reactivity of CH3. Resonance-enhanced multiphoton ionization (REMPI) was used to measure CH3 concentrations 4 mm above the substrate, in a system where the filamentto-substrate distance was varied from 7 to 16 mm [151]. The methyl radical

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Figure 9 Species mole fractions measured by MBMS sampling at the surface in a hot-filament reactor as a function of methane fraction in the feed gas. (From Ref. 15.)

concentration was a factor of 3 lower when the separation distance was 7 mm than when it was 16 mm. REMPI was used in a similar reactor system to measure concentrations of CH3, CH4, and C2H2 at different substrate temperatures [152]. By incorporating the concentration data with measured film growth rates, an apparent activation energy of 0.17 eV in CH3 concentration was determined, and no measurable substrate temperature dependences were observed for CH4 and C2H2. Absolute concentration profiles for CH3 as a function of distance from the filament were measured [153] using cavity ring-down spectroscopy (CRDS) [154]. A peak in CH3 concentration was detected several millimeters from the filament, indicating that this species is formed by gas-phase reactions rather than heterogeneous filament chemistry, as shown in Fig. 10. The CH3 concentration was also observed to increase linearly with susceptor temperature. Measurements of CH4 concentrations using CARS [155] and atomic hydrogen using REMPI [25] have shown that, near the filament, the up-

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Figure 10 Spatial profiles of CH3 density and absorbance in a hot-filament reactor at two different susceptor temperatures. (From Ref. 153.)

stream and downstream spatial profiles are the same. In other words, the concentration profiles of CH4 and H are independent of whether the measurements are made upstream and downstream of the filament. The conclusion to be drawn from this result is that, indeed, mass transport in hotfilament reactors is completely dominated by diffusion, and convection plays a secondary role at best. Models of diamond growth in hot-filament reactors have confirmed that growth rate is independent of filament-substrate orientation [28,156]. Spatial temperature distributions have been measured using thermocouples [14], BOXCARS [150], and LIF [157]. These different experimental techniques consistently show a very sharp temperature drop from the filament to the surrounding gas. For example, LIF temperature measurements showed a drop from 2600 K on the filament to 1400 K 1 mm from the filament, in a reactor operating at 30 torr. The lower the operating pressure, the more pronounced is the apparent temperature discontinuity between the filament and adjacent gas. As shown in Fig. 11, BOXCARS measurements found that, for a 2870 K filament and 20 torr operating pressure, the tem-

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Figure 11 Gas temperature in a hot-filament reactor with 1% CH4 in H2, for filament power of 2.7, 2.0, and 1.5 kW. The open squares indicate the filament and substrate temperatures for 2.0 kW filament power. (From Ref. 150.)

perature dropped to 2600 K within 0.1 mm of the filament. This effect is well known as was first discussed by Langmuir [18], and it is observed in many thermal systems operating at low pressure; the discontinuity is observed within one or two mean free paths (75–125 ␮m at 20 torr) where continuum heat transfer theory is not applicable.

B.

Plasma-Assisted Deposition

A popular technique for determining the composition of plasmas is optical emission spectroscopy (OES). High-temperature plasma systems such as dc arcjets show elevated levels of CH and C2 when compared with systems such as microwave, and these emissions are useful in determining the presence of specific species and for use as a process monitor [158]. The use of OES as a sensor for process control in low-pressure dc arcjet [159] and microwave reactors [160] has been investigated. For the microwave system it was found that there was a linear relationship between C2, CH, and H(␤) emissions throughout the plasma. Molecular beam mass spectrometry has also been used to determine absolute species concentrations near the substrate in microwave [161] and

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arcjet [162] plasma reactors. In the 20-torr microwave system, the effects of hydrocarbon source (CH4 and C2H2), hydrocarbon concentration, and substrate temperature on the gas-phase species concentration distribution near the substrate were studied. As illustrated by the data in Fig. 12, over the range of inlet carbon mole fractions considered, the composition near the substrate was independent of the specific source gas, indicating that the plasma was very efficient at scrambling the species during transport to the substrate. The composition was also found to be insensitive to substrate temperature, so that, although the film growth rate was temperature dependent, the gaseous species were governed by upstream processes that did not depend on the details of the heterogeneous kinetics. Regardless of the hydrocarbon reactant gas, when the mole fraction of carbon in the feed was less than 1%, CH4 was the dominant species detected near the substrate, whereas C2H2 was dominant for inlet mole fractions greater than 1%. Atomic hydrogen was found to be relatively insensitive to inlet carbon mole fraction, making up approximately 0.07% of the gas mixture. In the arcjet study [162], a 1% mixture of CH4 and H2 was passed through a 1 kW arc into a 200 torr reactor. It was found that a significant fraction of the inlet CH4 was converted to C2H2 and C2H4 and that the C2H2 concentration near the substrate grew approximately linearly with CH4 flow as the amount of CH4 in H2 was raised from 0.3 to 1.5%. Attempts were made to measure CH3 in that work, but it proved impossible to distinguish between actual CH3 and that produced as a fragmentation product. Actinometry has been used by a number of investigators to measure the relative ground state concentrations of species, most notably atomic hydrogen, using Ar as the actinometer [163–165]. It was observed by Mucha et al. [163] that, in CH4-H2-He-Ar mixtures, an increase in CH4 gave rise to a decrease in the H concentration, and the addition of oxygen resulted in an increase in H, possibly due to passivation of the reactor walls. Spatially resolved relative concentrations of atomic hydrogen were measured by Reeve et al. [165] in a dc arcjet reactor using a CH4-H2-Ar reactant mixture with no substrate present. It was observed that the H concentration dropped rapidly with distance from the plasma torch exit, reaching a relative value 30% of its initial maximum within 6 cm. The actinometry data, integrated along the line of slight, were found to be in excellent agreement with predictions of a one-dimensional model containing detailed pyrolysis chemistry. One drawback of actinometry, particularly in systems with appreciable electron densities, is the effect of the noble gas on plasma chemistry. Zhu et al. [166] carried out experiments in a microwave system with a CH4 /H2 plasma, and found that, upon addition of a noble gas, the emission intensity of various species changed, and the magnitude of the effect depended on the specific noble gas species introduced. It was determined that if a noble gas

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is to be used as an actinometer, its concentration should be kept below 1%. Ground state concentrations of atomic hydrogen have also been measured using third-harmonic generation [167,168]. The amount of atomic hydrogen present was seen to increase with plasma power, while it decreased as CH4 was added. Another nonlinear technique, resonant degenerate four-wave mixing, was used to measure CH and C2 concentrations and gas temperature within the boundary layer in a convection-dominated plasma reactor [169]. Measured CH profiles compared well with predictions obtained from a onedimensional stagnation-point flow model in which the experimentally determined temperature profile was used. Other work in plasma-assisted systems has been directed at determining concentrations of stable species such as C2H2 and CH4 using Fourier transform infrared spectroscopy (FTIR) in a microwave plasma reactor [170] and CARS in a diffuse rf plasma [155]. The quantitative differences in species’ concentrations measured in these two reactor types illustrate important distinctions in the gas-phase chemistry induced by the different energetic sources. In the microwave system, only C2H2 and CH4 were detected when the hydrocarbon constituted less than 1% of the inlet gas stream, whereas in the rf plasma no acetylene could be detected for comparable inlet conditions. Based on known detection limits it was deduced that, in the rf system, less than 20% of the inlet CH4 was converted to C2H2. As rf power was increased, the measured concentration of CH4 decreased, indicating that more gas-phase conversion was occurring. Efforts at measuring temperature in plasma systems have met with partial success. Early measurements using Langmuir probes in an arcjet system operating between 100 and 400 torr greatly overestimated the local temperature, and this was attributed to the disturbance of the plasma by the probe [171]; OES measurements in the same system gave temperatures that were 35–45% of the values measured by the probe. No substrate was present in that experiment, so it is difficult to extrapolate from the observed results to an actual deposition system. Measurements in a dc arcjet system at 60 torr using a floating double probe found that electron temperatures ranged from 2.3 eV at the exit of the plasma torch to 0.4 eV in the downstream (near the substrate) and peripheral regions of the plasma [172]. Electron densities in that system ranged from 6 ⫻ 1010 cm⫺3 near the plasma torch

< Figure 12 Mole fractions of species measured near the substrate in a microwave reactor as a function of the carbon mole fraction in (a) acetylene feed and (b) methane feed. Reactor pressure (20 torr), microwave power (850 W), and substrate temperature (825⬚C) were held constant. (From Ref. 161.)

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to 1 ⫻ 109 cm⫺3 in the downstream region, indicating that charged species concentrations were small compared with the 3 ⫻ 1017 cm⫺3 mixture number density. Determination of the gas kinetic temperature using OES of H2 and CN was carried out by Chu et al. [173]. LIF of CN was used to compare the rotational temperature obtained with OES with the gas kinetic temperature. It was found that the rotational temperature was an accurate measure of the gas kinetic temperature, even at pressures greater than 10 torr, and it was concluded from this that the rotational distribution is a better choice for temperature measurements than vibrational or electronic populations because of the more rapid thermal equilibration of the rotational population. One of the first detailed analyses of C2 and CH optical emission in a dc arcjet operating under diamond growth conditions with a CH4 /H2 mixture was carried out by Raiche and Jeffries [174]. Through examination of emission spectra, they concluded that the emission was likely due to chemiluminescent reactions; discrepancies in temperatures derived from emission spectra (5000 K) and those obtained from LIF measurements (2100 K) [175] were attributed to lack of thermodynamic equilibration of excited state populations. Rotational and vibrational excitation temperatures were determined in a dc arcjet reactor with a CH4 /H2 /Ar mixture, and a substrate located 1 in. below the exit of the plasma torch [176]. Although it was found that temperatures converged at the substrate and that rotational temperatures for C2 and vibrational temperatures for CH closely tracked the gas temperature, the vibrational temperatures for C2 and rotational temperatures for CH were anomalously high. Analysis of those results indicated that, in the plasma bulk, emission by CH was produced primarily by chemiluminescent reactions, while C2 was produced by electron-impact excitation. The general conclusion from that work was that OES of C2 provided an accurate means of obtaining spatially resolved gas kinetic temperatures. C.

Combustion Flame Deposition

Optical emission has been used in combustion synthesis to detect species such as CH, C2, H, and O in one system [177] and OH, CH, and C2 in another [178]. Yalamanchi and Harshavardhan observed that the primary combustion zone displayed the strongest emission from the carbon-bearing species, and the emission intensities of CH, H, and O dropped sharply downstream of this zone, while C2 emission remained fairly constant. Diamond growth was reported when CH emission was significantly stronger than C2 emission in the primary combustion zone. Hirose et al. [178] also examined emission from the center of the primary combustion zone and found that conditions optimal for optically transparent diamond correlated with an in-

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crease in OH emission and a decrease in C2 emission. In subsequent work, emission from C2 at 510 nm was correlated with diamond growth in a C2H2/ O2 flame [179]; as can be seen in Fig. 13, C2 emission increased with the fuel-to-oxygen ratio, reaching a maximum when the ratio of the fuel flow rate to the oxygen flow rate was 1.1. This maximum in C2 emission corresponded to a maximum in the deposition rate. Subsequently, diamond films were grown using a MAPP/O2 mixture, and OES spectra from OH, CH, and C2 were measured [158]. MAPP gas in a mixture of methyl acetylene, propadiene, and liquefied petroleum gas. By examining the relative intensities of the CH and C2 emissions, it was found that when the MAPP and oxygen flow rates were manipulated such that the ratio of the C2 ⌬␯ = 0 transition to the CH A-X transition was between 1.2 and 1.6, well-faceted diamond films could be grown. Ground state species have also been measured using LIF and mass spectrometry [180] and GC [181]. The mass spectrometer probe sampled gas from the center of the primary combustion zone; the main gaseous spe-

Figure 13 Emission intensities of C2 and CH, and deposition rate as a function of stoichiometry in a C2H2 /O2 combustion flame reactor. (From Ref. 179.)

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cies detected in this region were CO and H2. Samples taken near the burner showed C2H2 and the carbon-bearing radicals to be in near equilibrium. As oxygen flow rate was increased, C2H2 concentration decreased near the combustion zone, while H2 remained nearly constant. The LIF experiments were performed with no substrate present and it was found that maximum OH fluorescence intensities were nearly independent of distance from the combustion zone. Flame temperature and the concentrations of CO, CO2, H2O, and OH have been measured during atmospheric-pressure diamond growth using FTIR [182]. Distinct differences in temperature and composition were observed depending on whether or not a substrate was present; the deposition flame was found to be wider and cooler than the free flame, with the gas temperature lowered by as much as 700 K with the substrate present. In both flames, CO was located primarily in the main combustion zone, while H2O, CO2, and OH were found mostly in the outer flame region. A large radial temperature gradient, 700 K/mm, was measured across the diamond growth zone. The steep temperature and composition gradients in many combustion torch systems, such as this one, point to the difficulties inherent in growing large-area, uniform diamond films using combustion synthesis. Obtaining the appropriate gas-phase composition with little or no radial variations points to the need for flat-flame burners and burner-stabilized flames [183–185].

VI.

REACTOR SCALE MODELING

Numerical and analytical solutions of the governing conservation equations for momentum (fluid flow), mass, and energy (temperature) have led to many insights concerning the mechanisms and conditions under which diamond may be grown by chemical vapor deposition. Modeling many types of diamond reactors has proved successful primarily because the principal hydrocarbon sources used are CH4 and C2H2, and as discussed in Sec. II, the pyrolysis and combustion mechanisms for these fuels are well understood for the stoichiometries used, and thermodynamic and thermophysical data for the various gaseous species are known. Also, as discussed in the following, the reactor configurations and operating conditions used in dc arcjet, rf plasma, combustion, and hot-filament systems lend themselves to geometric simplifications, which in turn make the numerical models tractable, even with very detailed homogeneous and heterogeneous chemistry. The onedimensional models of these reactors have proved successful in describing qualitative (species and temperature profile shapes, likely growth precursors) and quantitative (diamond growth rate, species concentrations) features in

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systems where charged species (plasma) chemistry does not play a significant role. There is a need, however, for more detailed modeling whereby multidimensional effects are captured and ion-neutral chemistry is considered so that systems containing nonthermal plasmas, such as microwave reactors, may be adequately described. A significant factor complicating reactor models in the presence of the energy source. Whether it is the arcjet issuing from a dc plasma torch, the hot filament(s), or the microwave or rf plasmas, assumptions must invariably be made in constructing a physical model of the source. And, not surprisingly, the particular assumptions strongly affect the predicted temperature and species distributions within the reactor. Because each source type is handled differently, the discussion here is broken up according to reactor type: hot filament, plasma assisted, and combustion. Hot filament is the most studied diamond reactor type, both experimentally and theoretically, and it will be discussed first. A.

Hot-Filament Reactors

Most of the modeling efforts have focused on determining the temperature profile and, in particular, the species distribution in the region between the filament and substrate to identify likely diamond growth precursors and to develop and validate deposition mechanisms. The models have also been used to examine the role played by the filament in initiating gas-phase chemistry. Theoretical studies of hot-filament reactors may be roughly divided according to whether one- or two-dimensional models were used. The onedimensional models typically include detailed gas-phase and gas-surface chemistry and have been used to gain insight into the chemical kinetics governing diamond deposition and the relationship between mass transfer and chemistry. Two-dimensional models generally contain limited gas-phase chemistry and often do not contain deposition mechanisms at all. These models yield information on the details of mass, momentum, and energy transport in reactors. One of the first detailed studies of the chemistry in a hot-filament system was carried out by Goodwin and Gavillet [186]. It was assumed that the flow between the filament and substrate behaved as an ideal stagnation flow; the gas composition at the filament was determined using homogeneous kinetics and an experimental observation indicating that CH4 and C2H2 were present in roughly equal concentrations [14]. Figure 14 shows an example calculation of species concentration as a function of height above the substrate from this work. The availability of film growth rate data and the lack of an accepted deposition mechanism led Goodwin and Gavillet to examine the fluxes of individual hydrocarbon species to determine their

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Figure 14 Calculated mole fractions as a function of height above the surface in a hot-filament reactor (for all species greater than 0.1 ppm). (From Ref. 186.)

feasibility as growth precursors. An upper bound, mass transfer–limited growth rate of each hydrocarbon species was calculated, and it was calculated that only CH3, CH4, and C2H2 were present in sufficiently high concentrations at the surface to account for measured growth rates; the conclusion was that one of these three species must be responsible for deposition in the hot-filament environment. This result is consistent with the postulated deposition mechanisms that were being developed, specifically that one or both of CH3 and C2H2 were the species leading to film growth. Molecular beam mass spectroscopy data obtained by Hsu in a hotfilament reactor was the first quantitative measure of major species concentrations in a diamond deposition system [15,187]. By sampling through a pinhole in the center of the substrate, Hsu measured near-surface concentrations of CH4, C2H2, CH3, and H as a function of inlet CH4 concentration. (See Sec. V.A for more discussion of Hsu’s experiments.) A modeling study was subsequently carried out to examine Hsu’s system [28]. In that work, calculations were performed for H2-only and CH4 /H2 feed gases, using a one-dimensional stagnation flow model to describe the region between the

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filaments and the substrate. For the hydrogen system it was found that, as filament temperature was varied between 1800 and 2600 K, good agreement with Hsu’s data [187] was obtained when (1) the H and H2 near the filament equilibrate around the filament temperature and (2) the heterogeneous abstraction and termination reactions (1) and (2) were included. A comparison between the experimental and numerical results is shown in Fig. 15. When the heterogeneous reactions at the surface were not accounted for, atomic hydrogen mole fractions were overpredicted by two orders of magnitude. This result demonstrates the importance of the gas-surface chemistry in determining the gas-phase composition near the surface, and it also demonstrates the significant mass transfer limitation in hot-filament reactors. That is, the overall kinetic rate of destruction of H by surface reactions is much faster than the rate at which H can be transported to the surface by diffusion. The ratio of these two time scales, diffusion to kinetic, is defined as the Damko¨hler number (Da); for the hot-filament system the effective Damko¨hler number for atomic hydrogen is on the order of 10–20, depending on conditions, confirming that the system is, indeed, mass transfer limited. Numerical results were also calculated for inlet CH4 concentrations between 0.4 and 7.2% [28]. To obtain good agreement with the experimental data [15] it was necessary to implement a simple filament poisoning model,

Figure 15 Experimental [187] and theoretical [28] results for near-substrate atomic hydrogen mole fraction in a hot-filament reactor containing only hydrogen.

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whereby it was assumed that heterogeneous H2 dissociation on the filament varied linearly from a maximum when no hydrocarbon was present to a minimum at 7.2% CH4. The calculated results from that study, together with the measured compositions, are shown in Fig. 16. As can be seen in Fig. 16a and b, it was determined that the predicted gas-phase composition did not depend strongly on whether or not a temperature discontinuity between the filament and surrounding gas [150] was used. However, when no filament poisoning was assumed, regardless of the temperature discontinuity, the calculated results for gas composition were in complete disagreement with Hsu’s data [15]. The conclusion from the results was that the hydrocarbon blocks reactive sites on the filament surface, and the extent to which sites are blocked depends on the amount of the hydrocarbon present. Hsu’s observation that, to maintain a constant filament temperature, current must decrease as inlet CH4 increases, confirms this supposition. Additional experiments and analyses were carried out to examine the effects of hydrocarbon source (CH4 versus C2H2) and substrate temperature (255 ⱕ Ts ⱕ 825⬚C) on gas composition near the substrate [27]. As with the previous study [28], the numerical model exhibited good qualitative and quantitative agreement with experiment for a variable CH4-H2 feed composition and a fixed substrate temperature. For low inlet methane fractions it was predicted that most of this species was converted to C2H2, but at higher inlet CH4 fractions significant conversion did not occur. Agreement between theory and experiment was not as good when the CH4 feed was replaced by C2H2. When the inlet carbon fraction was less than 1%, there was good quantitative agreement, suggesting that the model developed earlier [28] is applicable for C2H2 feed when there is little filament poisoning. However, the calculations significantly underpredicted (by as much as 60 times) nearsurface CH3 and CH4 concentrations at higher inlet C2H2 concentrations. The large amounts of CH4 and CH3 observed experimentally by McMaster et al. [27] suggest that facile decomposition of C2H2 occurred even when atomic hydrogen concentration was reduced by filament poisoning. The predictions of the model were relatively insensitive to the extent of the poisoning (and hence, the degree of H2 dissociation), and it is likely that heterogeneous decomposition of C2H2 on the filament is the explanation for the discrepancy between the model predictions and the observed data.

> Figure 16 Experimental [15] and theoretical [28] results for gas-phase species distribution at the substrate for a filament temperature of 2620 K and a temperature discontinuity at the filament of (a) 900 K and (b) 0 K.

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A discrepancy was also found regarding the dependence of near-surface H concentration on substrate temperature. At low inlet CH4 fraction (0.4%) and relatively high substrate temperature (825⬚C), there was good agreement between theory and experiment. But the one-dimensional calculations indicated that near-substrate H concentration should monotonically increase by almost a factor of 10 as Ts was lowered to 255⬚C, whereas the experimental data indicated only a modest rise in H. It was found that by including a simple radial diffusional loss term for H in the model to account for multidimensional effects, the predicted values for H at the substrate were brought into close quantitative agreement with experiment. The effect of substrate temperature on species distribution was also examined [188] for a different set of experimental data discussed in Sec. V.A [150]. As with the earlier study [27], it was found that the atomic hydrogen concentration was predicted to decrease drastically with increasing substrate temperature. In these calculations, for 600 ⱕ Ts ⱕ 1000 K, the mole fraction of CH3 at the surface rose by a factor of 5, whereas for substrate temperatures above 1000 K the CH3 mole fraction was only weakly dependent on Ts. By examining the predicted CH3 mole fractions at the surface with and without heterogeneous deposition chemistry, it was computed that for Ts ⱕ 950 K, there was a 14.2 kJ/mol activation energy for CH3 formation with surface chemistry and a 12.2 kJ/mol activation energy without surface chemistry. It was concluded that the exponential increase in CH3 mole fraction at the surface with increasing temperature was purely a gas-phase effect and could not be correlated with heterogeneous chemistry. Multidimensional, that is, two-dimensional and axisymmetric, calculations have been performed by a number of investigators to determine the role of heat and momentum transport in diamond growth and to relate predicted spatial nonuniformities to film growth rate and thickness variation. One of the first theoretical studies of heat transfer in a hot-filament diamond reactor was carried out by DebRoy et al. [156]. A vertical reactor was set up in that work and the filament was designed so that axisymmetric behavior could be assumed. It was found that, whether the filament was located above or below the substrate and whether the gases were introduced above or below the substrate, there was little variation in film growth rate. The model predicted the diffusion velocities of important species such as CH3 and H to be greater than any forced or natural convection velocities, demonstrating that concentration and thermal gradients are primarily responsible for species transport in hot-filament systems. This result has been confirmed by other investigators using one-dimensional models in which the inlet bulk velocity was varied by over an order of magnitude with no measurable effect on near-substrate composition or growth rate [28,188]. A subsequent study was carried out using the same axisymmetric reactor geometry to examine the

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effect of atomic hydrogen on heat transfer [189]. It was determined that, for a given filament temperature, the substrate temperature in He was significantly lower than that in either pure H2 or a 1% CH4-H2 mixture and that small amounts of CH4 had no appreciable effect on the atomic hydrogen profile. In that work the predicted temperature profiles were in good agreement with measured values. Also, heterogeneous recombination of H was predicted to result in significant substrate heating due to its relatively high flux and the 4.5 eV exothermicity of the net recombination reaction to form H2. Because the sole energy source for the gas (and sometimes the substrate) typically consists of, at most, several discrete filaments, work has been done to study the effect of the filaments on substrate temperature uniformity. Wolden et al. [190] calculated temperature profiles in a system consisting of up to three parallel, cylindrical filaments oriented parallel to a silicon substrate in order to determine the relative contributions of radiation, conduction, and convection to substrate heating. It was found that predicted substrate temperature profiles were in reasonable agreement with measured values, and, in agreement with Tankala and DebRoy [189], it was determined that surface H recombination significantly affects absolute substrate temperature. Substrate temperatures were primarily determined by radiation flux, indicating that conduction and convection play secondary roles in the surface heat transfer process. Substrate temperature was predicted to be highest directly under the filaments, with appreciable gradients in the direction perpendicular to the filament axes. Through numerical experimentation it was found that a two-filament configuration could be designed that would yield relatively uniform substrate temperatures. A two-dimensional model containing a reduced gas-phase kinetic mechanism consisting of 10 species and 12 reactions has been developed [191]. Closed-form expressions for heterogeneous H production on the filament and for film growth rate were included in the model. Atomic hydrogen production on the filament was assumed to occur via reactions analogous to (1) and (2), and the relevant kinetic coefficients were adjusted to yield agreement with measured gas-phase H concentrations. At low pressure it was predicted that the H production rate on the filament was proportional to H2 concentration, and this result, coupled with tungsten filament data [192], yielded an H2 dissociation activation energy of 1.6–1.9 eV for filament temperatures between 2000 and 2500⬚C. At higher pressures, H concentrations appear to reach saturation. The two-dimensional reactor model was applied to three different experimental systems [27,149,150]. It was found that the temperature discontinuity at the filament had little effect on the results, which is consistent with earlier one-dimensional studies [28,186]. Also, total carbon near the filament was reduced relative to other regions of

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the reactor due to thermal diffusion effects. In general, it was concluded that the model adequately predicted the species’ concentrations and film growth rates in the different experimental systems. B.

Plasma-Assisted Reactors

Lack of quantitative data for temperature and composition in dc arcjet reactors has led investigators to use models to predict macroscopic observables such as film growth rate and to examine near-substrate gas composition for potential growth precursors. Using a modified mechanism with CH3 as the only growth precursor [59], Goodwin [193] modeled the growth environment of Raiche et al. [34] as a one-dimensional stagnation flow. It was determined that, although there were appreciable concentrations of atomic carbon near the substrate, the growth rate data of Raiche et al. could be adequately reproduced by the modified Harris mechanism. The uncertainty regarding the most probable growth precursor (CH3 versus C2H2) and the predicted high fraction of atomic carbon in dc arcjet systems (because of H supersaturation) led other investigators to propose a mechanism for the deposition of diamond and graphitic carbon in which all three species—CH3, C, and C2H2 —could participate [36]. The mechanism was incorporated into a stagnation flow model for a subatmospheric dc arcjet and used to investigate the dependence of growth rate and graphitic content on the degree of H2 dissociation and the CH4 concentration in the feed. It was predicted that CH3 was the predominant growth species when little of the H2 in the plasma torch underwent dissociation and that C became the dominant species at higher dissociation levels. The third growth species, C2H2, did not play a role in diamond growth under the conditions considered with less than 1% CH4 in the feed, but at higher input CH4 levels, the C and CH3 incorporation rates were only slightly higher than that of C2H2. In a subsequent study [194], the dependence of diamond growth rate on hydrocarbon injector location was modeled. As shown in Fig. 17, it was predicted that, for CH4 feed, growth rate could be increased by almost a factor of 2 by relocating the injector from a point near the plasma torch exit to just outside the substrate boundary layer. The growth rate increased as the injector was moved toward the substrate because this increased the near-substrate concentrations of C and CH3. An experimental study of the effect of injector location was carried out [165], and higher growth rate and improved film quality were observed when the hydrocarbon injector was located near the substrate. A two-dimensional model of the reacting gas flow, heat transfer, and electrodynamic phenomena in a subatmospheric dc arcjet has been developed [195,196]. Reaction rate coefficients for two irreversible reactions describing electron-assisted dissociation of H2 and CH4 were obtained in that

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Figure 17 Predicted diamond growth rate as a function of hydrocarbon injector height above the substrate (Xinj) in a dc arcjet reactor for two different mole fractions of atomic hydrogen exiting the plasma torch. (From Ref. 194.)

work by solving the Boltzmann equation for the electron energy distribution function; the coefficients were then used in the gas-phase kinetic mechanism, which consisted of 15 species and 76 reactions. Instead of a detailed deposition mechanism, flux boundary conditions for H and CH3 were derived in closed form. The model predicted the temperature to peak along the discharge axis (the symmetry axis) and to decay smoothly in the radial direction to the electrodes. The model also predicted the deposition rate, as measured by CH3 flux, to vary significantly over the substrate surface. Interestingly, the flux nonuniformity was pressure dependent: at 150 torr the growth rate was minimum at the center and increased monotonically by over a factor of 2 at a radius of 1 cm. At 75 torr, however, the growth rate was maximum at the center, and it decreased by a factor of almost 3 at a radius of 0.8 cm

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before increasing again at distances greater than this. These results were attributed to the pressure dependence of the CH3 distribution in the reactor. Diamond deposition in an atmospheric-pressure rf plasma reactor has also been modeled [197,198]. A nonreacting (except for hydrogen chemistry), axisymmetric flow model coupled to two-dimensional electromagnetic field equations was used to calculate the velocity and temperature fields in the reactor. The temperature field was then used in a one-dimensional stagnation model to describe the processes occurring within the concentration boundary layer. The boundary layer thickness was chosen to lie at the 4000 K isotherm because chemical equilibrium was believed to exist at temperatures above this, that is, in the free stream. In the first study [197] a detailed surface mechanism was not used. Instead, it was assumed that H recombined at the surface to form H2, and C and C2 were assigned sticking probabilities of unity. In the second study [198] a detailed deposition mechanism was developed in which all CHx species (x = 0–3) were possible growth contributors. The predicted growth rate increased strongly as the boundary layer thickness decreased. For relatively thick boundary layers resulting from moderate jet velocities, growth was dominated by CH3, and for thin boundary layers growth was dominated by C. Because of the difficulties involved in modeling nonthermal plasma systems, fewer theoretical studies have been performed on microwave reactors than on dc or rf reactors. As a preliminary step in modeling the twodimensional (axisymmetric) behavior of microwave reactors, Hyman et al. [38] carried out detailed zero-dimensional calculations by solving the Boltzmann equation to determine the electron energy distribution. This equation was coupled to transient equations describing ion and neutral species chemistry. It was presumed that the simulation modeled the time-dependent reactor behavior at the center of the plasma ball; mass and energy transport effects were accounted for in this zero-dimensional model by including estimates for diffusion and conduction driving forces in the governing species and energy equations. For a reactor pressure of 40 torr and power deposition of 30 W/cm3, the model predicted a very rapid electron density buildup for the first several microseconds: it rose from 2 ⫻ 109 cm⫺3 at 0.01 ␮sec to 5 ⫻ 1011 cm⫺3 at 3 ␮sec, but increased by only another factor of 2 when the time increased to 2 msec. Once the gas reached its equilibrium temperature of ⬇3000 K after 2 msec, electron processes became unimportant relative to thermal processes in determining the chemical evolution of the gas. Atomic hydrogen concentration also reached equilibrium within 2 msec, constituting over 20% of the neutral gas mixture in a system that initially contained 98.75% H2, 1% CH4, and 0.25% O2. Most of the C1 species reached equilibrium values after approximately 4 msec: CO was the dominant C1 species, at approximately 0.3%, followed by C at 0.2%. Methyl

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radical was present (at 0.01%) but at lower concentrations than both CH and CH2. Acetylene was predicted to be present in concentrations comparable to atomic carbon. The appreciable atomic hydrogen concentrations predicted to exist within the plasma ball are considerably higher than those found in laboratory microwave reactors [161] but may be characteristic of the conditions in the commercial ASTeX system being modeled. C.

Combustion Reactors

Analysis of combustion flame deposition has focused on the feasibility of using different hydrocarbon fuels, e.g., CH4, C2H2, C2H4, MAPP, and determination of the relationship between gas composition and film growth rate. Atmospheric deposition of diamond in premixed C2H2-O2-H2 and CH4-O2 strained flames has been modeled using a stagnation flow approximation [199]. Using a lightly sooting combustion mechanism [6] and a 35-reaction deposition mechanism, it was predicted that optimal growth conditions occurred when the burner-to-substrate distance was small, and the flame was lifted from the burner surface and stabilized on the deposition surface. The model was found to be in good agreement with experimental data available for the C2H2-O2-H2 flame [200]. It was also predicted that, because of the high gas velocities, temperatures in the C2H2 flame were higher than the theoretical adiabatic flame temperature; it was postulated that the reason for this behavior was the relatively long time required for C2H2 to dissociate to its equilibrium concentration. Concentrations of CH3 near the substrate were high enough in the C2H2 flame to account for observed growth rates. In contrast, temperatures in the CH4 /O2 flame were always lower than the adiabatic flame temperature, and while the gas velocity affected the flame location, it had little effect on peak temperature. In the CH4 flame, the fractions of CH3 and H near the substrate were approximately five times lower than those produced by the C2H2 flame. The bulk of the CH3 produced in the methane flame never reached the surface; instead, it was rapidly converted to C2H2 through bimolecular reactions. It was concluded that, even under optimal conditions, diamond growth rate was considerably lower in atmospheric methane flames than in acetylene flames. To increase film uniformity, combustion systems are often operated at relatively low pressure [183,184]. In a combined experimental and theoretical study of diamond growth, films were deposited at 35 torr to explore conditions that would simultaneously yield moderate growth rates, high film quality, uniformity, and large area coverage [201]. The gas was assumed to behave as an ideal stagnation flow, and the governing equations were coupled to a lightly sooting combustion mechanism [6] and a reduced deposition mechanism in which CH3 was the growth species and O and OH acted to

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abstract surface-bound hydrogen. The temperature profile predicted by the model was in close agreement with the profile obtained from OH rotational temperature data, and this was attributed in part to the large postflame reaction zone. Relative OH concentrations were obtained using LIF, and when these were normalized to the theoretical value at a single point (3 mm from the burner), the measured and predicted profiles were in good agreement. It was also found that, when normalizing the experimental OH concentrations, the presence or absence of heterogeneous chemistry in the model had no apparent effect. Because of this, the measured OH concentrations could not be used to evaluate the accuracy of the surface kinetic mechanism.

VII.

SUMMARY

This chapter has reviewed the state of understanding of the processes controlling the CVD of diamond. Gas-phase chemistry in this system is understood rather well, owing to much prior work in the combustion community. Much more contentious has been development of a mechanistic view of the elementary surface reactions leading to diamond growth. Indeed, our view is that a number of growth mechanisms and important growth precursor species can be operative depending upon details of the growth environment. Although there is still wide disagreement about the detailed, elementary steps in the deposition process, it appears that CVD diamond growth, and even defect formation, can be described quite well by reduced models. Such models, although not rigorous in detail, are useful in engineering reactorscaling studies and process optimization. Outstanding issues in our understanding of CVD diamond include elementary models for the differing growth rates observed on the different crystal faces of diamond. These different growth rates are key in controlling morphology and crystallite grain structure in polycrystalline diamond [202]. Another area still in need of better understanding is the initiation and control of diamond nucleation on nondiamond substrates. Although the nucleation of diamond has been widely characterized, fundamental and predictive models are still lacking.

ACKNOWLEDGMENTS It is a pleasure to acknowledge financial support of our work on CVD diamond by the Materials Science Program at DARPA, contract N00014-932002, and partial support has also been provided by Texas Instruments. The work performed at Sandia National Laboratories was also supported by the

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United States Department of Energy under contract number DE-AC0494AL85000. We have benefited greatly from collaboration and discussions concerning this work with Drs. Richard Woodin, Robert Kee, Ellen Meeks, Wayne Weimer, Wen Hsu, Huimin Liu, James Butler, David Goodwin, and John Angus.

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W Zhu, A Inspektor, AR Badzian, T McKenna, R Messier. J Appl Phys 68: 1489, 1990. FG Celii, HR Thornsheim, JE Butler, LS Plano, JM Pinneo. J Appl Phys 68: 3814, 1990. HR Thorsheim, FG Celii, JE Butler, LS Plano, JM Pinneo. In: R Roy, R Messier, JE Butler, JT Glass, eds. New Diamond Science and Technology. Pittsburgh: Materials Research Society, 1991, p 207. DS Green, TG Owanao, S Williams, DG Goodwin, RN Zare, CH Kruger. Science 259:1726, 1993. T Mitomo, T Ohta, E Kondoh, K Ohtsuka, Y Habu. J Appl Phys 70:4532, 1991. KR Stalder, RL Sharpless. J Appl Phys 68:6187, 1990. SW Reeve, WA Weimer. J Vac Sci Technol A 12:3131, 1994. HN Chu, EA Den Hartog, AR Lefkow, J Jacobs, LW Anderson, MG Lagally, JE Lawler. Phys Rev A 44:3796, 1991. GA Raiche, JB Jeffries. Appl Opt 32:4629, 1993. GP Smith, JB Jeffries. Electrochem Soc Proc 91-8:194, 1991. SW Reeve, WA Weimer. J Vac Sci Technol A 13:359, 1995. RS Yalamanchi, KS Harshavardhan. J Appl Phys 68:5941, 1990. Y Hirose, S Amanuma, K Komaki. J Appl Phys 68:6401, 1990. K Komaki, Y Masaaki, I Yamamoto, Y Hirose. Jpn J Appl Phys 32:1814, 1993. Y Matsui, A Yuuki, M Sahara, Y Hirose. Jpn J Appl Phys 28:1718, 1989. Y Matsui, H Yabe, Y Hirose. Jpn J Appl Phys 29:1552, 1990. PW Morrison, JE Cosgrove, JE Markham, PR Solomon. In: R Roy, R Messier, JE Butler, JT Glass, eds. New Diamond Science and Technology. Pittsburgh: Materials Research Society, 1991, p 219. NG Glumac, DG Goodwin. Mater Lett 18:119, 1993. JS Kim, MA Cappelli. Appl Phys Lett 65:2786, 1994. KF McCarty, E Meeks, RJ Kee, AE Lutz. Appl Phys Lett 63:1498, 1993. DG Goodwin, GG Gavillet. J Appl Phys 68:6393, 1990. WL Hsu. Quantitative analysis of the gaseous composition during filamentassisted diamond growth. Proceedings of Second International Symposium on Diamond Materials, Washington, DC, 1991, p 217. B Ruf, F Behrendt, O Deutschmann, J Warnatz. J Appl Phys 79:7256, 1996. K Tankala, T DebRoy. J Appl Phys 72:712, 1992. C Wolden, S Mitra, KK Gleason. J Appl Phys 72:3750, 1992. YA Mankelevich, AT Rakhimov, NV Suetin. Two-dimensional model of a HFCVD reactor. Proceedings of Fourth International Symposium on Diamond Materials, Reno, NV, 1995, p 687. T Otsuka, M Ihara, H Komiyama. J Appl Phys 77:893, 1995. DG Goodwin. Appl Phys Lett 59:277, 1991. DS Dandy, ME Coltrin. Appl Phys Lett 66:391, 1995. YA Mankelevich, AT Rakhimov, NV Suetin. Diamond Relat Mater 4:1065, 1995. YA Mankelevich, AT Rakhimov, NV Suetin. Plasma Phys Rep 21:872, 1995.

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197. 198. 199. 200. 201. 202.

SL Girshick, BW Yu, C Li, HH Han. Diamond Relat Mater 2:1090, 1993. BW Yu, SL Girshick. J Appl Phys 75:3914, 1994. E Meeks, RJ Kee, DS Dandy, ME Coltrin. Combust Flame 92:144, 1993. M Murayama, S Kojima, K Uchida. J Appl Phys 69:7924, 1991. NG Glumac, DG Goodwin. Combust Flame 105:321, 1996. C Wild, P Koidl, W Mu¨ller-Sebert, H Walcher, R Kohl, N Herres, R Locher, R Samlenski, R Brenn. Diamond Relat Mater 2:158, 1993. M Yoshikawa. Diamond Films Technol 1:1, 1991.

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5 Thermally Assisted (Hot-Filament) Deposition of Diamond Joseph E. Yehoda Diamonex, Inc., Allentown, Pennsylvania

I.

INTRODUCTION

The earliest reports of CVD diamond growth by hot-filament chemical vapor deposition (HFCVD) were published in the early 1980s by Matsumoto et al. [1,2]. A simple W filament was used in a flow tube, the substrate being heated both by the filament and by an external furnace. Since that time, the number of papers dealing with HFCVD has increased manyfold. Figure 1 shows the number of yearly publications dealing with hotfilament, thermal filament, or HFCVD as compiled in the DIAmond Database [3]. It shows an incubation period of approximately 5 years followed by a very rapid increase as research groups within and outside Japan discovered HFCVD. In this chapter, I will give a brief description of HFCVD followed by a more detailed look at the practical aspects of this deposition technique, focusing on filament processes, substrate heating effects, filament contamination, and distribution of species. Other hybrid methods of HFCVD will be discussed along with issues of reactor scale-up. Other reviews dealing with HFCVD have already been published [4,5]. The growth chemistry will not be specifically addressed here. The reader is referred to Angus et al. [6], Butler and Woodin [7], and Goodwin and Butler [8] for a more detailed treatment. II.

DESCRIPTION

Hot-filament CVD can be described as a light bulb. In very much the same way a light bulb uses a refractory filament in a low-pressure environment, 119

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Figure 1 Graph showing the number of publications dealing with hot-filament or thermal filament or HFCVD versus the year in which they were published. The data for 1999 are only through the first 6 months.

HFCVD also uses a filament, activated with either a dc or ac current, to cause the filament to glow (Fig. 2). At temperatures above approximately 1700–1800⬚C, the hydrogen in this low-pressure atmosphere undergoes a thermal dissociation reaction. It is this dissociation of molecular hydrogen into its atomic species that makes diamond growth possible. The atomic hydrogen (H 0) can then interact with the small percentage of hydrocarbon gas, frequently CH 4 , to form methyl radicals (CH3) via the reaction CH 4 ⫹ H 0 → CH3 ⫹ H2

(1)

This provides the most important active species for diamond growth [9–11]. The H 0 also has two other primary functions: (1) to etch nondiamond carbon from the growing film and (2) to surface terminate in H to prevent its collapse into a reconstructed graphitic surface, essentially shutting down the diamond growth completely.

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Figure 2

III.

121

Schematic diagram of the HFCVD process showing the basic elements.

FILAMENTS

The primary role of the filaments in HFCVD is to provide a means of dissociating diatomic hydrogen (H2) into atomic hydrogen via the reaction H2 ⇔ H 0 ⫹ H 0 ⫺ 4.5 eV

(2)

From Eq. (2), it can be seen that the forward dissociation reaction is endothermic, absorbing energy as it occurs. Unlike conventional CVD processes that rely solely on thermal energy to initiate a reaction, for CVD diamond growth H 0 is a key ingredient. The filament also participates in decomposition of the hydrocarbon species but more indirectly through the production of H 0. The filaments also provide a secondary role, heating the substrate to the deposition temperature for diamond growth. Alternative means of heating or cooling can also be implemented to decouple the thermal effects of the filament on the substrate, but this cannot be completely decoupled because of the role of H 0 recombination [reverse of Eq. (2)]. The advantage of in-

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dependently controlling the substrate temperature is to maintain optimum growth conditions. As will be seen in Sect. III.C, the heating of the substrate is primarily through H 0 recombination on the surface and secondarily through radiation from the incandescent filaments. Because Eq. (2) is endothermic, the energy requirements for dissociation should be visible during the CVD process, specifically on the energy supplied to the filaments. Jansen et al. [12] showed the effects of an unreactive gas such as He, compared with H2 and D2 , on the power dissipation of Re filaments. Compared with vacuum, there was only a small increase in power dissipated by the filaments, via convection and radiation, when He was used. When a gas such as H2 or D2 was introduced, the power dissipated in the filaments to maintain a constant filament temperature increased threefold. The result was the generation of H 0 and the energy expended, in dissociation of the diatomic hydrogen, was reflected in the increased power dissipation of the filaments; see Eq. (2). Thus the onset of power loss was associated with H 0 atom production. Sommer and Smith [13] investigated the effects of filament emissivity, filament resistance, and power consumption for W and Re filaments in CH 4-H2 and C2H2-H2 as gas chemistry systems. The filaments were observed to become ‘‘active’’ at a temperature ⱖ 1800⬚C. Evidence for this activity was the production of H 0 through thermal dissociation [Eq. (2)]. In other works [14,15], a similar effect of thermal dissociation of hydrogen on the power supplied to the filaments was observed. Some energy loss can happen at lower temperatures but is believed to be associated with increased vibrational and translational energy pathways for H2 rather than dissociation processes [14]. Again, comparison of power loss of Re filaments in vacuum, He, D2 , and H2 showed the onset of power loss associated with the endothermic hydrogen dissociation reaction [14], similar to that which was observed for W filaments [13]. A.

Filament Material

For a filament material to be a good candidate for HFCVD, it should have several important properties: (1) a high melting temperature of the metal or carbide, (2) resistance to attack by H 0, and (3) mechanical stability at the operating temperatures required for diamond growth. To date, the most successfully used filament materials have been W [13,16–18], Ta [17–19], and Re [12,14,18]. Other materials such as Pt [20] and C [21,22], have also been attempted but with only limited or no success. W and Ta are good carbide formers and also high-temperature materials. Carbon has low solubility in Re, so Re does not carburize, but its melting temperature is very high (3180⬚C). Table 1 gives the melting tem-

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Table 1 Melting Point of Various Filament Materials and Their Carbides Filament material

Tmelting (⬚C) 3410 2860 ⬇2600 2996 ⬇3400 3880 3180

W W2C WC Ta Ta2C TaC Re

peratures of different filament materials and their carbides. Ta can be operated at higher temperatures than W by virtue of its higher temperature carbide, and it is also mechanically less prone to deformation than W [17]. Re has been shown to retain its shape better than other filament materials [18], giving a longer lifetime; however, its cost may be prohibitive. To a large extent, the choice of filament material has been shown to be independent of most deposition parameters [18]. Where it has been shown to make a difference, though, is in what methane concentration, [CH 4 ], and filament temperature result in a maximum growth rate. This has beens shown to depend on filament material [18]. Before the peak in growth rate is observed, the growth rates between similar filament materials appear similar [18,20].

B.

Filament Processes

Filaments such as Ta and W require a carburization step before they can be effectively used for diamond deposition. Because they are good carbide formers, and carbon incorporation is unavoidable, a carburization step helps stabilize the filaments before growth is started. This carburization step is normally performed for two reasons. The first is that because the lattice constants of the carbides are typically larger than that of the pure metal, the filaments will distort dimensionally, lengthening for straight filaments or twisting for spiral filaments. This can change the filament geometry, subsequently affecting the growth. The second reason for carburization is to stabilize the filament electrically. The subcarbides and carbides have different electrical resistivities than the pure metals. A consequence of this is a change in the power required to maintain the filaments at a constant temperature, Tfil . As an example, the resistivities of Ta (12.5 ␮ ⍀ cm), Ta2C (80

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␮ ⍀ cm), and TaC (25 ␮ ⍀ cm) are seen to vary significantly from one another. Until the filament has reached equilibrium, because of the material changes caused by carburization along with the effects of the temperature coefficient of resistance, the power required for maintaining a constant filament temperature will change. Carburization is performed by heating the filaments in an atmosphere of hydrogen and a small percentage of carbon-containing gas, typically CH4. During this process the filament ‘‘removes’’ C from the ambient atmosphere of the reactor, forming a carbide from the surface inward. In the early stages of carburization, the filament can be composed of three distinct materials: a metal core surrounded by a subcarbide annulus that in turn is surrounded by a carbide ring. Figure 3 shows this schematically. The process can be tracked by analysis of the residual gases within the chamber, where the CH4 can be observed to decrease as the filament is heated.

Figure 3 Representation of a filament at successive stages of the carburization process. (a) The pure metal (M) filament; (b) partially carburized filament showing a metal core surrounded by a subcarbide annulus (M2C) followed by the metal carbide outer layer (MC); (c) a fully carburized filament composed of only the metal carbide.

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A negative effect of this carbide formation is an increase in the brittleness of the filaments. This is particularly problematic with W and Ta and less so with Re due to its lack of carbide formation. This can shorten the lifetime of the filaments, especially if the filaments are cycled over large temperature ranges, e.g., room temperature to several thousand degrees Celsius. C.

Filament Effects on Substrate Heating

Just as the forward reaction in Eq. (2) requires energy, its reverse reaction will deposit energy during the recombination of H 0 into H2 . The effects of substrate heating during HFCVD have been studied, experimentally and through modeling [15,23–25]. Homogeneous chemical interactions and diffusional mixing govern the [H 0 ] in the gas phase [15]. Simple probes, constructed using thermocouples, have been utilized to detect H 0 recombination (heating) [15,22,24]. Measurements of the [H 0 ] and Tprobe were made as a function of filament-substrate distance. Studies of the Peclet numbers for mass transport and heat transfer showed that (1) diffusive rather than convective mass transport was dominant and (2) conductive heat transport dominates over convective transport [23]. Using mass transport as an example, the Peclet number is defined as the ratio of the convective mass transport to the diffusive transport: Pe =

convective uL = diffusive D

(3)

Values of Pe ⬇ 0.08 << 1 were determined, implying that diffusion transport dominates. The [H 0 ] values that were measured and modeled in pure H2 and 1% CH 4 in H2 agreed well with each other. In the case of CH 4 addition, the amount of [H 0 ] present was observed to be less than that in pure H2 . Homogeneous gas-phase reactions were ruled out while changes in the filament were suspected. Further verification of homogeneous gas-phase reactions not being significant was provided by the [H 0 ] profile shape not changing from pure H2 to additions of 1% CH 4 [24]. Power inputs into the filaments were observed to decrease with the methane additions as well as an indication of less [H 0 ] being generated [12]. In a comprehensive study of substrate heating effects, H2 , He, N2 , and Ar were used as ambients (without hydrocarbons) to characterize the substrate heating effects [25]. Temperature increases as high as ⬇250⬚C were observed in H2 over He or the other gases, H 0 recombination being the cause. Similar temperature increases have been measured and also ascribed to H2 recombination [22]. Pressure effects were also studied and showed an op-

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timum range of 25–30 torr to operate within. At pressures higher than this, gas-phase recombination started to dominate over substrate surface recombination. For lower pressures, it was suggested that mixed flow regimes of viscous and molecular flow contributed to less efficient transport of H 0 to the substrate. For the geometry of the filament and substrate in this work, less importance was given to heat transport through radiation, but for more conventional geometry, radiation was believed to be more important. Heat flux in the reactor toward the substrate can be classified in order of importance: H 0 recombination > thermal radiation >> conduction > convection. Modeling of a three-filament system showed a 14% increase in Tsub when comparing the effects of H 0 recombination over radiation [26]. The same effect of substrate heating due to H 0 recombination has been observed in Diamonex’s 12-in. reactors. In this case, the substrate temperature in vacuum is approximately 500⬚C lower than that when H2 is introduced into the process chamber at typical filament temperatures for CVD diamond growth. D.

Filament Contamination

The main source of impurities in HFCVD films is incorporated hydrogen and metal from the filaments. Hydrogen can be incorporated from a fraction of a percent to several percent as an impurity [27–30]. This is not totally unexpected given that the typical growth ambient can be anywhere from 90 to 99% H2 . Metal contamination is normally lower, several tens of parts per million atomic (ppm-a) to hundreds of ppm-a. Using elastic recoil spectroscopy, differences in the [H] between the growth and substrate sides of thick (500 ␮m) diamond films were measured [30]. Both as-grown and polished samples were investigated. It was found that for the unpolished case, the substrate side had approximately 3.4 times more H incorporated (6.5% to 1.9%). When both the growth and substrate sides were polished, the substrate side was larger by only about 1.6 times, 4.2% for the substrate side and 2.6% for the growth side. The larger concentration on the substrate side was attributed to more nondiamond carbon that was believed to be where the H was bonding. One should remember that the substrate side, by virtue of nucleation and columnar growth, has a higher number of grain boundaries and associated defects. This can provide a greater number of sites where incorporated H can reside. The effect of the surface roughness on [H] was believed to be partially a geometrical effect of H being trapped by the roughness as it was ejected from the surface region toward the detector. Although this work used microwave CVD for the diamond deposition, the salient features of [H] in the diamond are believed to be appropriate to HFCVD as well.

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The question of how much incorporated H comes from the H2 gas and how much is from the hydrocarbon gas was investigated using isotopic labeling studies utilizing H2 , CH 4 , deuteruim (D2), and deuterated methane (CD4) during growth [27]. Both microwave CVD and HFCVD were used, with little difference found in the level of incorporated H. Experiments suggested that the incorporated hydrogen did not originate from H attached to the hydrocarbon gas. However, the results pointed to another, as yet undefined, source of H contributing to incorporation. One of the consequences of the filaments being operated at high temperature is the evaporation of filament material during the diamond deposition process. With the exception of Re filaments, which do not form carbides, the other filament materials such as W and Ta evaporate less material as a carbide than as a pure metal; this is a consequence of higher melting temperatures and lower vapor pressures for the carbides. Impurities have been characterized by a number of methods; SIMS, RBS, EDX, and NAA. SIMS is one of the most popular and sensitive techniques. Matrix effects and the lack of reliable ‘‘standards,’’ however, usually complicate its quantitative interpretation. RBS and EDX lack sensitivity for anything but the most contaminated films. NAA is quantifiable, with the only stipulation that access to a source of neutrons is necessary. There is not an extensive literature on filament contamination. It was recognized and characterized early for Re filaments [12], where large amounts of Re (up to 2000 ppm-a) were detected via SIMS. The level of filament contamination was observed to be a strong function of filament temperature. Ta and W impurities have been detected in HFCVD films deposited on Si [31]. RBS showed W contamination from 10 to 80 ppm-a at 2000⬚C, whereas for an equivalent filament temperature for Ta, the contamination was over 1000 ppm-a. It was also found that the Ta contamination was significantly reduced if a precarburized filament was used. The lower evaporation rate of TaC compared with Ta was believed to be the cause. The distribution of metal contamination in the HFCVD diamond films has been observed to decrease as the film grows thicker [32]. The main explanation for this phenomenon is the early nucleation, coalescence, and growth of diamond. Because the first stages of growth involve a nucleation stage, the growth of diamond is slow compared with the evaporation rate of metal from the filaments. As the film coalesces to form a continuous film, the growth rate stabilizes and reaches equilibrium with the evaporation rate of filament material. The net result is a continuous contamination level throughout the rest of the film. More recent studies have used NAA to quantify the level of contamination in HFCVD diamond films [33]. It was found that the highest levels of metal contamination occurred with Re filaments, followed by Ta and then

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W. This is shown in Table 2 for diamond deposited using these three different filament materials. Of the three filament materials, Re exhibits the highest level of contamination, by three to four orders of magnitude. Others [12] have observed the higher levels of Re contamination as well. As one would expect, higher filament temperatures resulted in higher levels of contamination via an increased evaporation rate: 0.279 ␮g cm⫺2 sec⫺1 for TaC at 2400⬚C compared with 0.00248 ␮g cm⫺2 sec⫺1 for TaC at 1950⬚C [33]. It is interesting to note that the calculated evaporation rate of WC, at 1950⬚C, was approximately a factor of 2 higher than that of TaC at the same filament temperature. However, its contamination level was substantially lower, 4.6 ppm-m (0.3 ppm-a) for W compared with 37 ppm-m (2.5 ppm-a) for Ta. The explanation for this difference, which has been observed by others, was the difference in how WC evaporates compared with TaC [33]. In WC, the C primarily evaporates, whereas for TaC, the Ta and C evaporate more or less equally. Gas chemistry effects on metal contamination have also been investigated to a limited extent. The obvious consequence for the addition of O2 , or other gases that allow operation at lower Tfil , is the lower evaporation rate that is present. Care needs to be exercised in using O2 in an HFCVD reactor, however. It has been shown that W and Ta filaments are stable against oxidation with added oxygen as long as a gas composition of C/(C ⫹ O) > 0.5 is maintained [34]. E.

Reactions with the Filaments

As long as the filament surface remains free of deposited C, which is excess carbon not involved in the carburization of the filaments, the dissociation of

Table 2 Metal Contamination, in Parts Per Million Atomic (ppm-a), in CVD Diamond Deposited Using the Three Different Filament Materials: Re, W, and Ta Contamination (ppm-a) Filament Re W Ta

Re

W

Ta

348 0.039 0.11

NA 0.30 0.17

<MDA 0.026 2.5

MDA for Re is 0.01 ppm-a. Source: Data courtesy of Dr. Robert Shaw, Oak Ridge National Laboratory.

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H2 into atomic hydrogen proceeds without interruption. When the level of carbon in the gas phase becomes greater than a critical value, dependent on Tfil , deposition of carbon onto the filament surface occurs [13,19,35,36]. This deposition is commonly referred to as ‘‘poisoning’’ or ‘‘sooting.’’ Filament poisoning results in a reduced ability to transform H2 to H 0. The effects are reduced growth rate, morphology change, and reduced crystal size in the deposited film [36]. Sommer and Smith [37] thermodynamically modeled the filament as a substrate and defined a phase field where graphitic deposition occurred. This was done for the CH 4 /H2 and C2H2 /H2 chemistries using W and Re filaments [13]. Addition of reactive gases, such as oxygen, has been found to lower the Tfil where C deposition occurs. The same chemistries with the addition of O2 were also modeled [38]. It was observed that at sufficiently high filament temperatures, no deposited C phase occurred on the filaments. However, when the filament temperature was low and/or at higher [CH 4 ], the filament would become covered with a graphitic deposit. This graphitic deposit, commonly called ‘‘soot,’’ is really a microcrystalline C. This type of surface is no longer conducive to the dissociation of diatomic hydrogen, effectively shutting off the source. This has been found in attempts to use carbon filaments [21,22]. When the filament poisoning is not too advanced, cleaning at high Tfil and low or no added CH 4 can in most cases clean the filaments to such a degree that they can still be used. If the C layer is too thick, however, no amount of H 0 cleaning will lead to recovery. A hysterisis in the filament poisoning has been observed and characterized in terms of filament temperature, gas flow, and [CH 4 ] [36]. Figure 4 shows this for three different methane flows, where the filament temperature is observed to increase as the filament surface becomes covered with soot. Others have also seen this change in filament behavior as the [CH 4 ] was changed [13,19,38]. It has been observed that growth with poisoned filaments will result in a smaller grain size as well as lower growth rates. In most cases, the onset of changes in the filaments will be detected by a sudden apparent increase in the Tfil (Fig. 4), followed by a decrease in the substrate temperature. These two seemingly contradictory behaviors can easily be explained as follows. As the filaments start to build up a layer of carbon on their surface, the emissivity of the filaments is increased. This increase is perceived by an optical pyrometer, typically used to measure Tfil , as an increase in temperature. The subsequent decrease in Tsub is the result of the lower level of H 0 production, and as shown earlier in Sec. III.C, the H 0 recombination on the substrate is the primary mode of heating. Through careful monitoring of the decomposition conditions, the region of filament poisoning can be avoided.

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Figure 4 Data showing the hysteresis in filament temperature as the methane fraction is varied for different total flows. This behavior is related to coverage of the filament by nondiamond carbon. (From Ref. 36.)

IV.

DETECTION AND DISTRIBUTION OF SPECIES

The detection of species during the HFCVD growth process has long been of interest. By probing the environment around the filaments and substrate, researchers have hoped to gain more insight into the growth process. A variety of probes have been used for detection of species at the filament and substrate. Infrared (IR) laser absorption has been used to detect species during HFCVD using 0.5% CH 4 in H2 [39]. Acetylene (C2H2) was found to be the most abundant species compared with CH 4 : 1.6 ⫻ 1015 cm⫺3 versus 2 ⫻ 1014 cm⫺3. The presence of CH3 was also detected with an estimated concentration of 5 ⫻ 1013 cm⫺3. Other species such as ethylene (C2H4) have measured concentrations of 6 ⫻ 1012 cm⫺3. The detection of C2H2 and CH3 could support either as a precursor to growth of CVD dia-

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mond. Other hydrocarbon species were not detected by this method because of its sensitivity level. Methods that rely on sampling of the growth gases have been used. Mass spectrometry was used to sample the surface/near–surface region of a Si wafer during growth [40]. A chemical kinetics model was then used to assist in interpreting the measurements. Calculations were done as a function of distance for CH 4 in H2 . CH 4 and C2H2 were monitored. Because of the short lifetime of some species, they could not be detected directly by mass spectrometry. Indirect monitoring could be used, assuming that the presence of certain peaks was mainly due to them. For example, 2H = H2 2CH3 = C 2H 6 C 2H = C 2H2 This is one of the shortcomings of this type of technique. The gas temperature was also measured as a function of distance from the filaments. Using conventional thermocouples, the gas temperature was found to drop rapidly, to ⬇600 K, at a distance of 1 mm from the filaments. From their measurements and modeling, it was suggested that CH3 or C2H2 is primarily responsible for growth. Another optical method using lasers was used to detect the distribution of H 0 in HFCVD [41]. Resonance-enhanced multiphoton ionization, better known as REMPI, uses a focused laser to excite different levels in a species that are then detected. Profiles of H 0 versus Tfil showed that increasing filament temperatures resulted in higher levels of atomic hydrogen. Addition of CH 4 showed that the [H 0 ] decreased as the [CH 4 ] was increased. For the highest levels of [CH 4 ] this behavior was found to be reversed, the result of poisoned filaments. Although no proof of the growth species could be obtained, measurements of the [H 0 ] opposite the substrate showed behavior indicative of diffusional transport. Flow rate variations also supported this type of transport. Molecular beam mass spectrometry has also been used to measure growth species at the substrate surface [42]. Unlike conventional mass spectroscopy, this method was able to detect free radical as well as stable species. Using three parallel filaments, concentrations of H, H2 , CH3 , CH 4 , and C2H2 were measured. Measurements of H 0 at the substrate confirmed a ‘‘superequilibrium’’ state over what the normal H 0 equilibrium mole fraction would be for the substrate temperature. At [CH 4 ] ⱕ 1%, the [H 0 ] was stable, whereas [H 0 ] was found to decrease dramatically for [CH 4 ] > 1%, confirm-

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ing what has been observed before [41]. This drop in [H 0 ] was more than an order of magnitude for an increase from 0.4 to 7.2% CH 4 . At the lower concentrations of methane, C2H2 was observed to be the dominant species. This was found to change as [CH 4 ] was increased; [C2H2] decreased with [CH 4 ] dominating and [CH3 ] steadily increasing, but at a slower rate as [CH 4 ] increased further. It was determined that there was a difference in the concentration of species if a single filament was used as opposed to an array. The reasoning was that a single filament allows more CH 4 to flow past without interacting with the filament. This is most obvious in the lower [C2H2 ] and [CH3 ] being detected. This also reconciled differences in species concentrations measured by others [41]. Coherent anti-Stokes Raman spectroscopy (CARS) has been used to measure both concentrations of species and temperature in rf-PACVD and HFCVD [43]. Upstream and downstream measurements were made of [CH4] from the filaments as a function of filament temperature. The lower concentration of CH 4 observed downstream was attributed to rarefaction of the gas by the filaments. Lifetimes of the H 0, before recombination, were found to be significantly longer (⬇0.5 sec) than those of other species that had lifetimes on the order of 100 ␮sec. This shows the dominance of H 0 as a species at the substrate. Two-photon laser-induced fluorescence (LIF) has been used to detect [H 0 ] profiles as a function of filament-to-substrate distance in HFCVD [44]. Measurements over a total pressure range of 1.5 to 100 mbar (1.1 to 75 torr) were made. Pressure effects were observed and found to give a saturation in [H 0 ] versus distance for pressures >10 mbar (75 torr). At a lower pressure, 1.5 mbar, the [H 0 ] was significantly lower, nearly 50% at the filament. Higher filament temperatures resulted in higher concentrations of H 0, falling off monotonically as a function of distance from the filament. The effects of filament diameter were explored for Ta filaments of 0.3, 1.0, and 2.0 mm diameter. At constant filament temperature and % CH 4 , the larger diameter filament resulted in a higher level of H 0 generation. This is believed to be an effect of available surface area; the larger surface area can support a higher number of dissociation events per unit area. As in previous studies [22,41], addition of CH 4 resulted in a reduction of [H 0 ]. The effects of excessive methane concentration were also observed here. The filament temperature was observed to increase by 80⬚C while the [H 0 ] decreased rapidly. The Tfil effect is not a true temperature change but a change in emissivity brought about by sooting of the filaments as explained before. The change in [H 0 ] was thought to be due to consumption in the gas phase. This supports later observations of the same effect [36].

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Other materials besides Ta were investigated—W and Ir—but carburized Ta was reported to generate higher [H 0 ] than Ir. CARS has been used to determine [H2 ] and temperature distributions in HFCVD as a function of distance from the filaments [45]. Temperature distribution measurements of the H2 were made as a function of distance from the filaments for three different powers. It was observed that there was a substantial drop in temperature as one moved away from the filaments. Similarly, the gas temperature above the substrate was found to be over 500 K hotter than at the substrate surface. [H 0 ] values were calculated from the temperature distributions and the [H2 ] from CARS. Deficits in expected [H2 ] were attributed to [H 0 ]. [H 0 ] fractions as a function of distance from the filaments and filament power were shown. Mole fractions of 50 to 20% were calculated for distance at the filament to ⬇7 mm away (1% CH4 ). It was shown that the [H 0 ] is in superequilibrium except very near the filaments when compared with thermal equilibrium values, verifying earlier work [42]. There was also a substantial drop between the gas temperature and the filaments and substrate. Others [42] have used two-dimensional finite element modeling [46] to interpret HFCVD experiments. Gas-phase chemistry, filament catalysis, surface interaction for growth, and how these affect [H 0 ] generation-recombination were considered. Based on the model, gas-phase chemistry was determined not to be primarily responsible for the [H 0 ]. Only a 30% drop in [H 0 ] at the substrate, compared with the [H 0 ] at the filament, implied that gas-phase recombination is not dominant. From others [41], two activation energies of ⬇150 kJ/mole for Tfil > 2250 K and 330 kJ/mole for Tfil < 2100 K were found. The activation energy at the higher temperature was believed to be due to a chemical reaction. An expression for the H 0 production was developed. The saturation effect observed by others was predicted by this expression. In addition, the decrease in [H 0 ] when CH 4 was added was predicted. Fourier transform infrared (FTIR) analysis of the gas during growth has also been used in an attempt to study the gas species in an HF reactor with a rapidly rotating substrate [47]. Rapid substrate rotation was studied at various deposition pressures and found to affect only the Raman signal. At 200 torr the quality improved, but no effect was observed at 20 and 400 torr. At 20 torr the pumping action of rotation on the gas is marginal at best, but at higher pressures this improves. A competing effect of H 0 recombination opposed the uniformity of H 0 species over the substrate at the highest pressures. Absolute [CH3 ] values have been measured using cavity ring-down spectroscopy (CRDS) [48,49]. In CRDS a laser pulse is reflected back and forth between two mirrors. These form a cavity where the laser pulse is

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circulated between the mirrors. Depending on the absorption of the medium within the cavity, the decay will be governed by this, and the decay time (ring-down time) can be determined. From this absorption the concentration can then be calculated by knowing the cross section for interaction. The [CH3 ] shows a maximum at ⬇2 mm from the filaments and is dependent on substrate temperatures. This maximum, seen in Fig. 5, is related to thermal diffusion effects, Sore´t diffusion. The higher Tsub results in higher [CH3 ] for the same Tfil . Detailed measurements near the substrate surface showed an increase in [CH3 ] by a factor of 2.8 for an increase in Tsub of ⬇2: 600 to 1200⬚C, a linear increase. An activation energy of 4.2 ⫾ 0.2 kcal mole⫺1 was found that agrees with other measurements [50]. Measurements of [CH3 ] at constant Tsub with Tfil from 2000 to 2550 K showed an increase followed by a saturation in [CH3 ] at ⬇2500 K. Others have also observed this [50,51].

Figure 5 Profiles of CH3 radical concentration, as a function of distance from a W filament, for two different substrate temperatures using CRDS. The gas flow is from left to right. Note the strong dependence of [CH3 ] on substrate temperature. The lines through the data represent modeled results. (From Ref. 49.)

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This study used a single W filament. This could be the difference in some of the measurements; more CH 4 is able to move around the filament and not be affected by its presence. This behavior was observed in other work [42].

V.

HYBRID METHODS OF HFCVD

In addition to the conventional form of HFCVD, other hybrid methods have been developed. These have typically involved applying a bias to the substrate, either positive or negative, and generally dc. Radio frequency biasing has been reported [52], but there has not been much follow-on work in this area. Some of the earliest work on bias-assisted HFCVD was done using a positively biased substrate [53–61] and is referred to as electron-assisted CVD (EACVD). As the name implies, electrons from the hot filaments are drawn to the substrate when a positive bias is applied. The filaments are strong sources of thermonic electrons at the normal operating temperature for HFCVD. High growth rates, 3 to 7 ␮m/hr, and enhanced nucleation densities have been reported when using EACVD [53,54,58]. In the earliest work on EACVD, growth rates of 3–5 ␮m/hr were reported for bias voltages of 150 V [53,54]. Ten-fold increases in nucleation were also observed. Attempts to apply negative bias were not successful. It was speculated that the growth enhancement took place on the substrate surface and not in the gas phase because of the small probability of interaction between electrons and gas molecules. The increase in nucleation density was also cited as related more to surface processes than to gas-phase processes. The biased HFCVD process was further characterized electrically as a diode; the filaments are strong emitters of electrons, with electrons flowing easily toward the substrate, whereas the substrate is not an electron source [56]. Positive and negative biases were applied and the results studied. It was common, regardless of polarity, that nothing occurred until a plasma was formed and that higher levels of bias were necessary to achieve this. Different morphologies were observed depending on the bias conditions, and the reverse bias case resulted in nonuniform deposits. Using EACVD, thick diamond films of 500 ␮m have been grown at rates of 7 ␮m/hr [58]. Again, the presence of a plasma was found. It was suggested that greater H 0 generation occurred, and it was not e⫺ bombardment that was responsible for the growth rate. Raman and IR measurements showed characteristics of diamond films, with properties improving as the film thickness increased.

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To further understand the mechanisms of EACVD, optical emission spectroscopy (OES) and IR absorption measurements were carried out during HFCVD with positive applied bias to evaluate the nucleation density [60]. OES measurements showed no increase in hydrocarbon species with applied bias and a very minor increase in H 0. This increase was not enough to account for the observed increase in nucleation density. The IR absorption intensity also showed no increase for growth species. Thus, it was concluded that the gas phase was not affected even though an increase in nucleation density was observed. Surface processes were postulated to be responsible. Negative biasing has also been applied to the substrate [62]. Nucleation enhancement was observed; however, it was nonuniform across the substrate, being higher around the edges. This effect was attributed to the substrate holder providing a more conductive path for charged species compared with the Si-wafer substrate. Subsequent modifications resulted in uniform nucleation. Nucleation densities were observed to increase from 104 to 109 cm⫺2. It was believed that the negative biasing results in positive ion bom⫹ bardment of the substrate by C ⫹, CH⫹ 3 , H , etc. species. Scanning electron microscopy (SEM) cross sections showed a disordered layer below the diamond film. Building upon this observation, selective area nucleation was achieved by using a grid above the substrate. The mesh grid acted as a ‘‘funnel,’’ directing the species responsible for the nucleation in a pattern. The grid mesh size was found to have a direct effect on the selective area nucleation density. In the case of EACVD, the bias is normally applied during the entire deposition. For a negative applied substrate bias, such as what is used for biased-enhanced nucleation (BEN), the bias is applied only during the initial stages of growth until sufficient nuclei are formed. At this point it is turned off, and normal HFCVD growth is continued. Spectroscopic ellipsometric study of the initial stages of biased-enhanced CVD identified four stages of the process [63]. These were carburization, etching, incubation, and nucleation. Observation revealed that during these four distinct processes, the plasma changed in a systematic way as well. Another unique hybrid method employing a hot filament has been used to deposit diamond. Good-quality CVD diamond was obtained, using a substrate that rotates sequentially between a hot filament and a graphite sputtering target [64]. The best diamond with this method was achieved under conditions of high [H 0 ]. Aside from the unique character of this method, combining a CVD and physical vapor deposition (PVD) technique, it attests to the importance of surface reactions of CVD diamond deposition and the importance of H 0.

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SCALE-UP AND COMMERCIALIZATION OF HFCVD REACTORS

Hot-filament reactors lend themselves to scale-up. Unlike microwave reactors, hot-filament reactors have no fundamental restriction of wavelength to limit the usable area over which to deposit [12]. The important considerations are filament diameter and shape, filament array size, and power requirements. Although the scale-up is conceptually straightforward, dealing with problems of the stability of large filament arrays and the movement that occurs is a challenge. The issues of filament spacing and filament-to-substrate distance have been addressed [12,65]. Ideally, it is desirable to maintain the spacing between the filaments to approximately the filament-to-substrate distance [65]. This allows a uniform distribution of H 0 to impinge onto the substrate, resulting in more uniform deposits of diamond. In addition to Diamonex’s 12-in. HFCVD reactors [66], others have developed HFCVD reactors for deposition over large areas for application in thermal management [29,66] (Fig. 6) and tool coatings for planar as well as round tools [67–69].

Figure 6 CVD diamond used as a heat spreader in a multichip module substrate for a supercomputer thermal management application. Note the 20-mm-square unpolished diamond pieces in the foreground and the polished pieces on the board. (Courtesy of Dr. Paul J. Boudreaux, Laboratory for Physical Sciences, College Park, MD.)

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CONCLUSION

Considerable knowledge has been gained since the early attempts at HFCVD. Large multizoned reactors have been developed for deposition over areas as large as 12 inches in diameter for such commercial applications as thermal management, tools, and protective coatings. Growth rates have also increased. With the application of active cooling during deposition, to carry away the heat of recombination and radiation, filaments operating near 2800⬚C are possible. Rates approaching ⬇19 ␮m/ hr have been reported [19] for single-filament systems and ⬇5 ␮m/hr for multifilament ones [70]. Unique configurations have allowed depositions onto spherical surfaces [71] as well. With continued scale-up to larger areas and increases in deposition uniformity and rates, the focus now shifts to improvements in other areas of diamond processing. For CVD diamond to become a commodity material in the thermal management arena and other areas, the whole processing stream requires simultaneous development to open commercial markets and carry us forward.

ACKNOWLEDGMENTS I would like to thank Dr. Bob Shaw for providing data on the ppm-a contamination, Dr. Daniel Morel for providing data to replot Fig. 4, Mr. Edward Wahl for Fig. 5 plus additional literature, and Dr. Paul Boudreaux for supplying Fig. 6. In addition, I would like to thank Diamonex, Incorporated for providing me with the time and encouragement to write this chapter and Dr. Fred Kimock for his suggestions while proofreading the manuscript.

REFERENCES 1. 2. 3. 4. 5. 6. 7.

S Matsumoto, Y Sato, M Kamo, N Setaka. Jpn J Appl Phys 21:L183, 1982. S Matsumoto, Y Sato, M Tsutsumi, N Setaka. J Mater Sci 17:3106, 1982. Data from DIAmond Database, Danish Technical Institute. The search criterion of hot filament or thermal filament or HFCVD was used. R Haubner, B Lux. Diamond Relat Mater 2:1277, 1993. C-P Klages, L Scha¨fer. In: B Dischler, C Wild, eds. Low Pressure Synthetic Diamond. Berlin: Springer-Verlag, 1998, p 85. JC Angus, A Argoitia, R Gat, Z Li, M Sunkara, L Wang, Y Wang. Philos Trans R Soc Lond A 342:195, 1993. JE Butler, RC Woodin. Philos Trans R Soc Lond A 342:209, 1993.

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6 Plasma Torch Diamond Deposition Joachim V. R. Heberlein University of Minnesota, Minneapolis, Minnesota

Naoto Ohtake Tokyo Institute of Technology, Tokyo, Japan

I.

INTRODUCTION

Deposition of diamond films using a thermal plasma has some process characteristics that are fundamentally different from those of all the other deposition methods. The thermal plasma generated either by an electric arc or by a radio frequency induction discharge (rfi), has extremely high energy densities (up to 108 J/m3) and temperatures (typically above 10,000 K), and this feature allows rapid dissociation of any substance or gas and high-rate generation of vapor-phase deposition precursors. As a consequence, high deposition rates are achieved and deposition at atmospheric pressure is possible. The advantages of thermal plasma chemical vapor deposition (TPCVD) have been recognized for the deposition of silicon carbide, silicon, and high-Tc superconductors [1], but only the promise of attaining high rate deposition of diamond using this process has led to strong further development efforts. Both thermal plasma generation methods, rfi and dc arc, were used to deposit diamond early on [2,3], but, at present, rf discharge reactors are more prominently used for process characterization, while the efforts in scaling the process to commercial size concentrate on dc arc reactors. For many applications of diamond coatings, economics is an overriding issue. Examples are diamond-coated tools or diamond heat spreaders in microelectronic applications. Economic studies of the scaling of the diamond deposition process have shown that the total deposition rate (in g/hr) is the most important factor in determining the cost of diamond-coated tools 141

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[4], and for these applications, arcjet deposition is the most favorable coating method. Linear growth rates of up to 1 mm/hr and total deposition rates of more than 0.2 g/hr have been reported in small 10-kW reactors [5]. In addition, the carbon utilization efficiency (carbon in the diamond film over carbon introduced into the system) with more than 8% and the specific energy requirement with less than 43 kWhr/g [6] are more favorable than with any other method [7], leaving the cost of the higher gas flow rates the one operational variable that is higher than with other deposition methods. Because of the issue of economics, most research in arcjet diamond deposition has focused on developing an understanding of the factors influencing the deposition rate. However, following the directions of the investigations with the other diamond deposition methods, there is now a strong research effort addressing items such as control of film texture, control of the film-substrate interface properties to improve adhesion on substrates of interest, and deposition at lower temperatures. In this chapter, we first describe the concept of arcjet diamond deposition in detail and then review the operational characteristics of arcjet plasma generators. A review of the principles of the arcjet diamond deposition process follows using representative results of models and of diagnostic experiments, including descriptions of the influence that various operating parameters have on the film growth. This is followed by a review of the most significant developments of deposition reactors. Concluding, we present a brief analysis of some of the present research directions.

II.

DESCRIPTION OF CONCEPT

In plasma torch diamond deposition, the torch generates a thermal plasma consisting of a mixture of argon and hydrogen in varying proportions providing a source of atomic hydrogen and of heat for dissociating the deposition precursors. There exist numerous different configurations through which this task is achieved. Figure 1 shows a schematic of a typical system consisting of a dc arc between a rod type cathode and a cylindrical nozzletype anode. The plasma gas mixture enters the arcing region from the base of the cathode, is heated and expanded by the arc discharge, and leaves the anode nozzle at a high temperature and low density and with a high velocity. In the plasma jet, heat exchange with the surroundings lead to a cooling of the plasma, a reduction of the jet velocity, and a recombination of the ionized and dissociated species. Figure 2 shows some typical contours of temperatures and velocities in an argon-hydrogen plasma jet obtained with a plasma torch with a 6-mm-diameter nozzle and operated at a power level of 40 kW [8]. The temperature and velocity distributions can vary widely depending

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Figure 1

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Schematic of thermal plasma CVD process.

on the torch power, plasma gas composition, and chamber pressure. Arc powers can range from 100 W to more than 100 kW, and 40 to 90% of the electric power is transferred to the plasma, depending on the specific design and the operating conditions. Argon-hydrogen ratios can also vary widely from 10% hydrogen to 100%. Increasing the amounts of hydrogen usually leads to increased electrode erosion with possible film contamination and to lower density jets with larger boundary layer thicknesses. Deposition precursors are usually added downstream of the nozzle because most hydrocarbons can form volatile compounds with thermionic cathode materials, leading to strong erosion. Deposition of diamond requires the presence of atomic hydrogen and either atomic carbon or hydrocarbon radicals. Consequently, the substrate must be placed at a position where the hydrogen in the plasma and the deposition precursors are largely dissociated, i.e., where the temperature in the jet is above about 4000 K if equilibrium conditions exist in the jet. The deposition process depends on the rates of the recombination processes in the boundary layer. Ideally, one would like to have frozen chemistry in the boundary layer to preserve high concentrations of atomic hydrogen and of atomic carbon, and the thinner the boundary layer the more closely will this condition be approximated.

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Figure 2 Temperature and velocity fields in an argon-hydrogen plasma jet at 1 atm. The torch nozzle exit is at z = 0. (From Ref. 8.)

The fluid dynamic boundary layer thickness ⭸ is a function of the free stream velocity u, and the gas density ␳ 0 and viscosity ␮ 0: ⭸ ⬀ (␮ 0 /␳ 0u)0.5

(1)

Besides the fluid dynamic boundary layer, one needs to consider the thermal boundary layer, and the concentration boundary layer. For the conditions of a high-temperature, high-velocity free jet impinging on a cooled substrate, the velocity and thermal boundary layers are often considered to coincide. However, for a mixture of gases with quite different densities and diffusion coefficients, such as argon and hydrogen, the concentration profile in the boundary layer may differ from the velocity profile. This fact is expressed by a value for the Schmidt number, Sc = ␮ 0 /( ␳ 0 D) (where D is the diffusion coefficient) that is not equal to one. Figure 3 illustrates the importance of the boundary layer thickness control. The distributions of the important chemical species in the boundary

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Figure 3 Temperature (a) and mole fraction (b) profiles for selected species in the substrate boundary layer for two different free stream velocities of an argonhydrogen-methane jet resulting in two different boundary layer thicknesses. (From Ref. 9.)

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layer of an argon-hydrogen-methane jet for two different free stream velocities and corresponding boundary layer thicknesses are shown [9]. The boundary layer edge has been assumed to coincide with the 4000 K isotherm, and equilibrium conditions are assumed at that location. It is apparent that the atomic hydrogen concentration at the substrate surface increases by an order of magnitude if the boundary layer thickness is decreased from 2 to 0.4 mm. Furthermore, the deposition mechanism can change during this decrease in boundary layer thickness from CH3 dominated to C dominated. This fact is illustrated in Fig. 4, where mole fractions of the important species for diamond growth at the substrate location are shown (Fig. 4a), as well as the growth rates for the different precursor species, both as a function of boundary layer thickness [9]. Besides controlling the boundary layer thickness by increasing the plasma velocity (i.e., increasing torch power or plasma gas flow rate or decreasing the chamber pressure), increasing the jet density can have similar effects (i.e., increasing the chamber pressure or changing the type of gas for the same velocity). One can have the paradoxical situation that reducing the amount of hydrogen in the jet and replacing it with the same volumetric flow rate of argon can actually lead to higher atomic hydrogen densities at the substrate surface due to stronger boundary layer compression [10]. Typical boundary layer thicknesses encountered in atmospheric pressure plasma jet diamond deposition range from approximately 0.5 to 2 mm. Lower pressures in the deposition chamber will increase the boundary layer thickness for the same jet velocity but also reduce the chemical reactions in the boundary layer. It is obvious that control of the boundary layer conditions is crucial for the deposition of diamond using thermal plasma chemical vapor disposition (TPCVD). However, a thin boundary layer leads to strong heating of the substrate by the hot plasma jet requiring effective substrate cooling to ensure the necessary control over the substrate surface temperature. While the high energy density of the thermal plasma allows very high deposition rates, it also brings some challenges for the process designer: there are usually strong radial nonuniformities associated with thermal plasma jets. These nonuniformities have the consequence that the high diamond growth rates exist over a small area, and strong radial variations of the film growth rate and the film morphology are observed. Also, the heat flux to the substrate is nonuniform, requiring special care in the substrate holder design to ensure a uniform substrate temperature. Various approaches have been pursued to increase the area of uniform deposition, such as reducing the pressure in the deposition chamber, which leads to a widening of the jet, spreading the arc jet magnetically, or moving the substrate. Most of these approaches require some sacrifice of the deposition rate. Also, re-

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Figure 4 Mole fraction distributions in the boundary layer (a) and diamond growth rate (b) for different boundary layer thicknesses. (From Ref. 9.)

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ducing the pressure carries the penalty of increased pump power with it. As can be seen in the discussion of the different plasma jet deposition reactors (Secs. IV. and V.), the principal design challenge is to preserve the advantages of this deposition method by transforming the high linear growth rates over a small area into uniform deposition over a large area while maintaining high overall deposition rates. The process characteristics of arcjet diamond deposition have several additional consequences: (1) A larger variety of precursors can be used; e.g., besides the commonly used hydrocarbons, various organic liquids can be used because the high temperatures will lead to rapid dissociation. (2) A variety of substrate materials can be used because the growth rate is frequently higher than the diffusion rate into the substrate material. However, this feature has somewhat limited benefits as the adhesion on many substrates is inadequate, and deposition on different substrates without good adhesion offers little advantage. (3) The high growth rates and high deposition precursor densities can result in highly stressed and sometimes very rough films and high secondary nucleation rates. Figures 5 and 6 illustrate these features, Fig. 5 showing diamond films obtained with several organic liquids used as deposition precursors and deposited at growth rates between 100 and 500 ␮m/hr [5]. Figure 6 shows some typical Raman spectra obtained from films deposited at high growth rates, indicating the relatively high purity of sp3 bonds [11]. Figure 7 shows a homoepitaxial film grown with methane at a growth rate of up to 220 ␮m/hr, depending on the crystal face [12]. The upper photograph shows the original diamond, and the lower one shows the crystal after 30 min of deposition. Although this homoepitaxial film is of excellent quality, the thickness that can be deposited remains limited due to the appearance of defects and secondary growth [13]. Although it is clear that the film characteristics can vary widely, the common features of these films are the high growth rates and the high purity of diamond as shown by the Raman spectra.

III.

PRINCIPLES OF PLASMA TORCH DESIGN

Plasma torch designs are adapted to the specific application, and they vary widely according to power, arc current, and energy density desired. For example, a cutting torch provides a transferred arc, highly constricted with a very high peak temperature (in excess of 15,000 K) for effective melting of the material, whereas a torch dissociating a gas and heating it to an average temperature of 4000 K for a chemical process will have a highly turbulent jet with a very wide temperature profile with a relatively low peak temperature. In the diamond deposition application, the torch has to disso-

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Figure 5 SEM photographs of diamond films obtained with various liquid precursors: (a) acetone, (b) dichloromethane, (c) benzene, (d) carbon tetrachloride, (e) lacquer thinner, and (f) PCB compound. (From Ref. 5.)

ciate the hydrogen and provide sufficient energy for dissociation of the hydrocarbons. This review is limited to torches that are suitable for this purpose and operate in the power range between 1 and 100 kW. The arc discharge requires a cathode, an anode, and some kind of stabilization mechanism for the arc column. Furthermore, the arc discharge requires sufficiently high gas temperatures in the arc column to ensure adequate electrical conductivity (at least 10,000 K when no metal vapors are present). Under these conditions the electrons are heated by the applied electric field, rapidly achieve a Maxwellian distribution, and a sufficient number of high-energy electrons exist for ionizing collisions with atoms to

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Figure 7 SEM photographs of a laser-cut diamond crystal (top) and the same crystal after 30 minutes in an arcjet reactor showing homoepitaxial growth. (From Ref. 13.)

< Figure 6 Typical Raman spectra obtained with diamond films from ethanol (a) and from acetone (b). (From Ref. 5; spectra courtesy of Dr. J. Butler.)

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supply additional electrons and make up for those that have been lost through recombination or diffusion. Compared with other discharges, the arc discharge operates with the highest current values (1 A to more than 100 kA), the highest current densities (in the order of 105 A/cm2), and the lowest discharge voltage gradients (typically 5 to 40 V/cm). A.

Torch Cathode

The arc cathode has to provide the electrons to the arc column for transferring the current, and two dominant cathode types are used in plasma torches: the hot cathode, usually in the form of a rod or a button consisting of a refractory metal, and the cold cathode, usually consisting of a copper surface that is intensely cooled. The hot cathode provides electrons through thermionic emission; i.e., the temperature at the tip of the cathode is high enough that a sufficient number of electrons is emitted from the metal crystal lattice. The most frequently used cathode material is tungsten with the addition of a material such as thorium oxide that has a very low work function (around 2.6 eV compared with 4.5 eV for tungsten), thus increasing the number of electrons emitted at a given temperature. There is little movement of the arc attachment spot because the preferred attachment is the site of the highest electron emission, i.e., for a uniform material the site of the highest temperature. Typical spot temperatures are close to the melting point of tungsten (3680 K), and the dominant cooling mechanism of the spot is the emission of the electrons [14]. Because a substantial amount of heat is going into the cathode (in the order of 5% of the torch power), additional cooling of the cathode is usually provided (e.g., water cooling through internal cooling channels); however, if the cooling reduces the attachment spot size or temperature, increased erosion will result [15]. For operation with an inert gas such as argon, the thermionic cathode experiences little erosion at current levels up to 1000 A. Operation with hydrogen or an argon-hydrogen mixture will increase the erosion rate because of the higher heat fluxes associated with the more constricted hydrogen arc. Oxidizing, halogenated gases and hydrocarbons lead to strong cathode erosion because of the formation of volatile tungsten compounds. Thermionic cathodes are found in torches operating at power levels from 100 W to 100 kW. Cold cathodes are used in torches of intermediate power levels from 50 kW to 10 MW and for currents of up to 3 kA. The emission mechanism typically involves some evaporation and ionization of the cathode material, and the attachment spot is usually very unstable. Strong cooling of the cathode surface by a high-velocity water flow on the back surface results in a highly constricted arc attachment spot, and a forced motion of this spot will

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distribute the erosion by evaporation over a larger area. The motion of the arc attachment is accomplished by controlling the gas flow over the cathode surface (e.g., swirl flow) and/or by applying magnetic fields to force a rotation of the arc attachment. The cathode material is usually copper or a copper alloy because of its high thermal conductivity. Evaporation of the cathode material leads necessarily to erosion and possibly contamination of a film, but these effects can be minimized for arc currents below 2000 A. B.

Arc Column

The arc column is inheritantly unstable because any disturbance of the current path through the plasma results in an increase in arc voltage and generation of magnetohydrodynamic (MHD) instabilities that can lead to arc extinction. Stable operation therefore requires a power supply with an opencircuit voltage significantly higher than the arc voltage and some design for a stabilization mechanism. Most torches use either convective stabilization, where a cold gas flow surrounding the arc forces the arc to remain in a preferred position of minimal heat loss, or wall stabilization, where proximity of a water-cooled wall to the arc forces it to the preferred position, or a combination of both. Convective stabilization has the consequence that an increase in arc current results in a widening of the discharge path or an increase in the plasma electrical conductivity or both, leading to a decrease in arc voltage (falling V-I characteristic) and requiring a current control in the power supply. The voltage gradient in the arc column is strongly dependent on the arc gas and the arc stabilizing design. An inert gas with a low thermal conductivity such as argon offers arcing with the largest arc diameter and the lowest voltage gradient, and the addition of hydrogen decreases the arc diameter and increases the voltage gradient dramatically due to the high thermal conductivity and specific heat of hydrogen. The consequence is that for the same torch diameter and the same arc current a thicker cold gas boundary layer exists if hydrogen is added to the plasma gas, leading to a strong temperature drop in the jet when the cold boundary layer mixes with the arc heated plasma. Higher arc currents and smaller nozzle diameters can avoid this temperature drop. C.

Anode

The function of the arc anode is to collect electrons from the arc plasma to allow current transfer to the power supply. However, the high current densities of the arc require intensive cooling of the anode. Heat fluxes between 5 and 20 kW/cm2 are encountered, and the total heat transfer can range from 5 to more than 50% of the torch power, depending on torch design. Ac-

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cordingly, high cooling water flow rates are required, and the water velocities and water pressures at the back surface of the anode must be high enough to avoid film boiling. Usually, motion of the arc attachment is used to distribute the anode heating over a larger portion of the anode surface. The anode heat flux and the erosion are dependent on the constriction of the arc attachment, and a gas with high thermal conductivity and high specific heat such as hydrogen results in increased erosion. Also, a thick cold boundary layer between the arc and the cold anode surface forces the arc to constrict more, resulting in increased erosion. D.

Torch Design

Most torches with a thermionic rod cathode have the cathode tip placed at the converging entrance section of a cylindrical channel. The channel wall may be the anode surface, or it may be a section separating the anode from the cathode to assure longer arc lengths. Figure 8 shows the schematics of two different torch designs with thermionic cathodes. A torch designed for plasma spraying is shown in Fig. 8a; the torch is operated at atmospheric pressures at power levels up to 40 kW, and mixtures of argon and hydrogen can be used as plasma gas. The torch shown in Fig. 8b has been designed for space propulsion; hydrogen or hydrazine is heated by a low power (1 to 1.5 kW) arc, and the plasma is accelerated to high Mach numbers in the diverging section of the nozzle into a low pressure or vacuum ambient. Both types of torch design have been used for diamond deposition. The plasma gas is introduced at the base of the cathode with or without a swirl component, flowing toward the cathode tip, where part of it is heated by the electric current in the arc while the remainder forms the cold boundary layer along the channel wall. The heating of the plasma gas by the arc decreases its density by possibly two orders of magnitude, resulting in strong acceleration of the plasma flow. From a fluid dynamic point of view, the arc acts as a type of converging nozzle. The anode attachment on the inside wall of the channel is usually unstable resulting in fluctuations of the arc length with a frequency of a few kilohertz to a few tens of kilohertz, depending on torch design. For the application of diamond deposition, these fluctuations are of no major consequence because the characteristic processing times are on a larger time scale. The plasma exits the channel in a jet that has, in the case of an atmospheric pressure environment, velocity and temperature distributions similar to those shown in Fig. 2 [8]. A converging-diverging or a diverging nozzle is added at the exit of the plasma torch when supersonic flows are desired or when the deposition reactor is at a low pressure. In the case of a torch such as the one shown schematically in Fig. 8b, with a jet issuing into an environment at pressures less than 1 Torr, nozzle exit velocities of 13 km/sec at temperatures of around 5000 K can be achieved [16].

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Figure 8 (a) Schematic of a plasma torch designed for atmospheric pressure plasma spraying: rod cathode at the left, anode nozzle with powder injection holes at right. (b) Schematic of plasma torch designed for space propulsion applications. (Part (a) courtesy of Praxair Surface Technologies; part (b) courtesy of NASA Lewis Research Center.)

Cold cathode torches typically position the cathode and anode cylinders coaxially side by side with the plasma gas entering through the gap between the electrodes with a swirl component (see Fig. 9). Usually, a solenoidal magnetic field is employed to act on the arc electrode attachments generating arc motion and reducing electrode erosion. The cathode is frequently used as the downstream electrode. The jets leaving such a torch usually have lower peak temperatures and velocities, and strong turbulence will make the profile more uniform. A nozzle is added when higher flow velocities are desired. However, for operation with high percentages of hydrogen as the plasma gas, use of thermionic cathodes is generally preferred because of easier control of electrode erosion [17].

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Figure 9

Schematic of a swirl-stabilized cold cathode dc plasma torch.

Another design consideration besides power and desired velocity distribution is the arc heating efficiency of the torch, defined as the fraction of the electrical energy input, the product of current and arc voltage, I ⫻ V, which ends up as enthalpy flow in the plasma jet. This efficiency is determined by measuring the energy loss QL to the cooling water:

␩ = 1 ⫺ QL /(I ⫻ V)

(2)

Typical arc heating efficiencies range from 40 to 70% for torches with rodtype electrodes and from 70 to 90% for torches with cold electrodes. The efficiency increases with increasing gas flow rate and decreases with increasing arc current. Torch designs offering higher voltage operation have higher arc heating efficiencies as long as the length of the arcing channel does not exceed the length for establishing fully developed flow. IV.

CHARACTERIZATION OF THE PLASMA JET AND THE SUBSTRATE BOUNDARY LAYER

A.

Description of Atmospheric Pressure Plasma Jets

The plasma jet has been characterized for a number of configurations by using diagnostics and modeling. Also, because the plasma torches used for

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diamond deposition have in general been developed for different applications such as plasma spraying or other materials processing tasks and for plasma propulsion, the characterization performed for these applications can be transferred to some extent to the diamond deposition process. However, one has to keep in mind that for different torch designs and operating conditions, the jet characteristics differ considerably and one has to be very careful when generalizations are attempted. Because of the strong nonlinearity of all plasma properties, the way the plasma gases and deposition precursors are heated and mixed can have a strong influence on the jet behavior. For example, mixing cold hydrogen with arc-heated argon will result in significant temperature drops in the jet and low degrees of hydrogen dissociation, and diamond deposition results obtained under these conditions cannot be compared with those obtained with arc-heated hydrogen. Some indication of the jet behavior can be found by calculating the jet power Pjet or the enthalpy flux after mixing of the reactants ˙ ⫻ have) Pjet = ␩ (I ⫻ V) = (m

(3)

where m ˙ is the total mass flow rate and have the average enthalpy of the mixture. Because in the temperature range between 2000 and 4000 K the equilibrium degree of dissociation changes drastically, a small change in the ratio of input power over mass flow rate can have a strong effect on the diamond deposition conditions. A value for have can be used to determine an equilibrium value for the degree of dissociation, and for arc-heated hydrogen this value will give a lower bound for the actual value, whereas for argonheated hydrogen, this value will present an upper bound. For the characterization of atmospheric pressure plasma jets, local thermal equilibrium (LTE) has been assumed in most cases. Also, time-averaged values are usually determined, although the fluctuations and instabilities may lead to somewhat distorted values [18]. Figure 2 gives such time-averaged LTE values of the temperature and velocity distributions in a plasma spray jet. Subsonic flow exists at the nozzle exit, and the plasma composition can be assumed to be close to chemical equilibrium at this location. Jets of this type have been well characterized concerning their time-averaged characteristics both experimentally and through models. For example, considering an argon jet issuing into an atmospheric pressure argon environment, it has been found that temperature and velocity distributions derived from spectroscopic and enthalpy probe measurements are reproduced by a standard low-Reynolds-number turbulence model for the jet and that they exhibit selfsimilarity with a Gaussian profile for radial distributions of temperature and axial velocity [19]. However, even for time-averaged conditions, chemical nonequilibrium exists.

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There are usually three effects that lead to nonequilibrium conditions in the jet: (1) jet inhomogeneities caused by fluctuations and turbulence, (2) diffusion due to strong radial gradients, and (3) different relaxation times for the temperature equilibrium and chemical concentration equilibrium. Jet fluctuations are caused by arc anode attachment instabilities; i.e., a movement of the anode attachment downstream followed by a restrike of the arc upstream close to the cathode will result in variations of temperature, velocity, and composition at the nozzle exit. Figure 10 illustrates these fluctuations with a sequence of 100 nsec exposure time images of an atmospheric pressure arcjet. These variations will enhance the effect of large-scale turbulence and breakup of the laminar core of the jet because of the strong shear layers at the jet boundaries and the strong density differences between the plasma and the cold surrounding gas. The entrainment of the cold gas results in a decrease of the average temperature and velocity, but the rate of mixing of the cold gas with the hot plasma and the establishment of average conditions are relatively slow. This effect has been demonstrated experimentally by Pfender et al. [20], and a modeling description has been presented by Huang et al. [19]. A consequence is that one can find degrees of ionization and of dissociation that are far above the equilibrium values according to the average temperature. Figure 11 illustrates how the non-equilibrium conditions can affect temperature measurements in an argon-helium

Figure 10 High speed images (100 nsec exposure time) of an atmospheric pressure arcjet indicating jet instabilities.

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Figure 11 Comparison of radial temperature profiles in an atmospheric pressure plasma jet obtained spectrometrically and using an enthalpy probe, indicating discrepancies of the results. (From Ref. 21.)

arcjet [21]. Temperatures derived from enthalpy probe measurements reflect the average energy content in the jet, and the spectral emission can be enhanced through nonequilibrium electron density distributions. Furthermore, the strong nonlinearity of the increase of the emission of radiation with temperature results in radiation measurements averaged over the line of sight that are higher than the associated average temperature. The effects of radial diffusion have also been well demonstrated experimentally and through modeling. Very high radial temperature and concentration gradients lead to radial diffusion of electrons, ions, and dissociated species out of the jet and molecular species into the jet, resulting in a higher concentration of molecular species in the central high-temperature portions of the jet and a widening of the distribution of electrons and dissociated species. Models for plasma jets with rigorous treatment of diffusion effects have been formulated [22,23] and combined with a kinetics formulation to determine the jet chemical composition [24]. The effect of lagging of the chemical reactions (recombination) compared with the drop in the gas temperatures results in conditions of a ‘‘super-

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equilibrium’’ or higher densities of ionized and dissociated species than equilibrium relations would predict for the measured or calculated gas temperatures [25,26]. This includes significantly higher electron densities and atomic hydrogen densities compared with equilibrium conditions. The reason for this effect is that the temperature is determined by elastic collisions among all the plasma components, resulting in relatively short relaxation times once mixing has been achieved, while the electron-ion recombination reactions are largely determined by three-body collisions, which are considerably less frequent. This effect is stronger for supersonic jets where strong deviations from chemical equilibrium already exist at the nozzle exit, or for jets issuing into low-pressure environments [25,26]. Under these conditions, the nozzle design can have a significant influence on the transport of atomic hydrogen in the jet, and ideally, the nozzle design, torch power and plasma gas flow rate have to be optimized together [26]. On the other hand, the lower velocities in the jets of radio frequency torches (in the order of 10 to 30 m/sec) result in conditions much closer to chemical equilibrium. B.

Low Pressure Plasma Jets for Diamond Deposition

These arcjets have been to a large extent characterized with respect to diamond deposition, and the plasma temperatures and excited species distributions have been the primary focus of the investigations. Several measurements have been made in low-power (around 1 kW), laminar flow jets exhausted into a low-pressure chamber (around 5 to 200 torr) [27,28]. The methane has been introduced upstream of the arc and the low-current arc has been operated in a hydrogen-methane atmosphere. The small dimensions of the torch have resulted in very short residence times of the gas molecules in the plasma region (10 ␮sec), and the low arc power limited the enthalpy increase. Both emission spectroscopic and laser spectroscopic (LIF) measurements have been reported. Gas temperature values of approximately 5000 K at the axis approximately 5 to 10 mm from the nozzle exit have been derived from emission from C2 bands [27,28], and LIF measurements on CH bands resulted in axial temperature values of 2100 to 2500 K [28,29]. The authors explain that the temperatures derived from the CH band measurements are the true heavy species temperatures because of the relatively long lifetimes of the CH excited species and that the C2 band radiation is influenced by chemiluminescence effects. No atomic hydrogen lines and no atomic carbon lines are seen, and a chemical kinetics model shows that no dissociation equilibrium is obtained under these conditions. In a similar arcjet reactor with methane and hydrogen flow through the arc, but operating at somewhat higher power levels (1.6 kW), strong emission of atomic hydrogen and atomic carbon lines has been observed up

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to 18 mm from the nozzle exit [30,31]. Farther downstream, emission from C2 and OH bands becomes dominant. A comparison with optical spectra from a microwave plasma shows the contrasting dominance of H2 and CH emission with the microwave plasma. A similarly strong emission of atomic hydrogen lines has been observed in a reactor operated with hydrogen at power levels up to 1.43 kW, with the hydrogen jet exhausted into a chamber having a background pressure of 0.35 torr [16,32]. Temperatures derived from LIF measurements on an atomic hydrogen line show values of approximately 4800 K at the axis near the nozzle exit dropping to 1800 K at an axial position 20 mm downstream, with some temperature recovery farther downstream. These temperatures are obtained with somewhat lower hydrogen flow rates compared with the measurements reported in Ref. 28, explaining the discrepancy. Velocity values derived from the Doppler shift of the LIF signals show peaks of about 13 km/sec near the nozzle exit, dropping to about 11.5 km/sec at 20 mm from the nozzle. A strong dependence of temperature and velocity on arc power is found: nozzle exit temperature values increase from about 1800 K at 0.8 kW to 4800 K at 1.43 kW. Laser-induced fluorescence measurements on CH radicals in an arcjet reactor operating with an argon-hydrogen mixture at a power level of 1.6 kW, with methane injected into the plasma flow inside the nozzle downstream of the arc, show temperature values ranging from 1800 K at the nozzle exit to about 2200 K at a position 20 mm downstream for the rotational temperatures and from 2700 K to about 2300 K for the vibrational temperatures [33]. It is not clear why the rotational temperatures should increase in the jet with increasing distance from the nozzle upstream of the recovery region in the boundary layer. These values for low-power arcjets are in strong contrast to measurements in medium-power plasma jets (larger than 5 kW), although less characterization has been performed in such reactors. The low-power arcjet measurements have been made some distance from the arc, and mixing between the hot plasma and the cold gas in the boundary layer has occurred to some extent. As pointed out in Sec. III., the low-current hydrogen arcs have small diameters and most of the gas is not heated by the arc. Mixing of the cold gas with the arc reduces the plasma temperatures in the jet. The atomic hydrogen mole fraction in these reactors can vary widely, depending on the fraction of the total hydrogen flow that is heated in the arc. In the mediumand high-power arc torches, the lower velocities and larger plasma volumes lead to a more uniform heating of the plasma gas and in general to higher temperatures at the nozzle exit (see Fig. 2). Ohtake et al. [34] present temperature measurements and temperature and flow field calculations for a 9kW reactor in which a supersonic jet exits a nozzle in front of the cathode,

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and the anode attachment occurs to another jet from a torch located at a 90⬚ angle (see Sec. V. for details). In this reactor, peak temperatures of 9847 K have been measured at the axial location where the anode jet attachment occurs, i.e., right at the end of the arc, using line intensity ratios. The pressure has been 200 torr, and local thermodynamic equilibrium (LTE) has been assumed. This temperature drops to about 3550 K close to the substrate. The methane is introduced from the background gas in the reactor by entrainment. Obviously, there is much dissociated hydrogen at the boundary layer edge, verified by a strong atomic hydrogen spectrum. The C2 spectrum is very strong above the substrate, and a chemical kinetics model indicates C2H2 and CH2 as the major precursor species. There are few measurements characterizing the boundary layer conditions in front of the substrate because of the small spatial extent of this boundary layer (typically in the order of 1 mm or less). Most boundary layer characterization has therefore relied on modeling. Measurements in lowpower supersonic arcjets show the effect of a shock in front of the substrate leading to an initial temperature increase from approximately 2300 K to a peak value of approximately 3100 K at a position about 2 mm in front of the substrate [33]. C.

Diamond Deposition Reactor Models

Several models exist describing different arcjet reactor configurations and relating the diamond growth rates to the arcjet and boundary layer characteristics. The principal difficulties encountered are the formulation of an upstream boundary condition and the mixing of the reactants and the entrainment of the surrounding atmosphere. Because the entrainment is usually neglected, and the mixing is usually assumed to be instantaneous, the principal difference between the models is the upstream boundary condition, i.e., the temperature, velocity, and concentration profiles at the torch nozzle exit. A model for the arc in the anode nozzle would provide an upstream boundary; however, such models have so far had to rely on significant simplifications because the arc attachment to the anode wall with superimposed parallel flow is a three-dimensional time-varying phenomenon, and only two-dimensional steady-state descriptions are available at present for a limited set of conditions [35,36]. Results of a model by Ohtake et al. [34] give a good impression of the conditions in an arcjet deposition reactor. A 9-kW reactor for which experimental data have been obtained is modeled with a uniform jet inlet temperature of 9847 K (according to measurements), a uniform inlet velocity of 2366 m/sec, and a background pressure of 200 torr. The results are shown in Fig. 12, the streamlines (Fig. 12a), the axial velocity distribution (Fig.

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Figure 12 Results of simulation of a hydrogen arcjet in a diamond deposition reactor: (a) streamlines, (b) axial velocity distribution, and (c) temperature fields. (From Ref. 34.)

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12b), and the temperature distribution (Fig. 12c). The axial temperature drops to about 3400 K and the axial velocity to about 350 m/sec at a position 10 mm above the substrate (120 mm from the inlet). Chemical equilibrium is assumed in the jet up to a position 10 mm above the substrate. Results of a chemical kinetics calculation across the 10 mm show that C2H2 is the most likely diamond deposition precursor species. However, it is likely that superequilibrium exists in the jet with respect to hydrogen dissociation, and higher concentrations of atomic hydrogen would lead to an increase in C and CH3 in the boundary layer. Coltrin and Dandy [37] present an extensive investigation of the chemistry in an arcjet similar to the low-power arcjets just described. Again, a uniform reactor inlet temperature (i.e., temperature at the torch exit) of either 2500 or 3300 K and a uniform inlet velocity of 2000 m/sec are assumed, but the nonequilibrium dissociation is taken into account by considering various degrees of dissociation from 2.6 to 95%. The background pressure is 30 torr, and the CH4 is assumed perfectly mixed with the hydrogen jet shortly downstream of the inlet. The results show that the CH4 equilibrates rapidly with the hydrogen and that the mole fractions of the atomic hydrogen and the principal deposition precursor species are essentially constant up to the boundary layer edge. An increasing degree of hydrogen dissociation at the reactor inlet results in an increasing mole fraction of atomic carbon because of the fast hydrogen abstraction reactions from hydrocarbon molecules and in a decreasing mole fraction of CH3. Increasing the amount of methane injection results in an increase in C2H2. The effect of increasing the inlet gas temperature from 2500 to 3300 K while the degree of hydrogen dissociation is kept constant is a reduction of atomic carbon and an increase of CH3. These results demonstrate that virtually all kinds of deposition mechanisms can be encountered in arcjet diamond deposition, dependent on jet temperature, the degree of hydrogen dissociation, and the hydrogen-to-methane ratio, all of which can be controlled over a wide range by the reactor design and operation. The same authors demonstrate this by calculating the growth rate for different methane injection locations in the same reactor configuration [38]. Location of the methane injector just outside the boundary layer (at approximately 1 cm from the substrate) is found to result in the highest diamond growth rates because at this location the mixing of CH4 with atomic hydrogen results in rapid formation of CHx radicals serving as the main growth species, while insufficient residence times keep the formation of acetylene low. These calculations are for methane injection on the axis and instantaneous mixing with the hydrogen flow. In reality, one has to allow some time or distance for the mixing of the CH4 with the hydrogen.

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Modeling results for a high-power reactor (98 kW) are presented by Kolman et al. [39]. An argon-hydrogen jet is considered with the temperature and mass fraction distribution at the reactor entrance taken from a plasma nozzle flow model for the same plasma torch operating conditions [26] (see Fig. 13). The hydrocarbon distribution at the reactor entrance has been assumed to be in equilibrium according to the temperature at the inlet. Two cases are considered, subsonic flow (Mach number = 1 at the inlet) and supersonic flow (Mach number = 2.92). The pressure at the reactor chamber exit is 35 torr. Figure 14 compares the results obtained for the subsonic jet (graphs on the left-hand side) with those of the supersonic jet. The axial distributions of temperature, velocity, pressure, and density from the nozzle exit (at the left side of each graph) to the substrate are displayed in the top graphs, and the mass fraction distributions of atomic hydrogen and various carbon-containing species are shown in the other two graphs. A gradual decrease of the atomic hydrogen concentration is observed, largely due to diffusion. The higher temperatures in the subsonic case lead to a dominance of atomic carbon in most of the jet expansion region. A strong temperature increase in the recovery zone in front of the substrate, particularly in the case of the supersonic jet, is obvious. Figure 15 shows the boundary layer profiles for the same quantities from a point 2 mm in front of the substrate. The drop in atomic hydrogen due to heterogeneous recombination on the substrate leads to an increase in acetylene concentration compared with atomic carbon as had been shown by Coltrin and Dandy [37]. It is interesting to notice that this drop is less pronounced in the case of the supersonic jet because of the strong temperature increase in the bowshock and because of the very thin boundary layer of 0.4 mm. Figure 16 shows the radial profiles of the gas-phase species at the substrate location and of the temperature, total heat flux, heat flux by conduction, and diamond growth rate on the substrate surface. The substrate heat flux is calculated considering the two major contributions to the energy transfer, heat conduction and surface recombination: qsub

冉冊 ␭ cp

with

eff

冉冊

␭ =⫺ cp =2

eff

dh ⫹ fs dz

冘 imax

(sihi)

i

␭/cpsub ␭/cpgas ␭/cpsub ⫹ ␭/cpgas

␭ = thermal conductivity, cp specific heat at constant pressure i = number of gas phase species si = destruction rate of species i on the substrate [kg/s m2]

(4)

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Figure 13 Radial profiles of temperature, pressure, axial velocity, and atomic and molecular hydrogen mass fraction of an argon-hydrogen plasma jet at the nozzle exit for subsonic (top) and supersonic flow conditions. Profiles are calculated in Ref. 26 and used for jet calculation as presented here in Ref. 39.

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Figure 14 Axial profiles of temperature, axial velocity, pressure, and density (top graphs), and of mass fractions of hydrogen, carbon, and several hydrocarbon species (middle and bottom graphs) for a subsonic (left) and a supersonic argon-hydrogen jet as calculated in Ref. 39.

Figure 15 Axial profiles across the substrate boundary layer of temperature, pressure and density (top graphs) and of mass fractions of hydrogen, carbon and selected hydrocarbons (bottom graphs) for a subsonic (left) and a supersonic argon-hydrogen jet as calculated in Ref. 39.

Figure 16 Radial profiles at the substrate surface of mass fractions of hydrogen, carbon and selected hydrocarbons (top graphs) and of temperature, total heat flux and heat flux by conduction, and total diamond growth rate g (bottom graphs) for a subsonic (left) and supersonic argon-hydrogen plasma jet as calculated in Ref. 39.

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hi = specific enthalpy of gas species i fs = fraction of reaction heat transferred to substrate, assumed to be 0.6 in these calculations Clearly, the major contribution to the total heat flux is the hydrogen recombination energy released to the substrate. The model for the surface kinetics does not include formation of graphite. In this model laminar flow has been assumed, and turbulence will widen the jet and reduce the temperature and density gradients in the jet fringes.

D.

Scaling Relations and the Effect of Pressure

An approach for deriving scaling relations for arcjet diamond deposition reactors is presented by Goodwin [40,41]. Based on a simple boundary layer analysis and the film growth model by Harris [42], rules are derived for optimizing free stream velocity and operating pressure. This analysis shows that in most arcjet reactors the atomic hydrogen concentration is sufficiently high that it no longer strongly influences the growth rate, a result confirmed by detailed computations by Kolman et al. [43]. But the atomic hydrogen concentration does play an important role in reducing defect densities. Defects are assumed to result predominantly from sp2 bond formation. The atomic hydrogen concentration at the surface is in a first-order approximation proportional to [(up)ds]0.5, where u is the free stream velocity, p the pressure, and ds the substrate diameter. However, the free stream velocity is limited by the plasma torch design and operation, and the pressure has an optimum value because too high pressures strongly increase homogeneous recombination of atomic hydrogen. In a similar type of one-dimensional analysis using the heat and mass transfer analogy, Young [17] finds that the total mass deposition rate is proportional to the torch power. Increasing the substrate diameter requires an increase of the torch power proportional to ds1.5 to keep the same linear growth rate. This result is illustrated in Fig. 17, where deposition area and linear growth rate are shown as a function of torch power. Increased torch power allows an increase of the deposition area (see left figure), and this increase more than compensates for the decrease in linear growth rate of the film (right figure) if one considers the total deposited mass. Based on this analysis, Partlow et al. [4] find that strong cost benefits can be gained by scaling to a 100-kW reactor, with further scaling providing smaller gains. The predicted production costs of diamond films as a function of the output power are calculated, and it is concluded that it is necessary to use a plasma torch larger than 100 kW in a gas recycle mode to decrease the cost of toolgrade diamond to the $5/carat level.

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Figure 17 Increase in deposition area with increasing power (left) and decrease in linear growth rate for the increase in deposition area. (From Ref. 4.)

A figure of merit for arcjet diamond deposition is presented by Bigelow et al. [7]. This figure is defined as the hydrogen concentration at the substrate divided by the torch power. An optimum pressure of 200 torr is found to maximize the hydrogen concentration at the substrate. At higher pressures homogeneous recombination losses will start to dominate. Such an optimum pressure has been found experimentally by Lu et al. [44] in a reactor where three arcjets are combined to cover a larger area (see Sec. V.). However, in this experiment the total mass flow rate of the plasma gases has been constant and not the velocity. The optimum pressure has been 270 torr for this reactor (see Fig. 18a). A similar optimum pressure for maximizing deposition rates has been reported (see Fig. 18b) by Hirata and Yoshikawa [45], although for their reactor the optimal pressure has been significantly lower (around 50 torr). However, these type of analyses do not represent the low-power arcjet deposition reactors at very low pressures with very high flow velocities. High deposition rates have been obtained under these conditions as well [32]. One may conclude that no one analysis is applicable for all arcjet reactors and that even for one reactor, the analysis applicable for the center of the substrate may not be correct for the outer parts of the substrate. Also, pressure variations affect not only the boundary layer. The arcjet becomes

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Figure 18 (a) Linear growth rate dependence on deposition chamber pressure [44]. (b) Total mass deposition rate dependence on deposition chamber pressure. (From Ref. 45.)

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less constricted and longer when the pressure is reduced from 1 atmosphere, and the heat as well as the mass is transferred to a larger portion of the substrate. Large area deposition will probably require reduced pressures.

V.

SPECIFIC PLASMA TORCH DEPOSITION REACTORS

There have been numerous efforts devoted to developing dc arcjet deposition reactors because of the promise of obtaining high deposition rates. In this section, several of these developments are described with the objective to present an overview of the different approaches to solve the problems associated with this method. Table 1 presents a summary of the specific developments described in this section. This table cannot be a complete representation of all arcjet diamond deposition developments, but it lists a representative sample.

A.

Common Features of Arc Jet Deposition

Diamond deposition using a dc arcjet was first reported by Kurihara et al. [2]. The plasma torch used simply consists of a tungsten cathode rod, a cylindrical anode made of pure copper and a dc power supply. They initiated a plasma jet consisting of Ar, H2 , and CH4 at 100–400 torr. The diameter of the anode nozzle was 2 mm and the distance between the cathode rod and the anode wall 1 mm. The substrate temperature was kept at 1000– 1500 K. They reported a growth rate of the diamond film of 180 ␮m/hr. Kurihara et al. [46] succeeded in forming functionally gradient films consisting of diamond/WC, diamond/Mo, etc. The WC or the Mo particles are melted by the plasma jet and sprayed onto a substrate, just as in a plasma spraying process. This plasma spraying process is combined with the diamond deposition process as shown in Fig. 19. The composition of the film changes from WC or Mo to diamond over a film thickness of 40 ␮m. The adhesive strength of the gradient composite film is better than 150 kgf/cm2. Loh and Cappelli [32] reported a supersonic plasma jet synthesis method that focused on reducing the thermal boundary layer effects in diamond deposition. They use two 35,000 L/min vacuum pumps in order to produce a process pressure as low as 10–100 Pa (0.07–0.7 torr). Figure 20 shows a schematic of the apparatus, a supersonic arc jet operating with hydrogen expanded to the low-pressure atmosphere. CH4 is introduced at the end of the expansion nozzle. The characteristics of this experiment are described in Sec. IV. The diamond film grown in this process on a molybdenum substrate at 820 ⫹ 30⬚C with a CH4 concentration in the jet of 0.3%

Table 1

List of Major Arcjet and rf Plasma Diamond Deposition Results

Type

Output (kW)

Gas (ᐍ/min at 20⬚C)

Pressure (torr)

Growth rate (␮m/h)

Fujitsu Tokyo Inst. Tech.

dc dc

1.8 9.0

100–400 200

80 930

Univ. of Minn Tokyo Inst. Tech.

dc dc

14.0 10.7

250 50

60 200

10 28.4

Univ. of Minn.

dc

19.3

100–760

1000

4

dc dc rf (4 MHz) rf (3.4 MHz) dc dc

1–3 1 60 40

CH4(0.01–0.2) ⫹ H2(5–20) CH4(0.08) ⫹ H2(1.5) ⫹ Ar(6.5) CH4(3.5–10) ⫹ H2(10–15) CH4(0.06) ⫹ H2(1.5) ⫹ Ar(6.3) (CH3)2CO(2 ml/min) ⫹ H2(18) ⫹ H2(1.7) ⫹ Ar(24) CH4(0.03–0.05) ⫹ H2(10) CH4(0.005) ⫹ H2(0.5) CH4(0.1–1.2) ⫹ H2(12) ⫹ Ar(60) CH4(0.8) ⫹ H2(20) ⫹ Ar(80)

NA NA

dc dc ⫹ rf dc dc

3.75 50 100 100

Institution

Stanford Chemnitz Univ. Tech. NIRIM Toyota Central Res. Ctr. Norton Texas Instruments and Olin Aerospace Kitachi Koki Univ. of Tokyo Westinghouse Univ. Sci. & Tech. Beijing NA: not announced.

Deposition area (cm2) 0.26 5

Remarks

Separate torch Triple torch 1 Cathode–3 anode Liquid source

Ref. 2 6 52,53 54 5

0.1 15 760

3 2 60

34 4 3.2

Supersonic plasma jet Hollow cathode Use induction coil

32 47 3

150

30

77

Use induction coil

48

CH4 ⫹ H2(⫹Ar?) NA

NA NA

NA NA

>80 320

Magnetic field enhanced Supersonic plasma jet

59 60

CH4(0.08) ⫹ H2(2) ⫹ Ar(20) CH4(0.3) ⫹ H2(15) NA CH4(0.04–1.2) ⫹ H2(8–12) ⫹ Ar(6–10)

44 250 NA NA

NA 1 4 40

3.2 168 730 97

On rotating substrate On rotating substrate Recycle mode Magnetic field, recycle mode

55 56 4 50

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Figure 19 46.)

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Schematic diagram of functionally gradient film deposition. (From Ref.

Figure 20 Schematic drawing of supersonic plasma jet CVD apparatus for diamond. (From Ref. 32.)

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displays mostly {111} facets. The growth rate of the film has been 1–10 ␮m/hr, a very high value considering the low operating pressure. Stiegler et al. [47] report diamond synthesis with a hollow cathode arc jet CVD process. A schematic diagram of the apparatus is shown in Fig. 21. A hot refractory hollow cathode is made of tungsten, and the arc discharge occurs between the hollow cathode and a ring anode with possible discharge transfer to the substrate. The substrate temperature is kept at 973–1123 K by controlling the current to the substrate. They report that this apparatus produces high charge carrier densities (e.g., electron densities of 0.5–2.0 ⫻ 1011/cm3). The growth rate of the film has been 2 ␮m/hr over a deposition area of about 4 cm2. Matsumoto et al. [3] first reported rf induction thermal plasma diamond deposition. The arrangement of the deposition experiments is comparable to that shown in Fig. 22. They use a mixture of Ar and H2 (35 L/min Ar ⫹ 12 L/min H2), Ar (17 L/min), and Ar and CH4 (8 L/min Ar, 0.1–1.2 L/min

Figure 21 Schematic diagram of hollow cathode arcjet setup for diamond synthesis. (From Ref. 47.)

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Figure 22 Schematic diagram of rf plasma CVD apparatus for diamond deposition. (From Ref. 48.)

CH4) as sheath, plasma, and carrier gases, respectively. The rf frequency is 4 MHz and the output power 60 kW. The growth rate of the diamond film has been approximately 60 ␮m/hr over a deposition area of 3 cm2. Kohzaki et al. [48] report large-area deposition of diamond films using an rf thermal plasma torch with an inner quartz sleeve of 65 mm diameter. The rf frequency is 3.4 MHz and the output power 40 kW. The process pressure is 150 torr. The growth rate of the film has been 30 ␮m/hr over a deposition area of 77 cm2 (12 in.2). They have obtained free-standing diamond films and have used them for tribological applications by brazing the free-standing films on steel materials.

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High-Rate Diamond Deposition

High-rate synthesis has always been one of the central objectives of arcjet diamond deposition process developments. A schematic of the arc jet apparatus featuring high-rate deposition reported by Ohtake and Yoshikawa is shown in Fig. 23 [6,49]. The apparatus mainly consists of a dc arc discharge torch, its associated power supply, and a reaction chamber. The plasma jet consisting of Ar and H2 is generated by a dc arc discharge. Typical operating conditions are 100 V and 90 A. CH4 is mixed into the plasma jet by en-

Figure 23 Schematic of separate-anode-type torch plasma jet diamond depositon reactor. (From Ref. 6.)

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trainment enhanced by the vortex flow of the plasma gas. The plasma torch consists of separate cathode and anode assemblies that are placed at right angles to each other, and current flow is from a plasma jet exiting the anode assembly to the perpendicular plasma jet exiting the cathode assembly. The diameter of the cathode is 2 mm. To protect the cathode rod and the anode from erosion, only Ar is fed into the flow channel surrounding the electrodes. The cylindrical anode is made of oxygen-free copper, and the diameter of the anode nozzle is 3.5 mm. The distance between the cathode nozzle and the substrate has been varied from 100 to 150 mm. Figure 24 shows the appearance of the plasma jet during diamond deposition. The plasma jet impinges on the substrate where the diamond is deposited. Figure 25 shows a scanning electron microscope (SEM) picture of diamond deposited for a deposition time from 1 to 10 min. Figure 26 shows the variations of the nucleation density and average size of diamond crystallization with deposition time. The substrate has been lapped with 15␮m diamond paste. The substrate is then exposed for 1 min to an Ar ⫹ H2 plasma jet in order to remove the diamond dust particles remaining on the substrate surface. It can be observed that diamond has already deposited after 1 min; however the nucleation density increases with increasing deposition time for approximately 8 min. The deposited diamond forms a continuous film after 10 min. Figure 27 shows SEM photographs of the surfaces and the laser cut cross-sectional views of films that were deposited at different CH4 concentrations. The deposition time has been 1 hr for all samples. For a CH4

Figure 24

Appearance of plasma jet during diamond deposition.

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Figure 25 (a–d) SEM photographs showing deposit at different deposition times. (From Ref. 49.)

concentration of 3%, a diamond film of 150 ␮m thickness was deposited within 1 hr, and the surface of the film was covered with triangular or rectangular automorphic diamond facets. When the CH4 concentration was increased to 5%, the maximum thickness of the film was about 700 ␮m and the diamond film had a large surface roughness. When the CH4 concentration was as high as 15%, cauliflower-like particles were observed on the film surface. The growth rate of the film decreases to about 100 ␮m/hr if we neglect the huge graphite particles grown on the film. Raman spectra of the films obtained at CH4 concentrations of (a) 3%, (b) 4%, (c) 8%, and (d)

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Figure 26 Variations of nucleation density and average particle size with deposition time.

15% are shown in Fig. 28. The Raman spectra from the films deposited at CH4 concentrations of 3% and 4% have only one sharp peak at 1333 cm⫺1. When the CH4 concentration is increased to 15%, diamond, graphite, and amorphous carbon are detected in the Raman spectrum from the deposit. The most suitable deposition conditions for high-rate synthesis of diamond are reported to be a CH4 flow rate of 0.08 SLM, an H2 flow rate of 1.5 SLM, giving a CH4 concentration of 5.3%, and a substrate temperature of 950⬚C. Figure 29 shows the surface and the cross-sectional view of the diamond film obtained under these deposition conditions. The diamond film has large surface roughness, however, and many different diamond automorphic facets can be seen on the surface. The maximum thickness of the diamond film is 930 ␮m, indicating the very high growth rate of 930 ␮m/ hr obtained by this method.

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Figure 27 (a–d) SEM photographs of surfaces and laser-cut cross sections of films deposited at different methane concentrations.

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Figure 28 Raman spectra of diamond films deposited at CH4 /H2 concentrations of (a) 3%, (b) 4%, (c) 8%, and (d) 15%.

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Figure 29 (a, b) SEM photographs of surface and cross-sectional view of highrate synthesized diamond film. (From Ref. 6.)

The relation between linear growth rate and CH4 concentration using this apparatus is shown in Fig. 30. Conversion efficiency (i.e., percentage of the carbon atoms in CH4 that formed diamond) is also plotted as a function of CH4 concentration. The linear growth rate increases with the CH4 concentration; however, the conversion efficiency has a maximum at at CH4 concentration of 4%. The decrease at higher CH4 concentrations may be caused by the deposition of nondiamond carbon. The gas flow rate also has an effect on the linear growth rate and the conversion efficiency (see Fig. 31). The CH4 concentration has been kept constant in these experiments. The growth rate saturates at H2 flows of 1.5 L/min, then decreases with further increasing H2 flow rate, mainly due to the decrease of the gas temperature. Figure 32 shows relations between the linear growth rate and the

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Figure 30 Relation between linear growth rate and conversion coefficient and CH4 concentration (H2 flow rate, 1.5 lpm; Ar flow rate, 6.5 lpm; power, 9 kW; chamber pressure, 25 kPa; substrate temperature, 1000⬚C; deposition time, 1 hr).

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Figure 31 Relation between linear growth rate and conversion coefficient and gas flow rate (Ar flow rate, 6.5 lpm; methane concentration, 4%; power, 9 kW; chamber pressure, 25 kPa; substrate temperature, 1000⬚C; deposition time, 1 hr).

conversion efficiency and the applied discharge power. Growth rate and conversion efficiency appear to be increasing more than linearly with torch power. Scale-up of deposition reactors to high power levels is generally accepted to reduce production costs. Following their scaling analysis, Young [17] and Partlow et al. [4] reported on the operation of a 100-kW system with a Westinghouse Marc 3 hot cathode swirl stabilized plasma torch. The plasma is expanded through a nozzle into the deposition chamber, which is

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Figure 32 Relation between linear growth rate and conversion coefficient and output power (H2 flow rate, 1.5 lpm; Ar flow rate, 6.5 lpm; pressure, 25 kPa; substrate temperature, 1000⬚C; deposition time, 1 hr).

kept at a pressure between 10 and 50 torr. The gas is recycled after going through a heat exchanger. Lu et al. [50] also reported on a 100-kW dc arcjet installation for deposition of diamond films at costs as low as $4/carat level. They used a magnetic field–enhanced ‘‘W’’ type of rotating arc (see Fig. 33) that provides large area uniformity for not only composition but also temperature distribution in the jet in front of the substrate. The deposition area is reported to be 97 cm2. Gas recycling and coolant recycling are employed in this facility.

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Figure 33 Schematic diagrams of (a) magnetic field–enhanced rotating plasma torch and (b) rotating arc. (From Ref. 50.)

C.

Large-Area and High-Quality Diamond Deposition

Enlargement of the deposition area has been mainly carried out by scale-up of the plasma torch itself as described in Sec. V.B. However, other ideas to enlarge the deposition area have also been reported.

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189

Lu et al. [44,51,52] described a triple torch plasma reactor, which is shown in Fig. 34. The plasma generator consists of three identical dc plasma torches operating with an argon-hydrogen mixture at a total power level of about 36 kW. The three coalescing plasma jets impinge on a water-cooled substrate. A water-cooled gas feeding probe is located above the region where the three jets merge. This arrangement results in efficient mixing of the H2/CH4 reactant mixture introduced through this probe with the plasma. The three coalesced jets offer a larger plasma volume than most dc reactors and higher plasma flow velocities than the rf reactors. To improve temperature uniformity, the substrate holder has been shaped to allow nonuniform cooling of the backside of the substrate [53]. Although a uniform growth rate has been achieved in this way, the film morphology has varied with

Figure 34

Schematic of triple torch plasma reactor. (From Ref. 52.)

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varying radius. However, providing additional methane to the outer portion of the coalesced jets through entrainment resulted in uniformity of film thickness and morphology over an area of approximately 35 mm diameter. Average linear growth rates of 100 ␮m/hr have been obtained [53]. Hirata and Yoshikawa [45,54] describe a unique plasma torch that uses three symmetrical anodes with one cathode as shown in Fig. 35. Each electrode can be moved along its axial direction by rotating a thread mounted at its end. The diameter of the plasma jet increases with increasing displacement y of the anodes from the center (see Fig. 36). According to Raman spectra taken from each radial portion of the film (Fig. 37), it can be seen that the quality of the diamond film is good all over the 60-mm-diameter substrate. Effects of process pressure on deposition rate (g/hr) and the surface profile are shown in Figs. 18b and 38, respectively. The maximum deposition rate (about 1 ct/hr) has been obtained at a process pressure of 6.7 kPa. The conversion efficiency of the carbon atoms in the source gas to diamond has been as high as 15% in this case. Although the surface uniformity has not been improved by this three-anode technique, the deposition area has increased by a factor of 5 compared with the deposition with the single-cathode single-anode torch. Noto and Mori [55] proposed enlarging the deposition area in terms of rotating the substrate during arc jet diamond deposition as shown in Fig. 39. The center of the substrate is shifted from the center axis of the plasma jet. The rotation speed of the substrate is kept at 15 rpm. The deposition area increases by a factor of 4 when the center of the plasma jet is shifted a quarter diameter from the center of the substrate. This idea demonstrates a convenient way to enlarge the deposition area, but Raman spectra from the diamond film (Fig. 40) indicate that the film contains small amounts of amorphous carbon, resulting from the deposit that grows in the peripheral part of the deposition region where the atomic hydrogen concentration and the substrate temperature are lower. Eguchi et al. [56] described diamond synthesis using a hybrid torch on a rotating substrate as shown in Fig. 41. The induction coupled plasma is coupled with a dc arcjet (‘‘hybrid plasma torch’’ [57]). The maximum substrate size has been 300 mm in diameter. The rotation speed has been 40 to 400 rpm. The temperature variation has been as small as 8 K per cycle, when the rotating speed of the substrate is 40 rpm. The diamond has grown over almost the entire surface of the rotating substrate. Yin et al. [58] reported diamond deposition on tungsten wires using the same rotating deposition system. Uniform diamond films approximately 1 ␮m thick are obtained on the wire with a diameter of 0.2 mm at a rotation speed of 450 rpm. Lu et al. [59] have applied a magnetic field to the arcjet in order to enlarge the plasma jet. A schematic illustration of the apparatus is shown in

Plasma Torch Diamond Deposition

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Figure 35 (a, b) Schematic illustration of one-cathode, three-anode plasma torch apparatus for diamond deposition. (From Ref. 45.)

Fig. 42. The magnetic field is applied to the dc arc to force a rotation, and the rotating arc produces a plasma jet uniform over a larger area. An additional magnetic coil with an auxiliary anode is mounted above the substrate. This arrangement increases the atomic hydrogen concentration near the substrate and also contributes to improving the uniformity of the diamond film.

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Figure 35

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Continued

The deposition area has been larger than 78 cm2 (i.e., 10 cm in diameter), film thickness has been 500 ␮m, and the surface roughness has been approximately 5 ␮m after surface polishing. The grain size of the diamond has been as small as 20–50 ␮m for a film 500 ␮m thick. The diamond film prepared by this apparatus has a high optical transmission (t > 70%) and also provides high thermal conductivity (>2000 W/m/K). Diamond films produced with this apparatus have already been commercialized as heat sinks. McKenna et al. [60] present optical-quality high-growth-rate diamond deposition by supersonic arcjet CVD, focusing on generation of thick freestanding diamond films for optical components and infrared windows. The schematic of the deposition setup is shown in Fig. 43. They reported that they deposited an optical-quality diamond film 700 ␮m thick over the entire surface of an 8-in. (20-cm) substrate. A free-standing diamond dome was also produced by this method. The diameter of the dome was 2.5 in. and

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193

Figure 36 Diameter of plasma jet versus displacement of anodes for different axial distances x between the cathode nozzle exit and the anode jet. (From Ref. 45.)

the thickness of the diamond film 700 ␮m. Process conditions were not given, but Raman spectroscopy and x-ray diffraction results for film indicated that the film had strong 具110典 orientation with very high film quality. D.

Liquid Source Diamond Deposition and Oxygen Addition Effect

Ohtake and Yoshikawa [61] reported the effect of oxygen addition in dc arcjet diamond deposition. They reported that the etch rate of graphite by the O2-Ar plasma jet was about 130 times larger than that by an H2-Ar plasma jet, and the rate of diamond etching by the O2-Ar plasma jet was about 55 times larger than that by the H2-Ar plasma jet. Consequently, the ratio of the etch rates of graphite and diamond obtained using the O2-Ar plasma jet was as high as 56, which is more selective etching of graphite in comparison with that by the H2-Ar plasma jet. The relationship between the oxygen concentration and the growth rate of diamond films is shown in Fig. 44. It can be seen that the growth rate decreases with increasing oxygen concentration. Figure 45 shows SEM pictures of diamond films deposited with oxygen concentrations of 0 and 33%. It can be seen that for a concentration of 33%, the crystals form films without pores, and the surface roughness is reduced. Figure 46 shows micro-Raman spectra of the diamond films that are deposited with oxygen concentrations of 0 and 33%. Both spectra have small peaks from amorphous carbon at 1500–1600 cm⫺1. The full

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Figure 37 Raman spectra taken from different radial positions of the diamond film (Mo substrate 60 mm in diameter). (From Ref. 45.)

width at half-maximum (FWHM) of the peak from diamond deposited with oxygen is 7.5 cm⫺1. The value is about 0.67 times as large as that from the diamond film deposited without oxygen. Figure 47 shows the thickness profile of the diamond film. It can be seen that the thickness of the film is about 200 ␮m. The film appears white due to the light scattering from the surfaces and the grain boundaries in the film. A diamond film with 1.2 mm thickness has been prepared in a deposition time of 20 hr. The surface roughness of this film was about 150 ␮m. Diamond deposition using arcjets with liquid precursors was reported by Han et al. [5]. The schematic of the apparatus is shown in Fig. 48. The best results are obtained with acetone and ethanol as liquid precursors injected into the arcjet plasma. The liquids are injected using an atomizing probe located at the center of the substrate, opposing the plasma jet in a

Plasma Torch Diamond Deposition

Figure 38 Ref. 53.)

195

Effect of process pressure on surface profile of diamond film. (From

counterflow arrangement, or from the side with the atomizing probe 2 mm above the substrate [62]. High linear growth rates of more than 1 mm/hr have been achieved when the organic fluids are injected in the counterflow arrangement into an argon-hydrogen plasma jet. It was observed that using acetone resulted in smaller diamond particles than ethanol [62]. When the liquid is injected from the side of the plasma jet, high diamond growth rates and carbon conversion efficiencies are obtained only when the liquid is atomized close to the substrate and liquid droplets are actually entering the boundary layer. This situation has been described in a three-dimensional model that includes the fluid dynamics of the plasma jet; the atomization, transport, and evaporation of the liquid; the gas-phase chemical kinetics, and the surface chemical kinetics [43]. The very high growth rates observed experimentally can be explained by the model as a result of the high mass

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Figure 39 55.)

Large area diamond deposition with a rotating substrate. (From Ref.

transport of deposition precursors in liquid form into the boundary layer, and the availability of oxygen and OH radicals to ensure film quality. E.

Effects of Substrate Bias on Arc Jet Diamond Deposition

Substrate biasing has been shown to be one effective way to accelerate the growth rate and to enlarge the deposition area of the diamond film. Substrate

Plasma Torch Diamond Deposition

197

Figure 40 Raman spectra of a diamond film with a rotating substrate at different radial positions (in mm). (From Ref. 55.)

bias effects in dc arcjet diamond deposition have been investigated by Matsumoto et al. [63] by using the setup shown in Fig. 49. The positive bias voltage is applied to the substrate or to the ring electrode near the substrate. The bias voltage has been ⫹100 to ⫹400 V, with a current flow of 0.5 to 5 A. The change in the appearance of the plasma jet with the bias is shown in Fig. 50. It is clear from Fig. 50b that a glowlike discharge extends from the tail of the plasma jet to the substrate, and the optical emission from the plasma jet is significantly enhanced especially near the substrate. The discharge changes to a transferred arc mode when bias is further increased, and because the transferred arc causes significant electron heating of the substrate, the substrate becomes overheated. Figure 51 shows the thickness profiles of the diamond films deposited with three different bias voltages. The growth rate of the diamond film increases by more than a factor of 2 when the bias current to the substrate reaches 2 A. In case of bias current of 3 A, the center region of the film is no longer diamond but graphite due to the large heat flux caused by the transferred arc initiated between the cathode and the substrate. These results show that the substrate biasing technique

198

Figure 41

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Schematic of hybrid plasma torch. (From Ref. 56.)

can have an important effect on increasing the growth rate of diamond but that it will remain difficult to improve the uniformity of the diamond film. Baldwin et al. [64] also reported the effect of substrate biasing on the growth rate of diamond films. From emission spectroscopic measurements, it was determined that the bias leads to an increase in the concentration of atomic hydrogen near the substrate. The growth rate increased by a factor of 7 when the substrate was biased at 170 V and a current density of 4.9 A/cm2 was obtained. They measured the two-dimensional distribution of atomic hydrogen emission and concluded that the increased growth rate can

Plasma Torch Diamond Deposition

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Figure 42 Schematic drawing of magnetic field-enhanced arcjet diamond deposition apparatus. (From Ref. 59.)

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Figure 43

Schematic model of supersonic arcjet CVD setup. (From Ref. 60.)

be attributed to an increased flux of atomic hydrogen to the growth surface resulting from an elevated electron temperature that increases the dissociation near the surface.

VI.

CONCLUSIONS AND CURRENT RESEARCH ISSUES

Arcjet diamond deposition encompasses a large diversity of approaches, probably more than any other diamond deposition method. The different approaches vary in how the atomic hydrogen is generated, how the deposition precursors are generated, and how the atomic hydrogen and the dep-

Plasma Torch Diamond Deposition

201

Figure 44 Relationships between growth rate of diamond films and the ratio of oxygen flow rate to methane flow rate. (From Ref. 61.)

Figure 45 SEM photographs of diamond films deposited (a) without and (b) with oxygen addition (33% of methane flow). (From Ref. 61.)

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Figure 46 Micro-Raman spectra of diamond films deposited at oxygen concentrations of (a) 0% and (b) 33%. (From Ref. 61.)

osition precursors are transported to the substrate. Because of this variety of approaches, it is difficult to arrive at general conclusions. The one common feature of all arcjet deposition methods is the relatively high growth rate of the films, and it appears that deposition reactors can be designed in which neither mass transport nor the gas-phase chemistry but rather the surface reactions are the limiting factors for the deposition rate. Furthermore, scaling

Figure 47

Thickness profile of diamond film deposited with oxygen.

204

Figure 48 Ref. 5.)

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Schematic of counterflow liquid injection plasma reactor. (From

to large deposition areas and high overall deposition rates can be accomplished. Approaches have been demonstrated to solve the inherent weaknesses of the arcjet deposition method—the nonuniformity of the plasma jet leading to nonuniform distributions of film thickness, and the high heat fluxes to the substrate requiring substrate cooling—but more work on re-

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Figure 49 Schematic drawing of substrate bias enhanced arcjet diamond deposition setup. (From Ref. 63.)

actor design for large-area high-rate deposition is anticipated. The major research issues associated with arcjet diamond deposition are essentially the same as those for all deposition methods; however, the special conditions of an impinging plasma jet may require different approaches for a solution. We see the areas that need to be further investigated: (1) the control of film morphology under high growth rate conditions, (2) the adhesion of

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Figure 50 Change of appearance of plasma jet with substrate biasing (a) no bias and (b) 280V, 4 A. (From Ref. 63.)

Figure 51 Thickness profile of diamond film deposited with three different bias voltage. (From Ref. 63.)

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207

the films on a variety of substrates, and (3) the deposition at low temperatures while maintaining a high growth rate. The control of film morphology requires mapping in the four-parameter space of carbon precursor concentration–atomic hydrogen concentration– total mass transport rate–substrate surface temperature, those regions associated with a certain texture of the growing film. It also requires control over secondary nucleation. Extensions of the maps of the ␣-parameter, which indicates the preferred direction of growth, to higher growth rate conditions and gas chromatography measurements giving information on the associated boundary layer chemistry can form the basis for this information [65]. Further experiments along these lines are necessary for arcjet deposition and for experiments with additional reactants such as oxygen and halogens. Such investigations will enhance the ability to tailor characteristics of highgrowth-rate diamond films for specific applications. Well-adhering diamond films have been obtained for some substrate materials, e.g., silicon or molybdenum; however, for many substrate materials of interest, adhesion is relatively poor. Being able to obtain well-adhering films will reduce the cost of diamond coatings for some applications and therefore allow wider utilization of the advantageous diamond characteristics. Arcjet diamond deposition makes the adhesion more difficult because the high growth rate is usually associated with an increased number of defects and with higher stresses. An understanding is needed of the relationship between defect and stress formation and the deposition conditions. Approaches such as the three-step deposition process in which an intermediate diamond-metal composite film is deposited between the substrate and the diamond film [66] may be a solution for some applications; however, the cost constraints will favor single-step processes for adhesion enhancement, possibly involving special substrate pretreatment such as deposition of a plasma sprayed intermediate layer of molybdenum [67]. Increasing the number of chemical reactants to include oxygen and halogens may be of interest for adhesion studies as well. A whole new world of applications for diamond films would open up if films could be deposited at high rates and at low temperatures. Film growth at low temperatures has involved use of oxygen or halogens, and rates have been very low. Arcjet deposition at temperatures of 550⬚C with deposition rates of 40 ␮m/hr [67] and even at 400⬚C with about 10 ␮m/hr growth rate have been achieved, but adhesion of these films has been rather poor. Approaches involving different surface chemistries may be necessary. Because arcjet deposition necessarily involves rather high heat fluxes, it may be possible to deposit diamond with this technology only on substrates that have a high thermal conductivity, but too few experimental data exist so far to reach any conclusion on this matter.

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7 Microwave Plasma-Assisted Diamond Film Deposition Timothy A. Grotjohn and Jes Asmussen Michigan State University, East Lansing, Michigan

I.

MICROWAVE PLASMA DISCHARGES

Microwave plasma-assisted diamond synthesis has been demonstrated over a wide operating pressure regime from a few millitorr to 1 atmosphere. The maximum film deposition rates vary from less than a tenth of a micrometer per hour at the low pressures of 10 mtorr to well over 10 ␮m/hr at operating pressures of 200 torr or greater. As the operating pressure is changed the behavior and properties of a typical microwave discharge vary significantly. At the low pressure of 10 mtorr to a few tens of torr the discharge usually fills the entire discharge chamber and is a relatively cold (gas temperature) nonequilibrium discharge where the electron temperatures are over 10,000– 20,000 K and the gas temperatures are less than 500–1500 K. As pressure is increased to 50 torr and above, the electron temperatures decrease and the gas temperatures increase. The discharge contracts and separates from the chamber walls as pressure is increased and takes on a ball-like or spherical shape that depends on the excitation electromagnetic fields and the geometry of the chamber. At higher pressures the gas temperatures usually are in excess of 1500 to 2000 K and the microwave discharge becomes a more spatially inhomogeneous discharge. More specifically, at higher pressures, the microwave discharge, similar to low-frequency and DC arcs, becomes a thermally inhomogeneous discharge. It has a hot central core with sharp thermal gradients existing between the discharge center and surrounding walls. Microwave energy is readily coupled into the electron gas in the hot discharge center because of 211

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its reduced neutral gas density, and neutral gas species are also easily ionized and excited in the hot discharge region. Major energy losses from the higher pressure discharges occur by heat conduction, convection, and radiation. The large temperature gradient causes heat conduction losses to become an important loss process. This loss mechanism includes the contribution to the heat conductivity by molecules, atoms, electrons, and ions as they diffuse to the walls. And also includes chemical reactions such as the transport of dissociation energy and ionization energy to the discharge/arc fringes by the free radicals and ions. Owing to the highpressure environment, electrons, ions, and free radicals recombine quickly outside the hot central core and thus convert their dissociation, ionization, and excitation energy into thermal energy. The result is a discharge with a radially varying gas temperature, ionization rate, and volume recombination rate. Gas temperature, ionization, dissociation, etc. are highest in the center of the discharge, while volume recombination and deexcitation of the different species increase radially away from the discharge center as the cooler, denser gas regions near the walls are approached. The central discharge core gas temperatures vary with gas type and pressure but typically are in excess of 2000 K, while temperatures external to the discharge are controlled by wall temperatures and the gas temperatures of the gas flowing around the discharge. This chapter reviews the studies that have been done on microwave plasma-assisted chemical vapor deposition (CVD) of diamond. As described earlier, this deposition occurs across a range of plasma discharge types extending from low-pressure nonequilibrium discharges to higher pressure, thermal-like discharges. This chapter is organized so that the general diamond deposition environment is first described; then a generic description of a typical plasma-assisted diamond deposition reactor is developed. Next, the details of several specific deposition systems are reviewed. Finally, details of the various microwave plasma-assisted diamond deposition processes and chemistries are examined. The approach used to organize the many diamond deposition results for microwave CVD systems is a control model approach where the deposition process is viewed in terms of input, internal, and output variables. The specifics of this approach are given in Sec. III.B. First though, Sec. II describes the general plasma chemistry environment that must be created to deposit diamond. II.

MICROWAVE PLASMA-ASSISTED CVD OF DIAMOND DEPOSITION ENVIRONMENT

The role of the microwave plasma-assisted machine in the deposition of diamond is to create the chemical/thermal environment needed for diamond

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deposition. This environment for the standard hydrogen-methane deposition process has the following attributes. A.

Substrate Temperature

For diamond deposition the temperature of the deposition surface is generally in the range from 400 to 1100⬚C with the more typical values being 700–1000⬚C [1–3]. This range of substrate temperatures allows surface phenomena including various adsorption, desorption, and abstraction reactions to occur that lead to diamond growth. Too high a substrate temperature converts the diamond to graphite. Obtaining the correct substrate temperature often requires the design of substrate holders that incorporate either heating or cooling. B.

Atomic Hydrogen

The appropriate chemically reactive species need to be supplied to the growth surface. Two types of radicals are needed. First, atomic hydrogen is needed so that the surface is almost entirely covered with hydrogen to permit growth in the diamond phase of carbon and not the graphite phase. Second, appropriate carbon-containing growth species must be supplied to the growth surface. The ratio of the atomic hydrogen flux to the carbon growth species flux is typically 1000–10,000 for the deposition of high-quality diamond [4]. This need for the large flux of atomic hydrogen prevents the use of standard CVD where the substrate temperature provides the energy to dissociate the molecular species. At the typical substrate temperatures of 700– 1100⬚C the dissociation rate of hydrogen is very low. Hence, the hydrogen must be dissociated by a hotter thermal source located away from the substrate (e.g., a hot filament) or by a plasma discharge that dissociates molecular hydrogen by either electron impact dissociation or thermal dissociation due to a high gas temperature in the discharge. In the case of microwave CVD reactors the plasma discharge serves to dissociate the hydrogen via either electron impact dissociation or a combined electron impact dissociation and gas heating–produced thermal dissociation. Typically, the lower pressure discharges (few tens of torr) have higher gas temperatures (>2000 K) and thus thermal dissociation of hydrogen is the dominant dissociation process. C.

Carbon-Containing Radicals

The appropriate flux of carbon-containing growth species to the deposition surface is needed. The conditions of diamond deposition using microwave

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discharges are typically in the pressure range from 1 to 200 torr and gas discharge temperatures ranging from slightly above the substrate temperature (⬃1100–1500⬚C) to above 3000⬚C. Under these conditions in microwave discharges, the dominant carbon-containing radicals important to diamond growth are CH3 and C2H2 [3,4]. The methyl radical 1CH3 is generally acknowledged to be the most important species for diamond growth and is most often obtained from the methane (CH4) input feed gas. The CH4 chemical reactions in the typical diamond deposition environment (high gas temperature and significant atomic hydrogen concentrations) occur primarily as neutral-neutral chemistry rather than via electron collision processes, which are more important for the hydrogen dissociation. Almost always, the carbon chemistry reactions occur on a time scale much shorter than the residence time of the deposition gas in the discharge chamber for microwave CVD reactor systems. Hence, the carbon chemistry is typically assumed to have reached an equilibrium condition for the discharge gas temperature and atomic hydrogen concentration found in the discharge.

D.

Deposition Uniformity

Once a vapor-phase environment containing a substantial amount of atomic hydrogen and an appropriate number of carbon growth radicals is created adjacent to a temperature-controlled substrate, diamond growth can proceed. One of the major issues for the design of microwave plasma-assisted CVD diamond deposition machines is creating the appropriate and uniform vaporphase environment and temperature over the entire deposition surface. Several factors influence the uniformity of the deposition including the uniformity of the substrate temperature profile and the uniformity of the discharge located adjacent to the substrate. Substrate temperature profiles can be controlled or influenced through the appropriate design of the substrate holder cooling or heating. The uniformity of the discharge is an even more complex matter. The size, shape, and uniformity of the discharge are controlled by a number of factors including the discharge chamber shape and size, the discharge kinetics including recombination of charged species in the volume (via volume recombination) and/or on the surfaces (via surface recombination), the generation of radicals in the discharge, and the loss of these radicals in the discharge and on the surfaces surrounding the discharge. Many of the differences in the performance between different microwave diamond deposition CVD systems are concerned with the area or size of the deposition surface across which good uniformity is achieved.

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III.

MICROWAVE PLASMA MACHINE DESCRIPTION, PROCESS VARIABLES, AND PERFORMANCE

A.

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A generic microwave plasma-assisted diamond CVD system is shown in Fig. 1. The subsystems include the gas flow rate control system, the vacuum pumping/pressure control system, the discharge chamber and substrate holder, the microwave power supply system, and the microwave energy coupling system, i.e., the microwave applicator subsystem. These subsystems work in unison, generally under computer control, to provide the deposition environment outlined in the previous section. A description of the basic operating purpose and design of each of these subsystems is provided in the following paragraphs. 1.

Gas Flow Rate Control Subsystem

The gas flow rate control system consists of first the gas cylinders containing the feed gases. Because of the sensitivity of the deposition process to impurities in the discharge plasma and the desire to minimize impurities in the deposited diamond, the feed gases should be of high and ultrahigh purity. The flow rate of each gas is controlled with a mass flow controller. The total flow rate ranges in the various systems and processes from tens to thousands of sccm. These controlled flow rate feed gases are then mixed together and delivered to the discharge chamber. 2.

Vacuum Pumping/Pressure Control Subsystem

The vacuum pumping/pressure control system as shown in Fig. 1 is used to pump the reacted gas from the deposition chamber in a continuous manner and to maintain the desired pressure in the deposition chamber. Most diamond deposition systems operate during deposition in the pressure range from a few torr to 200 torr, although values outside this range have certainly been reported. These common pressures of a few torr to 200 torr can be maintained at the flow rates used by using a mechanical roughing pump. The pressure in the deposition chamber is maintained by using an adjustable (throttle) valve located between the pump and the deposition chamber. The pressure is measured with a pressure gauge, most often a capacitance manometer. A control system automatically adjusts the throttle valve to achieve the desired pressure in the deposition chamber. Safety precautions included in the design of the pumping system are first a dilution of the hydrogendominated exhaust gas at the exit of the mechanical pump using a nitrogen

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Figure 1 Microwave plasma-assisted diamond CVD system showing gas flow control, vacuum pumping/pressure control, discharge chamber/substrate holder, microwave power supply, and applicator subsystems.

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purge. The nitrogen dilution is used to reduce the hydrogen concentration to a nonflammable level at the exit of the mechanical pump. A second safety feature often included is a safety interlock system that prevents the pressure in the processing system from exceeding a preset level when hydrogen is present in the system. 3.

Discharge Chamber/Substrate Holder Subsystem

The next subsystem is the discharge chamber/substrate holder unit. The purpose of this system is to confine the plasma discharge and to position the substrate surface for optimum deposition. In the simplest case this consists of a microwave transparent tube that confines the discharge and controls the spatial variation of the processing gas flow. A platform within the tube holds the substrate. In realistic systems this subsystem generally requires some of the most careful detailed design in order to optimize the diamond deposition process. Several design variables of this subsystem work in an interacting manner to establish a plasma discharge shape and size that produces uniform plasma-assisted deposition across the substrate surface. The first set of design variables to be considered is the substrate holder that is designed to have a controlled, uniform, and repeatable substrate temperature. Such controlled temperature is acquired in some systems through active heating or cooling of the substrate holder. Typically, active heating of the holder is required when deposition is done at low pressures (less than 60 torr) or with lower microwave power levels. Conversely, systems that operate at higher pressures (greater than 80 torr) and high input microwave powers often require active cooling of the substrate holder. It is also found in some designs that substrate heating relies solely on heating from the plasma discharge itself with no additional active heating or cooling utilized. This type of substrate holder system is referred to here as a thermally floating system. It is important to note here that when operating in a thermally floating configuration the substrate temperature is determined by the pressure and microwave power. The second set of design variables in the discharge chamber/substrate holder subsystem comprises the size and shape of the discharge chamber and the location of the substrate holder. The discharge chamber is typically constructed of a fused silica bell jar or window and additional stainless steel walls. The fused silica portion of the discharge chamber provides the transparent material for microwave power coupling while providing a gastight chamber. The shape and size of the fused silica/stainless steel confinement region, along with the size and location of the substrate holder, strongly influence the discharge location and shape. Also important to the discharge size and location is the magnitude of the input microwave power and its heating profile. A typical example of how

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the experimental substrate temperature, Ts , and plasma volume, Vd , vary with the discharge pressure and input absorbed microwave power, Pt , for a microwave plasma-assisted CVD system is shown in Fig. 2 [5]. The solid lines shown in Fig. 2 have been experimentally measured for a system operating with a 7.5-cm-diameter substrate holder. In this figure the lower limit on the plasma volume, Vd(min), is determined by the discharge volume required to just cover the substrate holder. The upper limit of plasma volume, Vd(max), occurs when the plasma discharge begins to touch the discharge chamber wall, i.e., it just fills the discharge volume. Note that when the hot or bright part of the discharge comes in contact with the walls it can cause substantial wall heating. Thus this condition when Pt is greater than the Vd(max) boundary in Fig. 2 should be avoided. The discharge chamber size for this plot is 12.5 cm in diameter. The general trend in this plot is that as the pressure, p, increases the microwave power absorbed into the discharge

Figure 2 Diamond deposition reactor operating field map showing the substrate temperature in a thermally floating substrate system (no active cooling or heating of the substrate). This experimental plot is for a system with a 12.5-cm-diameter quartz dome and 7.5-cm-diameter silicon substrate described in Refs. 5 and 8.

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must also increase to maintain a constant plasma volume. The other trend is that the temperature of the thermally floating substrate holder/substrate is determined primarily by the pressure and to a less extent by the input microwave power and flow rate. Plots such as the one given here in Fig. 2 that experimentally quantify the power-pressure region of operation can be developed for any microwave diamond CVD system. Different systems when measured this way can be expected to show similar trends but quantifiably different experimental operating curves. More specifically, these experimental Pt , p, Ts operating curves can be expected to be different for each of the microwave diamond CVD deposition systems described in Sec. IV. The last set of design variables of this subsystem is the location of the feed gas injection port(s), discharge gas flow directors, and exhaust gas pumping ports of the discharge chamber system. Some considerations include having radially uniform feed gas injection and radially uniform pumping of the discharge gas. Further, in some systems, especially those operated at higher pressures and flow rates, the injection ports and gas flow direction surfaces are designed to help improve the uniformity and shape of the discharge and ultimately the deposited film uniformity. At low pressures the discharges are more diffuse and detailed flow design considerations are not as crucial. An overall design issue for the discharge chamber/substrate holder subsystem is the selection of materials that are compatible with the high temperatures and reactive chemistry of the discharge. Common materials used for the substrate holder include molybdenum, stainless steel, and graphite. These materials to various degrees can withstand the substrate deposition temperatures of up to 1100⬚C. The walls of the discharge chamber are often constructed of fused silica and stainless steel. Where possible, water cooling of the walls is also included in the deposition discharge chamber design, especially for the stainless steel walls. 4.

Microwave Power Supply Subsystem

A typical microwave power supply subsystem is shown in Fig. 3. The microwave power is generated by a magnetron power supply most commonly operating at the frequency of 2.45 GHz. Another frequency used for the larger diameter and higher power systems is 915 MHz. The microwave circuit shown in Fig. 3 has the output of the magnetron power supply connected to a circulator that serves to isolate and protect the power supply from any power that may be reflected from the microwave cavity applicator. The reflected power is sent to an impedance-matched dummy load that is typically water cooled. The net power going to the plasma reactor is measured as the incident power, Pinc , minus the reflected power, Pref . The absorbed input

Figure 3

Typical microwave power supply and waveguide circuit.

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power is then Pt = Pinc ⫺ Pref . Microwave power measurements are made using directional couplers inserted in the transmission line or waveguide between the circulator and the plasma reactor. The directional couplers sample a known fraction of the power flow in a given direction in the waveguide/ transmission line. This sampled power is then measured using power meters. Typical power supplies used in microwave plasma-assisted diamond CVD machines range from 100 W to 8 kW for the 2.45-GHz frequency regime and 6–60 kW for 915-MHz excitation. 5.

Microwave Applicator Subsystem

The last major subsystem is the microwave coupling system, i.e., the external microwave circuit and applicator coupling system. The components of this subsystem are a waveguide, cavity resonator, antenna, or plasma surface wave launcher that focuses or guides the microwave energy to create and maintain the plasma discharge. The variation of this coupling system is the fundamental difference between the many microwave plasma-assisted diamond deposition machine designs. Section IV of this chapter describes several such design variations. Also included in this subsystem are the tuning elements that match the impedance of the transmission line/waveguide to the reactor load. These tuning elements can include stub tuning adjustments, antenna/probe adjustments, resonant cavity size adjustments, and substrate position adjustments, to name a few. These adjustments not only control the impedance matching, which determines the amount of reflected power for a given input power, but also can influence the plasma discharge shape and size, which has a direct impact on the uniformity of the diamond deposition across the deposition surface. B.

Microwave Plasma Reactor Process Variables and Performance Variables

1.

The Multivariable Plasma Reactor

The performance of a microwave plasma diamond deposition reactor is a complex function of many experimental variables. Figure 4 displays a generic block diagram of a typical reactor where the nonlinear relationships between three groups of variables are schematically represented. The three basic groups are (1) input variables, U; (2) internal variables, X; and (3) output variables, Y. The input variables are defined as the variables that can be independently controlled by an experimental operator or reactor designer. As shown in Fig. 4 the input variables can be further subdivided into controllable input variables, U1 , such as operating pressure, methane concentration, gas flow rate, and deposition pressure; the reactor geometry variables,

222 Figure 4

Multivariate parameter space for microwave plasma-assisted diamond deposition.

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U2 , i.e., the variables concerned with the reactor size and geometry, substrate holder configuration, etc.; and deposition process variables, U3 , i.e., substrate material, deposition time, seeding procedure, etc. The internal variables are defined as the internal plasma reactor states such as gas temperature, electromagnetic field strength, and plasma density. The output variables, Y, can be divided into two groups: those concerned with the reactor performance, Y1 , such as film growth rate and carbon conversion efficiency, and those concerned with the film properties, Y2 , such as film morphology, texture, and film quality. Figure 4, displays a number of example input, internal, and output variables that are important in the diamond deposition process. In order to begin to understand the microwave plasma-assisted diamond deposition process, not only must the relationships between the input variables and the output variables be understood but also the relationships between the reactor internal variables and both the input and output variables must be established. The output variables are a complex function of both the internal variable vector, i.e., Y = h(X), and input variables vector, Y = g(U ). A comprehensive theory that describes the relations between these variables does not exist and is only beginning to be developed. However, knowledge of these complex relations is essential for improved reactor design and ultimately for precise reactor control. In this chapter the important input and internal reactor variables are identified. These variables are then related to the reactor experimental outputs such as reactor performance, Y1 , and film properties, Y2 . This systematic approach enables improved understanding of the plasma reactor system through the identification of the cause-and-effect relationships between input and internal variables and then of the output reactor performance. Changes in reactor inputs such as operating pressure and gas chemistry, and in the reactor size and configuration are then related to reactor performance. 2.

Input Variables

Table 1 identifies a number of typical reactor variables. The independent, controllable input variables, U1 , are substrate temperature Ts , pressure p, incident microwave power Pinc , and feed gas composition and total gas flow rate ft . Reactor geometry variables, U2 , are associated with the applicator and discharge size. Here we assume that the applicator, the substrate holder, and the discharge chamber are all cylindrical. Thus the pertinent dimensions are the applicator radius RA and height LA and the quartz/fused silica discharge chamber radius R c and height L c . The chamber volume is then Vc = ␲R 2c L c . The substrate holder and the substrate itself have radii of Rh and Rs, respectively. These are some of the critical dimensions associated with the design optimization of the reactor and the reactor geometry variables asso-

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Table 1 Experimental Variables for Microwave Plasma-Assisted Diamond Deposition Reactors Input variables U

Controllable input variables, U1

Reactor geometry variables, U2

Deposition process variables, U3

Internal variables X

Output variables Y

Reactor performance, Y1 Film characteristics, Y2

Deposition pressure Incident microwave power Feed gas composition Substrate temperature Total flow rate Applicator size and configuration Substrate holder location and size Electromagnetic mode and cavity tuning Quartz dome geometry Substrate material and size Substrate seeding and nucleation procedure Deposition time Absorbed microwave power Plasma volume Absorbed power density Linear growth rate Total growth rate Carbon conversion efficiency Film uniformity Film structural quality Film morphology Film texture

ciated with the U2 variable set. Lastly, the deposition process variables need to be considered including substrate material and size, seeding or nucleation procedure, and deposition time. 3.

Internal Variables

Examples of experimentally measured internal variables, X, are (1) the power absorbed by the reactor, Pt ; (2) the plasma discharge volume, Vd ; and (3) the absorbed power density, < P> = Pt /Vd . The discharge volume Vd is given by ␲R 2dL d where the active discharge radius is R d and the height is L d . The power absorbed by the reactor, Pt , is defined as the difference between the incident microwave power, Pinc , and the reflected power, Pref , i.e., Pt = Pinc ⫺ Pref . The discharge is usually separated from the discharge chamber walls and thus Vd < Vc . The discharge volume Vd is often adjusted (see Fig. 2) by varying the power absorbed so that deposition uniformity is

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achieved over the substrate surface. Other internal variables include neutral gas temperature, electron density and temperature, radical species concentrations, and gas residence time. 4.

Output Variables: Reactor Performance and Deposited Film Characteristics

A number of reactor process/performance figures of merit have been adopted to enable the evaluation of deposition process performance. These figures of merit, Y1 , are defined as follows: 1. 2. 3.

Linear growth rate (␮m/hr) is defined as the thickness increase of the diamond film (␮m) divided by deposition time (hr). Total growth rate (mg/hr) is defined as the weight increase of the substrate (mg) divided by deposition time (hr). Carbon conversion efficiency (CCE) is defined as the percentage of carbon atoms in the input gases that are converted into diamond. The equation for carbon conversion efficiency is CCE = Nfilm /Ninput where Nfilm is the number of carbon atoms in the deposited film and Ninput is the number of carbon atoms that entered the discharge chamber in the input gas flow.

The deposited film characteristics, Y2 , can include a wide range of properties including film uniformity, texture, morphology, thermal conductivity, electrical properties, and optical properties as well as others. The film characteristics that will be most closely tied to the microwave CVD machines in this chapter include film uniformity, film texture, and film morphology. The other film characteristics are examined in more depth in other chapters of this book. 5.

Quantifying the Input, Internal, and Output Variable Relationships

The sections that follow in this chapter quantify the relationships between the input variables and internal variables, X = f (U ), the input variables and output variables, Y = g(U ), and the internal variables and output variables, Y = h(X). In particular, Sec. IV establishes the range of reactor geometry variables, U2 , and some of the reactor performance relationships, Y1 = g(U2). Section 5 presents the output variables (both reactor performance and deposited film characteristics) as functions of the adjustable input parameters and the internal variables, i.e., Y = g(U1) and Y = h(X). Section VI describes the internal variables and their relationship to input variables based on experimental measurements X = f(U ), and lastly Sec. VII examines in more detail the internal variables based on modeling studies, X = f(U ).

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IV.

MICROWAVE PLASMA SOURCES FOR DIAMOND THIN-FILM DEPOSITION

A.

Basis for Comparison

Many different microwave plasma-assisted diamond deposition machines have been designed including tubular reactors, bell jar reactors, plasma jet reactors, ellipsoid reactors, plasma disk reactors, surface wave sustained reactors, and magneto microwave reactors. This section describes some representative reactors for the various types and gives a limited number of specifications for comparison of the reactors. The set of parameters selected for comparison includes microwave coupling structure, microwave frequency, discharge chamber size, substrate size, input microwave power range, and operating pressure range. The diamond deposition outputs (e.g., deposition rate) from each of the different reactor systems are only briefly described in this section. A detailed comparison of the diamond deposited by each system is not attempted because the different systems described here were designed on the basis of different objectives. Some of these design objectives have included designs focused on creating small inexpensive research systems, high-volume production systems, or low-substrate-temperature deposition systems. More detailed discussions of the actual diamond deposition outputs (e.g., deposition rate, film texture) will be undertaken in later sections of this chapter where the outputs will be studied as a function of input variables such as pressure, input chemistry, and flow rate.

B.

Selected Reactor Structures

1.

Tubular Reactor (NIRIM Reactor)

A schematic diagram of a typical tubular microwave reactor is shown in Fig. 5. The tubular microwave reactor was developed in the early 1980s by Kamo et al. [6] and has become the most common diamond film deposition reactor technology used for basic deposition research studies. As shown, the input gas, which is a mixture of hydrocarbon and hydrogen gas, is dissociated by the 2.45-GHz microwave energy coupled into the quartz tube inserted through a waveguide. A plunger is attached to the end of the waveguide to minimize the reflected power. The substrate is placed on a substrate holder located at the intersection of the tube and waveguide. Typical microwave power levels are 100 W to 1.5 kW and the pressure range is less than 80–100 torr. Typical quartz tube diameters are 4.5 cm or less and the substrate sizes are limited to 2–8 cm2. Tubular reactors are simple reactors to design and low in cost to construct, and as a result they have been used in many research investigations.

Microwave Plasma-Assisted Diamond Film Deposition

Figure 5

2.

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Tubular microwave plasma-assisted CVD reactor. (From Ref. 6.)

Microwave Cavity Plasma Reactor

The microwave cavity plasma reactor (MCPR) [7,8] developed at Michigan State University and Wavemat/Norton in 1986–1995 is shown in Fig. 6. Two design variations are shown including an early version (1987) in Fig. 6a and a later version (1989) in Fig. 6b. The microwave discharge is produced inside a quartz dome which is located at one end of a microwave cavity. The cavity is formed by a cylindrical wall and a movable top short defining the top end of the cavity. The microwave energy is transmitted from a 2.45-GHz microwave generator through a rectangular waveguide to a transition into a coaxial waveguide that ends as a length adjustable excitation probe in the cylindrical cavity. A hemispherical plasma discharge is created and is placed in direct contact of the substrate by adjusting the length of the probe and the location of the sliding short, i.e., L p and L s . The diameter of the microwave cavity is 17.8 cm and the diameter of the discharge region is 9–12 cm. Various substrate holders and substrate sizes can be used ranging from 5 to 10 cm in diameter. The sliding short height L s is most commonly adjusted to a length of approximately 21 cm when a 2.45-GHz microwave excitation is used. This cavity height produces a resonant

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Figure 6 Microwave cavity plasma reactor: (a) early version and (b) later version. (From Refs. 7, 8.)

microwave mode that has been identified as the TM013 mode. Typical power levels are 500 to 5000 W and pressures from 5 to 140 torr. Care is taken in the design of the gas inlet structure and substrate holder structure so that the input gas is well mixed with the discharge and to get uniform gas injection and radially uniform discharge chamber exhaust gas pumping. The substrate holder can be designed with various heights. In addition, various substrate holders have been designed that are thermally floating, cooled, and heated. Figure 6a shows an early version of the reactor, which had a discharge diameter of 9 cm and a smaller substrate diameter. Figure 6b shows an improved reactor version designed for use with up to 10-cm-diameter substrates. Also, this more recent unit operates at higher pressures up to 180 torr and powers up to 6 kW. A larger 915-MHz version of the MCPR with a microwave applicator/cavity diameter of 45 cm was also designed, constructed, and operated (1994 at Norton Diamond Film). This larger design has a discharge diameter of 33 cm and substrate diameter

Microwave Plasma-Assisted Diamond Film Deposition

Figure 6

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Continued

of up to 20 cm. It operates using 8–18 kW of microwave power generated by a 915-MHz power supply. 3.

ASTeX Bell Jar and High-Pressure Microwave Sources

The bell jar microwave plasma-assisted CVD reactor initially developed in 1987 [9,10] is shown in Fig. 7. The basic features of this reactor include a

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ASTeX bell jar microwave plasma-assisted CVD reactor. (From Ref. 9.)

silica bell jar that confines the plasma discharge. The initial designs used a 10-cm inner diameter bell jar and 7.5-cm diameter substrate holder. The microwave power generated by a magnetron supply is transmitted to the reactor using a rectangular waveguide. An antenna couples the energy from the waveguide into the reactor, which is cylindrical in shape. The position of the substrate could be moved and the substrate either was thermal floating or could be heated. The pressure range utilized was 40–70 torr and the power range for this unit was typically 1 kW. By 1992, ASTeX had improved the bell jar design and developed the ASTeX High Pressure Microwave Source (HPMS) as shown in Fig. 8 [10]. The former bell jar that confined the discharge and permitted the transmission of microwave energy was replaced by a silica microwave window. A plasma discharge was formed in the region between the silica window and the substrate holder. The position of the substrate could be adjusted to optimize the discharge-substrate interaction and the subsequent film uniformity

Microwave Plasma-Assisted Diamond Film Deposition

Figure 8

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ASTeX high-pressure microwave source. (From Ref. 10.)

on the substrate. The substrate could be either heated or cooled as needed. The pressure range in which this system operated was from 10 torr to above 120 torr. The power levels used ranged from 1 to 5 kW with later systems able to operate at powers up to 8 kW. The lack of magnetron power supplies above 8 kW at 2.45 GHz prevented the extension of this 2.45-GHz design to even larger areas at the higher pressures. ASTeX designed a 915-MHz system that permitted the use of the higher power 30–60 kW magnetron power supplies [10]. The 915-MHz system had substrate sizes as large as 30 cm. This unit was reported as depositing diamond at a rate of 10 ␮m/hr over a 20-cm-diameter substrate. The mass deposition of diamond approached 1 g/hr. 4.

UC Berkeley Bell Jar Reactor

A schematic diagram of the UC Berkeley bell jar microwave plasma-assisted CVD system [11–14] is shown in Fig. 9. The bell jar is 10.2 cm in diameter

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Figure 9

Bell jar plasma-assisted CVD system. (From Refs. 11–14.)

with an annular gas feed system and gas exhaust system. The substrate utilized had a diameter of 2.5 cm and was supported by a quartz sample holder at the position near the plasma ball. This reactor was used extensively to study diamond deposition from solid-phase carbon sources. 5.

France-LIMHP Bell Jar Reactor

A schematic diagram of the LIMHP reactor studied by Gicquel and coworkers [15] is shown in Fig. 10. The reactor is composed of a quartz bell jar 10 cm in diameter that is surrounded by a 25-cm-diameter Faraday cage that acts as a resonant cavity for the microwave energy. The microwave power is coupled into the Faraday cage via a waveguide and an antenna. The substrate holder, which is 5 cm in diameter, can be moved up and down to obtain an optimum interaction between the plasma discharge and the

Microwave Plasma-Assisted Diamond Film Deposition

Figure 10 Ref. 15.)

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LIMHP-France bell jar plasma-assisted diamond CVD system. (From

substrate leading to good deposition uniformity. The pressure range of this system is 20–120 torr and the input microwave power range is 600– 6000 W. 6.

Ellipsoidal Reactor

A schematic diagram of the ellipsoidal reactor developed by Funer et al. [16] is shown in Fig. 11. The microwave cavity is ellipsoid in shape with the microwave power input being located at the top. The power input from the waveguide to the cavity is done using a probe antenna. The design goal in this structure was to maximize the microwave electric field strength at the location where the plasma is desired, i.e just above the substrate. Using the ellipsoidal shape maximized the fields in this region by locating the end of the antenna at one focus of the ellipsoid and the desired plasma location at the other focus. This reactor configuration was constructed at both 2.45 GHz and 915 MHz. The 2.45-GHz system used 3–6 kW of power for operation in the pressure range from 35 to 150 torr. The substrate size for this system was 5–7.5 cm. The 915-MHz system was used to deposit diamond on 5- to 15-cm diameter substrates. The power for the 915-MHz system was 20–60 kW for the pressure range 35–150 torr.

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Figure 11

7.

Ellipsoid microwave plasma reactor. (From Ref. 16.)

Surface-Wave Microwave PACVD Reactor

A diagram of a surface-wave microwave plasma-assisted reactor [17,18] is shown in Fig. 12. The microwave energy is transmitted to the reactor through a waveguide to the waveguide surfatron. The discharge is confined in a fused silica vessel. The plasma is created and stabilized by adjusting the coaxial tuning stub and the waveguide tuning stub. The reactor operates at pressures of 1–60 torr with input power on the order of 1 kW. The substrate holder is heated and made with a molybdenum susceptor. The vertical position of the substrate holder is adjustable. The reactor size is a 2.5 cm inside diameter quartz tube and the substrate size is 2 cm in diameter. The surface-wave microwave plasma-assisted reactor was also scaled to 915 MHz [19]. The substrate holder diameter used in this configuration was 8.0 cm. 8.

Microwave Plasma Jet Torch System

Figure 13 shows a microwave jet torch reactor developed by Mitsuda and coworkers [20,21] starting in the late 1980s. The unit consists of a rectangular waveguide, a microwave transition unit, and a coaxial waveguide. The coaxial waveguide consisted of a 5.72-cm-diameter outer conductor and 2.0cm-diameter center conductor. Microwave energy was generated by a 2.45GHz generator with an output of 3.8–4.2 kW. The input gas mixture used consisted of hydrocarbon, hydrogen, and argon that flowed radially into the coaxial waveguide section and then passed through a nozzle (2.2 cm in diameter) and out of the reactor. A plasma jet was generated near the nozzle

Microwave Plasma-Assisted Diamond Film Deposition

Figure 12 18.)

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Surface-wave microwave plasma-assisted CVD reactor. (From Refs. 17,

at atmospheric pressure and the resulting dissociated species arrive at the substrate. The substrate/deposition area was 2.5–5 cm2. This design, because of the high pressure, yielded linear diamond growth rates of 30 ␮m/hr. This is one of the highest diamond deposition growth rates reported using microwave plasma excitation. 9.

Magnetomicrowave and ECR Plasma CVD Reactor

A primary motivation for the deposition of diamond at low pressures is to achieve deposition at low substrate temperatures and across large areas. By lowering the pressure, gas heating is reduced and hence the substrate heating is reduced. In addition, at lower pressures the plasma discharge size is larger for a given input power and the plasma also diffuses more freely without volume recombination. At lower pressures microwave plasma sources are often operated with the addition of magnetic fields to improve microwave power coupling to the discharge. The addition of magnetic fields of sufficient strength allows collisionless heating of the electrons by the microwave fields to occur via the electron cyclotron resonance (ECR) mechanism. The use of magnetic fields in reactors with respect to diamond deposition was summarized by Bachmann [10]. He indicated that at pressures exceeding 7 torr the electron collision rate in the plasma is too high to permit substantial

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Microwave plasma torch CVD reactor. (From Refs. 20, 21.)

ECR heating. It was also noted that the magnetic fields hardly affect the deposition results at these higher pressures. Further, it was noted that at pressures of 75 mtorr and below, where ECR starts to become important, the diamond growth is significantly affected and it becomes difficult to grow well-defined polycrystalline diamond without getting a mixture of other graphitic–amorphous carbon phases. Well-defined polycrystalline diamond films were deposited by Mantei and coworkers [22–24] using a magnetomicrowave plasma CVD reactor operating at 1–3 torr as shown in Fig. 14. This reactor was built and investigated for the low-temperature deposition of diamond films. As shown, a magnetic field was established using a 15-cm-diameter, 9 cm high NdFeB permanent magnet with a magnetic flux density of 0.42 tesla at the magnet pole face. The discharge was operated with either CW microwave energy or pulsed microwave energy. The substrates used were 2.5 cm in diameter.

Microwave Plasma-Assisted Diamond Film Deposition

Figure 14

V.

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Magneto-microwave plasma CVD reactor. (From Refs. 22–24.)

DIAMOND DEPOSITION PROCESSES/CHEMISTRIES IN MICROWAVE PLASMA-ASSISTED CVD REACTORS

This section describes the operation of microwave plasma-assisted diamond CVD reactors with respect to discharge chemistry. The focus in this section is on nongeometric input parameter variations. Whereas the previous section described reactors of various sizes, shapes, and designs, this section focuses on the general operation of microwave CVD reactors with respect to a variety of nongeometric input parameters including input gas composition, flow rate, and effect of impurities. The growth of diamond films can be divided into a two-step process beginning with substrate surface treatment or nucleation and followed by the growth process. Nucleation can be initiated through one of a number of processes including substrate surface scratching and bias-enhanced nucleation (BEN). The BEN process is usually performed in the same diamond

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deposition reactor as the diamond growth process. The BEN process consists of applying a bias voltage to the substrate to nucleate or start the diamond growth. This process is typically performed with a specific recipe that includes the bias voltage, bias time, and carbon percentage in the feed gas. The diamond deposition reactor operating conditions are then changed once the nucleation step is completed to facilitate diamond growth on the substrate. This section, as well as the rest of this chapter, focuses on the diamond growth process on a prenucleated substrate surface. Specifically, reactor design and operating conditions for bias-enhanced nucleation are not considered further in this chapter. The diamond growth process and results are discussed in this section with an emphasis on deposition done in microwave diamond CVD systems. In particular, the influence of gas chemistry, gas impurities, deposition pressure, and substrate temperature on the growth rate, quality, and texture of diamond deposited in microwave CVD systems is covered. Using the control formulation described in Sec. III.B, this section quantifies when possible the relationships between the controllable input variables, U1 , and the diamond deposition outputs, Y, for microwave diamond CVD systems.

A.

Simplified Surface Reaction/Growth Description for Microwave Plasma-Assisted CVD

The primary function of the microwave discharge is to create the radical species that participate in the growth of diamond. For example, diamond growth by using a hydrogen-methane mixture requires both atomic hydrogen and carbon-containing radicals. The microwave discharge serves to dissociate some of the molecular hydrogen into atomic hydrogen and to dissociate the methane molecules into CH3 and possible other radicals such as CH2 and CH. A general view of the deposition process [25] is one where atomic hydrogen is bonded to almost all of the surface. The primary mechanism that opens sites on the surface is abstraction of surface-terminating hydrogen by atomic hydrogen. The reaction and associated rate, Rabs⫺H , is given by CdH ⫹ H → C * d ⫹ H2 Rabs⫺H = k 1[H] where k 1 is the reaction rate constant and [H] is the atomic hydrogen concentration (flux) at the surface. The abstraction results in an open site on the diamond surface, which can be filled by either the adsorption of another atomic hydrogen or a carbon radical species (e.g., CH3). The reaction and associated rate, RadH , of hydrogen adsorption onto an open site, C * d , is

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C d* ⫹ H → CdH RadH = k 2 [H] A growth species can also be adsorbed on to the surface with the reaction and associated rate for an open surface site given by C* d ⫹ CH3 → CdCH3 RadC = k 3 [CHx ] Once the growth species is on the surface, it can proceed along one of two primary paths. The first path is thermal desorption from the surface leading to an open site on the surface again. The reaction and associated rate for a given adsorbed site are CdCH3 → C d* ⫹ CH3 R des = k 4 The other pathway is the incorporation of the adsorbed carbon species into the diamond structure. The general event that begins this mechanism in growth models is an abstraction of a hydrogen from the adsorbed carbon species. CdCH3 ⫹ H → CdCH2 ⫹ H2 Rabs⫺CHx = k 5 [H] When the species adsorbed on the surface is CH2 , the carbon is believed to change to having two carbon-carbon bonds. Subsequent hydrogen abstraction and carbon incorporations complete the incorporation of the original carbon atom into the diamond crystal. The conditions that determine the rate of the five mechanisms listed above are surface temperature, gas-phase atomic hydrogen concentration at the surface, and gas-phase carbon radical concentration at the surface. In steady-state conditions, this set of reactions can be combined to give a growth rate G given by [25,26] G = k3

ns nd

冉

k1 k1 ⫹ k2

冊

[CH3][H] k4 ⫹ [H] k5

(1)

where ns is the surface site density (2.61 ⫻ 10⫺9 mol/cm2 on (100) surfaces) and nd is the molar density of diamond (0.2939 mol/cm3). During the deposition process, the surface is understood to be covered nearly 100% with atomic hydrogen as carbon radicals are being deposited in the diamond (sp3) phase. Low hydrogen surface coverage results in sp2like terminations on the diamond surface, which lead to defects and if the

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hydrogen coverage is low enough graphitic/amorphous film deposition. An empirical model [25] for the defects, Xdef , incorporated during diamond growth is Xdef ⬀

G [H]n

where n is an empirical fit that is often selected at n = 2. For n = 2 the simplest defect concentration model is given by Xdef ⬀

[CH4 ] [H2 ]

Hence, the higher quality (lowest defect density) diamond is deposited when the carbon species concentration in the input gas flow (e.g., methane concentration/hydrogen ratio) is low. Other work [4,27] has established the condition for achieving diamond growth. One necessary condition is to produce a flux of atomic hydrogen on to the surface that exceeds the carbon incorporation rate into the film by a factor of approximately 7000–11,000. Hence a key function of the plasma discharge in microwave CVD reactors is to provide a flux of atomic hydrogen that exceeds the carbon incorporation rate by a factor in the range of 104. To summarize, the many processes occurring on the diamond surface include adsorption of atomic hydrogen and carbon-containing species, hydrogen abstraction from the surface, and desorption of carbon radicals from the surface. The important variables for the diamond deposition process, including the microwave plasma-assisted CVD systems being considered in this chapter, are (1) substrate temperature, (2) atomic hydrogen flux, (3) carbon radical flux and composition, and (4) other ‘‘impurity’’ species fluxes. The rest of this chapter focuses on the discharge chemistry and diamond deposition results for microwave plasma-assisted CVD systems. Microwave plasma-assisted diamond CVD reactor performance as described earlier in Sec. III.B can be looked at either as the input variable settings determining the film properties (the approach used in this section, Sec. V, of this chapter) or as the input variable settings determining the reactor internal variables (e.g., [H], [CH3 ]) and then the internal variables determining the film properties (the approach used in Secs. VI and VII of this chapter). A somewhat reduced process variable model as shown in Fig. 15 is used as the basis for the discussion in the rest of this section. The input variables are input reactant gas composition, input gas flow rate, substrate temperature, input microwave power, and pressure. The output variables to be assessed include growth rate, diamond film quality, and film texture. The approach in this section is to give a general discussion of the trends for diamond growth in microwave CVD systems for a pressure range

Microwave Plasma-Assisted Diamond Film Deposition

Figure 15 process.

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Reduced variable model of the microwave plasma-assisted CVD

from 1 to 200 torr for a variety of input gas chemistries. The key reactor input parameters and process quantities to achieve diamond deposition uniformly across a substrate surface are as follows: 1. 2. 3. 4.

5. 6.

Establish the desired input gas flow composition and rate. Establish and maintain a uniform and selected temperature across the deposition surface of the substrate. Establish the exit gas pumping rate to get the desired pressure. At higher pressures construct the input gas flow, discharge chamber, and exit gas flow to optimize the flow dynamics for uniform diamond deposition. Construct the reactor to prevent or minimize contamination of the plasma discharge from leaks and reactor materials via wall erosion. Input the microwave power to establish the plasma discharge. Optimize the input power magnitude, discharge chamber size and cooling, microwave power absorption profile, and substrate position to get uniform deposition across the substrate area.

The first generality in understanding the relationship of the deposition chemistry and output variables is the region of diamond growth with respect to input gas composition. The most commonly used input gas mixtures consist of hydrogen-, oxygen-, and carbon-containing molecules. Because the temperatures and activation of the gases in the plasma discharge are extensive, a primary determining factor for the film composition is the C, H, and O atomic molar composition of the input gas, regardless of the exact input

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species molecular composition. A useful summary of the input gas composition appropriate to grow diamond was developed by Bachman et al. in 1990 [1] and further refined in 1994 [28]. The plot in Fig. 16 shows such a ternary C-H-O diagram. The carbon deposition region exists very near and just above the H-CO line connecting 100% H with C-50% and O-50%, i.e., the crosshatched region shown in Fig. 16. The diamond growth region is very narrow to nonexistent on the right end of the H-CO line where [H] approaches zero and becomes wider on the left side of the H-CO line when [H] is larger. Once a specific input gas composition is selected in Fig. 16, the diamond deposition is still a function of a number of other variables. Several other variables are important including pressure, flow rate, and substrate temperature, as described in more detail in the following subsections.

B.

Methane-Hydrogen Deposition Discharge

It is useful first to summarize the general trends for diamond deposition using the simplest discharge chemistry consisting of methane and hydrogen. To do this, some background needs to be developed first. The diamond growth proceeds in a methane-hydrogen discharge as described earlier in this section primarily to supply the [H] flux to the substrate surface and carbon radical flux to the surface. The most important carbon flux in the microwave plasma considered here is the CH3 methyl radical. To deposit diamond, the [H] flux to the surface is quantified as being 7000 to 10,000 times larger than the carbon flux that is incorporated in the growing film [4,27]. When the [H] is larger than this factor, diamond is deposited on a diamond surface. Further, the larger the [H]/[CH3 ] ratio is at the growth surface, the less sp2-bonded carbon and defects are incorporated into the film and the higher is the diamond quality. The other general observation is that the growth rate is proportional to the [CH3 ] flux to the surface as indicated in Eq. (1). The general trends for the growth rate versus temperature, pressure, and methane percentage in microwave plasma-assisted diamond CVD systems are shown in Figs. 17, 18, and 19 respectively. The general trends are 1. 2.

3.

An increase in the growth rate as the pressure is increased [29] as shown in Fig. 17. An increase in the growth rate as the temperature increases up to a maximum, then a drop in the growth rate at higher temperatures [5,30] as shown in Fig. 18. An increase in the growth rate that is linear versus methane percentage at low methane percentages, that is sublinear versus methane concentration for moderate methane percentages, and that

Microwave Plasma-Assisted Diamond Film Deposition

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Figure 16 C/H/O diagram of diamond CVD developed by Bachmann et al. (From Refs. 1, 28.)

saturates versus methane concentration at higher methane concentrations. These trends can be seen in the experimental data shown in Fig. 19. After the saturation value is reached, the growth rate may drop slightly as the methane concentration is increased further. Typically, in this high methane concentration region, nondiamond carbon or diamond with extensive secondary nucleation is predominantly deposited [5,26]. 1.

Growth Rate versus Pressure and Methane Percentage

One objective of this chapter is to quantify some of the experimental data obtained for microwave CVD systems across a wide parameter space. An empirical model for the growth rate G is G ⬃ R␥ where R is the methane fraction. In work by Harris and Weiner [31] the value of ␥ was pressure

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Figure 17 The total weight gain and absorbed microwave power density versus pressure. Note that the data in the 30–80 torr range include 7.5-cm and 10-cmdiameter substrates. The data above 80 torr are for 5-cm-diameter substrates. (From Ref. 8.)

dependent, varying from ␥ = 1 at 20 torr to ␥ = 0.5 at 200 torr. This growth rate model was developed in a hot-filament deposition system. A similar model can be developed for the microwave deposition system. To develop such a model for the microwave system we will consider data across a wide range of pressure and methane concentrations. Some data showing deposition rate versus methane percentage and pressure are shown in Fig. 20 for pressures of 18, 25, 53, and 135 torr [5,26,30,32]. The temperature used for these growth rates is at or near the measured or generally expected temperature range where the growth rate peaks. The methane concentration (#/unit volume) in the plasma discharge is a function of the discharge pressure, the discharge temperature, and the methane percentage in the input gas flow. In a microwave plasma source the discharge gas temperature increases as the pressure increases (see Sec. VI.B), assuming the discharge volume stays approximately constant. The neutral density in the discharge gas is proportional to (pressure)/(gas temperature). An approximate fit to the neutral gas

Microwave Plasma-Assisted Diamond Film Deposition

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Figure 18 Diamond growth rate as a function of deposition temperature and methane concentration. (From Ref. 30.)

density versus pressure is given by density ⬃ (pressure)0.75 (see data in Sec. VI.B). Hence the density does not increase linearly with the pressure because of the gas heating that occurs as the pressure is increased. This is an empirical fit that models the discharge neutral density versus pressure. The full model for the growth rate is GTsmax = Cp0.75 R where C is a proportionality constant, p is the pressure, and R is the methane percentage. Figure 20 shows a plot of this model and experimental data for growth rates in microwave CVD system for deposition pressures from 18 to 135 torr. This model is for the region of methane concentrations where the growth rate varies linearly with R. The growth rate increases linearly versus the methane concentration for low methane concentrations, but increases beyond this linear region are characterized by the growth rate changing sublinearly versus methane increases as shown in Fig. 19. This can be understood by looking deeper at the carbon chemistry in the plasma discharge. The linear region at low methane concentrations is characterized by the growth species in the plasma

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Figure 19 Linear growth rate of diamond versus methane concentration. (From Refs. 5 (a) and 26 (b).)

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Figure 20 Comparison of growth rate model with experimental data from Refs. 5, 26, 30, and 32. The growth rate model equation is (growth rate = Cp0.75R). This model is valid for low methane concentrations and for a range of substrate temperatures near the substrate temperature that gives a maximum deposition rate.

(CH3) increasing linearly with the methane concentration. Once the methane concentration becomes large enough, the CH3 concentration no longer increases linearly with the methane concentration as shown in Fig. 21 [26]. The gas-phase chemistry present in the discharge converts much of the CH4 to C2H2. This boundary where the CH3 percentage changes from a linear relationship versus methane concentration to a sublinear relationship varies as a function of pressure. A plot of the region of linearity versus pressure is shown in Fig. 22 based on experimental data [5,26,30,32]. The region below

Figure 21 CH3 and atomic hydrogen concentration versus input methane percentage as modeled by Farhat et al. [26] for a pressure of 7000 Pa and a plasma gas temperature of 2850 K.

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Figure 22 Regions of growth rate versus methane percentage as a function of methane percentage and pressure based on the experimental data of Refs. 5, 26, 30, and 32.

the dashed line exhibits a linear growth versus methane concentration. This plot uses data for substrate temperatures in the range where the maximum deposition rate occurs versus substrate temperature. 2.

Quality versus Pressure and Methane Percentage

The quality of diamond films can be defined in a number of ways including the number of incorporated defects and the Raman signal. Quality can also be defined in terms of the intended application for the diamond. Some measures of quality include the number of defects incorporated in the diamond crystals, the number or density/rate of secondary nucleation sites, the size of individual crystals in the polycrystalline film, and the nature of the grain boundaries. The general trend is that the larger the hydrogen flux is to the surface and the slower the growth rate (carbon incorporation into the growing film), the higher is the quality. In terms of the Bachmann diagram, the closer the plasma composition moves toward the C-O line, i.e., toward the no-growth region, the higher the quality of the deposited film. Because the definition of diamond film quality often depends on the intended application of the film, a simple definition of quality will be adopted here. This definition of quality has two regimes: the higher quality deposition regime, which has well-defined crystals, and the lower quality regime, which does not have well-defined crystals; i.e., it is extensively renucleated and often referred to as cauliflower-like films. Alternatively, a quality transition can be defined as the transition from a low secondary nucleation value, where well-defined crystals are formed, to a high secondary nucleation value, where cauliflower-like growth occurs. This region of

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high-quality growth in a methane percentage and pressure parameter space is shown in Fig. 22 based on experimental data [5,26,30,32]. It is the region below the solid line in the figure. The cauliflower diamond growth region is above the solid line in Fig. 22. 3.

Growth Rate versus Substrate Temperature

The deposition rate of diamond from methane-hydrogen gas mixtures generally shows a maximum rate versus substrate temperature as seen earlier in Fig. 18. The temperature range of this peak is in the range 850–1150⬚C with the location of the maximum deposition rate being dependent on the pressure. Experimental results [5,26,30,32] have shown that the maximum growth rate temperature, Tmax , increases gradually with pressure as shown in Fig. 23. Some specific data for the growth rate versus substrate temperature that yields the maximum growth rate include work by Gicquel et al. [30] at 18 torr that gave peak values for substrate temperatures of 850– 950⬚C, Kondoh et al. [33] at 30 torr that gave peak values for substrate temperatures of 900–1000⬚C and Kuo [5,29] at 135 torr that gave peak values for substrate temperatures of 1050–1150⬚C. In even higher pressure, nonmicrowave CVD processes, the substrate temperature of maximum deposition rate at atmospheric pressure is 1200⬚C in work by Snail and Marks [34]. At temperatures less than Tmax , the growth rate dependence on substrate temperature is generally modeled with an Arrhenius expression using an associated activation energy Ea . The general growth rate expression is G ⬀ exp

冉 冊 ⫺Ea RT

Figure 23 Substrate temperature for maximum growth rate, Tmax , i.e., the shaded region, versus pressure from Refs. 5, 26, 30, and 32.

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where G is the growth rate, R is the gas constant, and T is the temperature in kelvin. In the temperature range 440–510⬚C, Ulczynski et al. [35] reported an activation energy of 14.6 kcal/mol in the pressure range 5–15 torr. Kondoh et al. [33] using a hot-filament system reported an activation energy of 23 kcal/mol. The data of Gicquel et al. [30] in the temperature range 700–850⬚C showed an activation energy in the range 11–16 kcal/mol. In fact, many results from growth rate measurements of polycrystalline diamond deposition show activation energies of 15–30 kcal/mol [4]. 4.

Growth Rate versus Flow Rate

A key parameter determining the importance of the flow rate is the residence time of the feed gas in the deposition chamber. The residence time, t, is given by t = V/F where V is the discharge chamber volume and F is the flow rate scaled to the pressure in the chamber. Example residence times in a typical discharge chamber range from 1 sec to a few minutes. For example, a 200 sccm (STP) flow is 7600 cc/min at 20 torr and 1000 cc/min at 150 torr. So if the discharge chamber volume is 1 L (1000 cm3) the gas residence time is about 8 sec at 20 torr and 60 sec at 150 torr. While the feed gas is within the plasma discharge region, it is undergoing chemical reactions and some of the carbon is being deposited as diamond on the substrate. A measure of how much of the carbon in the input feed gas is deposited on the diamond substrate is the carbon conversion efficiency. The carbon conversion efficiency increases as the flow rate is reduced as shown for some experimental data in Fig. 24 [29,36,37]. In terms of the effect of this carbon consumption (or sink) on the gasphase chemistry, lower flow rates lead to a gas-phase composition of the discharge that has a lower carbon content than present at higher flow rates. For example, if the input flow has a carbon input of 0.01 mole fraction and the carbon conversion efficiency is 25%, then the exit gas has a carbon concentration of 0.0075 mole fraction. Because of the long gas residence time in typical discharge chambers for diamond growth, the exit gas composition can be considered a close approximation of the carbon mole fraction in the chamber. Hence, to first order a lower flow rate is equivalent to a lower carbon concentration. This is particularly true when the carbon conversion efficiency is high. However, the possible anticipated higher quality diamond expected from lower carbon concentrations (i.e., lower flow rates/ higher carbon conversions) is often not observed because another effect of

> Figure 24

Carbon conversion efficiency versus flow rate. (From Refs. 36, 37.)

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lower flow rates and the associated longer gas residence times is that any leaks or chamber wall erosion will lead to larger impurity concentrations in the gas discharge. Such impurities can alter and sometimes degrade the deposited film process and properties. An example of the influence of flow rate is the work by Ralchenko et al. [37]. A microwave system using methane and hydrogen at 100 torr, 2.45 GHz and a substrate temperature of 720⬚C was utilized to grow diamond at flow rates ranging from 60 to 1000 sccm. They found the highest quality diamond films intended for millimeter wave windows were deposited at the higher flow rates. This result is suggestive of some impurity in the deposition process being reduced by the higher flow rate. 5.

Growth Rate versus Deposition Time

The growth rate as a function of the time is not constant for the entire duration of the film growth process. Initially the growth rate is slow as the film first nucleates and grows to cover the entire surface of the substrate. Next the growth rate increases as the film texture is formed and the crystals oriented with their fastest growth direction perpendicular to the substrate surface outgrow the other less favorable crystal orientations. Finally, once the film has become well textured, the growth rate becomes constant versus time. This phenomenon is indicated in Fig. 25a for growth at a pressure of 135 torr for 120 h [5]. The same effect was demonstrated in the work of Ralchenko et al. [37] at a pressure of 100 torr as shown in Fig. 25b. 6.

Dependence of Film Texture and Growth Parameter ␣ on Discharge Chemistry

As diamond grows, the shape of the crystals depends on the growth rate of the various surfaces of the crystals. A useful measure for understanding the relationship of growth on various surfaces is to study the growth along some of the primary directions in the diamond crystal structure. One finds that the growth rate along the three directions [100], [110], and [111] changes as a function of gas chemistry and substrate temperature [38]. The growth rate along the [110] direction is generally the fastest. As a result the {110} surfaces are rarely seen in the polycrystalline films grown in CVD reactors, including microwave reactors. This occurs because any (110) surfaces will grow out quickly, leaving other surfaces with slower growth rates defining the crystal. The growth rate in either the [100] direction or the [111] direction is next fastest depending on the growth conditions. Maeda et al. [39] did a study of the growth rate along these two directions in a microwave CVD

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Figure 25 (a) Linear growth rate of as a function of deposition time [5]. (b) Growth rate versus film thickness. (From Ref. 37.)

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reactor. The study (Fig. 26) was done so that the growth rates along the [100] and [111] directions were measured as a function of methane concentration and substrate temperature. A useful parameter for understanding how the growth rates along the various directions determine the crystal shape is the growth parameter ␣ defined as

␣ = 兹3

V100 V111

where the growth rates along the [100] and [111] directions are given by V100 and V111 , respectively. When ␣ = 1 or less, the [111] direction grows quickly and the individual isolated crystals formed are cubes with (100) surfaces as shown in Fig. 27. Fig. 27 shows the diamond crystals that grow for values of ␣ ranging from ␣ = 1 to ␣ = 3 [40]. Also shown in Fig. 27 is the direction of fastest crystal growth for the various ␣ parameter values. The direction of fastest growth is indicated by the arrow by each cubooctahedral shape. For ␣ = 3 or larger, the [100] direction grows most quickly and the crystal shape formed has (111) surfaces. Conversely, for ␣ = 1 or less, the [111] direction grows most quickly and the crystal shape is formed by the more slowly growing (100) faces. In the case of ␣ = 1 or less, the longest direction in the crystal is the [111] direction. For ␣ = 3 or larger, the longest direction in the crystal is the [100] direction. At an intermediate value of ␣ = 1.5 the longest direction in the crystal is [110]. A plot of the ␣ parameter versus methane concentration and substrate temperature from the work of Maeda et al. [39] is shown in Fig. 28. The picture becomes more complicated when a polycrystalline film is grown because many crystals intersect and overgrowth occurs. The growth rates along the [100] and [111] directions determine the texture of the film and the surface morphology of the film. The texture of the film is the crystal direction that is longest in the individual crystals of the polycrystalline film. The texture in polycrystalline diamond films develops because of the crystals which have an orientation that has a direction of fastest growth perpendicular to the substrate surface. These crystals overgrow the crystals with other orientations. This is shown in Fig. 29, where a random orientation of small crystals is shown at the bottom of the film. As the film grows, the crystals that grow with their direction of fastest growth perpendicular to the surface become taller than their competitor crystals. Ultimately, these crystals with their fast growth direction normal to the substrate in Fig. 29 overgrow the competition, ending the possibility of further growth of the other crystals with less preferred orientations. A reliable measure of the ␣ parameter can be obtained using a texture analysis of the polycrystalline films from x-ray diffraction measurements.

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Figure 26 Growth rate along the [100] direction (a) and along the [111] direction (b) versus substrate temperature for various methane concentrations. (From Ref. 39.)

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Figure 27 The cubo-octahedral shapes that result as the ␣ parameter is varied from 1.04 to 2.85. These are the shapes for isolated crystallites. (From Ref. 40.)

Measurements of the velocity of growth of diamond along various crystalline directions in microwave CVD systems have been made in work by Wild, Koidl, and their colleagues [41,42] as shown in Fig. 30 and by Maeda et al. [39] as shown in Figs. 26 and 28. The trend shown in these studies is that as the temperature increases the ␣ factor decreases. Also, these studies in general showed that as the methane percentage is increased, the ␣ factor increases. These figures display the general trends for ␣ only. The exact value of ␣ at a specific substrate temperature and methane percentage may change from reactor system to reactor system because different reactor geometries result in a different relationship between the input, internal, and output variables; i.e., the different reactor geometries discussed in Sec. IV have unique and different Pt , p, and Ts operating curves as discussed earlier in Sec. III.A.3. As will be noted in the following sections on the influence of various impurities, the addition of impurities also affects the growth along various crystalline directions and consequently the ␣ parameter value. The other property of polycrystalline diamond films strongly dependent on the growth rates in various directions is the surface morphology. The surface morphology can be defined as the crystal shapes, orientations, and

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Figure 28 Growth rate ratio ([100]/[111] growth rate ratio) versus substrate temperature for various methane concentrations. (From Ref. 39.)

sizes as observed on the top surface of the growing polycrystalline film. Relating the direction of maximum growth rate and ␣ with the surface morphology of polycrystalline films must be done with great care. To appreciate this relationship, consider some randomly oriented seed crystals grown with ␣ = 1. As the individual crystals grow, they will have a cubic shape similar to the shape shown for ␣ = 1 in Fig. 27. Once the cubes start growing together, the surface will initially have the appearance of many cubes all of random orientation with respect to each other and the substrate surface. As the film grows to a larger thickness, the 具111典 texture forms because for ␣ = 1 the [111] direction grows fastest (see the arrow direction for the ␣ = 1 shape in Fig. 27). So as the film grows perpendicular to the substrate surface, the [111] direction will dominate and clear cube shapes will no longer be clearly seen. Rather, the corners of the cubes formed by overlapping and overgrowing crystals will be seen on the top surface. As a general statement, what the surface of films thick enough to have developed texture looks like can be roughly estimated as that seen by looking back down along the direction of the arrow for the crystals in Fig. 27. Commonly, films with square {100} facets are desired, and these can be formed in two basic ways. The first way is to operate with ␣ near 1. This will produce the square shapes during the initial stages of growth when the film thickness is only on the order of the initial spacing between the seed

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Figure 29 Sketch of polycrystalline diamond film growth from isolated, randomly oriented crystals shown at the bottom of the figure. The dashed lines indicate the grain boundaries. The solid lines show the surface of the film at selected times. (From Ref. 40.)

crystals or nucleation sites. Specifically, randomly oriented seed crystals will grow into small cube shapes with ␣ = 1. Continued growth under low secondary nucleation conditions will form a 具111典 texture because this direction grows the longest dimension (fastest). So observing square (100) facets when the films are thin may indicate values near ␣ = 1. The square facets in this case have orientations that are not well aligned with the substrate surface, i.e., faces parallel to the growth surface. Another way to form square facets is to grow a thick film with a 具100典 texture. This is done by using ␣ value slightly less than 3. As the film grows thick, the texture forms and the [100] directions are perpendicular to the substrate surface. The value of ␣ slightly less than 3 leads to the square tops on the crystals in the film. See, for example, the square tops on the crystal shapes for ␣ = 2.0 and ␣ = 2.25 in Fig. 27. These square facets are well aligned parallel to the surface of the growing film because of the strong texture of the film. This is the growth condition that leads to smooth coplanar (100) faceted films. So care must be used in interpreting the ␣ parameter value from just the examination of the surface morphology of polycrystalline films.

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Figure 30 Growth parameter (␣) versus methane concentration for three substrate temperatures. An ␣ parameter of 1.5 gives a 具110典 texture and an ␣ parameter of 3.0 gives a 具100典 texture. (From Refs. 41, 42.)

Once the ␣ parameter has been mapped, two-step processes [43] have been developed that use an ␣ = 3 or near 3 to grow highly 具100典 textured films during the initial growth phase. This gives the film structure shown in Figs. 31a and 32b. Then for the second growth phase the growth conditions are changed so that the ␣ parameter is reduced in value. This increases the relative growth rate of the [111] direction relative to the [100] direction and the film growth fills in the valleys located between the (100) faces present in the initial growth phase. The resulting film has a top surface covered with (100) facets all reasonably parallel with the substrate surface as shown in Figs. 31b and 32b. Another factor that influences the surface morphology is the extent and influence of twinning that can occur. Wild and coworkers [42] indicated that the ␣ parameter also influences the formation and effect of twinning. They found that for ␣ > 2 the {100} facets are stable with respect to twinning.

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Figure 31 Schematic drawing of a two-step diamond deposition process. Step one grows the film so that is has a 具100典 texture, then step two grows the film so that smooth (100) faces dominate the top surface of the film. (From Ref. 43.)

Stable means that if a small twin occurs on a (100) face it will disappear as the film continues to grow. Conversely, an unstable condition is one where a small twin grows larger as the growth continues. The other stability condition noted in their work was that for ␣ < 1.5 the {111} facets are stable with respect to twins with an inclined twin plane. C.

Influence of Oxygen (Hydrogen-Methane-Oxygen Discharges)

The addition of oxygen to the input gas flow, either as molecular oxygen, O2 , or as another gas such as CO or CO2 , can be useful for diamond deposition. The use of some oxygen in the input gas (either O2 , CO, or CO2) generally yields films with larger grain sizes and less sp2 material. Also, the inclusion of oxygen has been shown to increase the deposition rate in some cases and the addition of oxygen allows deposition to occur at lower substrate temperatures.

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Figure 32 SEM pictures of a polycrystalline diamond film after step one (a) and after step two (b and c) as described in the caption of Fig. 31. (From Ref. 43.)

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A basic requirement to achieve diamond deposition is that the C/O ratio must be near one (more specifically, equal to or slightly greater than one as shown earlier in the crosshatched region of Fig. 16). For oxygen-rich discharges no diamond growth occurs and for carbon-rich discharges (except those with large atomic hydrogen concentrations) nondiamond carbon is deposited. Any excess oxygen will etch the carbon from the surface, preventing growth, and any excessive carbon in large amounts is deposited as nondiamond carbon films. In general, a trade-off exists between higher growth rates (and the associated lower quality) that occur on having slightly more carbon versus lower growth rates (and the associated higher quality) that occur at slightly higher oxygen concentrations. Some additional understanding of diamond deposition with oxygencontaining discharges can be achieved by considering the gas-phase chemistry. The highly activated, high-temperature discharge environment of diamond deposition drives the mixture of carbon and oxygen species in the reactor toward primarily a CO molecular composition. If the feed gas mixture has substantial percentages of oxygen and carbon present, most of the oxygen and carbon are converted into CO. Four statements can be made regarding the influence of oxygen on the diamond deposition process: 1. 2.

In general, with the addition of oxygen, the substrate temperature can be dropped 100–150⬚C without a loss of growth rate [10]. The use of oxygen changes the growth rate, under some conditions to a higher rate. Figure 33 shows the growth rate versus percent oxygen (O2) added in the feed gas flow [44]. The deposition conditions used in this study by Weimer et al. [44] consisted of a tubular reactor operating at a 21 torr pressure, 170 W microwave power, and a 97 sccm H2 flow rate. The top portion of the figure shows the growth rate with a 2 sccm methane flow. It can be seen that as the oxygen flow is increased from 0 to 0.06% in the feed gas, the growth rate increases by a factor of 1.6. A similar phenomenon occurs for an acetylene feed gas as shown in the lower portion of Fig. 33. Also observed is that as the oxygen percentage increases further the growth rate drops. This presumably occurs because as the oxygen content in the discharge is increased more CO is generated, leaving less active carbon species available for deposition. Further, as the feed oxygen percentage increases, more oxygen radicals are available to etch the surface. In another study [10] of the influence of oxygen on the growth rate, the gas-phase chemistries near C/O/H = 1:1:1 gave a maximum deposition rate. This can be seen in Fig. 34, where the deposition rate peaks at the C/O/H = 1:1:1 condition [10].

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Figure 33 Diamond growth rate versus oxygen percentage in the feed gas flow. The hydrogen gas flow rate was 97 sccm. (From Ref. 44.)

3.

The oxygen reduces sp2 incorporation in the film and also reduces secondary nucleation, which leads to larger crystals and altered surface morphology. This is believed to occur because of the increased etching effect of oxygen radicals on graphitic structure in the film [45]. It has also been noted by Harker and DeNatale [46] that the crystallite size increases as increasing oxygen content is

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Figure 34 Diamond growth rate versus C/H/O feed gas composition for two pressures of 70 and 140 torr. The feed gas composition of C/H/O = 1:1:1 gave the highest growth rate. (From Ref. 10.)

4.

added to the gas feed due to increased reactive etching rates during deposition that result in decreased crystal defect density. The introduction of oxygen into the feed gas influences the ␣ parameter (growth rates along the [100] and [111] directions), film texture, and film morphology. Figure 35 shows a plot of the parameter ␣ versus methane concentration at a fixed substrate temperature of 800⬚C [42]. The first of two observations to be made is that when oxygen is present in the discharge, variations in the methane concentration produce changes in the ␣ parameter in a manner similar to the no-oxygen case (i.e., ␣ increases as methane concentration increases). The second observation is that oxygen introduction with other conditions held constant produces shifts in the ␣ parameter and hence the texture and surface morphology. The change of ␣ (as indicated by film texture) with changes in the oxygen input flow was also demonstrated by Gu et al. [47]. In their study CO (0–10%) was added to a 100 sccm H2 and 1 sccm CH4 feed gas flow. The deposited films showed a large increase in the (100) XRD peak (more 具100典 texture) as the CO flow increased from 0 to 1%. Further, as the CO flow percentage in-

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Figure 35 Growth parameter ␣ versus methane concentration for two different carbon monoxide concentrations of 17 and 67%. The substrate temperature was constant at 800⬚C. (From Ref. 42.)

creased to 4% and 10% the (100) XRD peak decreased, indicating a reduction in the 具100典 texture. A full mapping of the ␣ parameter dependence on oxygen content, hydrogen content, carbon content, and substrate temperature has not been done [40].

D.

Influence of Nitrogen Gas on Diamond Synthesis

In the mid-1990s it was demonstrated experimentally that the addition of small amounts of nitrogen (N2) gas to the conventional CH4-H2 diamond film synthesis gas has an important impact on the CVD synthesis of diamond films [48–53]. For example [49], high N concentrations result in nanocrystalline and black films containing graphite or amorphous carbon, and very high N concentrations, i.e. 20% N concentration can completely inhibit diamond growth. In contrast, the addition of only 20–100 ppm of nitrogen can have a beneficial effect. At a deposition pressure of 20–60 torr, an N

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concentration of only a few tens of ppm stabilizes the formation of smooth, 具100典 textured diamond films. In particular, Locher et al. [48] using a tubular reactor demonstrated that at intermediate methane concentrations (1–2%) at 37 torr, the addition of several tens of ppm of N2 stabilized the formation of smooth 具100典 textured diamond films. When no nitrogen was added with the CH4 percentage held equal to 1.5%, the film deposited had fine grains indicative of a high secondary nucleation rate or high twinning rate. When the nitrogen input level has set to 60 ppm, well-defined (100) faceted crystals grew with 具100典 texture. The introduction of nitrogen also increases the growth rate along the [100] direction which shifts the ␣ parameter to a higher value. This was also shown in the tubular reactor experiments of Jin and Moustakas [49]. The texture of the films shifts from 具110典 to 具100典 when tens of ppm to a few hundred ppm of nitrogen is added. This is further demonstrated in a homoepitaxial study by Wild et al. [50], who showed that the addition of 10–50 ppm of nitrogen increased the [100] growth rate much more than the [111] growth rate. Hence, the addition of small amounts of N2 to the deposition process can be used to stabilize the 具100典 growth surface. At higher deposition pressures and higher input power densities, the deposition rate was observed to increase by a factor of 3–5. Muller-Sebert et al. [51], employing a tubular reactor that operated at a pressure of 167 torr, a deposition temperature 830⬚C, and a methane concentration of 3%, demonstrated that the addition of only 25 ppm of nitrogen changed the growth rate from 2.6 to 13 ␮m/hr. Asmussen et al. and Ayres et al. [52], using a microwave cavity plasma reactor as shown in Fig. 6b, also studied the influence of nitrogen concentration from 5 to 1000 ppm at pressures of 38 and 50 torr. They noted a variation in growth rate of less than 10% over the range 5–1000 ppm. The substrate temperatures used in this study were T = 850⬚C at 38 torr and T = 910⬚C at 50 torr. Examples of how the nitrogen addition influenced the surface morphology are shown in Fig. 36. These experiments indicate that, as in the tubular reactor experiments, the addition of small amounts (200– 400 ppm) of nitrogen stabilizes the growth of high-quality 具100典 faceted films. However, the actual threshold nitrogen concentrations and the variation in these threshold concentrations versus the other independent experimental variables differ considerably from the tubular reactor performance, suggesting that reactor geometry has an important impact on the deposition process in the presence of nitrogen impurities. It is also interesting to note that even though nitrogen has a strong effect on the growth process, only a very small amount of the nitrogen is actually incorporated into the film [49,53]. Typical values for the incorpo-

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Figure 36 SEM images of nine samples deposited with 200 sccm flow rate, 38 torr pressure, and 1% methane. Nitrogen gas-phase concentration and diamond Raman signal peak width are given at the top of each micrograph. (From Ref. 52.)

ration probability are 2 ⫻ 10⫺4 for the {100} faces and 7 ⫻ 10⫺4 for the {111} faces [53]. E.

Chlorine- and Fluorine-Based Deposition Chemistries

Diamond has been deposited with halogen gases and halogen-containing gases included in the feed gas flow. Halogen-containing gas mixtures including CF4 , Cl2 , CH3F, CH3Cl, C2H2Cl2 , C2H5Cl, C3F8, and others have been used to grow diamond [10,54]. Some of the advantages of using hal-

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ogens as noted in the literature include enhancement of growth rate, improvement of diamond quality, and reduction of growth temperature. The role of chlorine or fluorine in the deposition process is believed to be due to hydrogen abstraction from the surface. A model [55] for fluorine and chlorine is that the abstraction of the hydrogen from the surface is done more quickly by atomic fluorine and atomic chlorine at lower temperatures. This opens up sites more often for the attachment of a carbon species (such as CH3). The region of diamond growth for the C/H/Cl system in a microwave CVD system [10,56] occurs for a mixture of predominantly hydrogen with carbon composition percentages of 2–3% or less and chlorine composition percentages of 40% or less to get diamond. The region of diamond growth for the C/H/F gas composition was again for a mixture of predominantly hydrogen with C percentages of 2% or less and a fluorine composition percentage of 12% or less. The advantage of using halogen to lower the deposition temperature in hot-filament systems is well documented. Such an advantage is less clear in microwave CVD systems. Bachmann et al. [10,56] reported studies of C/H/F and C/H/Cl systems in which no distinct advantage in terms of growth rate or lower deposition temperature was found as compared with the C/H/O system. F.

Inert Gas/Methane/Hydrogen Deposition Chemistries

Two basic influences of adding a noble or inert gas to the input gas flow for diamond deposition have been identified. The first is an enhancement of the atomic hydrogen and the growth species CHx concentration in the plasma discharge by the addition of Xe. This work was done by Hosomi and coworkers [57]. They observed an increase in the deposition rate of diamond on adding 1% Xe to the feed gas composition of 1 part methane and 99 parts hydrogen. They used a microwave CVD system operating at 800 W 2.45 GHz, and 40 torr. The low excitation energy level of Xe resulted in a plasma discharge with a higher electron density. This then produced more atomic hydrogen and CH3 and a 50% increase in the deposition rate with the Xe addition. The second influence of inert gases occurs when large quantities of a noble gas are added to the input gas flow. In a series of studies [58,59] at Argonne National Laboratory, large percentages of argon in the input gas flow together with low hydrogen percentages have been used to deposit nanocrystalline diamond. Work by the Argonne group has shown that for Ar/H2 /CH4 (1% CH4) discharges the transition from a discharge containing no argon (hydrogen dominant) to one containing no hydrogen (argon dom-

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inant) is accompanied by fundamental changes in the plasma chemistry, growth process, growth rate, and deposited film properties. However, throughout the entire variation of hydrogen-argon compositions with a small percentage of methane (⬃1%), diamond is grown. The plasma chemistry is observed to change from a plasma dominated by CH3 and H radicals at high hydrogen concentrations to a plasma having a high C2 concentration at high argon concentrations. Corresponding to the discharge chemistry changes, the diamond growth scenario for 70–99% hydrogen is dominated by the CH3 growth species, for the 20–70% hydrogen region the growth rate is dominated by the C2H2 species, and for the low hydrogen content region (less than 20%) the growth is dominated by the C2 species [59]. The C2 species is postulated as both a diamond growth species and a diamond nucleation species. The use of a predominantly argon discharge with small amounts of CH4 (⬃1%) and small amounts of hydrogen (0 to a few percent) permits the deposition of very smooth diamond films with randomly oriented 3- to 10-nm crystallites of diamond. Such diamond is referred to as nanocrystalline diamond.

VI.

INTERNAL VARIABLES

Several researchers have studied the internal variables in microwave plasmaassisted CVD diamond deposition reactors. These studies have quantified some of the relationships of input to internal variables. Some of the internal variable quantities measured have been species concentrations, gas temperature, electron density, electron temperature, and microwave power absorption density versus various input parameters. In this section these internal variable studies are reviewed with an emphasis on the studies that quantified the internal variable values. In particular, optical emission studies that provide only relative signal levels or relative concentration levels are not considered in this review. A.

Species Concentrations

Mitomo and coworkers [60] used in situ Fourier transform infrared (FTIR) spectroscopy to measure the molecular species concentrations in the microwave discharge region. In their study they used a number of different input gas mixtures including CH4 ⫹ H2 , C2H2 ⫹ H2 , C2H4 ⫹ H2 , CH3OH ⫹ H2, C2H5OH ⫹ H2 , CO ⫹ H2 , CCl4 ⫹ H2 , and CH4 ⫹ O2 ⫹ H2 for the discharge. The reactor was a tubular unit, shown in Fig. 5, operated at 2.45 GHz with a 4-cm-diameter tube, 30 torr pressure, and 300 W microwave power. The carbon-containing species observed using FTIR included CH4 , C2H2 , C2H4,

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and CO. The CH4 and C2H2 species were observed under all the conditions studied, while C2H4 was observed only when higher concentrations of carbon input gases were used. Lastly, CO was produced and measured when oxygen was present in one of the input molecular gas species. The species CH3OH, C2H5OH, and CCl4 were not seen in the discharge, indicating that plasma conditions were effective at dissociating these molecules. As shown in Fig. 37, when the input gas contained no oxygen the dominant species for low percentages of input carbon gas flow (i.e., 0.5% or less) was methane and the dominant species for percentages above 0.5% was acetylene. This was true regardless of the molecular form of the input gas. Another observation was that the addition of oxygen to the discharge reduced the concentrations of CH4 and C2H2 in the discharge as compared with the levels when no oxygen was present. However, the CO species concentration increased as oxygen was added. Hence, the discharge conditions in microwave CVD

Figure 37 Concentration of CH4 , C2H2 , and C2H4 in a microwave discharge region as measured by FTIR absorption spectroscopy versus percent methane in the feed gas at an operating pressure of 30 torr with no oxygen in the feed gas. (From Ref. 60.)

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reactors favor the formation of CO; i.e., the addition of oxygen results in bonding of carbon with oxygen, forming CO. A mass spectrometric study by Weimer et al. [44] found similar results. They used a differential pumped quadrapole mass spectrometer to sample the exhaust gas from a microwave tubular reactor being operated for the deposition of diamond. The reactor had a 1.25-cm-diameter tube operating at a pressure of 21 torr, a microwave power of 170 W, and a frequency of 2.45 GHz. The input gas flow consisted of hydrogen, oxygen, and various carbon-containing molecules including CH4 , C2H2 , C2H4 , and C2H6 . The species detected in the exhaust gas included CH4 , C2H2 , CO, and H2O. Figure 38 shows plots of the various detected species as a function of the oxygen percentage in the input gas flow (0–3%). Once again, the dominant carbon species at low oxygen input was either CH4 or C2H2 . At oxygen flow rates of 1% or greater the dominant species was CO and the concentrations of methane and acetylene dropped as the oxygen flow increased. Using a molecular beam mass spectrometer that is capable of measuring radical and stable species in the discharge, Hsu [61] studied diamond deposition in an ASTeX microwave reactor (see Fig. 7). The experimental structure was constructed so that the sampling point of the discharge was a hole in the center of the substrate holder. The deposition conditions used during the mass spectrometer measurements included a substrate temperature of 1073 K, a pressure of 20 torr, and an input microwave power of 800 W. The species detected by the spectrometer included H2 , H, CH3 , CH4 , and C2H2 . The results, which are summarized in Fig. 39, show measured concentrations versus the methane input flow percentage from 0.2 to 3%. The two radicals measured were atomic hydrogen and the methyl radical, CH3 . The dominant carbon species at low methane input flow was methane, whereas at methane flow rates of 0.5% and greater the dominant species was acetylene. The measured hydrogen mole fraction was about 10⫺3. This, of course, is the measured value at the surface of the substrate holder where the discharge is sampled by the spectrometer. It was further estimated by Hsu that the H-atom mole fraction in the center of the discharge located above the substrate holder would be 8%. He also found that the hydrocarbon chemistry in the microwave system was largely unchanged from that found in thermal systems (i.e., hot-filament systems). This was due to the carbonhydrocarbon chemistry being driven by the gas temperature and the atomic hydrogen concentration. The primary effect of the plasma was suggested to be the dissociation of the hydrogen molecules to atomic hydrogen. Erickson et al. [62] measured in a unique microwave reactor configuration other radical species concentrations in a microwave discharge reactor. The measurement technique used was absorption spectroscopy. The species measured included CH3 and CH at a pressure of 20 torr in the discharge.

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Figure 38 Diamond deposition reactor exhaust gas composition versus oxygen percentage in the feed gas for input gas flows of 97 sccm hydrogen and (a) 2 sccm CH4 , (b) 1 sccm C2H6 , (c) 1 sccm C2H4 , and (d) 1 sccm C2H2 . (From Ref. 44.)

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Figure 39 Mole fraction of chemical species measured in a microwave plasma CVD system versus variation in the methane fraction in the feed gas. Measurements done using a molecular beam mass spectrometer. (From Ref. 61.)

Based on the measured values of CH3 and CH at 20 torr, the atomic hydrogen mole fraction was estimated to be 0.8% or less. Wouters and coworkers [63] looked at hydrogen discharges created in a 1.6-cm-diameter tubular microwave reactor operating in the pressure range from 2 to 40 torr. They used the two-photon laser-induced fluorescence (LIF) method to measure the atomic H density when this discharge was operated in a pulsed mode with a 40% duty cycle at 100 Hz using 200 W of power. The results obtained for the absolute atomic hydrogen density and mole fraction are shown in Fig. 40. They reported gas temperatures in the discharge region were 1600 K at 40 torr and 1200 K at 2 torr as measured by H-atom Doppler broadening. The atomic hydrogen mole fraction can be seen to vary from 8% at 2 torr to 2% at 40 torr. Atomic hydrogen mole fraction in an LIMHP-France bell jar microwave CVD reactor (shown in Fig. 10) was measured by Gicquel and coworkers [26,64]. They used the method of actinometry, where the emission signals are properly calibrated so that absolute densities can be obtained. Actinometry is a technique that looks at the strength of optical emission

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Figure 40 63.)

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Atomic hydrogen percentage and density versus pressure. (From Ref.

signals from the discharge. Specifically, the emission from atomic hydrogen and the emission from a gas added at a low concentration (single-atom gas such as argon) are both measured from the same discharge. If the electron excitation energy and cross section of excitation of the two emitting species are similar, then the density of the atomic hydrogen species can be determined because the density of the argon species is known from the input flow rate. Further, if the signal intensities are properly calibrated, the absolute densities can be determined. In this case the results obtained for the atomic hydrogen concentration are shown in Fig. 41 [26,64]. The system used for this measurement was a microwave resonant reactor with a 5-cmdiameter substrate and a 10-cm-diameter discharge region. The power density variation (6–30 W/cm3) was obtained by varying the pressure and the input power to obtain the same plasma volume as the pressure was increased from 18 to 100 torr. The power density and pressure are strongly coupled with pressure increases producing power density increases. As shown in Fig. 41a, the atomic hydrogen mole fraction increases from about 2 to 20% as the pressure increases. Figure 41b displays the variation of the atomic mole fraction of hydrogen as the methane concentration is increased from 0 to over 5%. Only a slight decrease is observed at the low power density of 9 W/cm3. At the higher power density of 22.5 W/cm3, no significant change in the atomic hydrogen concentration is observed as the methane concentration increases from less than 1% to 6%.

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Figure 41 Atomic hydrogen mole fraction versus the microwave power density in part (a) and versus methane concentration in part (b). (From Ref. 26.)

B.

Neutral Gas Temperature

The neutral gas temperature of the discharge in microwave plasma-assisted diamond deposition reactors has been measured in a number of ways including Doppler broadening of optical emission signals, Doppler broadening of LIF signals, coherent anti-Stokes Raman spectroscopy (CARS), and rotational temperature of optically emitting molecules. One of the most systematic studies of the gas temperature in a diamond deposition reactor has been done by Gicquel and coworkers [65,66]. They used all four of the techniques just listed to measure the gas temperature in an LIMHP-France bell jar microwave discharge reactor (Fig. 10) operating at 2.45 GHz. This reactor had a discharge diameter of 10 cm and a substrate diameter of 5 cm.

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The results found by measuring the line-of-sight Doppler broadened emission of atomic hydrogen are shown in Fig. 42. The gas temperature ranges from 1600 K at the low power density (18 torr) to 3500 K at the highest power densities studied, which correspond to a pressure of 105 torr. Measurements performed using laser spectroscopy techniques are shown in Fig. 43. The two techniques utilized were CARS to measure molecular hydrogen and two-photon LIF to measure atomic hydrogen. The CARS technique measures the rotational temperature of molecular hydrogen. The LIF technique measures the Doppler broadening due to atomic hydrogen translational motion. Both of these techniques can be performed with good spatial resolution. For the data shown in Fig. 43 the location of the measurement was in the center of the discharge at a distance of 20 to 25 mm above the substrate. The effect of methane addition on the gas temperature was also studied as shown in Fig. 44. The results obtained by the line-of-sight optical

Figure 42 Atomic hydrogen translation temperature versus microwave power density. The temperature was measured using Doppler broadening of hydrogen OES signals. (Adapted from Refs. 65, 66.)

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Figure 43 Gas temperature versus average microwave power density. Gas temperatures measured include atomic hydrogen temperature by two-photon LIF and hydrogen rotational temperature by CARS. (Adapted from Refs. 65, 66.)

emission measurements of the rotation spectrum of molecular hydrogen are shown in Fig. 45. The temperatures in this case range from 1300 K at 9 W/ cm3 to 1900 K at 22 W/cm3. These rotational temperature values are systematically lower than those found by the other techniques. Similar rotational temperatures versus pressure were also measured by Grotjohn et al. [67] for the MCPR reactor system of Fig. 6b. One variation of this reactor has a 5cm discharge chamber diameter and a 3-cm-diameter substrate holder. These results are shown versus pressure in Fig. 46. Some understanding of the difference in the temperature measurements can be obtained by considering the location and species being measured. The Doppler broadening measurement of atomic hydrogen is weighted toward the region that has the highest atomic hydrogen concentrations. That region is the center of the plasma, which has the highest gas temperature. Conversely, the molecular hydrogen, which is the species being observed

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Figure 44 Atomic hydrogen temperature (measured by LIF) and molecular hydrogen rotational temperature (measured by CARS) versus methane percentage in the feed gas. (Adapted from Refs. 65, 66.)

for the OES (optical emission spectroscopy) rotational temperature measurements, will have a higher density near the edges of the discharge where the gas temperature is lower. Hence, the line-of-sight rotational temperature measurements are weighted more toward the edges of the plasma discharge, which are expected to be cooler. C.

Electron Density and Temperature

The electron density in the discharges operated under conditions that deposit diamond have been measured. Grotjohn and coworkers [67] used a millimeter wave Fabry-Perot resonator operating at 30 GHz to measure the electron density in a 2.45-GHz microwave reactor operating in the pressure range from 10–60 torr. The results of the measurements are shown in Fig. 47 versus pressure. The density range is 1–5 ⫻ 1011 cm⫺3. In another investigation using a tubular reactor with a diameter of 2 cm, Tahara et al. [68] studied methane-hydrogen discharges in the pressure range from 0.1 to

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Figure 45 Molecular hydrogen rotational temperature versus average microwave power density. Temperature was measured using light-of-sight OES. (Adapted from Refs. 65, 66.)

5 torr. The tube was placed through the center of a 2.45-GHz tunable resonant cavity. The methane flow rate in the input gas flow was varied from 1 to 10%. As shown in Fig. 48, the plasma density, which was measured with a Langmuir probe, stayed approximately constant at 1 ⫻ 1011 cm⫺3 across the pressure range studied. The microwave power utilized was 350 W. The last internal variable quantity is the electron temperature, which was measured in the pressure range 0.1 to 5 torr by Tahara et al. [68] using the system described in the preceding paragraph. The electron temperature values varied from slightly above 3.5 eV at the lower pressure of 0.1 torr to about 2eV at the higher pressure of 5 torr. D.

Microwave Power Density

Another important internal variable is the power density of the plasma discharge. Power density is defined by knowing the absorbed power of the

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Figure 46 Molecular hydrogen rotational temperature versus pressure for a 5-cmdiameter discharge system. (From Ref. 67.)

discharge and dividing by the volume of the discharge. The volume is typically estimated from the region of most intense light emission by the discharge. An example plot of the power density versus pressure measured for the MCPR reactor of Fig. 6b operated with a 3- to 4-cm diameter discharge and 3.2-cm-diameter substrate holder is shown in Fig. 49 [67]. Even though the pressure is a primary determining factor for the power density, other factors such as substrate size and total plasma volume are also determining factors. For example, the power density of the microwave system studied here does not match exactly the power density of other microwave diamond CVD systems with different diameters of substrate holders. In work by Kuo and Asmussen [8], the power density found for a microwave reactor with a 7.5-cm-diameter holder at 60 torr was 15 W/cm3 (see Fig. 17). In another system [2,30,65,66], the power density for a microwave system with a 5cm-diameter substrate holder operating at 60 torr was 22.5 W/cm3. So at the 60 torr pressure and 2.45 GHz excitation frequency, microwave systems with substrate holder diameters of 3.2, 5, and 7.5 cm have power densities of 32, 22.5, and 15 W/cm3, respectively. This relationship indicates that larger diameter plasmas, which are needed to cover larger substrates, operate with a lower power density than smaller diameter plasmas.

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Figure 47 Electron density versus pressure for a microwave plasma-assisted diamond deposition discharge. (From Ref. 67.)

E.

Microwave Electric Field and Mode

The last quantity to be considered in this section is the measurement of the impressed microwave electric field strength and the spatial variation of the electromagnetic mode in diamond deposition reactors. The specific system considered here is the microwave cavity plasma reactor (MCPR) as shown earlier in Fig. 6b. The microwave electric field has been measured in the MCPR system by inserting a microcoaxial antenna probe as shown in Fig. 50 through holes drilled in a pattern along the applicator cavity walls, i.e., along the vertical or z direction and around the circumference. The microcoaxial antenna probe samples the electric field component normal to the wall, which in this case is the radial component. The antenna probe is inserted through the applicator cavity holes a small distance (⬃a few millimeters) so that only a small fraction of microwave power going into the applicator cavity is coupled into the sampling antenna probe (typically

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Figure 48 Electron temperature and plasma density versus pressure for a cavity resonance microwave hydrogen-methane discharge. (From Ref. 68.)

⬃10⫺6). This small fraction for the amount of power sampled by the antenna probe ensures that the probe does not perturb the field in the applicator. An example plot of the measured electric field strength versus cavity vertical position (z direction) is shown in Fig. 51 [69,70]. The symbols show the experimentally measured microwave electric field values in a discharge loaded applicator cavity. The dotted line is the expected strength of the radial field variation versus vertical position along the applicator cavity for the TM013 mode. A sketch of the ideal TM013 mode is shown in Fig. 52. Note in this figure that the electric field has three maximums along the longitudinal direction, which is also seen in the experimental data of Fig. 51. Although not shown in Fig. 51, when the microwave electric field is sampled around the circumference of the applicator cavity wall, the electric field strength is unchanged in agreement with the MPCR operating in a TM013 electromagnetic mode.

VII.

MICROWAVE DIAMOND CVD REACTOR MODELING

Microwave plasma-assisted CVD reactors for diamond deposition have been modeled in a number of investigations. The modeling of microwave CVD reactors needs to consider a number of factors including:

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Figure 49 Microwave power density versus pressure for 5-cm-diameter hydrogenmethane discharge used for diamond deposition. (From Ref. 67.)

1. 2. 3.

Electron gas–initiated reactions in the discharges Neutral chemistry (including thermally activated) reactions in the discharges Microwave field excitation, propagation/resonance, and absorption including the spatial patterns of microwave fields and microwave power absorption

First, a few preliminary comments regarding H2 /CH4 discharge and microwave discharge operation in the pressure range from 1 to hundreds of torr are in order. The dissociation reactions, which are so important to diamond deposition (i.e., dissociation of H2 and CH4), can be driven by either electron dissociation or thermal dissociation. The general trend as shown in Fig. 53 for all molecular gases is that at low pressures, the electron temperature is high and the gas temperature is low so electron dissociation dominates. Conversely, at high pressures, the electron temperature is reduced

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Figure 50 Details of the microwave electric field measurement probe and a cutaway view of a microwave cavity plasma reactor.

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Figure 51 Microwave electric field strength (radial direction) versus vertical position for a microwave cavity plasma reactor as shown in Fig. 50.

Figure 52

Sketch of TM013 electromagnetic resonant mode.

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Figure 53 Electron, ion, and neutral temperatures versus pressure for nonequilibrium (nonisothermal) and thermal-like plasmas. (From Ref. 10.)

and the gas temperature increases, resulting in increased thermal dissociation. The exact pressure range over which this transition occurs is dependent on many factors including molecular species type, other constituents in the plasma, and the plasma volume. One of the objectives in this section is to establish an understanding of this transition in the diamond deposition process. A.

Modeling Studies

Several researchers have studied diamond deposition in microwave plasmaassisted CVD systems. The key attributes that distinguish the various models are: 1. 2.

Spatial dimension of the solution [zero (one point), one, or two dimensional] Discharge chemistry model (hydrogen, hydrogen-methane, H-CO)

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Microwave power absorption profile (uniform, assumed profile, self-consistently solved profile)

Koemtzopoulos et al. [71] in 1993 reported on a model for microwave discharges that looked at hydrogen dissociation. The reaction rates were solved for by determining the electron energy distribution function (EEDF) using the Boltzmann equation. The model considered electron dissociation of the hydrogen as the primary dissociation mechanism. The model solved the electron density balance equation, the atomic hydrogen balance equation, and the power balance equation at pressures ranging from 15 to 100 torr. The geometry considered was a tubular reactor with the electric field and species concentrations assumed uniform throughout the plasma volume. The model showed that the electron distribution function is non-Maxwellian with the tail of the distribution function depleted by inelastic collisions. Further, it was demonstrated that even when 1% CH4 was added to the hydrogen discharge of EEDF did not change appreciably. This work also noted that the dissociation of methane by abstraction of atomic hydrogen (CH4 ⫹ H → CH3 ⫹ H2) is faster than electron dissociation at pressures as low as 20 torr with a gas temperature of 600 K and an atomic hydrogen fraction of 0.08. Hyman et al. [72] in 1994 developed a one-point numerical model of microwave plasma CVD diamond deposition reactors. The model solved the Boltzmann equation to determine the electron energy distribution function. A dominant energy loss mechanism for the electron gas was the vibrational excitation of the hydrogen molecules. The gas heating then occurred predominantly through vibrational-translational energy exchange. This model considered discharges consisting of carbon-hydrogen-oxygen mixtures. In the model the point of calculation was selected as the center of the plasma ball located above the substrate holder. Diffusion and heat conduction effects were accounted for by two boundary points fixed at the substrate condition and the wall/ambient condition. Their simulation example was given at 40 torr pressure, 30 W/cm3 microwave power density, and an input gas mixture of 98.75% H2 , 1% CH4 , and 0.25% O2 . Typical values of the plasma conditions simulated at time scales approximating steady state (after 4 msec of reaction time) are an electron temperature of 2.5 eV and a gas temperature of ⬃3000 K. In their model the initial gas mixture of H2 , CH4 , and O2 reacts to a mixture consisting of H2 , C2H2 , and CO (stable species) and H, C, CH3, and C2H (radical species). Hence the methane and oxygen molecules in the discharge are converted predominantly to C2H2 and CO molecules. Work by Tan and Grotjohn [69,73] on microwave plasma reactors for diamond deposition looked at the microwave fields and the absorption of the microwave energy by the discharge. They obtained full-wave two-di-

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mensional solutions of Maxwell’s equations to solve for the electromagnetic fields using the FDTD (finite-difference time-domain) method. The work simulated the resonant fields in a resonant cavity microwave reactor. Experimental measurements and simulations of the 2.45-GHz microwave fields showed close agreement. This model was limited to hydrogen discharges in the reactor. The reaction kinetics included electron dissociation and ionization processes of hydrogen, but thermal processes were either left untreated or treated in a very simple manner. The gas temperature in their model was set on the basis of experimental gas temperature measurements. This modeling work solved for the electromagnetic fields and the power absorption of the electron gas in the microwave reactor. Extensive modeling work on hydrogen and hydrogen-methane discharges has been done by Hassouni et al. [74–80] at LIMHP-CNRS in France. They developed one-dimensional discharge models for moderatepressure H2 and H2 /CH4 plasma discharges. They also developed a twodimensional model of H2 discharges using an assumed microwave power absorption profile. Their modeling work considered the electron energy, H2 vibrational energy, and total energy. The models use Boltzmann equation solutions to determine the EEDF, which is important for determining electron reaction rates because the EEDF is non-Maxwellian. The model also included gas heating in the discharge region. Extensive comparisons with good agreement are made of the simulated gas temperature and the experimentally measured gas temperature, which was obtained by CARS and Doppler broadening resolved OES. The hydrogen discharge considered in their modeling work included either 7 or 9 species and the H2 /CH4 model included an additional 12 neutral carbon-containing species and 9 ionic carbon species. The carbon chemistry for the pressure range considered (18– 100 torr) has been shown to be primarily governed by thermal chemistry with the gas temperature and the atomic hydrogen concentrations being the primary neutral carbon chemistry driving factors. The work by Tan and Grotjohn [69,73] on modeling the microwave fields in microwave diamond deposition reactors was combined with the work on hydrogen discharges by Hassouni et al. [74–80] to produce a twodimensional self-consistent microwave field and plasma discharge simulation for a moderate pressure (18–80 torr) hydrogen discharge reactor [81]. This model produced a self-consistent solution of the microwave fields in the plasma reactor, the absorption of the microwave energy by the discharge electron gas, and the hydrogen plasma discharge. The plasma model used was a three energy mode (gas, molecular vibration, and electron) with nine ⫹ ⫺ ⫺ species [H2 , H, H (n = 2), H (n = 3), H⫹, H⫹ 2 , H3 , H , and e ] model that accounted for the non-Maxwellian electron distribution function and had 35 reactions. Good agreement was obtained between the model results and the

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experimental data for gas temperatures and atomic hydrogen concentrations. The model was also able to predict plasma discharge (ball) size, shape, and location in the discharge chamber with good accuracy. The specific reactor simulated, as shown in Fig. 10, had a 25-cm-diameter microwave resonant cavity structure operating at 2.45 GHz with a silica bell jar of 10 cm diameter. The substrate holder inside the bell jar had a diameter of 5 cm as shown in Fig. 10. Example two-dimensional plots of the gas temperature, atomic hydrogen mole fraction, absorbed microwave power density, electron temperature, and electron density are shown in Fig. 54. Numerical simulations of microwave plasma reactors for diamond CVD have also been done by Funer et al. [82,83]. In their study microwave fields are modeled in two dimensions (r and z) using a finite integration technique to solve Maxwell’s equations for the reactor structure. The plasma model used was a cold plasma dielectric function description of the discharge where the density of the discharge was calculated on the basis of the local electric field and a fitting parameter ␥ that is adjusted to have the modeling results agree with experimental observations. Their work looked at using the numerical model to design an optimum reactor. The various geometric dimensions of the reactor are described by parameters P1 , P2 , . . . , Pn . An optimization is done to determine the set of parameter values that maximize the ratio of the electric field (兩E兩2) within the plasma region to the electric field strength (兩E兩2) in the region surrounding the plasma region. The optimum parameter set was determined using the method of ‘‘direction of steepest gradient’’ to find the optimum solution. The result of this study was the elliptical reactor described earlier in Sec. IV, Fig. 11 [16]. B.

Internal Variables: Modeling Results

From the various modeling efforts, a number of important understandings regarding microwave-assisted diamond CVD reactors can be extracted. The first is that the chemistry of neutral carbon species (e.g., dissociation of CH4 to CH3) is essentially driven by gas temperature and H-atom concentration. Hassouni et al. [74] demonstrated using a one-dimensional H2 /CH4 plasma model that for the pressures they studied (18 torr and above) the carbon chemistry is driven by thermal and atomic hydrogen [H] processes and not by electron excitation or dissociation of carbon species. Another understanding that can be drawn from the various modeling results is the relative importance of thermal dissociation and electron collisional dissociation of hydrogen. First, Fig. 55 shows the atomic hydrogen concentration under equilibrium conditions due to just thermal dissociation at temperatures from 1600 to 2800 K (dashed line) for the two pressures of 20 and 100 torr. The equilibrium molar fraction for a pressure of 20 torr

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Figure 54 Spatial distribution (versus r and z) of discharge characteristics at 2500 Pa and 600 W. (a) Gas temperature (K), (b) atomic hydrogen model fraction, (c) absorbed microwave power density (W/cm3), (d) electron temperature (K), and (e) electron density (⫻1011 cm⫺3). (From Ref. 81.)

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Figure 55 Hydrogen dissociation (molar percentage) versus gas temperature for hydrogen in equilibrium conditions (dashed line) and hydrogen in a plasma discharge used for diamond deposition (solid line).

goes from 0.038% at 1600 K to 1.1% at 2000 K to 41% at 2800 K. Data are also shown in Fig. 55 for a pressure of 100 torr. These quantities are taken from the work by Argoitia et al. [84]. In the two-dimensional simulations of a 2.45-GHz microwave plasma-assisted CVD reactor with a discharge size of approximately 5 cm diameter by Hassouni et al. [81] the simulation results yielded an average hydrogen molar fraction and gas temperature as a function of pressure as shown in Fig. 56. Note that as the pressure increases the gas temperature and the hydrogen molar fraction also both increase. If these gas temperature and hydrogen molar fraction values are now also plotted (Fig. 55), the solid line labeled 2.45 GHz is obtained. In Fig. 55, the lowest pressure of 18 torr shows that the hydrogen dissociation in the microwave CVD system is substantially greater that that expected from the gas temperature. Hence, at this lower pressure electrondriven dissociation of the discharge is an important process. At the higher pressures, the hydrogen molar fraction is approximately the same as or less than the thermal dissociation value based on the discharge gas temperature. Hence, at 40 torr and above the thermal dissociation of hydrogen becomes a dominant process. The modeled/measured value of the hydrogen dissociation is less than the equilibrium value because, in the reactor, the discharge chamber walls and cooler gas regions outside the active discharge volume provide sinks for atomic hydrogen via surface recombination and volume recombination. The influence of reactor scaling on the atomic hydrogen molar fraction is also interesting to consider. A larger diameter microwave diamond dep-

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Figure 56 (a) Plasma gas temperature versus pressure in a hydrogen-dominated diamond deposition discharge. (b) Atomic hydrogen percentage versus pressure in a hydrogen-dominated diamond deposition discharge.

osition reactor operating at 915 MHz with a substrate diameter of 15 cm was also simulated using the model in Ref. 81. The simulated data for the larger system are shown in Fig. 55 as a solid line labeled 915 MHz. It can be seen that at the higher gas temperatures of 2400 K and above the larger diameter 915 MHz system has an atomic hydrogen molar percentage that is closer to the thermal equilibrium values (dashed lines) than the smaller 5cm-diameter discharge 2.45-GHz system. Another important factor affecting the %H and the gas temperature at a selected pressure is the input microwave power. Table 2 shows the gas temperature versus input microwave power at a pressure of 18 torr in a

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Table 2 Simulated Plasma Discharge Quantities as a Function of Input Microwave Power at a Pressure of 2500 Pa Microwave input power (W) Discharge parameters Vp (cm3) Tg peak value (K) Tg average value (K) Tg peak location (K) Te peak value (K) Te average value (K) Te peak location (cm) MWPD peak value (W/cm3) MWPD average value (W/cm3) MWPD peak location (cm) ne peak value (cm⫺3) ne average value (cm⫺3) ne peak location (cm) xH peak value (%) xH average value (%) xH peak location (cm)

300

500

700

800

900

19 1,730 1,500 1.3 19,840 16,030 0.3 18.1 8.7 0.3 3.3 ⫻ 1011 2.0 ⫻ 1011 0.9 0.65 0.4 1.1

33.6 1,920 1,620 1.5 19,920 16,000 0.3 19.2 8.5 0.3 3.4 ⫻ 1011 2.1 ⫻ 1011 1.1 0.81 0.52 1.5

49 2,020 1,640 1.7 19,650 15,930 0.3 18.4 8.0 0.3 3.3 ⫻ 1011 2.1 ⫻ 1011 1.3 0.9 0.55 1.5

61 2,080 1,710 1.9 19,570 15,730 0.3 17.5 7.4 0.3 3.3 ⫻ 1011 2.1 ⫻ 1011 1.3 0.93 0.60 1.7

74.5 2,065 1,640 1.9 19,560 15,320 0.3 17.2 6.4 0.3 3.1 ⫻ 1011 1.8 ⫻ 1011 1.1 0.9 0.52 1.7

Source: Ref. 81.

hydrogen discharge [81]. The primary factors affecting the gas temperature and percent hydrogen concentration once a particular pressure is selected are the plasma volume and the plasma boundary temperature (substrate temperature and wall temperatures). In general, the larger the plasma volume (as determined by the discharge chamber size and the input microwave power), the higher will be the gas temperature. The variations of other internal variables versus microwave input power are also given in Table 2. A companion table showing the variation of the internal variables versus pressure for hydrogen discharges of similar volumes is Table 3. Tables 2 and 3 provide a picture of the internal variable values and their variation with the pressure and microwave power (two input variables). One final utility of the models is in the design and operation of a reactor to get a uniform deposition across large areas. It has been noted by researchers that the uniformity of the deposition is controllable by the adjustment of the substrate position, microwave tuning circuit, pressure, and amplitude of the input microwave power. For example, work described by Bachmann [10] showed that films can be grown in the same reactor that vary from thickest in the center of a wafer area, to relatively uniform, to

294 Table 3

Grotjohn and Asmussen Simulated Plasma Discharge Quantities as a Function of Pressure/Power Pressure (hPa), microwave input power (W)

Discharge parameters 3

Vp (cm )* Tg peak value (K) Tg average value (K) Tg peak location (cm) Te peak value (K) Te average value (K) Te peak location (cm) MWPD peak value (W/cm3) MWPD average value (W/cm3) MWPDav experiment (W/cm3) MWPD peak location (cm) ne peak value (cm⫺3) ne average value (cm⫺3) ne peak location (cm) xH peak value (%) xH average value (%) xH peak location (cm)

25–600

52–1000

84–1500

110–2000

44.1 1,990 1,640 1.7 19,680 15,900 0.3 18.3 8.0 9.0 0.3 3.4 ⫻ 1011 2.1 ⫻ 1011 1.1 0.87 0.55 1.5

40.7 2,600 2,100 1.7 cm 17,220 14,600 0.3 40.1 16.0 15.0 0.3 5.1 ⫻ 1011 3.1 ⫻ 1011 1.1 1.19 0.78 1.5

39.8 3,100 2,540 1.7 cm 15,680 13,600 0.3 67.8 25.0 22.5 0.3 7.4 ⫻ 1011 4.3 ⫻ 1011 1.1 2.91 1.66 1.7

45 3,200 2,760 1.7 cm 13,990 12,400 0.3 79.1 30. 30. 0.3 9.1 ⫻ 1011 5.3 ⫻ 1011 1.1 6.98 3.8 1.9

*Vp, plasma volume. Source: Ref. 81.

thickest at the edge of the deposition area. Such a dependence of the uniformity was also seen in the discharge itself in Ref. 81, where simulations with the substrate holder at three difference vertical positions yielded the results of Fig. 57. Specifically, variation of the substrate height produced changes in the gas temperature and in the shape of the plasma discharge region above the substrate. Raising the substrate holder is shown in Fig. 57 to flatten the plasma so that it is more uniform across the diameter of the substrate.

VIII.

CONCLUSION

Microwave plasma-assisted CVD machines create and control the chemical environment and substrate conditions for diamond growth. The appropriate chemically active environment supplies neutral fluxes, such as CH3 and C2H2 , that provide the carbon for the growth process and also supplies a high-density atomic hydrogen flux so that deposition occurs in the diamond

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Figure 57 Spatial distribution of gas temperature (K) at three substrate positions. (a) Lowered 1 cm, (b) nominal position, and (c) raised 1 cm. (From Ref. 81.)

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phase. The deposition machine must also control the substrate temperature to achieve the desired diamond film uniformity and properties. Since the early 1980s, when Kamo et al. [6] created the tubular reactor, substantial progress and major innovations have been made in the design and development of microwave plasma-assisted CVD machines. A wide range of machine types and sizes have been developed and have demonstrated successful diamond deposition. Using current technology and know-how, microwave plasma-assisted CVD is achieved over a wide experimental regime, including pressures ranging from 10 m torr to 1 atmosphere, microwave powers ranging from 100 W to 60 kW, and substrate diameters ranging from 2.5 to 30 cm. Today, microwave CVD systems can deposit diamond films uniformly across substrates as large as 30 cm in diameter and at rates of nearly 1 g/hr. By carefully adjusting the chemistry and controlling impurities, diamond films with the desired quality and morphology can also be synthesized. Considerable engineering has gone into the design of these systems, and reliable, automated operation is currently available for commercial applications. The approach utilized in this chapter was to view these diamond machines in terms of the relationships between the input variables, internal variables, and output variables. The relationships between these experimental variables are developed from both experimental studies reported over the past 15 years in the literature and modeling investigations of specific diamond deposition machines and their associated diamond deposition processes. Much has been learned from experimental and modeling investigations about the relationships between the input variables, such as pressure, gas flow rate and composition, and input microwave power, and the internal variables, i.e., chemistry, of the discharge. This understanding has come both from careful experimental measurements of the internal variables including gas temperatures, plasma density, radical densities, and microwave power densities and from careful modeling studies that can now solve for the plasma discharge kinetics and the microwave fields self-consistently in two dimensions. These studies, which were reviewed in this chapter, provide a very useful picture for the understanding of the engineering and scientific issues associated with the design of microwave plasma-assisted CVD machines and the diamond deposition process itself. Microwave plasma reactors are often used for fundamental scientific experimental investigations because microwave plasma-assisted machines operate without electrodes or filaments in contact with the discharge. Hence, electrode, filament, and other contamination issues can be minimized. For example, microwave plasma reactors have been extensively used to investigate the influence of impurities (even at levels as low as 10 ppm) on the deposition process and film properties. One result of these investigations has

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been the design and development of very reliable, low-maintenance microwave plasma-assisted CVD machines that have very high vacuum system capabilities as well as the ability to control impurity gases to levels below a few ppm. Thus applications that require high-quality diamond synthesis, such as diamond window synthesis as well as synthesis of electronic quality films, are now usually carried out using microwave plasma reactors. However, even with the advances and successes over the past 15 years in the areas of machine design and process understanding, many interesting design and process understanding issues remain. Some of these include understanding the influence of various impurities or additives on the deposition process, e.g., the influence of small amounts of nitrogen, boron, and oxygen across the range of deposition conditions. Other issues center around the design of deposition machines that permit ever more uniform diamond deposition across large areas while minimizing unwanted contamination or impurities from the machine itself, i.e., impurities from wall erosion, substrate erosion, and fused silica bell jar or window erosion found at the high temperatures and in the highly active chemical environments of the deposition process. REFERENCES 1. 2.

3. 4.

5.

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8 Combustion Synthesis of Diamond Colin A. Wolden Colorado School of Mines, Golden, Colorado

I.

INTRODUCTION

Combustion synthesis is one of the competing chemical vapor deposition (CVD) technologies for diamond film growth. It was first discovered in 1988 by Hirose and Kondo [1], who realized that acetylene flames produce copious amounts of atomic hydrogen and hydrocarbon radicals that are required for diamond growth. The discovery was subsequently confirmed at the Naval Research Laboratory [2] and has become the subject of intense study. It has been argued that combustion synthesis is the most flexible of the CVD alternatives because of its scalable nature, minimal utility requirements, and significantly reduced capital costs relative to plasma-aided processes [3]. In this chapter the development of combustion CVD will be reviewed from its inception using conventional welding torches to its present implementation with flat flame burners. The key experimental parameters and their impact on deposition are discussed in detail. The chemistry of combustion diamond CVD is discussed, highlighting studies that employed in situ diagnostics and detailed reactor modeling. Finally, combustion synthesis is contrasted with other CVD techniques in terms of both processing and economics.

II.

INVENTION: THE WELDING TORCH

A.

Description of System

Figure 1 shows the structure of an atmospheric oxyacetylene torch in its unperturbed state and in the configuration used for diamond deposition. 303

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Figure 1 Schematic diagrams of (a) the flame structure of an oxyacetylene torch and (b) the flame in a diamond deposition configuration.

There are three distinct regions in an acetylene flame: (1) the inner flame, (2) the acetylene feather, and (3) an outer diffusion flame. It is in the feather region that the substrate is placed for diamond growth. The most important parameter in combustion synthesis is the oxygen-to-acetylene ratio, defined here as R = O2 :C2H2 . At values of R near 1.0, a neutral flame is achieved, which is defined as the condition where the feather region just disappears because all the acetylene is consumed in the primary flame. The diamond growth regimes as a function of composition are outlined in Fig. 2. The highest quality diamond is obtained in slightly rich flames, R = 0.85–1.0 [4]. The value of R at which a neutral flame occurs is dependent on both burner design and total flow rate. Thus, for a particular experimental configuration the composition at the neutral flame condition may be shifted slightly, but the principles described in Fig. 2 still hold. The welding torch arrangement of Hirose has been used in numerous subsequent studies [5–13]. Polycrystalline diamond has been grown at rates up to 200 ␮m/hr [5] and thick (150 ␮m) homoepitaxial layers have been deposited [6]. Atmospheric torches have successfully produced large indi-

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Figure 2 Carbon deposition regions observed using atmospheric acetylene torches as a function of gas composition. (From Ref. 4.)

vidual crystals that approach 1 mm in diameter [7,8]. The drawback of the welding torch arrangement is that the deposited material is characterized by radial inhomogeneity [9] and often contains significant amounts of nondiamond carbon [10]. Because of these limitations, welding torches are being replaced by flat flame burners, which are more appropriate for large area deposition. Nevertheless, the wealth of data from experiments with atmospheric torches provided the foundation for the general understanding of combustion grown diamond that is described in the following. A more comprehensive summary of experiments performed using atmospheric torches can be found in an earlier review [11].

B.

General Considerations

1.

Chemistry

The composition of acetylene flames is much different from the traditional H2 /CH4 mixtures used in hot-filament and plasma CVD systems. However, the chemistry and the mechanism of diamond growth in combustion CVD

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are expected to be similar to those of other diamond growth systems. First, at R = 1.0 the acetylene flame is positioned in the direct center of the empirical growth regime diagram developed by Bachmann et al. [12] (see Chapter 4). The detailed chemistry of acetylene flames is discussed in detail in Sec. IV, but its essence may be distilled to the following two reactions: C2H2 ⫹ O2 → 2CO ⫹ H2 H2 ↔ H ⫹ H

⌬H⬚R = ⫺107 kcal/mol

(1)

Reversible: function (T, P)

(2)

First, nearly all of the oxygen and acetylene is rapidly consumed, producing carbon monoxide and hydrogen as described by the global reaction (1) [13]. The highly exothermic nature of this reaction results in flame temperatures >3000 K. At these temperatures a significant fraction of hydrogen molecules are converted into atomic hydrogen as expressed by global reaction (2) [14]. The degree of dissociation is strongly dependent on both temperature and pressure. Carbon monoxide is thermally stable and not expected to affect the growth processes under these conditions. A small fraction of the acetylene is converted into hydrocarbon radical species or remains unreacted. Thus, growth schemes discussed in Chapter 4 that suggest that diamond growth proceeds through the addition of hydrocarbon radicals in the presence of a superequilibrium concentration of atomic hydrogen may also be applied to combustion systems. Where filament and plasma systems employ electrical energy to create atomic hydrogen, combustion systems rely on the chemical energy stored in the acetylene molecule to generate heat and atomic hydrogen. 2.

Substrate Temperature

Substrate temperatures during the combustion CVD of diamond range from 950 to 1650 K. Because of these high temperatures, substrates have been limited to materials such as molybdenum, alumina, silicon, and diamond. Evaluating the true substrate temperature is difficult in all diamond CVD environments but especially so in combustion synthesis due to the extreme heat fluxes present. The two techniques most commonly used are optical pyrometry and thermocouples placed on the back side of the substrate. Pyrometry provides a good measure of the relative temperature of the substrate, but absolute values may be off by as much as 100 K due to uncertainties in emissivities. Care must be taken to position the pyrometer in order to avoid emission from the flame itself. Back-side thermocouples are affected by both the quality of the contact and the steep thermal gradients present. Both techniques work well for a single configuration, but caution is urged when comparing absolute temperatures obtained from different systems.

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Substrate temperature has a dramatic effect on two important properties: growth rate and morphology. Several authors [15–17] have observed that the growth rate increases exponentially with temperature as shown schematically in Fig. 3. The behavior shown by the curve in Fig. 3 is characteristic of combustion systems; however, its location may be shifted to the right or left depending on the operating conditions and the technique used to measure temperature. Weimer et al. [15] measured activation energies between 12 and 18 kcal/mol for diamond growth on individual crystal faces. Slightly higher values (16–23 kcal/mol) have been reported for polycrystalline films [16,17]. These values are in good accord with activation energies measured in hot-filament systems, indicating that the growth mechanisms may be similar [18,19]. As the substrate temperature increases, the growth rate reaches a maximum (Fig. 3). Increasing the substrate temperature beyond this point causes a rapid decline in both the quality and the growth rate [15–17]. In atmospheric torches the maximum growth rate occurs at substrate temperatures between 1450 and 1650 K [15,20]. In lowpressure (40–50 torr) flat flame burners the same growth rate behavior has been observed, but the maximum occurs at significantly reduced temperatures of 1050–1250 K [17,21]. Kim and Cappelli [21] suggested that the falloff at high temperature may be due to oxidation of diamond. An alter-

Figure 3 The effect of substrate temperature on growth rate observed in combustion CVD of diamond. (From Refs. 15–17, 20.)

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native possibility is that the growth precursor desorbs from the surface before having the opportunity to incorporate into the diamond lattice [22]. Substrate temperature also determines the diamond film morphology. The morphology of most films deposited by combustion CVD are typically dominated by {111} facets [20,21,23]. However, a number of researchers [17,20,23,24] have observed that at higher temperatures the morphology consists of {100} facets parallel to the substrate. As temperature increases, the growth habit changes from octahedron to cubic as shown in Fig. 4. The temperature where {100} faceting occurs was near the temperature where maximum growth rates were observed (Fig. 3) [17,20]. 3.

Reactant Composition

In atmospheric torches it has been observed that morphology also depends on reactant composition [25,26]. Decreasing the oxygen fraction has an effect similar to that of increasing substrate temperature as shown in Fig. 4. It was observed that the morphology changed from octahedron growth under oxygen-rich conditions to cubic growth as the acetylene content was increased [25,26]. The dependence on composition is in accord with observations of morphology variations with methane concentration in plasma reactors [27,28]. For flat flame burners this dependence on composition has not been reported, perhaps because the range of R where diamond is successfully formed is much smaller [17,21]. Of the two variables, morphology depends more strongly on substrate temperature than composition. C.

Modifications of the Welding Torch

In the welding torch operation shown in Fig. 1, diamond is often deposited in a small circle or in an annular ring. To increase the deposition area a

Figure 4 Schematic diagram showing changes in crystal growth habit as a function of both substrate temperature and reactant composition. (From Refs. 17, 20, 23–26.)

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number of modifications of the welding torch have been investigated, including turbulent flame operation, multinozzle burners, and enclosed flames. A few groups [29,30] have investigated operating the welding torch under turbulent flow conditions. The turbulent condition was achieved by increasing both the flow rate and the burner orifice. Despite some reports [31] of improved quality, it was generally concluded that the changes were not dramatic and not worth the costs associated with increased flow rates [29,30,32]. Some success was achieved with a multinozzle configuration was developed by Zhu and coworkers [33], although the morphology was not uniform over the deposition area. During atmospheric operation, diffusion of oxygen or impurities from the ambient may effect film quality. Attempts to minimize the effect by surrounding the torch with a coannular flow of inert gas have been studied [34,35]. Under these conditions the outer flame (Fig. 1) was suppressed, but no dramatic changes were observed in quality or growth rate. Another way to exclude the ambient is simply to enclose the torch in a vacuum chamber [36–39]. It was observed that the outer diffusion flame disappeared as there was no oxygen present and the deposition area was increased by 20% [36,37]. In addition, reducing the pressure to 300 torr increased the deposition area by 200%, but the growth rate decreased significantly. Morrison et al. [38] performed a systematic study of an enclosed flame at 700 torr and found that a low-temperature pretreatment step enhanced the nucleation density. Wang et al. [39] achieved some success using rastering techniques with an enclosed flame to coat larger areas.

III.

PRACTICAL IMPLEMENTATION: THE FLAT FLAME BURNER

A.

The Flat Flame Burner

1.

Burner Design

A number of groups [14,17,21,40,41–45] have addressed the issues of increasing the deposition area and improving uniformity through the use of flat flame reactors operated at both atmospheric and reduced pressure. Cooper and Yarbrough [40] first demonstrated diamond deposition in a commercially available burner at pressures between 25 and 40 torr. A schematic of a flat flame burner CVD for reduced pressure operation is shown in Fig. 5. Premixed gas enters a water-cooled burner and exits through a matrix that creates a radial uniform velocity profile with only an axial component. In practice this has been achieved by drilling 1-mm holes in a copper plate [21,41], and by using a honeycomb made of thin-walled silica tubes

310

Figure 5 pressures.

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Schematic of a flat flame burner CVD system operated at reduced

[17]. A flat, circular flame is formed stabilized below the burner surface as shown in Fig. 5. This is a very different structure than the conical flame that is associated with atmospheric torches (Fig. 1). The substrate is maintained at a certain temperature T and positioned at a distance L from the burner surface. This design was developed in the 1950s to measure flame velocities near extinction/ignition limits [46,47]. The burner’s characteristics of stability and geometrical simplicity that made it useful for that purpose are equally valuable for chemical vapor deposition. Atmospheric pressure flat flames are less stable and require more complicated burner design. Two examples that have been used include a coflow arrangement and a trumpet-bell design that are shown schematically in Fig. 6 [42]. Murayama and coworkers [43,44] used the coflow design with hydrogen as the external gas to stabilize their flame. Workers at Sandia have demonstrated the scalability of the trumpet-bell design [42,45]. Comparison of Figs. 5 and 6 shows another important difference between atmospheric and low-pressure operation. At low pressures the flame is stabilized on the burner surface, whereas atmospheric flames are substratestabilized flames located within a millimeter or two of the substrate. In lowpressure operation the substrate may be positioned at any distance from the burner, whereas in atmospheric systems the distance is constrained by the stability limits. In addition, in large-area atmospheric flames it was found that it was necessary to surround the substrate with equally spaced pillars to stabilize the flame [48].

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Figure 6 Two designs of atmospheric flat flame burners: (a) a coflow design and (b) a trumpet bell design. (From Ref. 48.)

2.

Radial Uniformity and Scalability

Regardless of operating pressure, the unique feature of this design is that films are produced that are uniform in both thickness and morphology. Figure 7 shows micrographs of surface morphology and a cross-sectional profile that demonstrate the radial uniformity achieved in flat flame burners. At low pressures, Glumac and Goodwin [41] demonstrated the scaleable nature of the system, producing uniform films over areas as large as 13 cm2. More recently, Hahn et al. [47] scaled up an atmospheric deposition system to 20 cm2. Another feature of the flat flame CVD reactor is that it is amenable to detailed kinetic modeling. Under proper operating conditions [49], the axisymmetric stagnation flow may be treated in one dimension using a similarity solution [50]. A number of groups have performed detailed kinetic modeling on these systems, which has provided insight into the deposition mechanisms. These studies are discussed in more detail in Sec. IV.

B.

Operating Conditions

1.

Reactant Composition

Low-pressure flat flame burners are operated with a value of R very near unity [17,21]. At atmospheric pressure, pure oxygen-acetylene flames are unstable. It has been found that the addition of hydrogen (18–25% by volume) while maintaining a C/O ratio ⬃1 was required to stabilize the flame and achieve diamond growth [42–45]. Because of the homogeneous nature

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Figure 7 Scanning electron micrographs (a–c) and cross-section profile (d) showing the radial uniformity of both morphology and growth rate achieved in flat flame burners. (From Ref. 17.)

of these flames, the composition range where diamond is deposited is much smaller than observed with the welding torch design [4]. Most researchers [42–45] report only a single composition that successfully produced highquality diamond. In low-pressure systems there is a small range where diamond is deposited [21,51]. The reason for the narrow range is shown in Fig. 8, where the equilibrium mole fractions of selected species are plotted as a function of composition. The three major species (CO, H2 , and H) are nearly constant across this range of R. For the minor species a very sharp transition is observed between R = 0.98 and R = 1.02. The concentration of carbon-containing species (C2H2 , CH3 , C) falls between four and seven orders of magnitude over this narrow regime. A concomitant increase in oxidation products (H2O, CO2 , O2) is also observed. Certainly, very good control of mass flow controllers is required for reproducible results using combustion synthesis. 2.

Operating Pressure

As already discussed, operating pressure has a major influence on burner design and flame stability. The pressure also influences a number of critical

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Figure 8 Equilibrium mole fractions of selected species in an oxyacetylene flame as a function of reactant composition R = O2 :C2H2 . Calculation performed at 40 torr with 5% argon.

issues including growth rate, temperature control, and deposition temperature. First, growth rates in atmospheric systems range from 25 to 40 ␮m/hr [44,45]. In comparison, growth rates in flat flame burners at ⬃45 torr have been reported between 4 and 5.5 ␮m/hr [17,21]. Although the gas density is about 15 times greater in atmospheric reactors, the growth rate is only a factor of ⬃7 times greater. More important with regard to economics, the carbon conversion efficiency (the fraction of acetylene atoms converted to diamond) is very similar in both cases. As discussed in Sec. II, growth temperatures in atmospheric systems are hundreds of degrees hotter than at low pressure. Substrate material selection is more limited for atmospheric flames, and these films are subject to the formation of large compressive stresses during cooling due to differing coefficients of thermal expansion [49]. Robust substrate temperature control is requisite for both controlling growth rate and achieving textured growth [17]. The proximity of the flame and substrate in atmospheric reactors re-

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Table 1 Comparison of Operating Flat Flames at Atmospheric and Reduced (40–50 torr) Pressures Aspect

Reduced pressure

Atmospheric pressure

Growth rates Carbon conversion efficiency Deposition temperatures Temperature control Flame stability Safety Vacuum chamber required Burner design

4–5.5 ␮m/hr Similar ⬃0.005% 400–1000⬚C Easy Yes Advantage Yes Simple

25–40 ␮m/hr Similar ⬃0.005% 700–1200⬚C Difficult No: requires H2 addition No Complex

Source: Refs. 17, 21, 42–45, 51, 52.

quires that energy must be removed at fluxes on the order of 500 W/cm2, requiring the use of elaborate cooling strategies [20,45,48]. In contrast, lowpressure reactors are nearly thermally neutral, and films have been deposited without any cooling present [41]. Simple control strategies can maintain the substrate temperature within a few degrees of a desired setpoint for hours of deposition [52]. Although atmospheric burner design is more complicated, an advantage is that no vacuum chamber is required. Table 1 summarizes some of the pros and cons of operating pressure in diamond deposition. C.

Applications

Combustion CVD was invented 7 years after the discovery of hot-filament and plasma techniques, and subsequently the majority of applied research has been performed in these conventional reactors. However, the studies that have been conducted demonstrate that combustion-grown diamond is comparable to material produced in other systems. Some of these examples are presented in this section with the intention of demonstrating the flexible nature of combustion CVD. 1.

Textured Film Growth

For a number of applications [53,54] films that demonstrate {100} texturing have several advantages. The combination of {100} growth conditions [27] and bias-enhanced nucleation techniques [55] has yielded highly oriented diamond films. Both the number and angle of grain boundaries are significantly reduced in these films relative to randomly oriented films [28,52]. Both the thermal [56] and the electronic [53] properties of diamond are

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adversely effected by the presence of grain boundaries. For example, the measured carrier mobility was three times greater in {100} oriented films than polycrystalline diamond [53]. In addition, {100} growth provides a means of planarizing the growth surface [52], enabling the use of conventional silicon technology to manufacture device structures without expensive grinding and polishing steps [54]. Figure 9 shows a scanning electron micrograph of a highly oriented {100} film that was produced by a two-step process. First, oriented nucleation was achieved using bias-enhanced nucleation techniques in a conventional microwave plasma reactor. The substrate was transferred to a low-pressure combustion reactor and grown for 3 hr [52]. In Fig. 9 one can see that a number of grains have coalesced, forming a very flat surface. 2.

Doping and Device Fabrication

Ravi and coworkers [57] demonstrated the high purity of combustion-grown diamond, producing films that had resistivities two orders of magnitude greater than natural diamond. The doping of diamond imparts semiconductor properties that are required for a number of applications [53]. Most of the limited work on doping of combustion-grown diamond has been carried out at the Naval Research Laboratory [58–61]. Glesener and coworkers [58]

Figure 9 Scanning electron micrograph of a highly oriented {100} film formed by a combination of bias-enhanced nucleation in a microwave reactor and textured growth in a low-pressure combustion CVD system. (From Ref. 52.)

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fabricated Schottky diodes by depositing boron-doped diamond on molybdenum. Further studies [59,60] indicated that high surface resistance was critical to form good junctions. The boron was added by bubbling part of the acetylene through a solution of diboric trioxide in acetone. Doverspike and coworkers [61] used an atomizer to entrain aerosol droplets that contained dopant species into the gas flow. Boric acid dissolved in methanol was used as a dopant solution. Recently, boron incorporation has been achieved without the use of a solvent. Trimethylborate is a high-vapor-pressure liquid that may be introduced by mass flow controllers at low pressure or with a bubbler for atmospheric operation [14]. 3.

Low-Temperature Deposition

Low-temperature processing is required for compatibility with a number of optoelectronic materials. In addition, low-temperature deposition minimizes the compressive stress that is formed when diamond is grown on material with differing coefficients of thermal expansion. Diamond deposition at rates of ⬃1 ␮m/hr on glass substrates was achieved at low temperature (750 K) in a low-pressure combustion reactor [51]. The low temperature was achieved by increasing the burner-substrate distance to 20 mm. Continuous, adherent films were deposited on Vycor and Pyrex glasses. The best films were optically transparent and no damage to the substrates was observed.

IV.

DEPOSITION CHEMISTRY

A.

Diagnostics

The chemistry of combustion diamond CVD has been primarily investigated using laser-induced fluorescence (LIF) and mass spectroscopy. The two techniques are complementary. Mass spectroscopy has been used to provide quantitative measurements of the major stable species, which are important for verifying kinetic models. In this technique a quartz microprobe samples gases at the diamond growth surface. Using mass spectroscopy, Wolden et al. [62] noted that the strong compositional dependence observed in a flat flame reactor was related to a sharp change in the acetylene concentration. On the other hand, LIF is a nonintrusive optical technique that has been used to detect radicals such as C2 , C2H, CH, and OH in the gas phase above the substrate. Researchers using plasma and hot-filament reactors have focused on C1 species such as methyl radical and atomic carbon as the dominant growth species [63,64]. However, evidence from combustion reactors suggests that C2 species are also very important. Three different groups [13,65,66] have noted a strong relation between C2 concentration profiles

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and diamond deposition rates. The role of CH is less clear, and OH appears to be of minor importance [65]. The work of Cappelli and Paul [65] suggested that C2H also plays an important role in the deposition process. B.

Reactor Modeling

An attractive feature of flat flame reactors is that they may be simulated using simple stagnation flow models with complex combustion kinetic mechanisms. Several workers have used this approach to model flat flames at diamond growth conditions [66–68]. Kim and Cappelli [67] argued that optimum diamond growth conditions result from a competition between hydrocarbon growth and oxidation. Simulations at Sandia indicated the importance of operating at high flame speeds to increase atomic hydrogen production [68]. A detailed kinetic mechanism containing 50 species and 218 reactions has been developed for the acetylene flame by Miller and Melius [69]. The model has been verified experimentally by Glumac and Goodwin [70] using mass spectroscopy and LIF at conditions slightly oxygen rich for diamond growth. Wolden and coworkers [14] performed a similar validation study at diamond growth conditions with a diamond substrate present. Figure 10 shows the profiles of selected species between the burner and substrate at diamond deposition conditions [14]. Acetylene and oxygen are rapidly converted to hydrogen and carbon monoxide as the gas exits the burner. At the high temperatures involved, a large amount of atomic hydrogen is produced. The concentration of H decreases near the surface due to recombination reactions with the diamond surface [71,72]. As noted in Sec. III, there is a very narrow composition window where diamond growth is achieved. Figure 11 shows the normalized concentration of selected species from model predictions plotted over a range of composition that spans the transition from graphite deposition to diamond deposition through etching [66]. The two species most often implicated in diamond growth, H and CH3 , hardly changed over this range. In contrast, the acetylene concentration decreased by 70%, which was the largest change observed for any species [66]. Although the mechanism is not fully understood, acetylene appears to be responsible for the sharp transition between diamond and graphite deposition.

C.

Alternative Fuels

Although acetylene is the most common fuel used for combustion synthesis, a number of alternatives have been examined including hydrogen [73], eth-

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Figure 10 Profiles of selected species between the burner (11 mm) and the substrate (0 mm) at diamond growth conditions: R = 1.00, P = 47 torr, Ts = 750⬚C, Uo = 600 cm/sec. (From Ref. 14.)

ylene [74], MAPP gas [75],* and methane [76]. The interest in other fuels is economic, due to the relatively high cost of acetylene. Diamond has been deposited successfully in each case, but the growth rates are significantly less than with acetylene. The superiority of acetylene is due to its high flame velocity and temperature. Table 2 compares these properties for a number of fuels. Examining Table 2, one finds that the flame temperature of acetylene is at least 350⬚C hotter than for the alternatives. All of these fuels produce hydrogen, but only atomic hydrogen is useful for diamond deposition. The importance of acetylene’s high flame temperature is shown in Fig. 12, which shows the dependence of hydrogen dissociation on both temperature and pressure. First, the temperature dependence is exponential. Thus, increasing the temperature from 2500 to 2900 K results in a fourfold increase in the H atom mole fraction. Besides growth rate considerations, modeling efforts

*MAPP gas is a commercially available mixture of about half liquefied petroleum gas (mostly propylene) and half C3H4 (a mixture of the two isomers methyl acetylene and propadiene).

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Figure 11 Variations of selected species as a function of reactant composition R = O2 :C2H2 over a range that spans the transition from graphite deposition to diamond-deposition to etching. (From Ref. 66.)

Table 2 Comparison of Adiabatic Flame Temperatures and Flame Speeds of Selected Fuels Fuel Acetylene, C2H2 Ethylene, C2H4 Hydrogen, H2 Propylene, C3H6 Methane, CH4

Adiabatic flame temperature (K)*

Flame speed (cm/sec)

2910 2565 2525 2505 2325

141.0 68.3 264.8 43.8 33.8

*Assumes base temperature = 25⬚C; oxidizer, air; equivalence ratio, 1.0.

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Figure 12 Equilibrium dissociation of atomic hydrogen as a function of temperature and pressure.

suggest that diamond quality increases quadratically with atomic hydrogen concentration [77]. Figure 12 also indicates that H-atom dissociation is enhanced at lower pressures in accordance with Le Chaˆtelier’s principle.

V.

COMPARISONS AND CONCLUSIONS

Although material deposited by combustion CVD has not been tested extensively, there is every indication that the quality is on par with that of diamond produced in hot-filament and plasma systems. Schottky diodes and high-energy particle detectors have been successfully fabricated using combustion-grown diamond. Issues of large-area deposition and uniformity have been addressed with flat flame burners. Growth rates are exceeded only by atmospheric plasma torches. Important features such as textured growth, boron doping, and low-temperature deposition have all been achieved in combustion reactors. Oriented nucleation, which has been achieved by substrate biasing in microwave and hot-filament reactors, has yet to be demonstrated in a combustion CVD system.

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Early reports concluded that combustion CVD was a much more expensive synthesis technique than plasma or hot-filament methods [78]. However, more recent analyses using data from a low-pressure flat flame burner indicates that the costs are very similar to those of microwave plasma CVD (M. Stonefield and C.A. Wolden, unpublished work). In comparison with plasma-aided processed, combustion CVD requires much less capital but has higher consumable costs because of the amounts of acetylene and oxygen required. In conclusion, the status of combustion synthesis of diamond using acetylene flames has been reviewed. The development of the technique from its inception using conventional welding torches to its present implementation using flat flame burners has been detailed. High growth rates and uniformity are characteristic of diamond deposition in flat flame burners. The design may be scaled to arbitrarily large areas. The quality of combustion diamond is comparable to that of material produced by other techniques. Economically, combustion CVD is competitive with plasma techniques. Combustion CVD requires less capital investment, but these savings are offset by high material costs. Substantial savings will be realized by improvements in growth rates and carbon utilization efficiency.

ACKNOWLEDGMENTS The author acknowledges the financial support of the National Research Council and Army Research Office during the writing of the manuscript. The author would like to thank Dr. John Prater of the Army Research Office for many helpful discussions and for stimulating my work in combustion CVD of diamond. Collaborations with the research groups of Professors Zlatko Sitar and Robert Davis in the Materials Science and Engineering Department at North Carolina State University were greatly appreciated.

REFERENCES 1. 2. 3. 4. 5. 6. 7.

Y Hirose, N Kondo. Program and Book of Abstracts, Japan Applied Physics 1988 Spring Meeting. Tokyo: Japanese Physical Society, 1988, p 434. LM Hanssen, WA Carrington, JE Butler, KA Snail. Mater Lett 7:289, 1988. KV Ravi. Diamond Relat Mater 4:243, 1995. Y Hirose, S Amanuma, K Komaki. J Appl Phys 68:6401, 1990. KA Snail, LM Hanssen. J Cryst Growth 112:651, 1991. G Janssen, WJP van Enckevort, JJD Schaminee, W Vollenberg, LJ Giling, M Seal. J Cryst Growth 104:752, 1990. T Abe, M Suemitsu, N Miyamoto, N Sato. J Appl Phys 73:971, 1993.

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24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42.

Wolden XH Wang, W Zhu, J von Windheim, JT Glass. J Cryst Growth 129:45, 1993. DB Oakes, JE Butler, KA Snail, WA Carrington, LM Hanssen. J Appl Phys 69:2602, 1991. LM Hanssen, KA Snail, WA Carrington, JE Butler, S Kellog, DB Oakes. Thin Solid Films 196:271, 1991. PW Morrsion Jr, JT Glass. In: G Davies, ed. Properties and Growth of Diamond. London: INSPEC, 1994, p 380. PK Bachmann, D Leers, H Lydtin. Diamond Relat Mater 1:1, 1991. Y Matsui, A Yukki, M Sahara, Y Hirose. Jpn J Appl Phys 28:1718, 1989. CA Wolden, RF Davis, Z Sitar, JT Prater. Diamond Relat Mater 7:133, 1998. RA Weimer, TP Thorpe, KA Snail. J Appl Phys 77:641, 1995. KA Snail, CM Marks. Appl Phys Lett 60:3135, 1992. CA Wolden, Z Sitar, RF Davis, JT Prater. Appl Phys Lett 69:2258, 1996. E Kondoh, T Ohta, T Mitomo, K Ohtsuka. Appl Phys Lett 59:488, 1991. C Chu, M D’Evelyn, R Hauge, J Margrave. J Appl Phys 70:1695, 1991. JJ Schermer, JEM Hogenkamp, GCJ Otter, G Janssen, WJP van Enckevort, LJ Giling. Diamond Relat Mater 2:1149, 1993. JS Kim, MA Cappelli. J Mater Res 10:149, 1995. CA Wolden, KK Gleason. Diamond Relat Mater 5:1503, 1996. GH Ma, Y Hirose, S Amanuma, M McClure, JT Prater, JT Glass. In: R Messier, JT Glass, JE Butler, R Roy, eds. New Diamond Science and Technology. Pittsburgh: Materials Research Society, 1991, p 587. KV Ravi, A Joshi. Appl Phys Lett 58:246, 1991. KV Ravi, CA Koch, HS Hu, A Joshi. J Mater Res 5:2356, 1990. K Hirabayashi, Y Hirose. Diamond Relat Mater 5:48, 1996. C Wild, R Kohl, N Herres, W Muller-Sebert, P Koidl. Diamond Relat Mat 3: 373, 1994. BR Stoner, SR Sahida, JP Bade, P Southworth, PJ Ellis. J Mater Res 8:1334, 1993. KA Snail, RG Vardiman, JP Estrera, JW Glesener, C Merzbacher, CJ Craigie, CM Marks, R Glosser, JA Freitas Jr. J Appl Phys 74:7561, 1993. JJ Schermer, LJ Giling, P Alers. J Appl Phys 78:2376, 1995. KA Snail, CL Vold, CM Marks, JA Freitas Jr. Diamond and Relat Mater 1: 180, 1992. JJ Scheimer, WA Elst, LJ Giling. Diamond and Relat Mater 4:1113, 1995. W Zhu, BH Tan, J Ahn, HS Tan. J Mater Res 30:2130, 1995. RC Aldredge, DG Goodwin. J Mater Res 9:80, 1994. T Abe, M Suemitsu, N Miyamoto. J Cryst Growth 143:206, 1994. M Murakawa, S Takeuchi. Surf Coat Technol 54/55:403, 1992. K Komaki, M Yanagisawa, I Yamamoto, Y Hirose. Jpn J Appl Phys 32:1814, 1993. PW Morrsion, A Somashekhar, JT Glass, JT Prater. J Appl Phys 78:4144, 1995. DY Wang, YH Song, JJ Wang, RY Cheng. Diamond Relat Mater 2:304, 1993. JA Cooper Jr, WA Yarbrough. Diamond Opt SPIE 1325:41, 1990. NG Glumac, DG Goodwin. Mater Lett 18:119, 1993. KF McCarty, E Meeks, RJ Kee, AE Lutz. Appl Phys Lett 63:1498, 1993.

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51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78.

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M Murayama, S Kojima, K Uchida. J Appl Phys 69:7924, 1991. M Murayama, K Uchida. Combust Flame 91:239, 1992. DW Hahn, CF Edwards, KF McCarty, RJ Kee. Appl Phys Lett 68:2158, 1996. J Powling. Fuel 28:25, 1949. WT Bielder, HE Hoeschler. Jet Propul 25:1257, 1957. CF Edwards, DW Hahn. Proceedings of ILASS-95 (Institute for Liquid Atomization and Spray Systems), Troy, MI, 1995, p 34. GH Evans, R Grief. Numer Heat Transfer 14:373, 1988. RJ Kee, JA Miller, GH Evans, G Dixon-Lewis. In: Twenty-second Symposium (International) on Combustion. Pittsburgh: The Combustion Institute, 1988, p 1479. CA Wolden, Z Sitar, RF Davis, JT Prater. Diamond Relat Mater 6:1862, 1997. CA Wolden, SK Han, MT McClure, Z Sitar, JT Prater. Mater Lett 32:9,1997. BA Fox, BR Stoner, D Malta, P Ellis, RC Glass, FR Sivazlian. Diamond Relat Mater 3:382, 1994. SK Han, MT McClure, CA Wolden, Z Sitar. Mater Res Soc Symp Proc 423: 281, 1996. SD Wolter, BR Stoner, JT Glass, PJ Ellis, DS Buhaenko, CE Jenkins, P Southworth. Appl Phys Lett 62:1215, 1993. JE Graebner, S Jin, GW Kammlot, B Bacon, L Seibles, WF Banholzer. J Appl Phys 71:5353, 1992. KV Ravi, CA Koch, DS Olson, P Choong, JW Vandersande, LD Zoltan. Appl Phys Lett 64:2229, 1994. JW Glesener, AA Morrish, KA Snail. J Appl Phys 70:5144, 1991. JW Glesener, AA Morrish, KA Snail. Appl Phys Lett 61:429, 1992. JW Glesener, KA Snail, AA Morrish. Appl Phys Lett 62:181, 1993. K Doverspike, JE Butler, JA Freitas Jr. Diamond Relat Mater. 2:1078, 1993. CA Wolden, Z Sitar, RF Davis, JT Prater. J Mater Res 70:2733, 1997. SJ Harris, DG Goodwin. J Phys Chem 97:23, 1993. BW Yu, SL Girshick. J Appl Phys 75:3914, 1994. MA Cappelli, PH Paul. J Appl Phys 67:2596, 1990. RJH Klein-Douwel, JJL Spaanjaars, JJ ter Meulen. J Appl Phys 78:2086, 1995. JS Kim, MA Cappelli. J Appl Phys 72:5461, 1992. E Meeks, RJ Kee, DS Dandy, ME Coltrin. Combust Flame 92:144, 1993. JA Miller, CF Melius. Combust Flame 91:21, 1992. NG Glumac, DG Goodwin. Combust Flame 105:321, 1996. CA Wolden, S Mitra, KK Gleason. J Appl Phys 72:3750, 1992. SJ Harris, AM Weiner. J Appl Phys 74:1022, 1993. NG Glumac, DG Goodwin. Appl Phys Lett 60:2695, 1992. JS Kim, MA Cappelli. Appl Phys Lett 65:2786, 1994. SJ Harris, HS Shin, NG Glumac. Appl Phys Lett. 66:891, 1995. JS Kim, MA Cappelli. Appl Phys Lett 67:1081, 1995. DG Goodwin. J Appl Phys 74:6888, 1993. Final report for DARPA Contract Number N00014-93-C2044, 1997.

9 Laser-Assisted and Optical Pumping Techniques for Diamond Synthesis Vish V. Subramaniam and Shashi M. Aithal The Ohio State University, Columbus, Ohio

I.

INTRODUCTION

Diamond growth by chemical vapor deposition (CVD) processes requires activation of the gas phase adjacent to a substrate. The previous chapters of this book have discussed several methods of providing this activation needed for driving chemical reactions in the gas phase. Among these are hot-filament CVD (HFCVD), flame synthesis, and plasma CVD. All three methods rely upon thermal heating or near-equilibrium effects to induce reactions in the gas leading to diamond growth. Consequently, it is not possible to exercise selectivity from among the various competing chemical processes for diamond growth. Selectivity of desired chemical channels or lowering of growth temperatures, for instance, requires that attention be devoted to how the growth medium is energized and reacted. Lasers offer a unique means of activating the molecules in the growth medium. They are potentially capable of reducing growth temperatures as well as providing selectivity in a reactive process. In this chapter, the use of lasers in diamond synthesis is discussed. Use of lasers for diamond synthesis has not always been motivated with the goal of commercialization. Rather, lasers have been used to create environments that enable detailed study of the gas (or condensed) phase chemistry. These can also lead to better understanding of some of the reacting channels occurring in the other, more commercially viable processes 325

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leading to process improvements. There are also other reasons that laserbased methods of diamond synthesis have been explored. These include the need to reduce substrate and gas (or liquid) temperatures during growth and to control and limit the codeposition of nondiamond carbon by selectively driving only the specific chemical channels that lead to diamond formation. In addition, lasers can be used to control diamond deposition patterns and enhance growth rates. Processes that meet these requirements are not necessarily the most economical as well. Hence, cost is not the only issue to consider when comparing laser-based methods with other better established CVD processes and General Electric’s high-pressure, high-temperature (HPHT) process. In order to appreciate the utility of lasers in CVD processes for diamond growth, it is necessary to understand how the energy added to a gas is redistributed within the various modes of its molecules. Gases comprise molecules and atoms and, in the case of plasmas, ions and electrons as well. These molecules, atoms, and ions in turn possess various internal modes of energy storage in addition to their translational (or what is called external) modes of motion. Figure 1 shows these various modes schematically. In addition to the three external degrees of freedom (i.e., translation in the three coordinate directions) that a particle possesses, molecules and molecular ions can store energy in rotation, vibration, and electronic excitation. Atoms and atomic ions can store energy only in electronic excitation in addition to their external modes. When energy is added to a gas in the

Figure 1 Schematic showing the different modes of energy storage for a diatomic molecule.

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form of simple heating, it first appears in the translational motion of the gas particles. Temperature is the common measure used to describe the average translational energy of the gas. The energy added by heating eventually makes its way into the other modes of molecular motion via collisions. Usually, exchange of translational energy between molecules takes place within a few collisions, and equilibration of energy between rotational and translational modes usually requires on the order of tens of collisions. In contrast, many collisions (on the order of thousands or many more) are required for the vibrational modes of molecules to equilibrate with rotational and translational modes [1–3]. Because the excitation of the vibrational modes is helpful in driving endothermic reactions, it can be seen that simple thermal heating is a circuitous and inefficient route to cause a gas to react. Thermal stimulation of a gas can be accomplished in a number of ways, including simple heating, electrical heating by partially ionizing it and then driving a current through the gas, or using a laser. It is usually inefficient and expensive to use a laser for thermal heating of a gas unless repetitive, very short duration pulse heating is required for a particular process. Lasers are also useful in instances where only the gas adjacent to a surface must be heated without heating the surface itself (see Fig. 2). In cases where the surface alone needs to be heated to drive a heterogeneous reaction, the gas must be transparent to the laser source whose energy is absorbed at the substrate-gas interface. This is often useful in the case where spot heating as opposed to bulk heating is required. Lasers drive chemical reactions by exciting specific transitions in a molecule. It may be pertinent to ask at this point whether or not a laser is necessary to excite a specific transition in a molecule. In other words, can one use an intense lamp (with an appropriate filter) to produce monochromatic (but incoherent) light to initiate reactions in gases? The answer of course is yes, and chemists were employing such techniques long before the invention of lasers to measure reaction rates [4]. However, inference of re-

Figure 2 Schematic showing the use of a laser to drive homogeneous gas-phase reactions by pyrolysis, photolysis, or laser excitation without heating of the surface.

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action rates in complex chemically reacting systems is rendered difficult for two important reasons. First, incoherent monochromatic sources such as intense lamps are limited in intensity because they are diffuse, i.e., emit light in all directions. Usually, the higher the intensity (i.e., energy per photon multiplied by the number of photons per unit area, per unit time), the higher is the reaction yield, which makes it easier to measure changes in concentrations. Second, production of extremely short duration pulses (say of duration nanoseconds to hundreds of nanoseconds) of sufficient energy to drive fast reactions is nearly impossible with an incoherent, monochromatic source. Lasers, on the other hand, are monochromatic sources that can produce high pulse energies with extremely short durations and sustain these characteristics over long distances because they are coherent. We now digress a bit and examine this property of coherence in some detail, following the development in Ref. 5. Two sources are said to be coherent if they emit light or photons of a given frequency ␯ (or energy h␯, where h is Planck’s constant), with nearly the same amplitude, and in phase with each other. An important consequence of coherence is that a maximum intensity is observed at a point in space where the phase difference between two waves or photons reaching that point is an integral multiple of 2␲. Another way of stating this idea is that the maximum intensity will occur when the path difference1 between two waves or photons is an integral multiple of the wavelength ␭ (= c/␯, where c is the speed of light). The minimum intensity occurs when the phase difference between the photons is an odd multiple of ␲, i.e., (2m ⫹ 1)␲, where m is an integer (= 0, 1, 2, . . .). Coherent sources thus exhibit the important property of interference. The appearance of fringes (i.e., alternating segments of maximum intensity and minimum intensity) is due to interference. Because light is a form of electromagnetic radiation, it can be repre→ sented at any point in space as a time-varying electric field E(t) = → → E0e ⫺i␻te i␾(t), where E0 is the amplitude, ␻ = 2␲␯ is the circular frequency, i = 兹⫺1, t is time, and ␾→(t) is the time-dependent phase. Thus, when two → photons represented by E1 and E2 interact, the resulting intensity can be expressed as a time average: →

→

→

→

→

→

I = 具E⭈E*典 = 具(E1 ⫹ E2)⭈(E* 1 ⫹ E*)典 2 →

→

→

→

= 具兩E1兩2 ⫹ 兩E2兩2 ⫹ 2 Re(E1 ⭈E*)典 2 where the angle brackets denote the time average, defined as 1

If the path difference is x and the phase difference is ␦, the two are related by ␦ = 2␲x/␭, where ␭ is the wavelength.

Laser-Assisted and Optical Pumping Techniques

具 f 典 = lim → t0

⬁

1 t0

冕

329

t0

f(t) dt

0

The symbol Re denotes the real part of a complex number, and the superscript * denotes the complex conjugate of a complex number. Now for simplicity, if we assume that the two fields are polarized,2 then their vectorial nature can be ignored. The intensity then becomes I = I1 ⫹ I2 ⫹ 2 Re具E1E*典 2 where I1 = 具兩E1兩2典 and I2 = 具兩E2兩2典. Thus, if t is the time required for one photon to travel via a path A and if (t ⫹ ␶) is the time required for a second photon to travel via path B, then the intensity due to interference is ⫹ ␶)典 = 2 Re(⌫12(␶)). The function ⌫12(t) is called the mutual 2 Re具E1(t)E*(t 2 coherence function or correlation function of the two fields. Analogously, ⌫11(t) is called the autocorrelation function. By definition, ⌫11(t = 0) = I1 and ⌫22(t = 0) = I2. The intensity is also written as I = I1 ⫹ I2 ⫹ 2兹I1I2 Re{␥12(␶)} where ␥12(␶) is called the degree of partial coherence and is given by

␥12(␶) =

⌫12(␶) ⌫12(␶) = ⌫ (0)⌫ (0) 兹 11 兹I1I2 22

If 兩␥12兩 = 1, we have complete coherence. If 兩␥12兩 = 0, there is complete incoherence, and if 0 < 兩␥12兩 < 1, there is partial coherence. Now, suppose that the interference pattern varies between the two limits set by Imax and Imin: Imax = I1 ⫹ I2 ⫹ 2兹I1I2兩␥12兩 Imin = I1 ⫹ I2 ⫺ 2兹I1I2兩␥12兩 The fringe visibility is then defined as ᭙=

Imax ⫺ Imin 2兹I1I2兩␥12兩 = Imax ⫹ Imin I1 ⫹ I2

When I1 = I2, then ᭙ = 兩␥12兩. Thus, for complete coherence, ᭙ = 1 and the fringes have a maximum contrast of unity, whereas for complete incoherence, ᭙ = 0 and the fringe contrast is 0 (i.e., there are no distinguishable fringes). We will now attempt to relate the degree of partial coherence to the characteristics of a source. Suppose the source emits an electromagnetic 2

Simply defined, polarization is a chosen direction of the electric field vector in the plane normal to the direction of propagation of the electromagnetic wave.

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wave whose field varies sinusoidally for a certain duration ␶0 and then changes phase abruptly. This can represent, for example, the case of an excited atom or molecule that emits radiation for a certain amount of time and then suffers a collision with another atom or molecule. This sequence of emission for a certain duration ␶0 followed by an abrupt change of phase is then repeated indefinitely. ␶0 is called the coherence time. The phase therefore may vary in a manner such as that shown in Fig. 3 for illustrative purposes. Suppose now that the light from this source represented by E(t) = E0e⫺i␻te i␾(t) is split into two beams and subsequently brought together to produce interference. Assuming that 兩E1兩 = 兩E2兩 = 兩E兩, the degree of self partial coherence is

␥(␶) =

具E(t)E*(t ⫹ ␶)典 具兩E兩2典

Substituting for E(t), we have

␥(␶) = 具e i␻␶e i [␾ (t)⫺␾ (t⫹␶)]典 = ei␻␶ lim → T

⬁

1 T

冕

T

e i [␾ (t)⫺␾ (t⫹␶)] dt

0

Figure 4 shows an illustrative plot of the phase difference ␾(t) ⫺ ␾(t ⫹ ␶) versus time. For the first time interval, 0 < t < ␶0, ␾(t) ⫺ ␾(t ⫹ ␶) = 0 when 0 < t < ␶0 ⫺ ␶. However, for ␶0 ⫺ ␶ < t < ␶0, the phase difference takes on some random value ⌬ between 0 and 2␲. Therefore, the degree of self partial coherence becomes

␥(␶) = e

i␻␶

= e i␻␶

1 ␶0

冕

␶0

e

i [␾ (t)⫺␾ (t⫹␶)]

dt = e

0

i␻␶

1 ␶0

再冕

␶0⫺␶

0

冕

␶0

dt ⫹

␶0⫺␶

冎

e i⌬ dt

1 {␶0 ⫺ ␶ ⫹ ␶e i⌬} ␶0

Each interval will have the same expression for ␥(␶), except that the value

Figure 3 Plot of phase ␾(t) versus time t for the example of a quasi-monochromatic source. (From Ref. 5.)

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Figure 4 Plot of phase difference, ␾(t) ⫺ ␾(t ⫹ ␶) versus time t for the discussion of coherent length and coherent time. (From Ref. 5.)

of ⌬ will be different. Because ⌬ is random, the time average of e (i⌬) is zero, and the average of ␥(␶) over all such intervals will be (1 ⫺ (␶/␶0)e i␻␶, whenever ␶ < ␶0. On the other hand, when ␶ > ␶0, the phase difference is always random so that its average over many intervals is zero. Hence, we have

␥(␶) =

or

再 再

兩␥(␶)兩 =

冉 冊

for ␶ < ␶0

0

for ␶ ⱖ ␶0

1⫺

1⫺ 0

␶ e i␻␶ ␶0

␶ ␶0

for ␶ < ␶0 for ␶ ⱖ ␶0

This function is shown schematically in Fig. 5. Since 兩␥兩 is equal to the fringe visibility ᭙ for two light waves of equal amplitude, it can be seen from Fig. 5 that ᭙ drops to zero when ␶ exceeds the coherence time ␶0. This means that the path difference between the two split light waves, say x, must not exceed the value of Lc = c␶0, where c is the speed of light. The quantity Lc = c␶0 is called the coherence length. Thus, for x > Lc, interference fringes will not be observed. Interference fringes can be observed only for x < Lc. In a radiating gas, the time between collisions of gas molecules is not constant but varies randomly from one collision to the next. However, an average time between collisions can be defined. Hence, ␶0 should be interpreted as an average value of the individual coherence times. The same holds true for the coherence length.

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Figure 5 Plot of degree of self partial coherence, 兩␥ (␶)兩 versus ␶ for the discussion of coherent length and coherent time. (From Ref. 5.)

We are now in a position to understand the crucial differences between lasers and ordinary, intense, incoherent sources. The first point to realize is that no source of light is ever strictly monochromatic. There is always a spread of frequency about some mean frequency due to natural broadening.3 It can be shown using Fourier analysis that the width ⌬␻ of the frequency distribution is given by ⌬␻ = 2␲/␶0 or ⌬␯ = 1/␶0 [5]. Conversely, we can also say that a spectral line of width ⌬␯ has a corresponding coherence time of ␶0 = 1/⌬␯, with a coherence length of Lc = c␶0 = c/⌬␯. This condition can also be expressed in terms of wavelength as Lc = ␭2/⌬␭ because ⌬␯/␯ = 兩⌬␭兩 /␭. For ordinary light sources such as lamps or discharge tubes, the line widths in the visible portion of the spectrum (say around 500 nm) are on the order of an angstrom [5]. The corresponding coherence length is then on the order of 5000 wavelengths or about 2.5 mm. This means that with such light sources, interference fringes would disappear beyond a distance of about 2.5 mm. In contrast, the line width of a gas laser can be as narrow as 103 Hz or less,4 which corresponds to a coherence length of about 300 km! Thus, coherent sources are capable of producing interference effects over much larger distances than incoherent sources. The other essential difference between incoherent and coherent light sources is the property of directionality. Ordinary lamps and discharge tubes, which produce incoherent light, radiate in all directions. In contrast, light

3

Natural broadening refers to the finite line width (centered around a specific wavelength) observed for a spectral line due to the finite radiative lifetime of a given excited state of an atom or molecule. The width associated with natural broadening has its origins in Heisenberg’s uncertainty principle, which gives a relationship between uncertainties in time and energy. 4 The corresponding line width for ordinary, incoherent light sources is on the order of 1010 Hz.

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from a laser can come very close to an ideal plane wave whose divergence is primarily due to diffraction effects [6]. Therefore, the high directionality of the laser beam can be used to focus it to extremely small dimensions and thus attain high power densities or intensities. For the aforementioned reasons, laser-based methods have a great potential to drive chemical reactions. It is more efficient to stimulate internal modes of gas molecules (i.e., the more reactive modes such as vibrational or electronic excitation) directly rather than relying upon thermal heating. The former relies upon sustaining thermodynamic disequilibrium between internal and external modes of molecular motion. Excitation of the internal modes with minimal excitation of the translational modes also leads to some control over selectivity, as we shall see later in this chapter. In contrast, thermal heating of a gas, results in states that are in thermodynamic equilibrium or in local thermodynamic equilibrium (LTE).5 Lasers, depending on how they are used, are capable of producing gaseous environments that can be in LTE or far from it. Processes that use this departure from LTE to induce selective growth of diamond or produce films of desired properties or characteristics are discussed later in this chapter. Their ultimate utility in industrial applications, though, must be evaluated with regard to cost.6 The use of lasers for diamond synthesis (or synthesis of other materials for that matter) can be grouped into general categories: (1) rapid heating and pyrolysis, shown schematically in Figs. 2 and 6; (2) ablation or physical vapor deposition (PVD), shown schematically in Fig. 7; (3) photolysis, shown schematically in Figs. 2 and 6; (4) laser excitation or optical pumping, shown schematically in Figs. 2 and 6; and (5) hybrid methods. An obvious use of a laser is for intermittent, rapid heating. Laser pyrolysis is included in this grouping, although there are some important differences. A laser can be used to heat a gas by irradiating surfaces in contact with the gas. This takes advantage of the fact that solid surfaces tend to absorb radiant energy broad band (i.e., over a continuous range of wavelengths) whereas gases tend to absorb discrete lines (i.e., at specific wavelengths). Such an instance of a solid surface being heated is encountered 5

Strictly speaking, the state of thermodynamic equilibrium is defined as one that is homogeneous, isotropic, and devoid of any gradients. However, most practical engineering situations involve flows and gradients. Therefore, the concept of local thermodynamic equilibrium or LTE is typically introduced as an approximation to allow a flowing gas exposed to gradients to be treated as consisting of infinitesimal regions that are nearly homogeneous, isotropic, and devoid of gradients. 6 We shall address the issue of cost later, as each technique is described. We hasten to point out that the economics of diamond is largely artificial, and therefore we will avoid using units of dollars per carat to discuss cost. Rather, we evaluate processes based upon energy cost expressed here in units of joules per carat ( J/carat).

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Figure 6 Schematic showing the use of a laser to drive gas-phase or heterogeneous reactions by pyrolysis, photolysis, or laser excitation while heating the surface locally.

when heterogeneous (i.e., gas-solid) reactions need to be driven. The laser wavelength must then be chosen so that the gas is transparent to this wavelength while the surface is not. A potential advantage over other methods of heating the surface is that the laser energy can be absorbed at the surface alone, with minimal heating of the bulk material. If the gas alone is to be heated, the laser energy must first be absorbed7 by the gas (at a specific wavelength or discrete wavelengths corresponding to vibrational or electronic transitions in the gas molecules). The energy initially absorbed in the internal modes is then rapidly redistributed to the external (translational) modes, thus raising the gas temperature and driving chemical reactions. This process, known as pyrolysis, can involve either specific constituents or all constituents of a gas mixture. Lasers can also be used to irradiate and vaporize a target material, with the vapor-phase products subsequently condensing on a surface placed near the target. We shall refer to this technique as laser ablation, and a schematic is shown in Fig. 7. In the literature, laser ablation is also known as laser physical vapor deposition or LPVD. This method has been used successfully to produce thin films of superconductors and other materials. The target or targets are usually pure materials or materials of fixed, known composition. Intense laser energy (usually in the ultraviolet) is focused on the target,

7

Laser energy can be absorbed by a gas molecule M either by resonant single-photon absorption or by multiphoton absorption. The former utilizes transitions between real energy levels in a molecule whereas the latter can also occur via virtual energy states: single-photon: h␯ ⫹ M(E1) → M(E2) where E2 > E1 multiphoton: nh␯ ⫹ M(E *) → M(E *) where E * 1 2 2 > E* 1 and E * 1 and E * 2 do not have to be real energy states belonging to the molecule M

Laser-Assisted and Optical Pumping Techniques

Figure 7

335

Schematic of laser physical vapor deposition or LPVD process.

causing portions of it to vaporize and in some cases ionize or react. The vapor then is made to condense on a substrate placed nearby (which may be heated or cooled), resulting in a thin film. In most cases, the laser also interacts with the vapor (which may or may not be ionized) emanating from the target. Thus, the laser ablation technique could be easily applied in conjunction with other techniques such as plasma CVD, hot-filament CVD, or flame synthesis, resulting in a hybrid method. The third category is photolysis, wherein multiphoton processes are used to break apart polyatomic molecules into smaller, radical fragments. Multiphoton absorption is a nonlinear process whereby two or more photons are absorbed by a molecule, resulting in dissociation of the polyatomic molecule into molecular or atomic fragments. The process can be written symbolically in the following form of a chemical reaction: Mn ⫹ p(h␯) → Ra ⫹ Sb

(1) ⫺34

where p photons of frequency ␯ are absorbed (h = 6.626 ⫻ 10 J-sec, is Planck’s constant) by a polyatomic molecule containing n (n = a ⫹ b) atoms. The result is that the molecule is taken to its dissociation limit and the resulting polyatomic fragments are R (containing a atoms) and S (containing b atoms). The two ways in which a multiple number of photons can be absorbed by a polyatomic molecule are shown schematically in Fig. 8. The photons do not necessarily have to access real energy levels within the molecule en route to the dissociation limit. The multiphoton process can access virtual energy states [4,7,8]. Further, the absorption process can be either sequential or simultaneous. An example of a naturally occurring multiphoton process is the dissociation of O2 in the earth’s upper atmosphere due to ultraviolet (UV) radiation from the sun: O2 ⫹ m(h␯) → O ⫹ O

(2)

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Figure 8 Schematic showing multiphoton dissociation (MPD) process in a polyatomic molecule. MPD processes can take place through interaction of the molecule with many photons either sequentially or simultaneously and can involve either real energy levels or virtual energy levels.

where m is at least 2 for photons with a wavelength of 193 nm.8 The O atoms subsequently recombine with O2 to form ozone (O3). This technique of photolysis is routinely employed by chemists to measure reaction rates involving specific molecules or radicals [4,7,8]. There are laser-based techniques that take advantage of the coincidence between the wavelength of the laser light and energy difference for a particular transition (either electronic or vibrational) in a given molecule. Because such an application typically does not involve high powers but rather the right wavelength, these techniques are collectively referred to here as laser excitation or laser-excited CVD. A listing of different lasers presently available along with their operating wavelengths is given for reference in Table 1. A broader term that encompasses incoherent light (such as UV lamps) as well as coherent (laser) light is optical pumping. The terms laser excitation and optical pumping will be used interchangeably throughout this chapter, even when a laser is used to create the optical pumping. In optical pumping of a gas, the absorption is usually by a resonant single-photon process:

8

The particular wavelength of 193 nm is also the wavelength at which the ArF (argon-fluoride) excimer laser lases. The wavelength of 193 nm is in the range of absorption for O2 via the Schumann-Runge bands [4].

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Table 1 Available Laser Sources and Their Respective (Commonly Found) Wavelengths Laser type

Wavelength

ArCl excimer ArF excimer KrCl excimer KrF excimer Frequency-quadrupled Nd:YAG XeBr excimer XeCl excimer Nitrogen laser XeF excimer 7-Hydroxycoumarin dye 4-Methylumbelliferone dye Esculin dye Argon ion laser Argon ion laser Frequency-doubled Nd:YAG Puronin B dye Na-fluorescein dye 2,7-Dichlorofluorescein dye Rhodamine 6G dye Acridine red dye Rhodamine B dye Helium-neon laser Ruby (Al2O3 doped with Cr2O3) Nd:YAG (Y3Al5O12) HF chemical laser DF chemical laser CO laser CO2 laser Free electron laser

175 nm 193 nm 222nm 248 nm 266 nm 282 nm 308 nm 330 nm 351 nm 450–470 nm 450–470 nm 450–470 nm 488 nm 514.5 nm 532 nm Yellow 530–560 nm 530–560 nm 570–610 nm 600–630 nm 605–635 nm 632.8 nm 692.9 nm and 694.3 nm 1.064 ␮m (dominant line) 2.7 ␮m 3.8 ␮m Multiple lines from 4.7 to 5.8 ␮m 9.4 ␮m, 10.6 ␮m Visible to ultramicrowave (mm) wavelengths

Mn(E1) ⫹ h␯ → Mn(E2)

(3)

where h␯ = E2 ⫺ E1, and E1 and E2 are energy levels within the molecule Mn, comprising n atoms. This is followed by collisional processes that lead to energy transfer and subsequent chemical reaction. Lasers have been used successfully to synthesize diamond particles, films, and diamond-like films. Although lasers have also been used to enhance and control nucleation, reduce the surface roughness, and improve adhesion of the film to the substrate, the focus of this chapter is on synthesis.

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It is not our intent to provide a general background on lasers or on their principles of operation. There exist several excellent books on the subject [9,10]. Laser operation and characteristics will be discussed only as and when specifically applicable to a particular process. The focus here is on the more nonstandard and novel applications of lasers for diamond growth, especially those that result in highly nonequilibrium environments. In other words, we explore the situations that can best be created by a laser and, in some cases, not by any other means. This chapter is organized as follows. Section II describes synthesis of diamond and diamond-like carbon reportedly resulting from rapid heating and/or cooling due to laser irradiation. Production of diamond-like carbon by ablation of a precursor target is described in Sec. III, followed by a discussion of use of laser CVD for diamond synthesis by photolysis of carbonaceous precursors in Sec. IV. Diamond synthesis by relatively low-power resonance absorption of laser energy (i.e., laser excitation) is discussed in Sec. V. A chapter summary is given in Sec. VI.

II.

RAPID HEATING AND COOLING

A.

Introduction

There are specific instances where laser beams provide an intense source of energy that results in heating of a target gas, solid, or liquid. Depending on the rate at which the incident energy is absorbed and redistributed per unit time, resulting temperatures and pressures can exceed thousands of kelvins and many hundreds of kilobars or more. Referring back to the (equilibrium) phase diagram for carbon (see Fig. 13), it can be seen that such conditions are conducive for conversion of nondiamond carbon to diamond. Even when the output power of a laser beam alone does not provide sufficient intensity or the required heating and compression, the beam can be focused to provide intense heating over a small region. The output beam from a laser is usually at least a few millimeters in diameter. When focused using a lens (of radius b < a) or focusing mirror, the ultimate radius of the beam of radius a can be estimated from physical optics to be [6,9] r0 = ␭ f/min{a, b}

(4)

where ␭ is the wavelength of laser light and f is the focal length of the lens or optical element used. In practice, however, the ultimate size of a focused laser beam is much larger than that given by Eq. (4) because of multimode emission from the laser and lens aberration. Now, if P is the power of the incident laser beam, then the intensity can be written as

Laser-Assisted and Optical Pumping Techniques

冕

339

a

I=

Ip(r)2␲ r dr

0

␲ r 20

When Ip is independent of r, we have I=

P ␲ r 20

(5)

We can also write Eq. (5) using Eq. (4) as I = Pa2/␲␭2 f 2

(6)

Usually, Ip depends on r in a Gaussian manner but Eqs. (5) and (6) can be easily rewritten for this case. Although Eq. (6) may not be quantitatively accurate for real laser beams for which Ip is a function of r, it does provide the correct trends. For instance, the intensity does scale inversely with the square of the laser wavelength and lens focal length and directly with the square of the initial (i.e., prefocusing) beam size. Thus, for a given laser output power, the intensity increases for shorter wavelength laser beams, smaller focal length lenses, and large initial beam diameters. B.

Gas-Phase Heating

An appropriate example of rapid gas-phase heating triggering reaction and ultimately leading to formation of diamond particles is the experiment of Buerki and Leutwyler [11]. This work combines both pyrolytic and photolytic decomposition of the gas phase. In this experiment, mixtures consisting of ethylene (C2H4), H2, and silane (SiH4) in compositions of 51.5–100%:0– 41.2%:0–7.2% were introduced vertically through a capillary nozzle into a reactor. These precursors were diluted in either N2 or Ar or both. The gas flow was then irradiated horizontally by a focused line-tunable continuouswave (cw) CO2 laser beam, 2–3 mm above the nozzle. Silane (a strong absorber of 10.6-␮m CO2 laser radiation) was used to elevate the gas temperature and to enhance pyrolysis or chemical decomposition of C2H4. Two processes that cause such gas mixtures to react are pyrolysis and photolysis. The process by which these small molecules decompose upon exposure to infrared radiation from the CO2 laser is known as infrared multiphoton dissociation or IRMPD [7]. Both SiH4 and C2H4 absorb infrared photons via multiphoton processes (of the type discussed in footnote 7 and shown in Fig. 8) triggered by the intense radiation field of the focused laser beam and are subsequently taken to their respective dissociation limits [7]. Inevitably, some of the laser energy is also transferred to the vibrational modes of these

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molecules, resulting in rapid gas heating via vibration-rotation-translation (VRT) and vibration-translation (VT) collisional energy transfer. Thus, some of these molecules are also pyrolyzed and decomposed. The authors report that 1 g of particles black in appearance were produced from C2H4 /N2 /Ar/ H2, C2H4 /N2, C2H4 /Ar, and C2H4 /N2 /H2 mixtures. The particles (on the order of 5–15 nm in size) were characterized by bright-field transmission electron microscopy (TEM) imaging and electron diffraction. Based on this analysis, the authors report finding diamond for the C2H4 /N2 gas mixture and a graphite-diamond mixture in all the other cases. In addition, these authors report that a gas mixture of C2H4 /N2 /SiH4 /H2 yielded diamond particles ⬃120 nm in size in one instance. Although it is encouraging that they appear to be able to distinguish between diamond and graphite through bright-field TEM imaging and electron diffraction analysis, some caution is warranted. Disordered graphite is known to masquerade as diamond, especially in electron diffraction patterns [12,13]. The only way to establish deposits unequivocally as being diamond is through Raman spectroscopy. As an example, the Raman spectrum of a diamond film containing graphite and disordered graphite synthesized using an oxyacetylene flame is shown in Fig. 9. This particular film can be seen to contain diamond (1332 cm⫺1 line), graphite (as can be seen from the ‘‘G’’ peak at 1580 cm⫺1), and disordered graphite

Figure 9 Raman spectrum of a diamond film synthesized using an oxyacetylene flame, displaying peaks identifying diamond and disordered graphite. (From Refs. 15–17.)

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(as evidenced by the presence of the ‘‘D’’ peak at 1343 cm⫺1). Unfortunately, no Raman spectra are presented in Ref. 11. This is understandable given the small size of the particles and the small sample, both of which would yield an extremely small signal (if any) in Raman spectroscopy. In the absence of such evidence, as many additional methods as possible of characterization of the physical properties (such as hardness) and chemical properties (such as reactivity to hydrogen or oxygen when heated, or exposure to acids) are needed. Again, this is difficult when sample sizes are small. Gas-phase reactions with C2H4 as the carbonaceous precursor required about 10 W of power (the residence time was about 1 msec and the pressure was 1 atm) [11]. Based upon the values given in Ref. 11, a characteristic J/carat value (not counting capital cost) can be computed for this case using the optimistic assumption that all of the 1 g of deposit yield is diamond. Reference 11 reports a linear growth rate of 5.7 ␮m/sec, and assuming this is all diamond, we can compute an equivalent spherical volumetric growth rate of (4/3)␲(5.7 ⫻ 10⫺6)3 m3/sec or 7.8 ⫻ 10⫺16 m3/sec. Given the density of diamond (3515 kg/m3) and that 1 carat = 0.2 g or 2 ⫻ 10⫺4 kg, the growth rate in carats per second is 7.8 ⫻ 10⫺16 ⫻ 3515/2 ⫻ 10⫺4, or 1.4 ⫻ 10⫺8 carats/sec. The power required for this process according to Ref. 11 was 10 W or 10 J/sec, so that the energy cost in joules per carat is 10/1.4 ⫻ 10⫺8, or 7.1 ⫻ 108 J/carat. The value of 7.1 ⫻ 108 J/carat is enormous, and it is important to put it in perspective by comparing with the corresponding energy cost for diamond synthesis using an oxyacetylene flame. For flame synthesis, assuming a linear growth rate of 100 ␮m/hr on a 1 cm2 surface area, we obtain a typical value9 of 8 ⫻ 105 J/carat. Thus, we can see that the energy cost of this particular pyrolysis/photolysis process is three orders of magnitude higher and has no apparent gain in quality of the diamond or in selectivity. It must be further emphasized that laser efficiency and capital cost have not been considered here. The joule per carat value, however, does provide an index for comparing these different processes. A more recent example of extreme gas-phase heating to the point of ionization is the laser-plasma technique developed by Konov and Uglov [14]. In this work, a powerful (2.5 kW) cw CO2 laser beam was focused using an NaCl lens ( f = 7 cm) into a chamber containing a flowing mixture of Xe, H2, and CH4 (in proportions of 300:30:1) at 1 atm. The authors report growth of diamond films 1 cm2 in area at a rate of 30–50 ␮m/hr on water9

Assuming a growth rate of 100 ␮m/hr over a circular spot 1 cm2 in area, the volume growth rate is 2.8 ⫻ 10⫺12 m3/sec or 4.9 ⫻ 10⫺5 carats/sec. Taking 39 W as that power required to raise a total flow of 1.8 ⫻ 10⫺4 kg/sec of an acetylene-oxygen mixture from 25⬚C to the ignition temperature of 305⬚C, the cost is 8 ⫻ 105 J/carat. It must be pointed out that this value is typical of a laboratory-scale oxyacetylene flame.

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cooled tungsten substrates, verified after growth using Raman spectroscopy. This growth rate is comparable to deposition using a laboratory-scale oxyacetylene flame, except that the power cost is higher by about two orders of magnitude. It must be pointed out, however, that this excessive power cost can be lowered if their process is optimized. This work is, however, very similar in nature to synthesis using the oxyacetylene flame except that conditions such as gas type and purity are more controllable. C.

Surface Heating

An alternative approach of using lasers to provide rapid heating has been demonstrated by several researchers [18,19]. In this instance, a stream of carbon black particles was exposed to CO2 and yttrium-aluminum-garnet (YAG) laser irradiation at various power densities and modes of operation (i.e., cw and pulsed). Conversion of carbon black particles to diamond is reported in Ref. 19. Again, no Raman spectra are given, but the authors claim that TEM imaging, x-ray, and electron diffraction data are able to distinguish diamond particles from disordered graphitic phases. Another report appears to confirm this finding based on TEM imaging, electron diffraction, x-ray photoelectron spectroscopy, and measurements of electrical resistivity [20]. In the latter work, a Q-switched Nd:YAG laser was used to irradiate a 200-nm-thick amorphous carbon (so called diamond-like carbon or DLC) film and to convert it to diamond. However, caution must be exercised about the credibility of these reported results given the lack of any Raman spectra. Further, an earlier study on pulsed Nd:YAG laser irradiation of amorphous carbon films actually reports conversion of the film to graphite at intensities of less than about 1 J/cm2 [21]. They confirm the structural change to graphite by Raman spectroscopy. Laser intensities of 4.5 J/cm2 were reportedly used in Ref. 20 and these intensities are not drastically different from those used in Ref. 21. It is also unlikely that the initial amorphous carbon films were very different. This comparison indicates that characterization methods other than Raman spectroscopy (such as TEM imaging and electron diffraction) may not be able to distinguish diamond from disordered graphite reliably. There has been an interesting attempt to use a laser to provide rapid heating of the surface layers of a single-crystal copper specimen, initially saturated with carbon. Because carbon is not soluble in copper, it can be driven out of the material with relative ease by heating. The technique described in Ref. 22 reportedly formed millimeter-size single-crystal diamond ˚ thick and were formed on the singlefilms. These films were about 500 A crystal copper substrate when irradiated with a laser beam. The presence of diamond was reportedly verified using Raman spectroscopy. This work was

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probably based upon the work of Ref. 23, which reported heteroepitaxial diamond growth by ion implantation of high-temperature carbon into a copper substrate. Unfortunately, neither the result reported in Ref. 22 nor that in Ref. 23 was reproduced in a subsequent attempt by Lee et al. [24]. Their approach essentially consisted of ion implantation of carbon at an ion energy of 50 keV and a flux of 1018 atoms/cm2 in a number of crystalline substrates [Cu(100), Cu(110), Cu(111), Ni(100), Ni(110), and single crystal Co]. The samples were then irradiated using separate laser wavelengths of 248 nm (KrF excimer laser with pulse width of 25 nsec), 308 nm (XeCl excimer laser with pulse width of 15 nsec), and 532 nm (frequency-doubled Nd:YAG laser with pulse width of 7 nsec) with power densities in the range of 1–6 J/cm2. The laser irradiation was carried out in vacuum and in the presence of nitrogen. No additional information was reported in their paper about whether or not the beam was focused or the spot size of the beams. Characterization by Raman spectroscopy, Auger spectroscopy, and TEM showed the resulting carbon films to be amorphous or composed of microcrystalline graphite. Lee et al. were therefore unable to reproduce the results of Refs. 22 and 23. Reference 24 appears to have reproduced all of the conditions reported in Ref. 22, but for the longest pulse width and perhaps the rise time of the laser pulse. In the experiments of Ref. 24, the longest pulse width was 25 nsec whereas the longest pulse width in Ref. 22 was 45 nsec. Because the pulse width affects the heat flux and total heat input into the surface, this could have affected the outcome of the experiments, with the rise time of the laser pulse being an important parameter. Figure 10 shows how two pulses can have different rise times while having the same total or integrated energy content. As we are dealing with pulse widths on the order of tens of nanoseconds, specific details such as rise time of the pulse and maximum pulse amplitude could be important in reproducing the experiments reported in Refs. 22–24. In other words, even if the heat addition over the duration of the laser pulse were the same in Refs. 22 and 24, the

Figure 10 Schematic showing two laser pulses having the same total or integrated energy while having different peak powers and rise times.

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rate at which the heat is added may have been important. Unfortunately, pulse shapes are not reported in either Ref. 22 or Ref. 24. In addition, it would be interesting to repeat these experiments in the presence of atomic hydrogen, as this could help stabilize a diamond surface in the act of formation. It is instructive to explore the heating depth and evolving surface temperature distribution when a material is exposed to laser irradiation. Laser radiation can be reflected, transmitted, or absorbed at a surface and at depths below the surface. Of these, only the absorbed energy affects the temperature or average energy of the solid material. The absorbed radiation may be viewed as the result of interactions between the incident photons and electrons and photons and phonons10 in the material. In dielectric materials, phonon-phonon interactions are dominant whereas in metals photon-electron followed by electron-phonon interactions are important. The process of heat transport within the material therefore establishes itself (in the classical sense of heat conduction) only after a certain time ␶ has elapsed. This initial relaxation time, ␶, is the characteristic time required for photon-phonon or photon-electron and electron-phonon interactions (i.e., collisions) to exchange energy and establish local thermal equilibrium. In other words, the relaxation time is the time that must elapse before a local lattice temperature or local electron temperature can be defined. In metals, the characteristic times for phonon-phonon, photon-electron, and electron-phonon interactions are on the order of picoseconds, and in dielectrics the phononphonon relaxation time is on the order of nanoseconds to picoseconds. Therefore, if laser pulse widths are shorter than nanoseconds, the microscale or short-transient energy transfer must be considered, and for subnanosecond time scales it is likely that the temperature field is discontinuous [25]. During these short times, propagation of thermal energy within a material often follows a hyperbolic or wave equation unlike the usual parabolic equation describing the diffusion of heat.11 This means that a temperature distribution can propagate as a pulse or wave through the material, as shown in Fig. 11, with transient peak temperatures being much higher than normally predicted by the heat diffusion equation. Values of the quantities ␶q (relaxation time 10

Phonons are the quantum particles corresponding to the discrete or quantized vibrational states in the lattice of a solid. Typical lattice frequencies ␯ are on the order of 1013 Hz and energies are on the order of E = h␯, where h is Planck’s constant. Phonons propagate at the speed of sound, which for most solid materials at room temperature is on the order of 10 to 100 km/sec. 11 Although the hyperbolic form of the heat equation was first pointed out by Maxwell in the nineteenth century [26], it remained obscure until Cattaneo revived the idea in 1948 and again in 1958 [27].

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Figure 11 Plot showing the distribution of nondimensionalized temperature ␪(x, t) = (T(x, t) ⫺ T0)/T0 versus nondimensionalized distance ␦ = x/2兹␣␶q, at a nondimensional time ␤ = t/2␶q. The parameter B = ␶T/2␶q, where ␶T is the characteristic time for a meaningful temperature to be defined at a point or the phase lag of the temperature gradient, ␶q is the characteristic time for a meaningful temperature gradient to be defined at a point or the phase lag of the heat flux vector, ␣ is the thermal diffusivity, and T0 is the initial temperature at t = 0. The limit when B = 0 corresponds to what is known as a thermal wave, i.e., one in which a temperature pulse with an overshoot propagates as a wave through the material medium. (From Ref. 25.)

for the temperature gradient to be established) and ␶T (relaxation time for a temperature to be defined) inferred from measurements are 0.4348 and 70.833 psec, respectively, for metallic copper [25]. However, the corresponding values for oxides are larger, and it must be borne in mind that copper will have an oxide layer when exposed to air. Such differences can be important in explaining the different results obtained in Refs. 22–24. The effects of heating at short time scales (i.e., on the order of nsec or smaller) can be considerably different from behavior at long time scales (or times greater than a nanosecond), and this in turn can alter the diffusion of carbon from the bulk material to the surface.

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Following the initial transient, the temperature response of a solid subjected to laser irradiation can be calculated for times on the order of tens of nanoseconds and greater. This is done by ignoring a part of the fast rising portion at the beginning of the laser pulse. In this instance, the heat flow in the material can be determined for most of the pulse duration of tens of nanoseconds using classical (Fourier-type) heat conduction. For a semi-infinite solid receiving a heat flux over a small, prescribed region on its surface, the transient temperature distribution is [28] T(x, t) ⫺ T(x, t = 0) = ⫺

q⬙x 0 erfc kT

1/2 2q⬙( 0 ␣Tt/␲) exp kT

冉 冊 x 2兹␣Tt

冉 冊 ⫺

x2 4␣Tt

(7)

where q⬙0 is the heat flux at the surface due to the absorbed laser energy, ␣T is the thermal diffusivity, kT is the thermal conductivity, x is the spatial coordinate, t is time, and erfc is the complementary error function. T(x, t = 0) is the temperature distribution following the fast transient portion of the laser pulse, after which time classical heat conduction occurs. The q⬙0 in Eq. (7) is a constant heat flux input into the surface. In reality, q⬙0 can be time dependent and varying even in the regime of classical heat conduction for the two pulse shapes shown in Fig. 10, so that Eq. (7) must be rederived in such an instance. In addition, the boundary condition (which yields the instantaneous value of q⬙) 0 must include a heat balance whereby heat is removed from the surface by radiation and convection. Hence, unrealistically high surface temperatures will be predicted by Eq. (7) if applied under conditions where radiative cooling of the surface is important. Although the situation described by Eq. (7) is not exactly that encountered in the experiments [22–24], it can nevertheless provide an indication of the temperature levels existing within the material during the period of laser irradiation. For illustrative purposes, temperature profiles given by Eq. (7) are plotted at various times in Fig. 12 for a laser intensity of 5 ⫻ 108 W/cm2, representative of the conditions existing in the experiments of Ref. 24. Because the rate of diffusion of carbon within the bulk Ni or Cu substrate material is temperature dependent, specifically varying as T 1/2, carbon initially near the surface would be driven out, aggregate, and condense to form a film. Although this would be expected to affect the growth rate of the carbon film at the surface, it is unclear what the effect of high local transient temperatures would be on the type of carbon aggregates thus produced. The nature of the resulting film could well be dependent on the rise time of the laser pulse.

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Figure 12 Temperature distributions calculated using Eq. (7) at various instants of time are shown here for an absorbed laser intensity of 5 ⫻ 108 W/cm2 for copper, representative of conditions in the experiments of Ref. 24.

Perhaps the most dramatic and as yet unsubstantiated claims have been the reports of diamond growth on a variety of substrates using CO2 as the carbonaceous precursor, with one or more laser sources (a CO2 laser, an excimer laser, and an Nd:YAG laser) [29–32]. It is important to point out that these claims were reported initially in the popular press, thereby circumventing the usual scientific peer review process. However, they are worth examining in view of what already exists in the published scientific literature and what is discussed in Secs. IV and V of this chapter. We will try to analyze this process, henceforth referred to as the QQC process (named after the industrial group that purportedly invented it). According to initial press releases, in the QQC process CO2 and N2 (as a shielding gas) are introduced in a plane stagnation flow over the substrate at an initial pressure of 1 atm. The process then consists of simultaneously irradiating a target surface to be coated, with simultaneous focused

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beams from a CO2 laser, excimer laser (of undisclosed wavelength), and an Nd:YAG laser, which then reportedly produces diamond on a variety of substrates including stainless steel, cast iron, and a variety of metals and ceramics [29–32]. What is more remarkable is the claim of growth rates on the order of 1 ␮m/sec (specifically, a 45-␮m diamond coating is reportedly produced over a 1.6 cm2 area within 45 sec). Although few details are provided in Refs. 29–32, it is still possible to explore the feasibility of this approach. We now analyze the QQC process to explore whether or not the conditions might even be conceivably favorable for diamond growth. The excimer lasers and YAG lasers used in the QQC process are capable of producing extremely short pulses on the order of 10 nsec, so that the peak power can be on the order of 20 MW12 or more. This implies a peak intensity of 20 MW/mm2 or 2 GW/cm2 for a spot size or focal area of 1 mm2. An estimate of the gas temperature can then be made if we assume that the laser heating is balanced by radiative loss from the gas. This yields an approximate value of 13,000 K for the gas temperature of the resulting thermal plasma. Ionization and dissociation processes will tend to lower this estimated temperature so that realistic temperatures are probably in the range of thousands of kelvins. In the reported experiments, the target surface is exposed to a high intensity of infrared and ultraviolet energy. This must result in flash evaporation, in a manner similar to what occurs in laser shock processing or explosive welding [33–36]. The flash evaporation of the substrate material can result in an implosive (compressive) force at the material surface in the gigapascal range, depending on the pulse energy.13 This effect is put to good use in laser shock processing to improve the mechanical properties of metallic surfaces of dense or porous materials and in explosive welding [33–36]. The resulting gas mixture composed of vaporized substrate material, CO2, and N2 is rapidly heated to temperatures high enough to ionize the constituents. Such an ionized, electrically conducting gas is called a plasma. Accompanying this rapid heating is the production of extreme pressures. For a Gaussian-shaped laser pulse, assuming an absorption coefficient of 0.1 (typical for plasmas in this range of temperature and pressure), Ref. 35 gives the following relation between the maximum pressure in kbar and the absorbed intensity expressed in GW/cm2:

12

This is obtained assuming a peak energy of 200 mJ and a pulse width of 10 nsec. ˙ mass per unit time. This is typically milliA surface undergoing flash evaporation loses m ˙ on the order of 102 kg/ grams of material over the pulse duration of 10 nsec, yielding an m sec. Assuming a shock velocity on the order of the speed of sound at the temperature of 13,000 K, or O(103) m/sec, this yields a force of magnitude 105 N, or a pressure on the order of 1011 Pa (100 GPa, or 1000 kbar) on a spot 1 mm2 in area.

13

Laser-Assisted and Optical Pumping Techniques

Pmax = BI 1/2

349

(8)

where B is a constant with a value on the order of 10. It is interesting to note that this expression yields a maximum pressure that is independent of laser pulse duration and wavelength and one that is dependent only on the laser intensity at the focal point. Therefore, it is evident that the local processing conditions (i.e., in the gas and on the surface) achieved by such powerful lasers are on the order of GPa of pressure and temperatures on the order of thousands of kelvins. Shown in Fig. 13 and Fig. 14 are the phase diagrams for carbon in the absence of a catalyst and in the presence of catalytic metals such as nickel and iron, respectively. It can be seen that the pressures and temperatures shown in Figs. 13 and 14 match those expected in the QQC process. Thus, the QQC process appears capable of producing conditions locally comparable to those encountered in the well-known hightemperature, high-pressure (HTHP) process used for commercial diamond growth [37]. This places the QQC process within the realm of possibilities. However, the technique must be reproduced and independently verified before its claims such as growth rates of 1 ␮m/sec over an area of 1.6 cm2 can be substantiated. According to the analysis presented here, such growth rates may be possible on surfaces approximately 1 mm2 in area.

Figure 13 Ref. 38.)

Phase diagram for carbon without the presence of any catalyst. (From

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Figure 14 Phase diagram for carbon in the presence of Ni catalyst (left) and Fe catalyst (right) at a pressure of 5.7 GPa. M, solid metal; L, liquid; G, graphite; D, diamond; C, carbide. (From Ref. 38.)

We can estimate the cost in terms of joules per carat for the QQC process, assuming that the growth rate of 1 ␮m/sec over a 1.6 cm2 area is indeed realizable. Using a pulse energy of 200 mJ/sec and volume growth rate of 1.6 ⫻ 10⫺10 m3/sec, we can calculate an energy cost of 71 J/carat, which is energetically much cheaper than diamond synthesis by one of the faster CVD processes, flame synthesis. D.

Heating of Surfaces Immersed in Liquids

The growth of some natural diamond (if not all of the larger crystals found in nature) is believed to occur in a state comprising solids immersed in

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liquids at extreme pressures and temperatures [38]. Nevertheless, synthesis of diamond by various deposition techniques has until recently largely focused on the gas phase alone. There have been a few attempts to grow diamond from a liquid phase or from solids submerged in the liquid phase [39–43]. Of these, Refs. 40–42 appear to be most intriguing in terms of potential application of lasers for diamond growth. In Cherian’s experiments [40–42], evidence for dissolution of diamond in a nickel crucible containing liquid NaOH at 1100 K and at atmospheric pressure is given, and more surprisingly, recrystallization of diamond back onto diamond surfaces upon ‘‘rapid’’ cool-down is also observed. As reported in Ref. 40, diamond crystallites consisting of chips and cleavages were dissolved in molten NaOH in a nickel crucible maintained at 1100 K in an oven. The crucible and its contents were then rapidly cooled to room temperature by removing them from the oven and placing in contact with a room-temperature metal surface or by cooling the crucible in room-temperature water. A cooling rate of ⬃1000⬚C/min was reportedly required for recrystallization to occur. Figures 15 and 16 show scanning electron microscopy (SEM) images of overgrowths that show the recrystallized diamond. Verification that the overgrowths are indeed diamond was carried out using several different characterization techniques, including microprobe Raman spectroscopy [40]. Reference [40] reports that careful experiments varying the quenching rate showed that the faster quenching rates yielded incomplete growth in the direction perpendicular to the substrate. Further, a metallic film of Ni was

Figures 15 and 16 SEM images of overgrowths that show the recrystallized diamond upon quenching an NaOH solution containing dissolved diamond particles in a nickel crucible. (From Ref. 41.)

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found on the overgrowths of diamond, suggesting the role of an Ni-C complex as an intermediate facilitating the growth of diamond. Evidently, some of the carbon in the initial diamond seed material dissolved into the liquid NaOH, formed complexes with the dissolved Ni (from the walls of the Ni crucible), and upon cool-down recrystallized as diamond on remnant diamond seed surfaces. More insight into mechanisms could have been gained if isotopic labeling had been used. For instance, 13C diamond particles (used in the dissolution part) and 12C diamond seeds (used in the recrystallization part) may have been helpful in identifying the exact sources and targets of dissolution and recrystallization, respectively. Alternatively, a carbonaceous source other than diamond (graphite, for instance) could have been used in the dissolution phase of the experiment, while a diamond or silicon seed particle (thoroughly characterized prior to use) could have been introduced during the growth/recrystallization or cool-down phase of the experiment. More recently, Zhao et al. [43,44] have demonstrated that diamond can be grown on diamond seeds from (Ni)-C-H2O mixtures at a pressure of 1.4 kbar and temperature of 800⬚C.14 Experiments typically used mixtures of 3 wt% powdered nickel, 95 wt% glassy carbon, and 2 wt% 0.25 ␮m sized diamond in water (50–100 wt% of the glassy carbon) in a pressurized and heated vessel. Run durations were typically 50–100 hr, the shorter durations yielding diamond particles several microns in size. The presence of nickel was reportedly crucial in obtaining larger aggregates of particles with sizes ranging from tens of microns to 100 ␮m. The typical particle morphology observed in these experiments is shown in Fig. 17 and can be seen to resemble the morphology of diamond particles produced by General Electric’s commercialized high-pressure, high-temperature process. The use of lasers in such liquid-phase experiments may be awkward, although specific wavelengths do penetrate certain liquids. For example, the green line of the argon ion laser can be transmitted through water. Therefore, it may be possible to use lasers to transmit through a liquid and trigger heterogeneous reactions at a liquid-solid interface. However, this can be exploited only after growth mechanisms are clearly understood. Another 14

Laboratory experiments (see H. C. Noltimier and V. V. Subramaniam, Laboratory chemical vapor deposition [CVD] experiments applied to the geological formation and age of natural diamond, Poster Paper BTH-1 presented at Session 152 [Experimental Petrology] at the 1995 Geological Society of America Annual Meeting, New Orleans, November 9, 1995) also suggest the beneficial role of water vapor in accelerating growth of diamond by hot-filament CVD on minerals such as almandine and olivine, both found as impurities in natural diamond. These minerals can act as nuclei for diamond growth in C-H-O systems (and even at the low pressures of 30 torr typical in HFCVD). The authors also give compelling arguments indicating that most natural diamond may form during transit in the diamond diatremes instead of forming at depth, as commonly thought.

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Figure 17 Typical particle morphology observed in the experiments of Ref. 43. Note the resemblance to the morphology of diamond particles produced by General Electric’s commercialized high-pressure, high-temperature process.

means of possibly initiating diamond growth from a laser-excited liquid is discussed in Sec. V.C.

E.

Summary

Use of intense laser irradiation for pyrolysis (and subsequent reaction) of the gas phase and rapid heating of surfaces has been discussed in this section. Where rate of heating is necessary and crucial, lasers may be capable of providing a unique avenue for diamond growth. However, capital and maintenance costs remain prohibitive, especially in the energy cost per carat. Some reported techniques such as the QQC process, if reproduced, appear competitive with other existing techniques based upon reported growth rates and should be examined more carefully. Lasers have also been used to irradiate powders of carbon black and convert some of these into diamond. A relatively unexplored area is the use of lasers to drive heterogeneous reactions on surfaces immersed in liquids. Use of lasers to excite liquids themselves and drive liquid-phase reactions is discussed in Sec. V.

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ABLATION

The use of lasers to produce rapid heating is well established. When this rapid heating of solid surfaces leads to vaporization of the material at the surface, this is known as ablation. The resulting vaporized material often constitutes an activated gaseous phase that can be subsequently reacted and modified to yield a product or can condense onto another surface to produce a solid layer with different microstructural properties. This process, also known as laser physical vapor deposition, was shown schematically in Fig. 7. Intense laser energy (usually focused) is directed toward a target material, causing it to vaporize. The resulting vapor or plume is a gas comprising atoms and molecules from the target and is often ionized. This technique is often used to produce thin films on substrates by directing the electrically conducting plume toward a biased substrate. LPVD or ablation has been used for the deposition of thin films of different materials. Of particular relevance is the use of such an ablative technique for the deposition of diamond-like or amorphous carbon films [45–54]. In these experiments, graphite is used as a target (except in the case of Ref. 54, where Lucite targets were also used) and different highenergy lasers such as excimer lasers or Nd:YAG lasers or CO2 lasers are used. Intensities on the order of 108 W/cm2 are usually required. It is well established that LPVD is capable of synthesizing diamondlike carbon (DLC) or amorphous carbon films from ablated graphite targets. The term amorphous carbon refers to a material with properties distinct from those of graphite but lacking the long-range crystalline order characteristic of diamond. DLC films are known for their hardness approaching that of diamond. Many of the properties of amorphous carbon materials can be accounted for by the structural model of graphitic islands interlinked by small percentages of diamond-like sp 3 bonds [55]. Davanloo et al. [55] report the growth of ‘‘amorphic diamond’’ from a laser plasma source. These authors provide sufficient evidence for differences between their material and DLC (such as structural size on the order of 100–200 angstroms and band gap of 1.0 eV) to warrant distinguishing between their material and other established DLC properties. Such small crystallite dimensions usually pose great difficulty in acquiring Raman spectra so that this characterization technique is ineffective in unequivocally indicating the presence of diamond in the present case. Their technique is a variant of LPVD. An Nd:YAG laser (Q-switched repetition rate of 10 Hz, 15 nsec pulse width) was used to produce a peak intensity of 5 ⫻ 1011 W/cm2 at a graphite target, in conjunction with an electric discharge of 10 A maintained between the target and a rod electrode placed nearby. The special nature of this ‘‘amorphic diamond’’ film thus produced on a germanium window is evident in Fig.

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Figure 18 Transmittance curves for an amorphic diamond–coated Ge window (25 mm diameter) compared with a bare Ge window. The film was reportedly 0.3 ␮m thick with an index of refraction of 2.1. The authors point out the fact that absorption from CH bands at 2940 cm⫺1 is absent. (From Ref. 56.)

18. As can be seen from Fig. 18, the transmittance is higher for the amorphic diamond–coated Ge window compared with the bare Ge window and shows complete absence of the C — H absorption band at 3.4 ␮m. Reference 55 further reports a hardness value of 13 GPa, compared with the value of 77 GPa (at a temperature of 290 K) for diamond [37]. The amorphic diamond of Davanloo et al. was thus clearly subjected to numerous such tests, which enabled them to confirm that their films indeed exhibited diamond-like properties. Although LPVD and plasma-assisted LPVD have been successful in producing DLC and amorphic diamond films, there have only been a limited number of reports regarding growth of diamond using this technique [56,57]. Latsch and Hiraoka have shown that diamond can be produced by LPVD from targets of polymethyl methacrylate (PMMA) when a reactive mixture of oxygen and hydrogen (ratio of concentrations not reported) is present at pressures between 0.5 and 0.9 torr. The authors report the following critical parameters: target to substrate distance = 3–6 cm, substrate temperature = 600⬚C, ArF excimer laser (193 nm), fluence = 190 mJ/cm2, and substrate

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bias = ⫺50 V [56]. The authors do not provide any information regarding any substrate pretreatment and report that ‘‘crystals started to appear after 10 minutes and thicker films were obtained for longer exposure times.’’ However, no SEM images are shown of the ‘‘films,’’ only of the isolated particles (see Fig. 19). Further, microprobe Raman spectra of the deposits (shown here in Fig. 20) indicate the presence of both ‘‘D’’ (at 1330 cm⫺1) and ‘‘G’’ (1597 cm⫺1) peaks. These peaks are usually indicative of graphite. Although the ‘‘D’’ peak usually occurs around 1343 cm⫺1, it can shift in some samples to the location where the diamond peak occurs. Therefore, caution must be exercised in interpreting Raman spectra especially when a broad peak near 1332 cm⫺1 and the ‘‘G’’ peak of graphite are simultaneously present. As an illustrative example, a Raman spectrum of a carbonaceous deposit produced from an oxyacetylene flame is shown in Fig. 21 [17]. The same film, exposed to atomic hydrogen (produced by a hot filament), removed the carbonaceous deposit, as can be seen from the Raman spectrum shown in Fig. 22 [17]. Given the uncertainty introduced by this fact, it is important to expose a film (or crystals) suspected to be diamond to H atoms at temperatures near 800⬚C in order to be sure that the deposit is indeed diamond. Subsequently, Polo et al [57] used ArF and KrF excimer laser ablation of graphite targets in hydrogen at 0.76 torr and reported growth of diamond particles 1–20 ␮m in size. The deposits were verified as diamond by Raman spectroscopy. The ablative method can be subject to problems of reproducibility. The composition of the target is often a critical parameter, as are the substrate temperature, position of the substrate relative to the target, substrate bias,

Figure 19

SEM image of isolated particles produced by LPVD. (From Ref. 56.)

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Figure 20 Microprobe Raman spectrum of the deposits from Ref. 56 showing the presence of both ‘‘D’’ (at 1330 cm⫺1) and ‘‘G’’ (1597 cm⫺1) peaks. This is indicative of disordered graphite rather than diamond.

Figure 21 Raman spectrum of a carbonaceous deposit produced from a flame. (From Ref. 17.)

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Figure 22 The film whose Raman spectrum is shown in Fig. 21 was exposed to atomic hydrogen (produced by a hot filament) [17]. This figure shows the Raman spectrum after exposure to atomic hydrogen. Note the disappearance of the feature at 1334 cm⫺1, which clearly demonstrates that the original film was not diamond.

and laser pulse energy. Of these, variability in the composition of the target has the largest influence on the resulting film or deposits. In some cases, ablation of the target can be accompanied by gross ejection of particulate solid material from the target that is then incorporated in a growing film. Based upon the scant information presently available regarding growth rates in LPVD, it is not possible to estimate the energy cost per carat for this process. Further research in this area is warranted, especially with regard to use of different combinations of target material and reactive gases.

IV.

PHOTOLYSIS

The process of photolysis, or the use of energetic photons to fragment a polyatomic molecule, was introduced in Sec. I. Usually, such processes require the presence of intense laser irradiation to initiate interaction between a molecule and one or more photons. As explained in Sec. I, this multiphoton interaction between molecule and photons may be sequential (i.e., the molecule may sequentially absorb each photon) or simultaneous, ultimately lead-

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ing to fragmenting of the molecule into smaller molecular or atomic fragments. This generally falls within the area of photochemistry [4,7,8]. The wavelength range typically used in photochemistry varies from the vacuum UV (below 200 nm) to the microwave region (1–10 cm). This range is chosen because of the typical absorption characteristics of molecules. Most small (three or four atom) polyatomic molecules have bond dissociation energies on the order of 1–10 eV. This corresponds to photon wavelengths in the UV-visible range. Light in this wavelength range is usually absorbed via electronic transitions in molecules. Wavelengths in the IR usually result in vibrational excitation because molecular vibrational states differ by energies on the order of 0.1 eV or less. Radiation in the far IR to microwave regions (10 ␮m to 10 cm) usually corresponds to excitation of the rotational energies of molecules. The wavelength range applicable to photochemistry is further restricted by the availability of materials for optical elements such as windows, lenses, and mirrors. Typical wavelength ranges and other properties for common optical materials are listed in Table 2. Table 3 lists some useful conversion factors because different units are used for convenience. For instance, when dealing with UV or visible light, wavelength units in nanometers are typically used. When dealing with radiation in the near IR to the far IR, units of microns (␮m) are used for wavelength and wavenumbers or cm⫺1 are used for frequency. In the microwave regions, wavelength units of millimeters or centimeters are used. It is important to delineate the difference between reactions occurring in photochemistry, thermally induced reactions (i.e., those caused by heating), and reactions initiated by extremely short-wavelength radiation such as x-rays or gamma rays. In thermal reactions (such as pyrolysis), molecules are dissociated or reacted from their ground electronic manifolds by vibrational excitation usually fed by energy from the external modes (i.e., translation and rotation). In contrast, photochemical reactions typically involve electronically excited states. In reactions initiated by x-rays and gamma rays, the route is often via ionization. In other words, molecules are ionized (i.e., charged by stripping them of one or more electrons) and subsequently react with other ions or neutral molecules. The difference between thermally induced reactions and photolytic reactions is apparent in the following illustration provided in Ref. 4. Consider the thermal decomposition of ethane: C2H6 ⫹ M → CH3 ⫹ CH3 ⫹ M where M is any other collision partner. Here, translational energy is transferred from M to C2H6 by impact, resulting in an intermediate15 fol15

The intermediate (C2H6)† is typically vibrationally excited and is known as a transition state. In contrast, the intermediate in photolytic reactions is usually an electronically excited state.

Table 2

Typical Characteristics of Optical Materials

Material Al2O3 (sapphire) BaF2 CaF2 Ge LiF MgF2 KBr KCl KF KI Si SrF2 SrTiO3 TiO2 (rutile) Source: Ref. 59.

Transmission Water solubility Melting range (g/100 mL of Knoop Density point (␮m) Index of refraction H2O) hardness (g/cm3) (⬚C) 0.15–5.5 0.5–13 0.12–10 1.8–22 0.12–7 0.11–8 0.21–37 0.18–25 0.16–15 0.27–42 1.2–15 0.12–11 0.395–5.0 0.42–5.3

1.768 1.475 at 0.546 ␮m 1.424 at 2 ␮m 4.116 at 2 ␮m 1.379 at 2 ␮m 1.378 1.538 at 2 ␮m 1.475 at 2 ␮m 1.39 at 0.257 ␮m 1.631 at 2 ␮m 3.458 at 2 ␮m 1.439 at 0.546 ␮m 2.409 2.613–2.909

Insoluble

2200

3.97

2053

0.12 1.6 ⫻ 10⫺3 Insoluble 0.27 7.6 ⫻ 10⫺3 53.48 34.7 92.3 127.5 Insoluble 0.011 Insoluble Insoluble

82 158 780 102 415 7 9

4.89 3.18 5.323 2.635 3.15 2.75 1.984 2.48 3.12 2.33 4.24 5.175 4.26

1280 1360 937.4 842 1266 730 776 846 682 1410 1450 2080 1825

5 1150 130 595 700

Cleavage plane

Thermal expansion (⫻10⫺6 per ⬚C) 4.5

(111) (111) (100) Poor a or c (100) (100) (100) (100)

18.4 6.1 35 9.2–13.4 38.4 36.6 32 43 3

(111) 10.6 C-axis: 9.943

Laser-Assisted and Optical Pumping Techniques Table 3

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Conversion Factors for Energy

1 eV

1 cm⫺1

␭ (angstroms)

1.6021 ⫻ 10⫺12 ergs/molecule 8065.73 cm⫺1 23.061 kcal/mole 96.487 kJ/mole 2.859 cal/mole 11.962 J/mole 1.9863 ⫻ 10⫺16 ergs/molecule 1.2398 ⫻ 10⫺4 eV/molecule 285915/␭ kcal/mole 12398/␭ eV/molecule

lowed by decomposition into CH3 molecules. In contrast, the primary photochemical channel for photolytic decomposition of ethane is C2H6 ⫹ h␯ → C2H4 ⫹ H2 proceeding via absorption of a photon by C2H6, leading to an electronically excited intermediate. As can be seen from this illustration, the products resulting from thermal reactions and photolytic reactions can be very different, showing how different products arise from different transition states. A photon absorbed by a molecule does not necessarily lead to a chemical change. The molecule certainly becomes excited upon absorbing the photon, but there are other loss processes that inhibit chemical change. For instance, the excited molecule could simply radiate the photon away by spontaneous emission. The molecule could also suffer a collision with another molecule while in this excited state. This may result in energy transfer to (into either internal or external modes of) the collision partner. Such processes are considered as losses because they do not result in dissociation of the target molecule or in chemical reaction, which is the primary goal of photolytic processes. In that sense, these loss mechanisms lead to inefficiencies in the photolytic process. The efficiency of a given photolytic process is qualitatively accounted for by the quantum yield, ␩q. It is defined as [60,61] ⌽q =

number of molecules undergoing the process number of photons absorbed by the system

(9)

In photochemistry, 1 mole (i.e., Avogadro’s number of 6.022 ⫻ 1023) of photons is called an Einstein. Typically, an overall reaction pathway may consist of several primary or elementary pathways and a quantum yield can be defined for each primary channel i:

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⌽i =

number of excited molecules that proceed via elementary channel i number of photons absorbed by the system (10)

If moderate or low light intensities are involved, the probability that an excited molecule will absorb more than one photon during its short lifetime is small. For these conditions,

冘

⌽i = 1

(11)

i

where i represents the ith primary photochemical pathway. Equation (11) is referred to as the Stark-Einstein law and holds only for low or moderate light intensities. Further, though ⌽i ⱕ 1, the overall quantum yield for a product, ⌽oq, can be much larger than 1 as is the case for chain reactions. The earliest attempt to use a laser to photodissociate a carbonaceous precursor and produce diamond met with failure [13]. Although success was reported initially [12,13], subsequent characterization of the growth material showed the deposit to be heat-treated carbon black [13]. At the time, both CH4 (methane) and C2H2 (acetylene) were suspected of being growth species and Kitahama et al. used 193-nm radiation from an ArF excimer laser to photodissociate C2H2 diluted (from 1 to 30%) with hydrogen. The pressure was kept in the range of 25–30 torr, and substrate temperatures in the range 400–800⬚C were explored. After growth durations of 2 hr during which time C2H2 was photolyzed using 193-nm pulses (100 Hz repetition rate and 50 mJ/pulse), growth of particles (later shown to be nondiamond carbon) was observed along scratches induced by substrate pretreatment.16 The authors do not explain why higher hydrogen concentrations were not used in their mixtures, especially given the fact that the photochemistry of acetylene at 193 nm is well known [62]. In fact, the photolysis products of pure C2H2 have been reported to yield diacetylene, ethylene, hydrogen, and a polymer [62]. It is quite possible then that higher hydrogen concentrations or presence of oxygen in the precursor gases would have yielded diamond growth in these early experiments. The initial claims of diamond growth by photolysis of acetylene were subsequently retracted [13]. Despite the initial setback for photolysis, Goto et al. [63] succeeded in producing diamond from a gaseous mixture of hydrogen flowing at 1000 sccm and carbon tetrachloride (CCl4) flowing at 1–10 sccm and irradiated by a focused ArF excimer laser beam. The pressure ranged from 6 to 50 torr, the repetition rate was 100 Hz, the pulse energy was 80–200 mJ, and the average power was 5–12 W. The beam was focused using an F:300 16

Substrates were pretreated as is common with other growth techniques, in this case using no. 1800 diamond powder to enhance nucleation and accelerate growth.

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cylindrical lens, and the authors report that configurations where the laser irradiated the substrate and was parallel to the substrate, were separately explored. The latter arrangement is shown schematically in Fig. 23. The authors report the formation of an amorphous carbon film after deposition durations ranging from 30 min to 3 hr. However, when the hydrogen stream was predissociated using a microwave discharge or a resistively heated hot filament, the authors report growth of a 1- to 3 ␮m-thick diamond film on silicon substrates heated to 450⬚C. The films were characterized by Raman spectroscopy, which revealed a discernible peak at 1333 cm⫺1 confirming the presence of diamond. The crystal structure was further confirmed by electron diffraction. This was the first reported instance of diamond growth using a laser-based process and one of the first to demonstrate that substrate temperatures did not need to be as high as 800⬚C. The authors report on the importance of atomic hydrogen and methyl radicals for diamond growth. This idea has received much support in reviews of diamond growth mechanisms [64–66]. Following the success of Goto et al., Tyndall and Hacker [67] reported on photolysis of over 20 compounds of organic precursors using focused (cylindrical lens with a focal length of 100 mm) KrF excimer laser radiation. Laser fluences of 150 mJ/pulse/cm2 were reportedly used along with substrate temperatures between 25 and 400⬚C, while chamber pressures were maintained between 1 and 5 torr. The authors report that temperatures in excess of 400⬚C resulted in dramatically decreased growth rates. The organic precursors were admitted into the growth chamber by passing a carrier gas (reportedly argon, helium, or hydrogen) over the reservoir containing the organic precursor. Of the organic precursors examined, the authors report that aliphatic carboxylic acids such as CH3CO2H (acetic acid) and

Figure 23 Schematic of experimental arrangement used in Ref. 63 to produce diamond films from photolysis of CCl4/H2 mixtures.

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H2C(CO2H)2 (malonic acid) yielded films containing diamond and disordered graphite after durations of 1.5 hr. The malonic acid had to be heated to 50– 70⬚C to provide sufficient vapor pressure to yield reasonable growth rates, but acetic acid could be used at room temperature. The authors do not specify which carrier gas or gases were used with these precursors. The Raman spectra of films obtained from these organic precursors display broad features at 1335 cm⫺1, which the authors claim to be diamond. However, this should be taken as insufficient verification, based upon the illustrative spectra shown in Figs. 21 and 22. As discussed earlier, this film shows the presence of a feature at 1332 cm⫺1, but this feature disappeared when the film was treated in atomic hydrogen (from a heated tungsten filament) after growth. Diamond films are usually quite resistant to etching by atomic hydrogen, and such disappearance of the well-known diamond feature in the Raman spectrum is not observed in true diamond films. On the other hand, graphitic films or films with disordered graphitic carbon show significant changes in their Raman spectra after postgrowth treatment in atomic hydrogen. Therefore, the spectra reported in Ref. 67 cannot be taken as irrefutable evidence of the presence of diamond. A postgrowth etch treatment of the film would have served as another means of verifying their claim. However, the authors of Ref. 67 do report on additional characterization of their deposits, such as electrical resistivity measurements and characterization by Auger spectroscopy. The electrical resistivity of these samples was greater than 109 ohm-cm (closer to the value for diamond, i.e., 1016 ohm-cm, than for graphite, i.e., 10⫺2 ohm-cm). Such additional characterization of the deposits is encouraging and bolsters the claims reported in Ref. 67. No SEM images of the deposits are shown, and therefore it is not clear whether the yield is a film covering a certain region of the substrate or consists of particles distributed over the substrate. In some instances, the choice of the carbonaceous precursor dictates the choice of growth technique. This is true in the case of growth of diamond from mixtures containing CO [68–70]. Use of CO as the carbonaceous precursor for diamond growth is of particular interest when isotopically pure diamond is desired. Diamond synthesized from a hydrocarbon source such as methane, but with a 13C content of 0.1% or less, is much more thermally conductive than diamond grown from CH4 with the natural abundance of 13 C of 1.1% [71]. Now, isotopically pure 12C and 13C are commercially produced as CO, and more processing steps are required to convert them to isotopically pure hydrocarbon sources. Consequently, 12CO will be cheaper than using 12CH4 in such an instance. Furthermore, because CO cannot be used in some conventional diamond growth systems such as HFCVD or oxyacetylene flame synthesis, growth options using CO as the precursor are

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limited. Consequently, plasma CVD or laser methods must be used when CO is the precursor. Growth of particles of diamond on seeded unheated monocrystalline silicon [(001) and (111)] substrates has since been reported from CO/H2 gas mixtures by photolysis of CO [68–70]. The photolysis of CO was accomplished using focused ArF excimer laser irradiation (the reader is referred to Ref. 70 for experimental details). Several orientations of the laser relative to the substrate were explored, as shown in Fig. 24, while the gas flow was directed perpendicular to the laser beam and toward the substrate. A CO flow of 0.7 sccm and H2 flow of 99.3 sccm were used, and the chamber pressure was maintained at 8 torr. Prior to growth, the substrates were thoroughly characterized using SEM imaging and energy-dispersive x-ray spectroscopic (EDS) analysis to ensure that no diamond particles remaining from the abrasive pretreatment used were present. Further, in order to distinguish seed particles from growth particles, the authors report using commercially available diamond grit (0–0.5 ␮m in size). The substrates were then thoroughly cleaned ultrasonically in acetone, rinsed with deionized water, and characterized before growth using SEM imaging and Raman spectroscopy. After run durations of 4 hr, irregularly shaped but faceted particles of size 5–10 ␮m of the type shown in Fig. 25 were observed. The morphology of these particles does not resemble that of diamond crystallites usually observed in other diamond processes (for example, see Fig. 28), suggesting that pure growth is involved here as opposed to the growth and etch processes simultaneously occurring in other CVD processes. Microprobe Raman spectra of these particles (see Fig. 26 showing a representative spectrum) exhibit a beautifully sharp diamond line at 1332 cm⫺1, with no discernible presence of graphitic or amorphous carbon. This work represents the first instance in which diamond growth is observed on unheated substrates by any known process, despite the slow growth rate. In some of their laser photolysis experiments, the H2 stream was dissociated using a tungsten filament resistively heated to about 2000⬚C [68–70]. As expected, the coverage of the particles is substantially increased, as shown in Fig. 27. The morphology of diamond particles produced by photolysis of CO in a hydrogen bath is significantly different from that of crystals normally grown by other CVD techniques. They are irregular in shape and resemble the 0- to 0.5-␮m diamond grit used for pretreatment of the substrates but are larger (5–10 ␮m in size). The irregularity in shape suggests the following. Because the resolution of SEM imaging is about 50 nm, it is likely that seed particles smaller than 50–100 nm went undetected. These small particles then would have acted as seeds around which diamond could grow, thus explaining the increase in size observed after growth. The typical cubooctahedral shapes (see Fig. 28) and other morphologies usually seen in other

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Figure 24

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Schematic of LCVD experiment. (From Ref. 70.)

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Figure 25 surface.

367

SEM images of diamond particles grown by LCVD on unheated

Figure 26 Typical Raman spectrum of diamond particles synthesized by LCVD on unheated surfaces.

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Figure 27 SEM image of increased coverage obtained by LCVD, in the presence of a predissociated hydrogen stream.

Figure 28 Typical cubo-octahedral morphology of diamond particles synthesized by hot-filament CVD.

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CVD systems are a result of growth-etch cycles. In conventional CVD systems, the presence of (relatively) large amounts of atomic hydrogen accelerates diamond growth by passivating the growing surface while removing nondiamond carbon and partially etching diamond. An excellent illustration is provided by the interrupted temporal history of growth of diamond around a 100-␮m seed particle from a CO/H2 gas mixture in a microwave discharge reported in Ref. 72 and reproduced here in Fig. 29. As can be seen, the early stages of growth on the seed crystal give the appearance of an irregular shape for the particle. The morphologies usually observed in other conventional CVD systems begin to become apparent in this case of a CO/H2 plasma only after a long period of time (50 hr) has elapsed [72]. The irregular morphology observed in Refs. 68–70 can then be understood because their experiments spanned only 4 hr. The laser photolysis experiments of Refs. 68–70 provide an excellent example of the use of lasers to drive reactions selectively, specifically those

Figure 29 An excellent illustration is provided by the interrupted temporal history of growth of diamond around a 100-␮m seed particle from a CO/H2 gas mixture at 45 torr in a microwave discharge reported in Ref. 72. (a) The seed crystal, (b) after 10 hr, (c) after 20 hr, and (d) after 50 hr of growth.

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that result in diamond formation while formation of the graphitic phase is suppressed. The choice of the ArF excimer laser as a source is dictated by the well-known multiphoton process that dissociates CO into C (31P) and ground state O(3P) atoms [73]. Once atomic carbon and oxygen are formed, they react as radicals with the surrounding molecular hydrogen resulting in the formation of desirable CHx species. It is important to note that if H2 were not present, copious amounts of C2, soot, and other nondiamond carbon would result [70]. This channel of C2 production from CO will be addressed further in Sec. V. More recently, it has been shown that optical pumping of CO/Ar gas mixtures with trace amounts of Fe or Ni catalyst results in growth of single-walled carbon nanotubes (see E. Ploenges et al. Carbon Nanotube Production in CO Laser Pumped Carbon Monoxide Plasmas. Paper AIAA2001-0651, presented at the 39th AIAA Aerospace Science Meeting and Exhibit, Reno, Nevada, January 8–11, 2001). In order to understand the laser-driven chemistry in the experiments reported in Refs. 65–67 better, we examine a simple chemical kinetics model of the gas-phase reactions expected to occur in the irradiated CO/H2 mixture. To enable a simple solution, the following assumptions are made. First, every CO molecule in the focal volume is assumed to have dissociated. Second, diffusion and convection are neglected in order to simplify the solution. From the flow rate of CO of about 1 sccm reported in Ref. 68, total pressure of 8 torr, and assuming a local gas temperature of 350 K, the initial number density of CO can be calculated to be ⬃2.2 ⫻ 1021 m⫺3. Similarly, the initial number density of molecular hydrogen based on its flow rate of about 99 sccm is 2.2 ⫻ 1023 m⫺3. Knowing the energy per photon,17 1.0 ⫻ 10⫺18 J and taking the energy per pulse as 50 mJ, the total number of photons in the laser-irradiated volume can be calculated. Assuming this volume to be about 1 mm3, the number density of photons is then approximately 4.8 ⫻ 1025 m⫺3. Because this is much bigger than the initial CO concentration of 2.2 ⫻ 1021 m⫺3 and assuming no more than three photons are required to dissociate a CO molecule, the first assumption is justified. Thus, the initial gas composition within the laser irradiated region can be taken to be nCO = 0 m⫺3, nH2 = 2.2 ⫻ 1023 m⫺3, and nC = nO = 2.2 ⫻ 1021 m⫺3. However, diffusion and flow will serve to replenish the laser-irradiated region with CO and H2 reactants. A more representative and realistic estimate of the gas composition can be obtained by scaling the initial concentrations of atomic carbon and oxygen with respect to the ratio of the irradiated volume to the

17

Because an ArF excimer laser was used in these experiments, the energy of a photon of wavelength 193 nm is (6.626 ⫻ 10⫺34 J-sec) ⫻ (3 ⫻ 108 m/sec)/(193 ⫻ 10⫺9 m) or 1.03 ⫻ 10⫺18 J.

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gas volume adjacent to the substrate. Taking the volume adjacent to the substrate to be about 1 cm3 and the irradiated volume as about 1 mm3, the initial composition for each successive interval is: nCO = 2.2 ⫻ 1021 m⫺3, nH2 = 2.2 ⫻ 1023 m⫺3, and nC = nO = 2.2 ⫻ 1018 m⫺3. With these initial values, the set of rate equations of the form dni = f (ni , nj ) dt

for all j

(12)

describe the evolution of concentration of species i, where ni and nj represent the number densities of the species listed in the reactions given in Table 4.

Table 4 Elementary Reactions and Rate Constants Evaluated at 300 K, Used to Simulate Gaseous Environment Existing Within the Laser-Irradiated Volume Adjacent to the Substrate in the Experiments Reported in Refs. 68–70 Reaction C ⫹ H2 → CH2 C ⫹ H2 → CH ⫹ H H2 ⫹ O → OH ⫹ H C ⫹ CO → C2O CH2 ⫹ H2 → CH3 ⫹ H CH2 ⫹ CO → C2H2 ⫹ O CH2 ⫹ CO → CH2CO H2 ⫹ C2O → CH2 ⫹ CO CH ⫹ H2 → CH3 CH ⫹ H2 → CH2 ⫹ H C2H ⫹ O → CH ⫹ CO CH ⫹ CO → HCO ⫹ C H ⫹ CO → HCO H ⫹ CO ⫹ H2 → CHO ⫹ H2 OH ⫹ CO → H ⫹ CO2 CH2 ⫹ CH2 → C2H2 ⫹ H2 CH3 ⫹ CH3 → C2H6 CH2 ⫹ CH3 → C2H4 ⫹ H CH2 ⫹ CH2 → CH3 ⫹ CH CH ⫹ H → C ⫹ H2 CH3 ⫹ H → CH2 ⫹ H2 C2H2 ⫹ O → CH2 ⫹ CO CO2 ⫹ O → CO ⫹ O2 CO2 ⫹ H → CO ⫹ OH CH3 ⫹ H → CH4

Rate constants 7.11 5.0 7.05 6.31 3.2 2.14 1.0 7.0 2.66 2.66 3.0 2.09 6.92 1.15 1.32 4.98 4.06 6.64 2.30 4.98 3.2 2.14 1.39 1.87 3.32

⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻

10⫺44 m3/sec 10⫺151 m3/sec 10⫺24 m3/sec 10⫺44 m3/sec 10⫺24 m3/sec 10⫺63 m3/sec 10⫺21 m3/sec 10⫺19 m3/sec 10⫺17 m3/sec 10⫺17 m3/sec 10⫺17 m3/sec 10⫺17 m3/sec 10⫺17 m3/sec 10⫺46 m6/sec 10⫺19 m3/sec 10⫺17 m3/sec 10⫺17 m3/sec 10⫺17 m3/sec 10⫺23 m3/sec 10⫺17 m3/sec 10⫺27 m3/sec 10⫺19 m3/sec 10⫺55 m3/sec 10⫺35 m3/sec 10⫺16 m3/sec

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The reactions listed in Table 4 are not meant to be exclusive but represent only one set of reactions thought to be important for the conditions reported in Refs. 68–70. Equations (12) then represent a set of coupled nonlinear equations for ni that can be solved numerically using a method such as that described in Ref. 75. In these calculations, the ArF excimer laser pulses are assumed to remain off for 50 msec (corresponding to a 20-Hz repetition rate) and have pulse durations of 20 nsec. Each pulse interval is hereafter defined as the pulse duration of 20 nsec plus the laser-off time of 50 msec. Compositions of all species (except CO, H2, C, and O) are updated for each interval from values calculated at the end of the previous interval. The compositions after 2 sec or 40 such intervals thus calculated are shown in Figs. 30–32. It can be seen that the carbonaceous species present in order of abundance are HCO, C, CO, CH3, CH2CO, CH4, CH2, C2H6, C2H4, C2H2, and CH. Among these, the least credible is the unusually high amount of atomic carbon present. This must be regarded as a fictitious result because

Figure 30 Compositions of various species calculated using the reactions in Table 4 are shown here after 2 sec or 40 intervals.

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Figure 31 Compositions of various species calculated using the reactions in Table 4 are shown here after 2 sec or 40 intervals.

recombination of C to form either C2 or CO was not included in our reaction set listed in Table 4. Further, the absence of nondiamond carbon either on the SEM images or in the Raman spectra is conspicuous in the experiments reported in Refs. 68–70. This strongly suggests that C2 species must not have been present in abundance in the gas phase because these are known to produce graphitic carbon. Species capable of removing nondiamond carbon or atomic hydrogen or atomic oxygen from CHxOy complexes bound to the growing diamond surface are also present. In order of abundance, they are HCO, C, O, OH, H, CH3, CH2CO, CH2, and CH. Of these, only the high concentration of C should be ignored for the reasons already mentioned. Given the state of present understanding regarding mechanisms of diamond growth [64], we can attempt to make some assessment regarding the identities of possible precursors important in diamond growth by photolysis of CO.

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Figure 32 Compositions of various species calculated using the reactions in Table 4 are shown here after 2 sec or 40 intervals.

Suppose the linear growth rate (i.e., growth rate normal to the substrate surface) is gr. Then, the number of carbon atoms added per unit time per unit area of the growing surface by the carbonaceous precursor, n˙ ⬙C , is given by n˙ C⬙ =

gr␳d mC

(13)

where gr is expressed in units of m/sec, ␳d is the mass density of diamond (3515 kg/m3), and mC is the atomic mass of carbon in kg (12 ⫻ 1.6605 ⫻ 10⫺27 kg). At the very least, for growth to occur, the flux of the carbonaceous precursor must exceed this quantity n˙ ⬙C for growth to continue. Thus, we have 1 ¯ ⱖ n⬙ ˙C nXC 4

(14)

where nX is the gas phase number density of the carbonaceous precursor,

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¯ = (8kBT/mX␲)1/2 is the random thermal speed. In the expression for and C ¯ kB is Boltzmann’s constant (1.3806 ⫻ 10⫺23 J/K), T is the gas temperature C, in the neighborhood of the growing surface, and mX is the molecular mass of the carbonaceous precursor. In using the expression for the random thermal flux in Eq. (14), it has been assumed that the velocity distribution function of species X is described by the Maxwell-Boltzmann distribution. Using Eqs. (13) and (14), the order of magnitude of the minimum concentration nX necessary to explain an observed growth of gr can be determined. For the specific conditions of the CO photolysis experiments reported in Refs. 68–70, let us take the growth rate to be 1 ␮m/hr, gas temperature T = 300 K, and mX to be on the order of 2 ⫻ 10⫺26 kg. For these values, Eq. (14) yields nX ⬇ 1018 m⫺3. Expected values of the gas composition for times on the order of an hour can be determined from calculated results such as those shown in Figs. 30–32 and compared with this minimum value of nX. Such an order of magnitude estimate shows that candidate growth species in diamond growth by photolysis of CO (excluding C and CH4) are HCO, CO, CH3, and CH2CO. Of these, CO can be eliminated as a likely growth precursor because it is an extremely tightly bound molecule and difficult to dissociate. CH3 emerges as a strong contender as growth species based upon what is known regarding growth mechanisms in other CVD systems [64]. However, the abundant presence of HCO and CH2CO cannot be overlooked, and these may well play a role in diamond growth by photolysis of CO. The other somewhat remote but possible candidate growth species is CH2, as its concentration is lower than that of CH3 only by about two orders of magnitude. Other species such as C2H6, C2H4, C2H2, and CH can be safely eliminated because they are present in substantially smaller amounts. Although the foregoing analysis yields some insight into the identity of the key carbonaceous precursor for diamond growth, it must be emphasized that it is inexact and can be viewed only as an order of magnitude estimate. Nevertheless, such analysis is useful for inferring trends and may suggest process improvements that lead to an increase in yield or growth rate. In this section, we have examined existing photolytic techniques for diamond synthesis. Of significance is the fact that growth of diamond particles has been realized under conditions where the substrate is not heated at all (see Refs. 68–70 on photolysis of CO), and growth of diamond films has been reported at temperatures as low as 450⬚C (see Ref. 63 on photolysis of CCl4). Given the strong interest in lowering growth temperatures [76], these represent significant advancements in the state of the art. It is also of significance to note that in the photolysis experiments involving CO there is evidence that selectivity has been achieved because nondiamond carbon was not codeposited. The absence of nondiamond carbon is conspicuous, and the microprobe Raman spectra show a particularly sharp diamond line

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at 1332 cm⫺1. All these photolysis techniques, however, appear to require predissociation of hydrogen in order to increase growth rates. Of these, the photolytic decomposition of CCl4 in a predissociated hydrogen stream appears closest to commercial realization. An estimate of cost can be made based upon the results reported in Ref. 63. Using their reported growth rate of 1 ␮m/hr but over an area of 1 cm2 (the actual deposition area was not disclosed in Ref. 63) and an input average power of 10 W, the energy cost is approximately 2 ⫻ 107 J/carat for a yield of 4.9 ⫻ 10⫺7 carats/sec.

V.

OPTICAL PUMPING

A.

Introduction

Optical pumping refers to the excitation of the internal modes of atoms or molecules. Light, which is not necessarily coherent, may be used to excite rotational, vibrational, or electronic states of atoms and molecules by what is known as resonant absorption. In contrast to the relatively higher power, multiphoton processes introduced in the earlier sections of this chapter, here we focus on single-photon resonant absorption. The term resonant absorption refers to the fact that there is an excellent coincidence between the frequency of the exciting radiation or light and the energy gap (divided by Planck’s constant) associated with a particular rotational, vibrational, or electronic transition. Further, in contrast to multiphoton processes, optical pumping or resonant single-photon processes are characterized by much lower intensities. Coherence of the exciting radiation is therefore not strictly necessary, although they are needed in practice in order to exceed threshold intensities for absorption. Such threshold absorption levels exist because there are losses due to quenching by collisional or radiative processes that must be overcome. Internal modes of diatomic molecules were introduced briefly in Sec. I. As discussed earlier, these comprise rotational, vibrational, and electronic means of energy storage for molecules. At equilibrium, the average energy in these modes can be described by a single temperature, T. Further, the equipartition theorem18 from statistical thermodynamics tells us that each squared term in the Hamiltonian (corresponding to the degrees of freedom associated with each mode of molecular motion) contributes on average kBT/ 18

The equipartition theorem states that each squared term in the Hamiltonian contributes kT/2 to the average energy. Examples of squared terms are kinetic energy of a particle, which scales as velocity squared and potential energy in a linear spring, which scales as displacement squared. In Hamilton’s formulation of classical mechanics, velocity and displacement are examples of canonical independent variables.

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2 to the average energy of a molecule. For example, there are three degrees of freedom in translation for an atom or molecule. Each appears as a squared term in the kinetic energy arising from the sum of the squares of the three components of velocity (i.e., 12 mC 2x ⫹ 12 mC 2y ⫹ 12 mC 2z ). Hence, the contribution from the translational motion to the total energy of the particle is (3/2)kT. Similarly, for a diatomic particle, the contribution from the rotational modes is kT (corresponding to two degrees of freedom in rotation), and the contribution from the vibrational mode is kT (corresponding to the potential energy and kinetic energy associated with the single degree of freedom in vibration). The essential point here is that the energy in each of these modes is dependent on a single quantity, the gas temperature. When the gas is out of thermodynamic equilibrium, the energy in these modes can be different and is no longer identified by a single temperature. This is of relevance to optical pumping because the resulting situation is one where the energy in the vibrational and electronic modes cannot be described solely by the gas temperature, which characterizes the rotational and translational modes. Equilibration of the energies in the various modes of molecules occurs by collisions. As explained in Sec. I, rotation and translation equilibrate within a few collisions. However, for diatomic molecules such as CO, NO, and N2, it takes many collisions before the vibrational modes equilibrate with the external modes (i.e., rotation and translation). The rate at which energy is exchanged by the various modes via collisions can be described by a rate coefficient, analogously to chemical processes. For example, one can speak of a rate coefficient for vibration-vibration (VV) energy transfer, vibration-translation (VT) energy transfer, vibration-rotation (VR) energy transfer, vibration-electronic (VE) energy transfer, and so on. Thus, each species under such nonequilibrium conditions should be thought of as a specific molecule in a particular vibrational state of an electronic manifold. An example is provided by the energy level diagram of CO shown in Fig. 33, which shows the ground electronic state of CO (X1⌺g⫹) along with its vibrational levels (denoted as the many horizontal lines within the curve). Also shown in Fig. 33 are other electronic states along with their vibrational levels. The rotational levels are not shown for clarity, but they would appear as additional horizontal lines in between successive vibrational levels. For CO at 300 K, the characteristic time for VT transfer19 is expressed as ⬃10 sec-atm for the v = 1 level, while the characteristic time for VV energy transfer is ⬃0.1 msec-torr. At 1 atm, this yields a characteristic time of 10 19

This VT rate is for CO-CO collisions. The corresponding values for CO-He and CO-Ar VT relaxing collisions depleting v = 1 and populating v = 0 are 4 ⫻ 10⫺3 sec-atm and 103 secatm, respectively.

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Figure 33

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Energy level diagram for CO.

sec for VT relaxation for the v = 1 level while its characteristic time for VV exchange is 76 msec. This means that at any given pressure in the collisiondominated regime, vibrationally excited CO will tend to retain energy in vibration for relatively long durations if VT processes are ineffective. Chemical reactions proceed from vibrationally excited or electronically excited states because these promote the necessary breaking of chemical bonds. Optical pumping provides a means of producing vibrationally or electronically excited molecules. This technique has been pioneered by Rich and coworkers [2,77–79], Brechignac et al. [80], and Urban and coworkers [81,82] for studying various nonequilibrium molecular energy transfer processes with applications to electrical discharges, flames, and supersonic expansions. In this section, we discuss in detail the use of this novel technique for diamond synthesis. Although other laser sources and precursor molecules can be targeted using the technique presented in this section, we focus specifically on the technique known as laser-excited CVD or LECVD already reported in the

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literature [70,83,84]. In this method, a CO laser operating on several lines (i.e., transitions) from v = 12 → v = 11 through v = 1 → v = 0, is directed on CO gas molecules in a slowly flowing 95% CO/5% CH4 gas mixture at room temperature. The laser energy is absorbed by the target CO molecules initially in the ground electronic state (X1⌺⫹) and redistributed via anharmonic VV exchange collisions primarily to the internal modes of CH4 as well as to higher vibrational levels within CO. Diamond particles similar in morphology to those produced in Refs. 68–70 were observed on monocrystalline silicon wafers over substrate temperatures ranging from ⬃600⬚C down to room temperature. In order to understand this technique better, it is necessary to provide some detailed background on the optical pumping of CO, a topic on which there exists a considerable amount of literature. At room temperature, most CO molecules are in their ground electronic manifold (X1⌺⫹) with a majority of them occupying the ground vibrational level v = 0. The equilibrium distribution of populations versus vibrational level is described by the well-known Boltzmann distribution: nv = nv=0e⫺(Ev⫺Ev=0)/kT

(15)

where nv is the number density of CO molecules in vibrational level v with energy Ev = ប␻(v ⫹ 12) ⫺ ប␻␹e(v ⫹ 12)2, nv=0 is the number density of CO molecules in vibrational level v = 0 with energy Ev=0, and T is the translational mode temperature. In the expression for the vibrational energy Ev, ប = h/2␲, ␻ is the frequency of the molecule as an oscillator, v is the vibrational quantum number, and ␹e is the anharmonicity. Equation (15) states that at equilibrium at a temperature T, most molecules can be found in level v = 0, with the population in higher vibrational levels decreasing exponentially with v. Therefore, if radiation from a CO laser operating on vibrational transitions other than v = 1 → v = 0 is directed on gaseous CO at room temperature, no absorption will result and the gas will be transparent to the laser irradiation. It is evident that for cold CO gas to absorb the radiation, either the laser must have some output on the lowest transition v = 1 → v = 0 (i.e., shortest wavelength) or the gas must be heated (so that upper vibrational levels have sufficient population to absorb the longer wavelength laser transitions). Commercially available CO lasers typically do not have output on this shortest wavelength transition, and therefore such a CO laser must be specially built [70,83]. When laser output on the v = 1 → v = 0 transition is present, CO gas molecules can now absorb this laser energy and populate the v = 1 level. These molecules in level v = 1 now absorb the laser output from the v = 2 → v = 1 transition and populate the v = 2 level, and so on. In this manner, CO molecules can be optically pumped up to vibrational level v = 12, or whatever may be the vibrational level corre-

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sponding to the longest wavelength laser transition. Collision-induced vibrational energy (VV) exchange processes then proceed according to CO(v) ⫹ CO(w) S CO(v ⫺ 1) ⫹ CO(w ⫹ 1),

wⱖv

(16)

This collisional vibrational energy exchange is favored due to the anharmonicity of molecules20 and serves to populate vibrational levels much higher than those initially populated by the laser irradiation. Levels as high as v = 40 in the ground electronic manifold of CO (corresponding to energies of about 10 eV) have been populated in this manner. This laser excitation followed by redistribution of the absorbed laser energy among the higher vibrational levels is known as anharmonic VV pumping. The resulting population distribution, henceforth referred to as the TRR distribution, is highly non-Boltzmann and was first derived by Treanor, Rich, and Rehm in 1968 [85]. For the limiting case of VV exchange collisions dominating VT exchange, the TRR distribution is [85]: nv = nv=0 exp

再

冎

(ប␻ v ⫺ 2ប␻␹ev) ប␻␹ev(v ⫺ 1) ⫺ kT kT1

(17)

where T1 is the ‘‘vibrational temperature’’ of level v = 1 defined by nv=1 = nv=0e⫺ប␻(1⫺2␹e)/kT1 or ប␻(1 ⫺ 2␹e) T1 = ⫺ nv=1 k ln nv=0

冉 冊

(18)

The form of Eq. (17) for the TRR distribution can also be derived from statistical thermodynamics in a manner analogous to that used to derive the Bose-Einstein or Fermi-Dirac distribution. This is done by maximizing the thermodynamic probability subject to the constraints that the total number of particles, total energy, and total number of vibrational quanta per molecule are fixed (i.e., conserved) [85]. Figure 34 shows a semilog plot of the normalized number density or population density as a function of vibrational quantum number for several cases. These are (1) the Boltzmann distribution as given by Eq. (15) but neglecting anharmonicity in the molecule, (2) the Boltzmann distribution 20

Anharmonicity refers to the fact that the vibrating bond between C and O atoms in the CO molecule exhibits departure from that of a harmonic oscillator. As a consequence, the gap between successive vibrational energy levels decreases as the vibrational quantum number (or vibrational energy) increases.

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381

Figure 34 Schematic showing a log-linear plot of normalized populations of molecules in vibrational level v versus vibrational quantum number (or vibrational energy) for three cases: (1) equilibrium, where the variation is given by the Boltzmann distribution [Eq. (15)] but without the effects of anharmonicity; (2) equilibrium, where the variation is given by the Boltzmann distribution [Eq. (15)] but including the effects of anharmonicity; and (3) nonequilibrium in which the average vibrational energy is different from the average translational energy.

including anharmonicity, and (3) the limiting TRR distribution as given by Eq. (17), with Tv ≠ T. It is important to point out that the concept of a vibrational temperature Tv that represents a meaningful average energy in vibration makes sense only when the variation of normalized number density versus vibrational quantum number is log linear. When departure from log linearity occurs, a single vibrational temperature cannot be defined for all vibrational levels. This is what happens in the case of the Boltzmann distribution including the effects of anharmonicity with Tv ≠ T or in the case of the ideal TRR distribution. The vibrational quantum number at which the number density attains a minimum for the TRR distribution can be determined by differentiating ln(nv /nv=0) from Eq. (17) with respect to v and setting it equal to zero. The result yields what is known as the Treanor minimum: vmin =

(1 ⫺ 2␹e) 2␹e

冉冊 T T1

⫹

1 2

(19)

A similar minimum exists for the Boltzmann distribution (i.e., equilibrium distribution) when the effect of molecular anharmonicity is included: (vmin)equilibrium =

(1 ⫺ ␹e) 2␹e

(20)

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Values of frequencies and anharmonicities for some diatomic species are given in Table 5. As can be seen, the anharmonicity, ␹e, takes on values that are usually less than or equal to 0.01. This means that (vmin)equilibrium ⬇ 1/2␹e ⬇ 50. Such high vibrational levels are so close to the dissociation limit that the quadratic behavior of anharmonicity is never observed under equilibrium conditions. Thus, at equilibrium, the populations of vibrational levels are nearly log linear with vibrational quantum number below the dissociation limit, even when the effect of anharmonicity is included. In contrast, the TRR distribution yields vmin ⬇ (82)(1/5) ⬇ 16 for CO for T1 /T ⬇ 5. Thus, for the species listed in Table 5, the TRR distribution yields a minimum in the number density variation when the vibrational quantum number is on the order of 10 and the vibrational temperature of level v = 1 is a few times higher than the translational or gas temperature. In reality, the TRR distribution is modified by the competing effect of VT relaxation. VT energy transfer scales with vibrational quantum number and hence becomes important at the higher quantum numbers. The degree to which vibrational nonequilibrium persists in a gas therefore depends on the competing strengths of VV and VT or other loss processes such as spontaneous emission. In molecules such as CO and NO, spontaneous emission is slower than VT processes at pressures of interest. In homopolar diatomic molecules such as O2 and N2, there is no spontaneous emission because these molecules possess no natural or intrinsic dipole moment. We therefore illustrate the realistic VV up-pumping process by considering VV and VT processes alone, with the rotational modes in equilibrium with the translational modes at temperature T. Consider a diatomic molecule A2 undergoing the following single-quantum processes: VV energy transfer: k w⫺1,w v⫹1,v A2(v ⫹ 1) ⫹ A2(w ⫺ 1) → A2(v) ⫹ A2(w) ← k w,w⫺1 v,v⫹1

Table 5

(21)

Frequencies and Anharmonicities for Some Diatomic Molecules

Parameter ប␻ (cm⫺1) ប␻␹e (cm⫺1) ប␻/2ប␻␹e Source: Ref. 86.

CO

H2

N2

NO

O2

OH

2169.8 13.3 82

4401.2 121.3 18

2358 14.1 84

1904 14 68

1580 12 66

3735 83 22

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VT energy transfer: kv⫹1,v A2(v ⫹ 1) ⫹ M → ← A2(v) ⫹ M kv,v⫹1

(22)

where the VV and VT rates are given in Refs. 75 and 79. The evolution of the population of level v is then given by the following rate equations, including spontaneous emission as a loss mechanism [2]: dnv = VTv ⫹ VVv ⫹ SRDv dt

(23)

where the terms on the right-hand side represent net VV transfer, VT transfer, and spontaneous radiative decay into level v. Expressions for each of these terms, for CO, are given in Ref. 75. Process (21) is shown schematically in Fig. 35 for two general molecules A and B. Now, if E(v) is the energy of molecules in vibrational level v, then E(v ⫹ 1) ⫺ E(v) > E(w) ⫺ E(w ⫺ 1) for w ⱖ v because of the effect of anharmonicity. Thus, if we treat the right-hand side of process (21) as the ‘‘products’’ and the left-hand side as the ‘‘reactants,’’ we have ⌬E = E(v) ⫹ E(w) ⫺ E(v ⫹ 1) ⫺ E(w ⫺ 1) = [E(w) ⫺ E(w ⫺ 1)] ⫺ [E(v ⫹ 1) ⫺ E(v)] so that ⌬E ⱕ 0 for w ⱖ v. ⌬E is called the resonance defect. This shows that the forward process of (21) is favored at lower temperatures because it is exothermic in the sense that the energy difference ⌬E flows out of the vibrational modes into the external modes of rotation and translation for w ⱖ v. On the other hand, the reverse of process (21) is endothermic in the sense that energy must be provided from the external modes to sustain it. This can be expected to occur only at high temperatures. Energy can be retained in the vibrational modes, therefore, if an external source (such as a laser or optical pump) provides energy to the vibrational mode

Figure 35 Schematic showing intermolecular vibrational energy transfer, preferentially transferring vibrational energy from the molecule with the more widely spaced energy levels to the molecule with the more closely spaced energy levels [2]. When both collision partners are molecules of the same species, then such VV transfer is called intramolecular vibrational energy transfer. The difference between ⌬v and ⌬w is called the resonance defect.

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to overcome loss processes such as process (22) or else process (22) is inhibited or minimized. Process (22) scales with vibrational quantum number v and temperature; i.e., the rate for vibrational deexcitation by VT transfer increases with increasing v and increasing T. Hence, as long as the energy corresponding to the resonance defect is removed either by having the gas flow or by having a suitable diluent such as argon, a low gas temperature can be maintained or VT losses can be lowered compared with VV exchange. Under these conditions, the solution of the rate equations (23) yields a fully VV pumped distribution and is indeed observed as shown in Fig. 36. The fully VV pumped distribution is observed in optically pumped gases as well as in common plasmas. It is, in fact, ubiquitous in plasmas containing tightly bound molecular species such as CO, NO, N2, or O2. In such plasmas, the mean electron energy is lowered because inelastic collisions between electrons and molecules dominate all other processes. Consequently, the electron (translational) energies in such discharges strongly resemble the fully VV pumped distribution shown in Fig. 36. The result is that a single electron temperature cannot be identified, and hence we must speak of electron energies and a corresponding electron energy distribution function or EEDF that is highly non-Boltzmann. These electron impact processes can be included in the rate equation formulation as given by Eq. (23) and are crucial in determining the chemical composition in a plasma. Process (16) is an example of intramolecular energy transfer, or transfer of vibrational energy between molecules of the same chemical species. Intermolecular energy transfer, or transfer of vibrational energy between molecules of different chemical species, also occurs. In both cases, energy is transferred preferentially from the molecules with widely spaced vibrational energy levels to those with more closely spaced energy levels. LECVD takes advantage of this point precisely. Further, this energy transfer is a result of molecular collisions and scales with pressure (or density) as long as relatively low external mode (i.e., translational and rotational) temperatures are maintained or as long as rates of population of vibrational levels by VV exchange collisions are favorable compared with the rates of depopulation of these levels by VT collisional processes. The effect of anharmonicity in a diatomic or small polyatomic molecule is such that any vibrational energy over and above the equilibrium value (corresponding to the translational temperature T ) is rapidly redistributed to higher vibrational states. Thus, molecular states at high vibrational levels can be populated, especially when the gas temperature is very low. The process, however, is not restricted to low gas temperatures and has been shown to occur at elevated gas temperatures on the order of 1500 K [87].

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Figure 36 Fully VV pumped distribution from Ref. 79 measured from an optically pumped mixture of 1% CO/Ar at a total pressure of 100 torr. Note that at low vibrational quantum numbers, the VV pumped distribution resembles the TRR distribution but instead of displaying a minimum exhibits a plateau known as the TRR plateau characterized by v ln(nv=0/nv) = constant. The distribution exhibits a sharp drop at the higher vibrational quantum numbers because the VT rates overwhelm the VV rates at high values of v.

B.

Optical Pumping of Gases (Laser-Excited CVD or LECVD) for Diamond Growth

Optical pumping of gases using a low-power laser can, under the right conditions, result in production of molecules with high vibrational energies. These molecules can then be made to react among themselves or transfer energy to other species to excite them to specific vibrational or electronic states and hence serve as huge heat baths for driving chemical reactions. A particularly dramatic demonstration of the power and usefulness of this tech-

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nique is the early work of Kildal and Deutsch [88]. At the time, laser sources in the mid-IR such as the CO laser were not as well developed as they are today. Consequently, Kildal and Deutsch [88] went to elaborate lengths to obtain some coherent output at ⬃4.7 ␮m by frequency doubling the 9.4 ␮m laser line from a CO2 laser. The resulting laser output at 4.7 ␮m is coincident with the lowest vibrational transition, v = 0 → v = 1, in CO so that CO can be vibrationally excited to level v = 1 at room temperature. Once this state is populated, of course, other higher vibrational levels can be populated via anharmonic VV pumping: CO(v = 1) ⫹ CO(v = 1) → CO(v = 0) ⫹ CO(v = 2), followed by CO(v = 1) ⫹ CO(v = 2) → CO(v = 0) ⫹ CO(v = 3), and so on. Kildal and Deutsch used this approach to optically pump various gas mixtures containing CO, where CO is used as the energy ‘‘donor’’: CO/ C2H2, CO/C2H2 /H2, CO/CO2, CO/N2O, CO/CS2, CO/CS2 /H2 and CO/OCS [88]. Further, by placing mirrors on the chamber containing these gas mixtures, Kildal and Deutsch were able to obtain lasing from the ‘‘acceptor’’ molecules in which population inversions (partial or total) were sustained by energy supplied from the optically pumped and subsequently vibrationally excited CO molecules. The fact that such transfer lasers could be produced was testament to the rapidity of intermolecular vibrational energy transfer versus loss of this energy to translational modes. A laser source at 4.7 ␮m (i.e., laser output on the CO fundamental v = 1 → v = 0) would have made the optical pumping of CO much easier. Similar energy transfer and VV pumping have been previously reported in CH4, CD3H, CD4, CH2D2, and CH3F [89]. The CO laser was invented as early as 1965 by Patel [90], but theoretical understanding of its operating principle would await the development of the theory of anharmonic VV pumping developed by Treanor, Rich, and Rehm in 1968 [85]. This theoretical development subsequently led to more powerful supersonic and cryogenically cooled CO laser sources [77–79]. Today, the CO laser is the most efficient gas laser, displaying efficiencies near 50%. Steady development in the 1980s and 1990s led to compact cryogenically cooled CO laser sources capable of significant output on the lowest vibrational transition (v = 1 → v = 0). This has been important in enabling the optical pumping of CO at room temperature. We begin with a description of the optical pumping of CO diluted in argon. It is necessary to understand optical pumping in this simple mixture before proceeding with a description of the LECVD process that utilizes the optical pumping of other cold CO-containing gas mixtures. An excellent review can be found in Ref. 2. Consider a mixture of CO/Ar (typically a few percent CO with the balance being argon) flowing at 100 sccm, total pressure of about 50 torr, and temperature of 300 K, irradiated by a CO laser operating multiline with some of its output on the lowest transition (v

Laser-Assisted and Optical Pumping Techniques

387

= 1 → v = 0). Usually, lasing on the lowest transition is difficult but can be relatively easily produced using an intracavity Q switch [70,82]. This usually results in about 100 mW output on the lowest transition, with a total output of about 5 W on all lines. With improved designs [91], cw (continuous wave) output with several watts on the lowest transition can be obtained. The CO in the CO/Ar mixture absorbs this radiation on the v = 1 → v = 0 transition, which populates the v = 1 energy level above its equilibrium value. This in turn enables laser output on the v = 2 → v = 1 transition to be absorbed, populating the v = 2 level above its equilibrium value, and so on. In this manner, levels v = 9 down to v = 1 are populated by absorption of energy from the laser beam. A typical spectrum of the CO laser emission is shown in Fig. 37. It is important to highlight the fact that this absorption process is a resonant, single-photon process and therefore does not require high laser powers or pulse energies. This absorbed laser energy is then redistributed to the higher vibrational levels by anharmonic VV pumping. The result is a fully VV pumped distribution as shown in Fig. 36. Note that only one por-

Figure 37 Typical spectrum showing output from a CO laser. This laser is capable of operating at about 10 W cw while also lasing on the v = 1 → v = 0 transition (leftmost peak). Each successive set(s) of peaks represents higher vibrational bands from v = 2 → v = 1 up to v = 10→ v = 9. (From Ref. 91.)

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tion of the TRR distribution is evident because VT rates scale or increase with vibrational quantum number and prevent the total inversion that is characteristic of the TRR distribution. Instead of a minimum, the real VV pumped distribution exhibits a near-plateau region over which vnv ⬇ constant, followed by a steep drop in the vibrational populations at the higher vibrational quantum numbers. The reason for both trends is that both VV and VT rates increase with v, but eventually VT rates exceed the VV rates that drive the up-pumping at the higher vibrational quantum numbers. A fully VV pumped vibrational population distribution in a flowing CO/Ar mixture results in population of vibrational states as high as v = 42, corresponding to energies of more than 8 eV [79]. This is significant because the dissociation energy of the CO molecule is about 11 eV. When a molecule such as CO is pumped to vibrational levels as high as v = 42, quite a bit of energy is engaged within the vibrational mode. This energy should be available to drive chemical reactions or for transfer to other modes of energy storage such as electronic excitation. Indeed, a host of energy transfer processes occur such as those that result in population of low-lying electronic states by VE (vibration-to-electronic) transfer [79,82]: CO(X1⌺⫹, v) ⫹ CO(X1⌺⫹, w) → CO(v⬘) ⫹ CO(a3⌸, w⬘), Ev ⫹ Ew > 6 eV ⫹

⫹

⫹

CO(X ⌺ , v) ⫹ CO(X ⌺ , w) → CO(X ⌺ , v ⬘) ⫹ CO(A ⌸, w⬘), Ev ⫹ Ew > 8 eV 1

⫹

1

1

CO(X ⌺ , v ⬇ 27) ⫹ M → CO(a ⌸, w⬘) ⫹ M) CO(X1⌺⫹, v ⬇ 40) ⫹ M → CO(A1⌸, w⬘) ⫹ M 1

3

(24)

1

(25) (26) (27)

Processes (26) and (27) represent direct collisional transfer to electronic states, one of which is the a3⌸ state, which is metastable with a radiative lifetime of 4.4–9.5 msec. Another electronic state, A1⌸, has a radiative lifetime of 10 nsec and therefore serves to limit the vibrational up-pump. It must be pointed out that around v = 42, 2[E(v = 42) ⫺ E(v = 40)] ⬇ [E(v = 1) ⫺ E(v = 0)], so that the following near-resonant process: CO(X1⌺⫹, v ⬇ 42) ⫹ CO(X1⌺⫹, v = 0) → CO(X1⌺⫹, v ⬇ 40) ⫹ CO(X1⌺⫹, v = 1) can occur with high rapidity, as does VT transfer (which scales with the vibrational quantum number v). While this is possible, the VE transfer via process (27) has been observed experimentally, and radiative emission from CO(A1⌸, w) → CO(X1⌺⫹, v) has been observed only after CO(X1⌺⫹, v ⬇ 42) is populated [79]. Thus, despite attaining energies near the dissociation limit, CO is not observed to dissociate because of the rapid VE transfer to

Laser-Assisted and Optical Pumping Techniques

389

the A1⌸ electronic state, followed by fast radiative decay to the ground electronic state or manifold [79]. Thus, infrared radiation goes into exciting the gas, while ultraviolet light comes out! In contrast, the a3⌸ by virtue of its relatively long lifetime suffers collisions and is either deexcited (collisionally quenched) or reacted.21 Processes (24) and (25) represent energy transfer by an associative mechanism referred to as vibrational pooling. Such processes have high probability of occurrence because they typically involve many combinations of molecular collision pairs with energies that add up to the required energy of a given excited electronic state. Such associative processes have been shown to be instrumental in producing ionization by vibrational pooling and may constitute a major source of ionization in CO-containing electrical discharges [92]: CO(X1⌺⫹, v) ⫹ CO(X1⌺⫹, w) →

再

CO⫹ ⫹ CO(X1⌺⫹, w⬘) ⫹ e⫺, ⫺ (CO)⫹ 2 ⫹ e

Ev ⫹ Ew ⱖ 13.6 eV

(28)

The lower pathway of process (28) resulting in the formation of the dimer ion is favored because it has a slightly lower ionization potential than CO. Regardless, the production of CO⫹ or (CO)⫹ 2 dimer ions usually leads to cluster ions of the form (CO⫹ ⭈ CO⭈ Cn) where n = (0, . . . , 11) [93]. In addition to the aforementioned energy transfer and associative ionization processes, chemical reactions such as the Boudouard reaction occur: {CO(X1⌺⫹, v)

or

CO(a3⌸, v⬘)}

⫹ {CO(X1⌺⫹, w) or CO(a3⌸, w⬘)} → C* ⫹ CO2, Ev ⫹ Ew > 6 eV

(29)

followed by: C ⫹ CO ⫹ M → C2O

(30)

C ⫹ C ⫹ M → C2 ⫹ M

(31)

The formation of C2 in the gas phase is generally thought to be undesirable for diamond formation. There is some work however, that suggests C2 could be a growth species for nanocrystalline diamond [94,95]. Past optical pumping experiments involving sufficient vibrational excitation of CO to drive the Boudouard reaction (29) leading to C2 formation via (31) have shown formation of graphitic soot [96]. Reaction (31) is one of the channels for Alternatively, there can be collision-induced E-V transfer from CO(a3⌸) into the CO(X1⌺⫹, v ⬇ 27) state, although it has not yet been observed experimentally by optical pumping.

21

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formation of soot in electrical discharges containing substantial amounts of CO. In a plasma, free carbon is produced by electron impact dissociation of CO as well as by reactions (29) and (31) where the appropriate CO(a3⌸) or vibrationally excited CO(X1⌺⫹) is produced by electron impact processes. In contrast, formation of C2 in the gas phase in an optically pumped mixture first requires the formation of atomic carbon via reaction (29), which has an activation energy of about 6 eV. Therefore, it is clear that formation of CO in the a3⌸ state [whose lowest vibrational level is isoenergetic with the v ⬇ 27 state of CO(X1⌺⫹) with an energy on the order of 6 eV] or CO in vibrational levels beyond v ⬇ 13 in the X1⌺⫹ state must be suppressed. The requirement that CO in vibrational levels beyond v ⬇ 13 in the X1⌺⫹ state not be populated stems from the fact that molecules in these levels can pool their energies to form some molecules in v ⬇ 27 of the X1⌺⫹ state or in the low vibrational levels of the a3⌸ state. In general, light molecules or molecules with many rotational modes are very effective in VT relaxing vibrationally excited CO [2,3]. Molecular hydrogen and water are two examples of strong VT relaxers [2,75]. Hence, it is very difficult to produce reactive vibrationally excited CO molecules by optical pumping in mixtures predominantly comprising H2 or H2O, which is typical of growth mixtures used in diamond synthesis by CVD. Rebello et al. circumvented this problem by using a mixture containing mainly CO but with some CH4, which is commonly used as a carbonaceous precursor in CVD processes for diamond synthesis. Diamond growth was reported from a gaseous mixture of 95% CO and 5% CH4, where the CO was optically excited using a Q-switched CO laser operating with its shortest wavelength output on the v = 3 → v = 2 transition [70,83]. These experiments were the first to demonstrate that diamond growth was possible without the need to hyperdilute the gas phase with hydrogen or some other etchant. Such a mixture has never before been reported to yield diamond growth by any other CVD process (HFCVD, plasma CVD, or flame synthesis), and may therefore signal the existence of alternative routes to diamond synthesis. We review their experiment here in detail. A schematic of the LECVD or laser-excited CVD experiment is shown in Fig. 38. A CO laser Q-switched at 200 Hz with the lasing lines shown in Fig. 39 was used to optically pump a flowing mixture of 95 sccm of CO and 5 sccm of CH4 at a total pressure of 50 torr. Of the 2.3 W output (on all lines) from the Q-switched CO laser, approximately 1 W was reportedly absorbed by the CO in the gas mixture [70,83]. Single-crystal Si(100) wafers approximately 2 cm2 in size were used as substrates and heated to a temperature between 600 and 700⬚C. The substrates were supported on a heated holder within the reactor and oriented upside down [83]. This was done to

Laser-Assisted and Optical Pumping Techniques

Figure 38 Ref. 83.)

391

Schematic of the LECVD or laser-excited CVD experiment. (From

take advantage of the buoyancy-driven or free convective flow induced by substrate heating, which tends to drive the gas upward. Such a means of mounting was also used in experiments where the substrates were not heated [70]. The substrates were physically abraded using diamond particles (4- to 8-␮m sized particles in the earlier work where the substrate was heated [83] and with particles 0–0.5 ␮m in size in the later work where the substrates

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Figure 39 Spectrum showing the lasing lines of the CO laser used in the LECVD experiments. This laser was Q switched at 200 Hz. (From Ref. 83.)

were not heated [70]) suspended in glycerol and subsequently cleaned in deionized water, acetone, and methanol, respectively. The authors reported that such a pretreatment was used to possibly reduce nucleation times and thereby enable short-duration experiments, as is typically done with other diamond growth techniques [70,83]. The substrates were then thoroughly characterized prior to growth using SEM imaging, and Raman spectroscopy (survey as well as with a microprobe). The substrates contained some residual abrasive particles only in a few isolated cases. However, these proved to be debris of the silicon substrate when analyzed using energy dispersive x-ray spectroscopic (EDS) analysis. Further, these debris particles did not show the characteristic diamond line at 1332 cm⫺1 in the corresponding Raman spectra. The authors carefully characterized the substrates before growth and reported on the formation of additional particles approximately 10 ␮m in size clustered together in groups that covered regions on the order of 50 or 60 ␮m2. Figure 40 shows SEM images of the substrate surface before and after growth. The fact that these growth particles were grouped together enabled Raman spectra to be obtained using a microprobe. A representative Raman spectrum and EDS spectrum are shown in Figs. 41 and 42, respectively. Of

Laser-Assisted and Optical Pumping Techniques

393

Figure 40 SEM images before and after growth in the LECVD experiment. (From Refs. 70, 83.)

significance is the fact that these experiments have been repeated under conditions where the substrate is not heated and similar diamond growth is observed [70]. Evidently, diamond growth by LECVD does not require the monocrystalline silicon substrate to be heated. During the LECVD growth process, there was no visible emission from the reactor chamber even when the substrate was heated because the resistively heated tungsten filament was hidden from view. However, there was radiative emission from the gas in the infrared. Figure 43 shows a low-resolution IR spectrum from the gas

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Figure 41 Typical Raman spectrum of the diamond particles synthesized by LECVD. (From Ref. 70.)

phase for the case where the substrate was not heated, displaying the overtone emission (i.e., ⌬v = 2) from vibrationally excited CO and emission from the ␯3 mode of CH4. The ␯3 mode is the asymmetric stretch mode where a single hydrogen atom vibrates against the CH3 group in the methane. An energy level diagram for CH4 is shown in Fig. 44 along with the corresponding low-lying CO vibrational energy levels. In addition, faint emission was observed from the ␯4 or bending mode of CH4 [70]. The ␯4 mode emission is particularly difficult to detect because it overlaps with ambient blackbody radiative emission at 300 K. These spectra serve to verify that CO is vibrationally excited and transfers energy to CH4 to excite it vibrationally as well. The population distribution in CO(X1⌺⫹) can be inferred by comparing the experimentally measured radiative emission with synthetic spectra and is shown in Fig. 45 [70]. It can be seen that the CO in the CO/ CH4 mixture under conditions of interest to diamond growth exhibits vibrational nonequilibrium but is not fully VV pumped. Using the slope of the population distribution for the lower vibrational levels in Fig. 45, a vibrational temperature T␯ = 2200 K can be inferred.22 There are some interesting similarities and differences between these diamond crystals and those observed in other CVD systems. In the first 22

Note that here the translational temperature T ⬇ 300 K ≠ T␯ = 2200 K.

Laser-Assisted and Optical Pumping Techniques

395

Figure 42 Energy-dispersive x-ray spectroscopic (EDS) analysis spectrum of the diamond particles synthesized by LECVD. (From Ref. 70.)

place, the morphology of these particles is clearly irregular but still faceted. It resembles the morphology of the particles obtained by photolysis of CO in the CO/H2 mixtures in LCVD (see Sec. IV and Refs. 68 and 69). There is also a strong resemblance of the morphology of the growth particles to that of the high-pressure diamond grit used in the abrasion pretreatment, except the growth particles are larger. The well-defined crystal habits displayed in diamond synthesized by other CVD techniques are due to the simultaneous presence of growth and etch channels. If pure growth occurred without the presence of any etch mechanisms, morphologies such as those in Figs. 25 and 29 would be expected, as discussed earlier in Sec. IV (see Figs. 25 and 29, associated discussion, and Ref. 72). The Raman spectra reveal that the growth particles are indeed diamond as can be seen from the sharp 1332 cm⫺1 line in Fig. 41. The fact that no graphitic lines (at 1580 cm⫺1 and/or at 1343 cm⫺1) are observed in the Raman spectrum is indeed conspicuous. Codeposition of nondiamond (graphitic) carbon is usually ob-

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Figure 43 Low-resolution IR spectrum from the gas phase, displaying the overtone emission (i.e., ⌬v = 2) from vibrationally excited CO and emission from the ␯3 mode of CH4. The ␯3 mode is the asymmetric stretch mode where a single hydrogen atom vibrates against the CH3 group in the methane. (From Ref. 70.)

served in diamond growth using other types of CVD processes and is clearly absent in LECVD. The EDS spectrum shows the presence of a small peak corresponding to oxygen. As this peak is observed only in diamond films grown using other CVD techniques in which oxygen or oxygen-bearing compounds are used in the growth gases [15–17,69], this suggests rather strongly that CO may play a role in diamond growth by LECVD. Such an oxygen peak is never observed in EDS spectra of diamond films exposed to ambient air. Therefore, it appears highly likely that oxygen is present on the diamond surface itself as a direct result of the specific LECVD growth environment and may in fact provide clues to growth mechanisms. Control experiments were also done to determine what the growth species might be [70,83]. Substrates having undergone the same abrasive pretreatment, and either heated to the same temperatures or unheated, were exposed to optically pumped 95% CO/5% H2 and 100% CO gaseous environments but showed no presence of diamond. These control experiments suggest that CH4 is the likely carbonaceous precursor. However, the CO

Laser-Assisted and Optical Pumping Techniques

397

Figure 44 Energy level diagram for CH4, along with the corresponding low-lying CO vibrational energy levels. (From Ref. 70.)

could have played a facilitating role as can be inferred from EDS analysis indicating the presence of oxygen on the diamond surface. Unfortunately, experiments involving 13CH4, which would have been more illuminating, were not done.23 As mentioned earlier, the same optical pumping technique has been applied to conditions where the substrate is not heated [70,84]. Earlier experiments [83] were conducted with a heated substrate and v = 3 → v = 2 23

The use of 13CO in the gas phase would have been problematic because the CO laser source would also have had to operate using the same isotope in order to take advantage of resonance absorption.

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Figure 45 Population distribution in CO (X1⌺⫹) inferred by comparing the radiative emission with synthetic spectra. (From Ref. 70.)

as the shortest wavelength lasing transition from the CO laser. As discussed earlier in Secs. V.A and V.B, there is a negligible population of CO molecules in the v = 2 state at room temperature so that laser absorption to trigger the VV pumping could occur only at an elevated temperature. In the more recent work [70,84], however, the CO laser was operated with some output on the v = 1 → v = 0 transition so that CO molecules at room temperature could be vibrationally excited. Indeed, as in the LCVD or laser photolysis technique discussed in Sec IV, diamond growth was obtained on unheated surfaces [70,84]. It is of significance that two completely different laserbased techniques (LCVD and LECVD) involving two completely different gas mixtures (1% CO in 99% H2 for photolysis and 5% CH4 in 95% CO for LECVD) yielded diamond growth on unheated surfaces. This also suggests that growth mechanisms in these completely different experiments may share common features. We shall address the subject of mechanisms shortly. Optical pumping experiments have also been conducted in mixtures of 5% C2H2 in CO [70,84]. A low-resolution emission spectrum from this experiment is shown in Fig. 46 and displays the ␯3 band of acetylene and faint emission from possibly the combination bands ␯2 ⫹ ␯ 15, ␯2 ⫹ 2␯ 05 ⫺ ␯ 15, ␯2 ⫹ 2␯ 14 ⫹ ␯ 15 ⫺ ␯ 14, ␯3 ⫺ ␯ 14, and ␯1 ⫺ ␯ 15 [97]. The spectrum ascribed to the

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Figure 46 Low-resolution emission spectrum from optical pumping of CO/C2H2 mixture showing the ␯3 band of acetylene and faint emission from possibly the combinations bands ␯2 ⫹ ␯ 15, ␯2 ⫹ 2␯ 05 ⫺ ␯ 15, ␯2 ⫹ 2␯ 14 ⫹ ␯ 15 ⫺ ␯ 14, ␯3 ⫺ ␯ 14, and ␯1 ⫺ ␯ 15 [97]. (From Ref. 70.)

␯3 band may also contain some emission from the ␯2 ⫹ ␯ 14 ⫹ ␯ 15 combination band. The ␯3 band of acetylene arises from its asymmetric stretch mode wherein a hydrogen atom vibrates against the associated C2H. As in the case of the optically pumped CO/CH4 mixture, the vibrational populations of CO can be inferred from the overtone emission spectrum. This is shown in Fig. 47 for the CO/C2H2 mixture, and appears to indicate that levels up to about v = 9 or v = 10 are populated. However, no diamond growth was obtained from optically pumped CO/C2H2 mixtures despite the obvious energy transfer from CO to acetylene [70]. The LECVD experiments reported in Refs. 70, 83, and 84 were independently reproduced in the Laboratoire d’E´nerge´tique Moleculaire et Macroscopique, Combustion (E.M2.C.) at E´cole Centrale Paris in France [98]. These results confirm diamond growth both on unheated silicon substrates as well as on heated substrates [98]. Additional experiments in which high-resolution spectra were obtained are reported in Ref. 98 as well. Figure

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Figure 47 Vibrational populations of CO inferred from the overtone emission spectrum are shown here for the CO/C2H2 mixture and indicate that levels up to about v = 9 or v = 10 are populated. (From Ref. 70.)

48 shows a high-resolution spectrum of the same bands of CO and CH4 that are displayed in Fig. 43 for the experiments reported in Refs. 70, 83, and 84. With 4 W of the incident 10.8 W cw laser power (on all lines) absorbed, Ref. 98 reported that emission measurements indicate that the CO alone (without addition of CH4) is pumped up to levels near v = 17, which corresponds to energies of about 4 eV. Upon addition of the CH4, emissions from CO molecules are observed only up to about v = 10, which corresponds to energies of about 2.5 eV. Note that in the latter case, formation of C2 in the gas phase is suppressed because reaction (29) requires an activation energy of about 6 eV. Reference 98 also presents detailed analyses using high-resolution emission and absorption spectroscopy. Careful analysis shows that the spectrum largely attributed to the ␯3 mode of CH4 actually contains other lines arising from the combination bands ␯3 ⫹ ␯4 → ␯4 and ␯3 ⫹ ␯2 → ␯2, also known as the ‘‘hot bands’’ of methane. From these spectra, a vibrational temperature T␯ of 1950 K was inferred [98]. Of significance is the fact that the detailed gas-phase spectroscopic studies of Ref. 98 indicate the presence only of CO and CH4 in both emission and absorption measurements. No evidence was found for any other chemical species or reaction by-products, at least within detection limits. Clearly, either re-

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Figure 48 High-resolution spectrum of the overtone bands of CO and ␯3 mode emission from CH4 from the E´cole Centrale Paris experiments. (From Ref. 98.)

action by-product concentrations were too small to be observed or reactions occurred on the growth surface. Diamond growth on unheated, seeded substrates has been reported using two completely different laser-based techniques (laser photolysis and LECVD) and using two very different gas mixtures (1% CO in H2 in the photolysis case and 5% CH4 in CO in the optical pumping case). These results beg the question of whether or not the two techniques share some commonality in growth mechanisms. At first glance, it appears they share

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no common features. Laser photolysis uses a ‘‘conventional’’ gas mixture for diamond growth and therefore can be explained using present understanding of diamond growth by CVD processes [64], which identifies the CH3 radical as the growth precursor. Once CH3 groups are added to a growing diamond surface, the atomic hydrogen is removed by the atomic hydrogen present in the gas phase. In contrast, LECVD uses a gas mixture that normally would not yield diamond growth if used in other conventional non–laser-based CVD methods. There cannot be an appreciable amount of atomic hydrogen in the LECVD environment, or else the CO would not VV pump [2,75]. Because the particle growth rates for the two methods are comparable (on the order of 1 ␮m/hr) as are the resulting morphologies and Raman spectra, we expect the carbonaceous precursor to be present in concentrations on the order of 1018 m⫺3 following the same reasoning as in Sec. IV. It is extremely difficult to infer growth mechanisms or detailed channels based upon the experiments reported thus far [70,83,84,98]. However, a reasonable reaction scheme can be formulated if all the known evidence is viewed collectively. This evidence will be briefly summarized at the outset. First, control experiments indicate no diamond growth either in the absence of laser excitation or when CH4 is absent from the gas mixture. Further, no diamond growth was obtained from optically pumped CO/C2H2 mixtures. Second, elemental oxygen is detected in the EDS spectra of diamond particles grown using LECVD as well as laser photolysis. This suggests that CO somehow acts in concert with CH4 during growth. Third, there is clear evidence of energy transfer from CO to CH4 as can be seen from the IR emission from excited states of CH4. Fourth, the LECVD experiments conducted at E´cole Centrale Paris detected only CO and CH4 and no other species (within detection limits) in their emission and absorption studies [98]. Fifth, the morphology of the irregularly faceted particles grown by LECVD is identical to those grown by laser photolysis. Finally, the particle growth rates appear to be insensitive to whether or not the substrate is heated. Based upon these six essential points, we attempt to formulate a possible mechanism. There have been several important attempts to elucidate the surface mechanisms responsible for diamond growth [64,65,99–102]. These mechanisms are relevant for conventional CVD techniques for diamond growth in a hydrogen-rich environment and have shown promise in providing a mechanistic understanding of growth on (100) surfaces. Many of the proposed mechanisms focus on the incorporation of CHx species on the surface, specifically the CH3 molecule (i.e., methyl radical) [64,65,99–101]. We therefore concentrate here on the possibility of extending these ideas to understand the LECVD process. However, it must be borne in mind that

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these mechanisms have been postulated for a hydrogen-rich ambient and not for the conditions typical of LECVD. The first point that must be addressed is the production of methyl radicals either in the gas phase or on the surface of seed diamond particles. Given the relatively high vibrational temperature of CO (⬃2200 K) produced by laser excitation and subsequent VV pumping, it is reasonable to expect the translational temperature of CH4 to be between 300 and 2200 K. Under these conditions, production of CH3 can occur via the following channels: Vibrationally stimulated thermal dissociation: CH4 ⫹ M → CH3 ⫹ H ⫹ M Vibrational pooling:

CH* 4 ⫹ CH* 4 → CH3 ⫹ H ⫹ CH4

(32) (33)

CO(v) ⫹ CH* 4 → [CH3COH]* → [C2H4O]* → [CH3CHO]*

CH3 ⫹ HCO CH3CHO CH4 ⫹ CO

(34)

where the * denotes an excited species. The formation of [CH3COH]* can proceed via an insertion reaction whereby a CO molecule inserts itself into a vibrationally excited CH4. Such insertion reactions involving AlO inserted in CH4, have been previously reported [103]. The last step of process (34) has been observed in studies of decomposition of oxirane [104]. It is also interesting to note that CH3CHO is more stable than C2H4O by about 27 kcal/mol or ⬃1.17 eV/molecule. But, there is an activation energy of ⬃57 kcal/mol or ⬃2.47 eV/molecule for the isomerization C2H4O → CH3CHO. This activation energy can be provided via the vibrational excitation of the reactant CO and CH4 molecules by pooling because energies up to ⬃2 eV are available from CO molecules near v = 10 (see Fig. 45). A compelling argument can be made for processes (33) and (34) based upon energy transfer considerations. It can be seen from Fig. 44 that the ␯3 mode of CH4 cannot be populated by intermolecular energy transfer from CO(v = 1) because its energy is higher than the energy corresponding to the v = 1 → v = 0 transition.24 However, intermolecular energy transfer can occur to the ␯2 and ␯4 states of CH4 via CO(X1⌺⫹, v = 1) ⫹ CH4 → CO(X1⌺⫹, v = 0) ⫹ CH4(␯2 or ␯4)

(35)

It can thus be seen that the ␯3 mode can be populated by VV up-pumping 24

Two-quantum transfer via processes such as CO(v = 2) ⫹ CH4 → CO(v = 0) ⫹ CH4(␯3) are possible but much less probable than transfer of single vibrational quanta.

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Table 6 Typical Characteristics of Low-Lying Energy Levels and VV Transfer in Methane at 2.5 Torr State

␯1 (symmetric stretch) ␯2 (symmetric bend) ␯4 (asymmetric bend) ␯3 (asymmetric stretch) 2␯2 2␯4 2␯3 2␯3 → ␯3 ␯2 ⫹ ␯4 ␯3 → ␯4 ␯3 → ␯2 ␯1 → ␯4 2␯4 → ␯2 ⫹ ␯4 ␯1 ⫹ ␯4 → ␯3

Characteristic time for VV transfer

Radiative lifetime

O(0.1–0.5 ␮sec) O(0.1–0.5 ␮sec) 1.1 ␮sec 1.6 ␮sec O(0.1–0.5 ␮sec) O(0.1–0.5 ␮sec) O(0.1–0.5 ␮sec) 0.92 ␮sec O(0.1–0.5 ␮sec) 0.72 ␮sec O(0.1–0.5 ␮sec) O(0.1–0.5 ␮sec) 1.6 ␮sec 0.22 ␮sec

>20 sec 13 sec 0.39 sec 37 msec — 0.20 sec — — 0.39 sec 25 sec 120 sec 8 sec — —

Source: Refs. 105–107.

within the methane initiated from either the ␯2 or ␯4 modes25 or by radiative decay from an excited state. In the latter case, an upper state could have been populated only by VV up-pumping within the methane. Once a specific excited state is populated, it can undergo one of several processes. It can radiate a photon (provided selection rules allow such a transition) and occupy a lower energy state or ground state. It can be collisionally deexcited to any lower state by a VT-type collision or collisionally excited to an upper state by intermolecular or intramolecular vibrational energy transfer. In CH4, the radiative lifetimes of the low-lying levels are longer than tens of milliseconds, as can be seen from Table 6 [105–107]. In contrast, VV transfer occurs within microseconds at pressures of interest to LECVD (i.e., PCH4 = 2.5 torr) [106]. Also, VT and VR collisional deactivation of these levels occurs on time scales of hundreds of microseconds or milliseconds at 2.5

25

The ␯2 and ␯4 levels of methane are isoenergetic with the v = 24 → v = 23 and v = 33 → v = 32 transitions in CO, respectively. Because such high vibrational levels are not significantly populated in CO (as can be seen from the overtone emission spectrum of CO), these methane energy levels must have been populated by off-resonance intermolecular energy transfer from v → v ⫺ 1 transitions in CO (with the v = 1 → v = 0 transition being the most likely one).

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torr [106]. Hence, if intermolecular energy transfer from CH4 back to CO does not depopulate the upper levels of CH4 appreciably, a compelling argument can be made for rapid VV exchange among CH4 molecules. We therefore expect CH4 molecules to be vibrationally hot. This is evident from the strong radiative emission from the ␯3 mode of CH4 despite the presence of rapid intramolecular VV transfer and self-absorption of radiation from the ␯3 mode by surrounding, cold CH4. It is therefore clear that vibrational energy from CO is rapidly transferred to CH4, thereby populating the ␯2 or ␯4 (or both) states. The presence of vibrationally excited CO and excited CH4 in the LECVD experiments has been inferred. These can lead to formation of CH3 radicals via processes (32) through (34). Similar reactions could occur between CO and CH4 molecules adsorbed on diamond seed surfaces as well, and there is not enough experimental evidence to argue for production of methyl radicals from the gas phase alone. Nevertheless, given such an initial source of production of CH3 radicals, the evidence gathered from the LECVD experiments collectively leads to two possible mechanisms. They are (1) growth from CH3 radicals with CO playing no part other than that of a spoiler and terminating growth and (2) growth by concerted action of CO and CH3 at the surface of the diamond seed particles. Let us consider these two possible mechanisms in some detail, especially from the perspective of experimental observations. For ease of discussion, we consider growth on the (100)-oriented surface. Once CH3 radicals are produced (via either gas-phase or surface processes), they can attach themselves to dangling bonds on the (100) surface as shown in Fig. 49. This can be written symbolically as: C•d ⫹ CH3 → Cd — CH3

(36)

• d

where C represents an activated site (i.e., dangling bond) on a seed diamond surface. Atomic hydrogen from the CH3 group can then be removed by successive attacks by other CH3 radicals: Cd — CH3 ⫹ CH3 → Cd — CH•2 ⫹ CH4(g)

(37)

In this manner, carbon can be successively added to and atomic hydrogen

Figure 49 Schematic showing attachment of CH3 radical on a dangling bond on the (100) surface of a diamond speed particle.

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removed from the surface by CH3 radicals alone. Molecular dynamics calculations have shown that a high fraction of CH3 radicals (more than 0.5 at normal incidence) can be adsorbed on (100) diamond surfaces over kinetic energy ranges from 0.5 to 2 eV [108]. Other processes for abstraction of H atoms can also take place. One such process occurs by attack from vibrationally excited CO as suggested previously [109]: Cd — CH3 ⫹ CO(␯) → Cd — CH2 ⫹ HCO

(38)

The other can occur by the following process (after abstraction of an H atom from each of the CH3 groups): Cd — CH2• ⫹ Cd — CH2• → Cd — C2H4

(39)

In this scenario, the CO serves the sole purpose of exciting CH4 and producing CH3. It can also play the role of a spoiler by occupying a dangling bond and establishing a ketone-type structure. This structure is stable (unless attacked by a radical such as CH3) and can in principle inhibit growth by the CH3 mechanism just discussed. The ketone and other possible surface structures are shown in Fig. 50. The second possible mechanism requires the presence of both CO and CH4. Here, CO is added to the surface (the activation energy for adsorption supplied by vibrational excitation) so as to form a ketone-type structure (see Fig. 50a): —O C•d ⫹ CO → Cd — C —

(40)

The adsorbed CO is then attacked by a methyl radical, resulting in the conversion of the double bond between C and O to a single bond by ␤scission:

Figure 50 Schematic showing attachment of CO on the (100) surface of a diamond seed particle, forming a stable ketone-type structure (a) and an ether-type structure (b).

Laser-Assisted and Optical Pumping Techniques

— O ⫹ CH3 → Cd — C — O — CH3 Cd — C —

407

(41)

The resulting ether-like structure is shown in Fig. 51. After subsequent Hatom abstraction via (37), (38), or (39), an aldehyde-type structure can form momentarily, leading to ␤-scission of the underlying CO bond. This should result in evolution of formaldehyde (H2CO), leaving behind two dangling bonds (i.e., two active sites): Cd — C• — O — CH2• → Cd — C• ⫹ H2CO(g) The two dangling bonds on the carbon now allow another layer to be grown by repetition of the preceding processes. Both mechanisms serve to explain some of the key observations in the LECVD experiments. Both can account for the presence of small amounts of elemental oxygen (see the EDS spectrum shown in Fig. 42), and both give plausible descriptions of growth in an environment depleted of atomic hydrogen. Of the two, however, the first appears to explain additional observations reported in Ref. 98. The result of hydrogen abstraction by methyl radicals in the first mechanism would result in the evolution of CH4 from the surface, which would be indistinguishable from the methane already present in the gas phase. This would explain why only CO and CH4 were detected in the absorption measurements reported in Ref. 98. The question remains why CH3 radicals or perhaps HCO went undetected. A possible answer to this question is that CH3 concentration levels (according to our estimates, methyl radical concentrations on the order of nCH3 ⬇ 1012 cm⫺3 or 1018 m⫺3 are expected, or about 1 ppm) were well below detection limits. By this latter argument, the second mechanism cannot be ruled out because

Figure 51 Schematic showing the result of attack by the CH3 radical on a ketonetype CO structure occupying a dangling bond on the (100) surface of a diamond seed particle.

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evolution of H2CO and HCO levels could have been below detection limits as well. Unfortunately, ultimate quantitative detection limits were not reported in Ref. 98 so that it is not possible to carry out further analysis of possible mechanisms. Given the current level of interest in synthesizing diamond at low substrate temperatures [76], both LCVD and LECVD appear to be significant advancements toward attaining this goal. Both laser-based techniques challenge the conventional myth that high substrate temperatures are necessary for diamond growth. Clearly, the environment of conventional diamond growth techniques is limited only by how energy is loaded into the gas mixture. Both techniques also offer some selectivity as can be seen by the conspicuous lack of codeposition of nondiamond carbon, prevalent in other CVD methods. LECVD also challenges our understanding of diamond growth mechanisms by displaying growth in an environment that is not rich in atomic hydrogen. Ultimately, that may be the reason why growth rates in the two methods are small—on the order of 1 ␮m/hr. For LECVD, as the absorbed power is on the order of 1 W, we may estimate the energy cost per carat as 1 J/sec ⫻ (1/10⫺12 cm3) ⫻ (1 hr ⫻ 3600 sec/hr) ⫻ (1/3.515) (cm3/g) ⫻ (0.2 g/carat) = 2 ⫻ 1014 J/carat. This value is many orders of magnitude higher than the corresponding value for diamond synthesis by an oxyacetylene flame. However, unlike LCVD and other methods of CVD diamond synthesis, the LECVD process scales with pressure and can be operated potentially at pressures on the order of 20 atm [77,83], so that the J/carat value can be reduced drastically. However, continuous films have yet to be produced by either LCVD or LECVD. The optical pumping technique shows tremendous promise for synthesis of other materials. For example, it has been shown that vibrationally excited nitrogen is important in the production of silicon nitride films [110]. Reference 110 reports that when silane was added to a flowing nitrogen discharge afterglow (where there is known to be copious amounts of vibrationally excited N2 molecules) and the reaction products made to impinge on a heated monocrystalline silicon substrate placed downstream, silicon nitride films were produced. In addition, reactions between the vibrationally excited N2 and silane in the afterglow led to formation of fine (micron-sized) particles of white silicon nitride powder [110]. Given the similarity in structure between CH4 and SiH4, it is likely that optically pumped CO/SiH4 mixtures could be used for deposition of silicon at low temperatures or for synthesis of silicon carbide. Indeed, Ref. 110 determined experimentally that about 15% of the vibrationally excited N2 quenching events resulted in excitation of the ␯3 mode of SiH4. Recently, a combination of optical pumping and application of a subbreakdown radio-frequency electric field has been shown to produce plasmas in CO/N2 gas mixtures seeded either with NO or

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O2 at total pressures ranging from 0.4 to 1.2 atm [111]. Such plasmas, although weakly ionized, contain substantial amounts of vibrationally excited CO and N2. The use of such plasmas for synthesis of novel materials remains to be explored. In this section, we have examined a laser excitation technique known as LECVD for diamond synthesis. Of significance is the fact that growth of diamond particles has been realized under conditions where the substrate is not heated at all [70,84] and without the need to hyperdilute the gas phase with hydrogen. In fact, diluents such as hydrogen poison the vibrational uppumping of CO and CH4, an effect that is central to the LECVD process. In the following section, we examine a potential means of extending the LECVD process to the condensed phase in order to increase growth rates. C.

Optical Pumping of Liquids

Energy transfer as well as the optical pumping of gases was discussed in Sec. V.B. Specifically, it was shown that small polyatomic molecules are very effective in retaining energy in their vibrational modes. For diatomic molecules, in the limit as VV exchange rates dominate VT and VR energy transfer rates, the population of various vibrational levels is described by the TRR distribution for anharmonic oscillators [see Eq. (17)]. As long as VV rates exceed VT, VR, and spontaneous emission rates, energy is effectively retained in the vibrational modes of molecules. It is important to point out that vibrational energy exchange among anharmonic oscillators is a collisional process. As long as the energy defect26 is carried away by a suitable cold bath, energy can be maintained for long times within the vibrational modes. This is irrespective of the pressure or density of the medium. In the gas phase, CO/Ar mixtures have been optically pumped in a manner so as to excite CO to very high vibrational states (near v = 40) at pressures of 20 atm [77]. Such strong vibrational excitation has also been observed in the liquid and solid phases. This is of significance if we are interested in driving chemical reactions, while maintaining some degree of control and selectivity over which reactions occur and to what extent. In this section, we describe extension of the LECVD technique described in Sec. V.A and V.B to the condensed phase. 26 Recall that the energy defect is defined as the energy difference between the total energy of the colliding molecules before the collision and that value after the collision. During anharmonic VV pumping, energy of magnitude equal to the energy defect is transferred from vibrational excitation to the external modes of translation and rotation. This results in eventual heating of the gas unless the gas is flowed or a suitable diluent is used to carry off this excess heat.

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There exists a considerable literature on optical pumping of CO at elevated gas pressures as well as in the liquid and solid phases [77,112– 118]. These studies have been largely motivated by interest in fundamental energy transfer processes, isotope separation processes, and development of energy transfer lasers. There exists a relatively good coincidence between the laser lines emanating from a CO laser operating on the abundant isotope 12 16 C O and the isotopic liquid phase mixture of 88% 13C16O and 12% 13C18O. Several researchers have used this coincidence to excite CO vibrationally in the liquid phase and in the solid phase [112–118]. Remarkably, the condensed phase CO behaves as though it were a dense gas within the liquid argon matrix or on the solid single-crystal NaCl (100) surface [112–117]. Processes encountered in the gas phase (as discussed in Sec. V.A. and V.B) also occur in the condensed phases, and very high vibrational levels near v = 40 in CO have been observed [112]. Further, energy transfer from CO to small polyatomic molecules has also been reported [112,117,119,120], and not surprisingly, vibrationally excited CO and O2 have been reacted to form CO2 in the liquid phase at temperatures near 88 K. This is indeed a dramatic demonstration of the extreme disequilibrium between vibrational modes and external modes created by optical pumping. Although diamond growth from such optically pumped CO/CH4 liquid mixtures has never been demonstrated, the successful LECVD experiments described in Sec. V.B are strong indicators that diamond growth in optically pumped liquids could meet with success. Further, measured rate coefficients for energy transfer in the liquid and gas phases for a variety of mixtures of interest to diamond synthesis are quite encouraging. Table 7 gives measured values of rate coefficients for gas and liquid phases at a temperature of 80 K, as reported [119,120]. Remarkably, the variation in rate coefficients for vibrational energy transfer between gas and liquid states is less than 10% for the molecules listed in Table 7. Now, the rate of energy transfer depends on the product of the rate coefficient and number densities of the colliding partners. Therefore, the rate at which intermolecular vibrational energy transfer occurs increases by many orders of magnitude because the liquid phase is much denser than the gas phase. This has the potential to increase yield and growth rates. As many single-crystal materials are grown from melts in the liquid phase, optical pumping in the liquid phase may finally lead to epitaxial, single-crystal diamond films. The latter possibility is further bolstered by the fact that multilayers of ␣-form solid, single-crystal CO can be deposited on NaCl (100) substrates epitaxially because the lattice mismatch is less than 0.5% [116]. Further, the solid CO has been vibrationally excited up to levels as high as v = 23 [114], and as high as v = 30 at 22 K, by optical pumping using a CO laser [116]. In fact, this up-pumping is so rapid in the solid phase as to yield a population inversion (i.e., there are greater

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Table 7 Measured Rate Constants for Vibrational Energy Transfer in the Gas and Liquid Phases at 85 K System N2-12C16O N2-13C16O N2-13C18O 13 18 C O-O2 13 16 C O-O2 12 16 C O-O2 13 18 C O-CH4 13 16 C O-CH4 12 16 C O-CH4 N2-CH4 12 16 C O-CH4 13 16 C O-CH4 13 18 C O-CH4 12 16 C O-CF4 13 18 C O-CF4 12 16 C O-CD4 13 16 C O-CD4 13 18 C O-CD4 12 16 C O-CD3H 13 16 C O-CD3H 13 18 C O-CD3H

⌬E (cm⫺1) 187 234 286 487 540 587 509 562 609 796

kLiquid (cm3/sec) (3.2 ⫾ 0.2) (1.2 ⫾ 0.1) (3.9 ⫾ 0.1) (1.54 ⫾ 0.02) (7.0 ⫾ 0.5) (4.2 ⫾ 0.1) (4.03 ⫾ 0.09) (2.08 ⫾ 0.05) (1.33 ⫾ 0.05) (1.3 ⫾ 0.1) (1.33 ⫾ 0.05) (2.08 ⫾ 0.05) (4.03 ⫾ 0.09) (8.6 ⫾ 0.1) (7.50 ⫾ 0.09) (2.48 ⫾ 0.04) (2.28 ⫾ 0.08) (1.47 ⫾ 0.03) (1.15 ⫾ 0.02) (1.58 ⫾ 0.04) (1.26 ⫾ 0.02)

⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻

kGas (cm3/sec) 10⫺15 10⫺15 10⫺16 10⫺17 10⫺18 10⫺18 10⫺15 10⫺15 10⫺15 10⫺16 10⫺15 10⫺15 10⫺15 10⫺14 10⫺16 10⫺13 10⫺13 10⫺13 10⫺12 10⫺13 10⫺13

(3.6 ⫾ 0.2) (1.1 ⫾ 0.1) (3.79 ⫾ 0.08) (1.50 ⫾ 0.03) (7.0 ⫾ 0.9) (4.1 ⫾ 0.2) (4.17 ⫾ 0.08) (2.07 ⫾ 0.06) (1.27 ⫾ 0.04) (1.5 ⫾ 0.2) (1.27 ⫾ 0.04) (2.07 ⫾ 0.06) (4.17 ⫾ 0.08) (1.98 ⫾ 0.04) (1.0 ⫾ 0.1) (4.60 ⫾ 0.08) (4.3 ⫾ 0.1) (3.5 ⫾ 0.1) (1.32 ⫾ 0.03) (3.3 ⫾ 0.1) (2.38 ⫾ 0.05)

⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻

kLiquid/kGas 10⫺15 10⫺15 10⫺16 10⫺17 10⫺18 10⫺18 10⫺15 10⫺15 10⫺15 10⫺16 10⫺15 10⫺15 10⫺15 10⫺13 10⫺15 10⫺13 10⫺13 10⫺13 10⫺12 10⫺13 10⫺13

0.97 1.09 1.03 1.03 1.00 1.02 0.97 1.00 1.05 0.87 1.05 1.00 0.97 0.43 0.75 0.54 0.53 0.42 0.87 0.48 0.53

⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾ ⫾

0.08 0.13 0.03 0.03 0.15 0.06 0.03 0.04 0.06 0.13 0.06 0.04 0.03 0.01 0.08 0.01 0.02 0.02 0.02 0.02 0.01

Source: Refs. 119, 120.

numbers of molecules in the higher vibrational states than in the v = 0 or ground vibrational state). We now describe an experiment that demonstrates some of the salient features of optical pumping of CO in the liquid phase [70]. A CO laser designed to operate cw (5 to 8 W on all lines) with some laser output on the v = 1 → v = 0 transition was used to pump CO in a liquid argon matrix. A schematic of the cell containing the cryogenic mixture is shown in Fig. 52. This cell is identical to that used in the experiments reported in Ref. 112, and details may be found therein. The output from the CO laser was focused into the center of the cryogenic cell containing a solution of CO in liquid argon, using a ZnSe lens (1 in. diameter, focal length of 9 in.). The liquid mixture was produced from an initially gaseous mixture of CO and argon, which was condensed upon being cooled by the liquid argon placed in a dewar immediately above the cell. A schematic of the mixing chamber

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Figure 52 Schematic of the cell containing the cryogenic mixture of CO and argon. (From Ref. 70.)

is shown in Fig. 53. The CO/argon mixture is prepurified before allowing it to condense into the cell. The purification procedure consists of using the cold finger connected to the mixing chamber. The gases are condensed into the cold finger and, after some time, allowed to evaporate back into the mixing chamber while a small part of the cold finger is still immersed in liquid nitrogen. This process is repeated 15 times. Reference 70 reported pumping of CO/argon gas mixtures where the initial partial pressure of CO in the gas phase was varied between 70 mtorr and 30 torr, while maintaining a total pressure of 2 atm. The CO was an isotopic mixture comprising 88% 13C16O and 12% 13C18O. This isotopic mixture was selected because of its excellent coincidence in the liquid phase with CO laser lines when the CO laser was operated on the normally abundant 12C16O isotope. Following the aforementioned purification procedure, the CO/argon mixture was condensed into the cell and irradiated by the cw CO laser beam. Power measurements before the cell were in the range of 3.5 to 5 W. Using a side port, IR emission was monitored from the optically pumped liquid CO. A representative spectrum of the first overtone (⌬v = 2)

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Figure 53 Schematic showing the mixing chamber used in optical pumping of liquid CO/argon mixture. (From Ref. 70.)

transitions from the liquid CO for an initial gas-phase CO partial pressure of 9 torr, after background blackbody subtraction, is shown in Fig. 54. It is important to note that this is not a low-resolution spectrum. Rotational lines within each vibrational band can be either totally absent (as in the case of CH4) or substantially narrowed in the liquid state as compared with similar gas-phase spectra. It is immediately apparent from the emission spectrum that states at least as high as v = 38 (see the energy level diagram for CO

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Figure 54 A representative spectrum of the first overtone (⌬v = 2) transitions from liquid CO in liquid argon, optically pumped using a CO laser. This spectrum was obtained for an initial gas-phase CO partial pressure of 9 torr and after background blackbody subtraction. (From Ref. 70.)

shown in Fig. 34) of the heavier isotope 13C18O are substantially populated. In addition, peaks corresponding to isotopes of carbon dioxide 13C16O16O, 13 16 18 C O O, and 13C18O18O are also observed. This is indicative of chemical reaction occurring among vibrationally excited CO molecules, possibly via channels (29). Production of CO2 has been observed previously but from vibrationally excited CO doped with O2 [112]. Assuming the Einstein A coefficients for spontaneous emission from these vibrational states are comparable between gas and liquid phases, relative populations can be inferred from the emission spectrum. This is shown in Fig. 55, displaying a fully VV pumped distribution in the heavier isotope. It is clear that many (if not all) of the processes observed in gas-phase optically pumped CO occur in the liquid phase as well. Anharmonic VV pumping resulting in highly vibrationally excited CO (levels as high as v = 38 or as energetic as 8 or 9 eV) is observed in both gas and liquid phases. Intermolecular energy transfer between CO and CH4 has been reported, although IR emission from highly excited methane has not yet been observed. Chemical reaction from vibrationally excited CO, and between CO and O2, yielding CO2 is observed in both the gas and liquid phases as well. Given this close similarity in the occurrence of key processes between gas and liquid phases and the success of the LECVD process for diamond synthesis, the likelihood that diamond can be synthesized from optically pumped liquid CO/CH4 /Ar mixture appears to be high. Should diamond synthesis occur in

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Figure 55 Relative populations of vibrationally excited CO in liquid argon inferred from the emission spectrum. This was obtained by assuming that the Einstein A coefficients for spontaneous emission from these vibrational states are comparable between gas and liquid phases. Note the fully VV pumped distribution in the heavier isotope. (From Ref. 70.)

such an optically pumped liquid mixture, it should be more rapid than in the gas phase because the rates of energy transfer scale as the square of the density. Finally, the production of flaw-free, cubic, solid CO as well as its extreme vibrational excitation by optical pumping resulting in population inversion bodes well for adsorbed CH4 species. Although growth of diamond films using such a technique has not been demonstrated, it is nevertheless worth exploring. Given the fact that many growth techniques for single crystals of other materials involve the liquid phase, this approach of optically pumping liquids appears promising for synthesis of single-crystal diamond. This is important before diamond can be considered as a candidate material for electronic applications.

VI.

SUMMARY

This chapter has discussed synthesis of diamond from gas and liquid phases using laser sources. The laser-based techniques include surface heating, py-

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rolysis, ablation (LPVD), photolysis (LCVD), and optical pumping (LECVD). The laser-based techniques do not necessarily supplant existing CVD methods but offer the prospect of lowering growth temperatures, selectively depositing diamond while inhibiting the deposition of nondiamond carbon, and perhaps enhancing growth rates. In the case of rapid gas-phase heating such as pyrolysis, the laser simply serves as a source of thermal heating and is therefore an inefficient means of activating the gas. In this instance, it does not provide any advantages such as selectivity or enhanced quality of the deposit. Ablation and heating of surfaces can benefit from laser sources because reactions may need to be driven locally, without bulk heating of the growth medium, target, or substrate. In contrast, photolysis and optical pumping techniques use attributes of molecular structure to drive specific reaction pathways to form products. This is difficult or not even possible using conventional growth methods. Many of these laser-based processes have already demonstrated diamond growth, albeit at different rates. Although capital costs vary widely, a useful measure of the relative efficacy of each process is the joule-per-carat value. This measure considers the power required for the process as well as growth rate simultaneously. The pyrolysis and photolysis techniques exhibit growth rates on the order of microns per hour, as does the optical pumping technique at low gas pressures. However these exhibit drastically different energy costs in J/carat: O(108), O(107)–O(1014), and O(1014), respectively. These should be contrasted with typical values of O(108) J/carat for HFCVD27 and O(106) J/carat for synthesis using an oxyacetylene flame.28 The laser-plasma technique is equivalent to but less efficient energetically than the conventional oxyacetylene flame, exhibiting growth rates on the order of 10 to 100 ␮m per hour at a power level of 2.5 kW. Of all these laser processes, however, the well-publicized but as yet unverified QQC process reports growth rates on the order of millimeters per hour (i.e., microns per second) at a cost of about 71 J/carat. Clearly, if cost is the prevailing factor, the QQC process appears to be the best (provided its claims are substantiated), while some of the laser pyrolysis and laser photolysis methods are competitive with HFCVD and oxyacetylene flame synthesis. It would be premature to eliminate optical pumping based on a comparative measure such as joules per carat. Optical pumping, unlike the other methods, inherently scales directly with pressure. Therefore, for approximately the same power expenditure, the growth rate can be significantly increased sim-

27

This value is based on a power expenditure of 100 W and deposition over a 1 cm2 area at 1 ␮m/hr. 28 See footnote 9.

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ply by raising the pressure. This would reduce the J/carat value for this process from the unreasonable O(1014) and make it competitive with the others. Further enhancement in growth rate is possible in the liquid phase, in principle, although diamond growth in an optically pumped liquid is yet to be demonstrated. Moreover, this method has the added virtue of lower growth temperatures as well as process selectivity. Some of the more nascent but novel approaches such as LECVD, laser photolysis, and the QQC process have been critically examined. Some appear promising in terms of scaling to higher growth rates, lower growth temperatures, and providing selectivity. Conventional CVD and some of the laser-based (such as pyrolysis and laser-plasma) methods are useful for substrates that can withstand high temperatures and the presence of large amounts of atomic hydrogen or oxygen. The more novel of the laser-based methods show some promise of being able to circumvent these difficulties. It is particularly noteworthy that the optical pumping technique is capable of activating gases over a wide a range of pressures, as well as liquids. There are precedents for growth of single crystals of various materials from the liquid phase. Optical pumping lays the groundwork for development of a new class of processes that employ laser excitation to drive energy transfer and chemistry in cryogenic liquids and may someday play a role in the production of single-crystal diamond films.

ACKNOWLEDGMENTS Partial support from grants MSS-9157303 and MSS-9102076 from the National Science Foundation, The Ohio State University College of Engineering, The Center for Materials Research, The Ohio Board of Regents Investment Fund Program, and the Directorate of Defense Research and Engineering (DDR&E) under the Air Plasma Ramparts MURI program managed by the Air Force Office of Scientific Research is gratefully acknowledged. The authors thank Dr. Gregory Hall, Chemistry Department, Brookhaven National Laboratory for many helpful comments and suggestions.

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10 CVD Diamond Solutions for Machining and Other Mechanical Applications Brian L. Cline Cline Innovations, LLC, Sterling, Massachusetts

James M. Olson Fairchild Semiconductor, South Portland, Maine

I. A.

INTRODUCTION Growth Engine for Advanced Cutting Tool Materials

The machining industry is always seeking a means of improving productivity and machined part quality. Over the years, this relentless demand has resulted in countless iterations of productivity improvements. Today, the machine tool industry produces automated high-speed machining centers that have the ability to machine complex shapes quickly with high accuracy and minimal operator assistance. These dramatic machine tool improvements create an interrelated demand for improved cutting tool materials that enhance productivity by extending tool life under increasingly aggressive machining conditions. Improvements to cutting tool materials are also needed for enhanced cutting tool performance in machining many advanced workpiece materials. For example, the aerospace and automotive industries are utilizing increasing quantities of lightweight materials such as high-silicon aluminum alloys, fiber-reinforced composites, and metal matrix composites (MMCs), which offer unique options for component design. Unfortunately, many of these enabling materials are very abrasive and difficult—if not impossible—to machine using conventional cutting tools [1–3]. 425

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This chapter contains an overview of how and why chemical vapor deposition (CVD) diamond technology is beginning to assume a key role in the materials evolution for advanced cutting tool and specialty wear part applications. Section I continues with a history of cutting tool materials development including high-speed steel, cemented carbides, hard coatings, and synthetic diamond materials. Section II overviews the issues and challenges associated with CVD diamond tool design and manufacture. This section also includes discussion of CVD diamond properties and application specifics that can affect the performance of CVD diamond cutting tools as well as common approaches to CVD diamond tool design. Section III is focused on microstructural features of CVD diamond that affect the performance of diamond coatings as well as freestanding diamond in mechanical applications. Section IV contains cutting performance information for various CVD diamond tool types used in a wide range of materials. The chapter closes with an overview of other types of mechanical component applications in Sec. V followed by a summary in Sec. VI. B.

Evolution of Conventional Cutting Tool Materials

1.

Carbon Tool Steels and Nonferrous Cast Alloys

Early industrial tooling materials included carbon tool steels—iron-based materials with a wear-resistant ‘‘case’’ surrounding a tougher FeC alloy. Although these materials display high fracture resistance, their low hardness and low wear resistance limit their wear life in industrial machining of metals and highly abrasive materials. The introduction of high-speed steels (containing varying amounts of W, Cr, V, Mo, and Co) led to the rapid replacement of carbon tool steels in metalcutting applications due to marked improvements in wear and fracture resistance. The added wear resistance and high-temperature hardness properties (‘‘hot hardness’’) of nonferrous cast alloys (containing varying amounts of Cr, W, C, and Co) allowed further improvements in cutting capabilities for selected metalcutting operations. 2.

Cemented Carbides Including Tungsten Carbide

The subsequent development of cemented carbides in the late 1920s provided an immediate advantage over traditional high-speed steels and cast alloys [4]. The combination of properties offered by cemented carbide cutting tools is typically attained by sintering large volumes of ceramic grains with 3 to 15% (by volume) of metallic binder and various sintering aids. Cobalt-sintered tungsten carbide combines wear-resistant, hard tungsten carbide (WC) ceramic particles with the fracture resistance of a ductile, metallic, Co-based binder phase. Many ‘‘tungsten carbide’’ grade formulations are

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readily available for a wide range of applications in the cutting tool and wear part industry. The metal sintering approach to engineering cutting tool materials bypasses the challenges of introducing the high hardness and wear resistance of otherwise brittle ceramic materials into cutting tools. Although WC-Co cutting tools have lower fracture resistance than high-speed steel, their mechanical properties are suitable for a very wide range of heavy-duty applications. The higher hardness and improved hot hardness characteristics of cemented carbides allow operation at cutting speeds three to four times higher than with high-speed steel. C.

The Historic Use of Diamond and Ceramic Cutting Tool Materials

1.

Single-Crystal Diamond

For decades, natural and high-pressure, high-temperature (HPHT) singlecrystal diamonds have been used for specialty cutting and wear applications. Single-crystal diamond tools are known to have unmatched edge quality and create excellent surface finish due to their precision, continuous diamond edges. Applications include woodworking, contact lens machining, jewelry manufacture, and nonferrous metal finishing. The cost and difficulty of fabricating tools of complex geometries limit the usage of single-crystal tips to simple shapes relative to other tooling materials. However, the hardness, thermal stability, and corrosion resistance of single-crystal diamond tooling continue to provide added value in many demanding industrial applications. Single-crystal tools are also limited by their low fracture resistance, anisotropic wear behavior, and morphological shape constraints relative to other forms of diamond. 2.

Polycrystalline Diamond Compacts

In the early 1970s, technology was developed that allowed the production of metal-sintered polycrystalline diamond (PCD) compacts in large, twodimensional flat plates sintered directly to a cemented carbide backing. Similar in construction to cemented carbide, PCD diamond tooling has significant advantages related to the high wear resistance of diamond grains combined with the fracture resistance afforded by the metallic binders used in sintering. Figure 1 contains scanning electron microscope (SEM) images that compare the two-phase microstructures of a cemented carbide cutting tool and a PCD cutting tool. The added hardness and wear resistance of the diamond grains in PCD relative to the tungsten carbide grains in WC-Co offer distinct advantages for PCD-tipped tooling. PCD tools are normally fabricated by radio-frequency or torch brazing flat, tungsten carbide-backed,

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polycrystalline tool tips directly onto a cemented carbide or high-speed steel tool body. After brazing in air, PCD tools are typically finish ground or cut to final shape by electric discharge machining (EDM). The performance advantages of PCD over tungsten carbide tools clearly outweigh the added cost of brazed PCD tooling in many nonferrous metal and abrasive nonmetallic machining applications. PCD is commonly used for machining aluminum, copper, brass, bronze, and cemented carbide in applications including turning, boring, profiling, grooving, milling, and holemaking [5]. 3.

Advanced Ceramics

Ceramic cutting tools are produced from a wide range of polycrystalline ceramic materials including aluminum oxide, cubic boron nitride (‘‘PCBN’’), and silicon nitride [6–9]. The hardness, chemical stability, and high wear resistance of these advanced ceramic cutting tools have demonstrated costperformance advantages over conventional cutting tool materials in applications ranging from abrasive and corrosive polymers to superalloy machining. PCBN-tipped tools are rapidly becoming the favored cutting tool choice in many high-throughput ferrous applications. Although the wear resistance, high-temperature corrosion resistance, and hot hardness of ceramic cutting tools are impressive, the application range of ceramic tooling is often limited by the lower fracture resistance of ceramic materials relative to other cutting tool materials. Special cutting edge preparation, whisker reinforcement, or other approaches are commonly used to improve the performance and broaden the application range of ceramic cutting tools. D.

Development of Coating Technologies for Cutting Tools

In the 1970s, thin-film deposition technology began to play a key role in furthering performance of commercial cutting tools [10]. Coated carbide and

< Figure 1 Structural similarities between cemented tungsten carbide and PCD diamond: SEM photomicrographs showing (a) the fractured cross section of a 6% CoWC cemented carbide at 5000⫻ magnification, (b) a polished cross section of a 6% Co-WC cemented carbide at 2000⫻ magnification, and (c) a 50⫻ image showing the construction of a PCD cobalt-sintered diamond cutting tool. Because both cemented carbides and PCD are two-phase materials composed of hard ceramic grains (WC or diamond, respectively) sintered in metal, they are commercially available in various compositions and grain sizes tailored for a wide range of applications. (From Norton Diamond Film/Saint Gobain Industrial Ceramics, Inc.)

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coated high-speed steel tools utilize hard coatings such as titanium nitride, titanium carbide, and aluminum oxide to enhance cutting performance. Most coatings are produced using CVD or physical vapor deposition (PVD) techniques. This ‘‘layer-composite’’ approach to cutting tool design couples the high-temperature wear resistance, corrosion resistance, and hardness advantages of advanced ceramic materials with the superior fracture resistance of the underlying tool body. Today, hard coating technology has evolved to the development of multilayered coatings in which individual coating layers offer unique performance-enhancing properties beyond single-layer structures [10,11]. Coating technologies for tungsten carbide and high-speed steel resulted in significant improvements in machining productivity and serve as the predecessors of CVD diamond-coated cutting tools. E.

Commercialization of CVD Diamond Technology for Cutting Tools

The relatively recent development of CVD diamond technology [12–14] has enabled further advances of diamond as a strategic material in the cutting tool industry. Like many new materials, CVD diamond has had its technical and commercial challenges. Today, however, the industry has achieved a track record of success and continues to develop processes that ensure consistency, reliability, and performance [1,2,15–23]. Presently, CVD diamond cutting tools are commercially available in two primary product forms: ‘‘thick-film’’ freestanding CVD diamond cutting tool tips and ‘‘thin-film’’ CVD diamond coatings. 1.

Thick-Film CVD Diamond Cutting Tools

Thick-film CVD diamond is vapor-deposited diamond manufactured in the form of solid, freestanding wafers of pure, binder-less diamond with typical thickness ranging from 150 to over 1000 ␮m. For most cutting tool uses, CVD diamond wafers are laser cut into hundreds of mirror-finish polished CVD diamond tips that are subsequently attached to cutting tools in a manner similar to cobalt-sintered polycrystalline diamond (PCD). The development of successful brazing techniques for thick-film diamond in the early 1990s bypassed the adhesion and substrate selection challenges of thin-film CVD diamond tools [8,23]. Figure 2a contains an image of two large-diameter, as-deposited, freestanding diamond wafers in addition to a collection of mirror-finished freestanding diamond materials. Figure 2b shows examples of finish-ground thick-film CVD diamond tooling (also known as diamond sheet tools [11,23]) adjacent to examples of aluminum workpiece materials. Thick-film CVD diamond cutting tools are engineered to compete

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Figure 2 Thick-film CVD diamond is vapor-deposited diamond that can be manufactured in the form of large-diameter, freestanding wafers of pure, binder-less diamond. The larger wafer shown in the background of image (a) is approximately 175 mm in diameter. For most cutting tool uses, CVD diamond wafers are laser cut into hundreds of mirror-finish polished CVD diamond tips [(a), foreground], which are subsequently attached to cutting tools (b) in a similar manner to cobalt-sintered polycrystalline diamond (PCD). Freestanding CVD diamond cutting tools are used for a wide range of applications including aluminum automotive component machining (b). (From Ref. 1.)

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with conventional PCD tools and are useful in a wide range of applications. As with PCD, thick-film CVD diamond tools are normally made with oversized tips that can be reground multiple times by diamond tool fabricators. Approaches to engineering thick-film CVD diamond-tipped tools are discussed further in Sec. II.D.2. 2.

Thin-Film CVD Diamond-Coated Cutting Tools

Thin-film diamond is CVD diamond that is deposited as a continuous, conformal coating directly onto a suitable substrate. The ability to deposit polycrystalline diamond coatings directly onto cutting tools enables the properties of diamond to be captured in shapes previously not available from nature or the diamond industry. In addition, the complete coating can eliminate the depth of cut limitations of thick-film CVD tools and PCD-tipped tools. Commercial diamond coatings generally fall in the thickness range of 5 to 35 ␮m. The diamond-coated tungsten carbide end mill depicted in Fig. 3 shows the complex shape, high-aspect-ratio coating capability presently available from the CVD diamond industry. Approaches to engineering thin-film CVD diamond-coated tools are discussed in Sec. II.D.1. Thin-film adhesion issues, challenges, and solutions are the topic of Sec. III.B.

Figure 3 Thin-film CVD diamond is vapor-deposited diamond deposited directly onto a component such as a cemented carbide cutting tool. This image contains a diamond-coated tungsten carbide rotary tool showing the complex shape coating capability now available in the CVD diamond industry. The end mill shown is 20 mm in diameter and 160 mm in overall length with a coated flute length of 110 mm. (From Ref. 15.)

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ISSUES AND CHALLENGES IN CVD DIAMOND CUTTING TOOL DESIGN AND MANUFACTURE

Capturing the unique properties of diamond in the design of CVD diamond cutting tools requires a knowledge of the application range and a fundamental understanding of the processes available to manufacture the tool. A broad-scope assessment of the complex properties-process-application interaction is critical because the performance advantage of a CVD diamond tool —if any—will depend not only upon the properties of the diamond itself but also on whether the chosen tool design and manufacturing process effectively capture the desired properties for the application of interest. A.

Critical Properties of CVD Diamond for Mechanical Applications

The key properties of CVD diamond for mechanical applications are not limited to the often-referenced hardness of diamond. The true challenge in CVD diamond tool manufacturing is capturing this potential within a functional tool that delivers reproducible performance. Table 1 provides a comparison of selected mechanical and thermal properties for PCD, single-crystal diamond, cemented carbide, and silicon nitride. Selected properties are summarized further in the remainder of this section. 1.

Hardness and Young’s Modulus

Diamond’s unmatched hardness and elastic modulus contribute to excellent wear resistance. Unlike metal-bonded PCD compacts and cemented carbides, diamond-like carbon (DLC), and many other hard coatings, CVD diamond maintains its hardness and wear resistance at elevated cutting temperatures. Diamond’s hot hardness is due in part to the high-temperature structural stability of its dense, polycrystalline construction coupled with the lack of metal binders that soften at elevated temperatures. 2.

Coefficient of Friction

CVD diamond’s low friction coefficient contributes to lower cutting forces, lower spindle power consumption, and less frictional heating in many cutting applications. The reduced cutting temperature that results from diamond’s high lubricity is viewed as a major advantage in applications where coolant elimination and higher speed operation are being considered. This property is not included in Table 1 because measured values of the coefficient of friction vary significantly depending on environment, surface roughness, and measurement technique. The coefficient of friction of polished CVD dia-

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Comparison of Thermal and Mechanical Properties for CVD Diamond and Other Hard Materials

Property Indentation hardness (GPa)

Young’s modulus (GPa) Tensile strength (MPa)

CVD diamond

Natural diamond

85–100 Technique unspecified Commercial data Ref. 90

50–100 Technique unspecified Commercial data Ref. 90

78.5 ⫾ 18.6 Vickers indentation Commercial data Ref. 91

56–102 Knoop indentation Normal load of 1–500 kg Ref. 92 1000–1100 Commercial data Ref. 90 1050–3000 Orientation dependent Measurement technique unspecified Typical commercial data Ref. 90

1000–1100 Commercial data Ref. 91 Growth face in tension: 500–800 (0.5 mm thick) Three-point bend geometry Estimated from Fig. 11 of Ref. 21 Nucleation face in tension: 800–1300 (0.5 mm thick) Three-point bend geometry Estimated from Fig. 12 of Ref. 21

PCD 50 Technique unspecified Commercial data Ref. 90

WC-Co cemented carbide 7.8–23.5 Vickers indentation Typical range Ref. 93

Si3N4 ceramic 7.8–17.7 Vickers indentation Range based on commercial data from two suppliers

21.5 Knoop indentation Ref. 92

776 Commercial data Ref. 90 1260 Measurement technique unspecified Commercial data Ref. 90

400–700 Ref. 93 700–1500 Typical range Ref. 93

120–330 Typical data Ref. 94 586–843 Range observed for three commercial grades Four-point bend with crosshead speed of 0.004 cm/s NIST evaluated data Ref. 95

Compressive strength (MPa)

16,000 Commercial data Ref. 90

7600 Commercial data Ref. 90

3000–7000 Typical range Ref. 93

>4000 Commercial data ASTM C773 Ref. 97

1.3 Commercial data Ref. 90

8680 average 16,530 maximum Natural octahedron containing no visible flaws or inclusions 10⫺6 m2 estimated load area Ref. 96 2.9 Commercial data Ref. 90

Transverse rupture strength (GPa)

1.2 Commercial data Ref. 90

0.6–3.0 Typical range Ref. 93

5.3–7.0 Commercial data Ref. 91 500–2200 Commercial data Ref. 90

3.4 Commercial data Ref. 90 600–2200 Commercial data Ref. 90

8.81 Commercial data Ref. 90 560 Commercial data Ref. 90

500–1100 Commercial data Ref. 90

600–1100 Commercial data Ref. 90

200 Commercial data Ref. 90

5–30 Typical range Ref. 93 20–120 Typical range for manufacturers quoted values Ref. 93 —

0.76–0.85 Commercial data Ref. 4, p. D116, Kennametal, Inc. 1.5–8.5 Typical values Ref. 94 7–43 Typical data Combined range for material types Ref. 94 —

Fracture toughness [MPa(m)1/2] Thermal conductivity at room temperature (W/m ⭈ K) Thermal conductivity at 200⬚C (W/m ⭈ K)

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Continued

Property Thermal expansion coefficient (ppm/K in 100–250⬚C range) Thermal expansion coefficient (ppm/K at 500⬚C) Thermal expansion coefficient (ppm/K at 1000⬚C) Mean thermal expansion coefficient (ppm/K in denoted range)

CVD diamond

Natural diamond

PCD

WC-Co cemented carbide

Si3N4 ceramic

1.2 Commercial data Ref. 90

1.2 Commercial data Ref. 90

4.2 Commercial data Ref. 90

—

—

3.8 Commercial data Ref. 90

3.8 Commercial data Ref. 90

—

—

—

4.5 Commercial data Ref. 90

4.5 Commercial data Ref. 90

6.3 Commercial data Ref. 90

—

—

—

—

—

4.5–8.5 Typical range for 0–800⬚C temperature range Ref. 93

2.8–3.7 Typical data for 20–1000⬚C range Ref. 94

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mond is generally superior to that of cemented carbides [24] and advanced ceramics [25] and is similar to values attained for single-crystal diamond (e.g., 0.05 [24]). The high lubricity is often compared with that of fluoropolymers.* 3.

Thermal Conductivity

High-quality diamond has the highest thermal conductivity of any material. As Sec. III.A will explain, the use of the highest crystalline quality CVD diamond is not necessarily the best overall solution for mechanical applications of diamond. Regardless, it has been demonstrated that freestanding diamond that has been engineered for mechanical applications can offer thermal conductivity over five times that of tungsten carbide and over 50% greater than that of PCD.† Although diamond’s high lubricity helps to avoid frictional heating effects, CVD diamond’s excellent thermal conductivity relative to other cutting tool materials acts as an additional safeguard in maintaining lower cutting temperatures by dissipating heat generated in the cutting zone. 4.

Thermal Expansion Coefficient

CVD diamond and single-crystal diamond have essentially identical thermal expansion characteristics, as Table 1 delineates. Diamond has a very low thermal expansion coefficient relative to most other cutting tool materials such as cemented carbide and particularly high-speed steel, especially in the 100 to 250⬚C range. This property can be beneficial in controlling the positional accuracy of a cutting tool relative to a workpiece during precision machining. Because of the high-temperature nature of commercial CVD diamond coating and brazing processes, attachment of CVD diamond to cutting tool materials such as cemented carbide requires strict attention to the thermal expansion mismatch. The residual thermal stresses that result from high-temperature attachment necessitate good interfacial adhesion for both braze fabrication of thick-film CVD diamond and direct thin-film coating. Section III.B contains a detailed discussion of diamond adhesion issues for thin-film cutting tools.

*According to E.I. du Pont de Nemours and Company, the coefficient of friction of Teflon is generally in the range of 0.05 to 0.20, depending on the load, sliding speed, and particular Teflon coating used. †Comment is based on Norton Diamond Film’s ‘‘PolyTurn’’ and ‘‘DiamaPak’’ cutting tool products, which were retracted from the market upon business closure.

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Fracture Strength

As Table 1 depicts, the compressive strength of CVD diamond is generally superior to that of single-crystal diamond and PCD. Unfortunately, the pure polycrystalline structure results in a material that is generally inferior in tensile strength. Even so, the tensile strength of freestanding CVD diamond is sufficient for a wide range of industrial applications, especially when incorporated into tool designs that accommodate the unavoidable fact that diamond is a brittle, ceramic-like material. The measured values of the Weibull modulus [21] indicate that the breadth of the strength distribution for bulk CVD diamond is similar to that for advanced ceramics such as silicon nitride. The observed values ensure that CVD diamond can yield the reliable, reproducible tensile strength necessary in many mechanical applications. 6.

Fracture Toughness

Fracture toughness is a property of a material that is frequently defined as resistance to crack propagation. High fracture resistance is necessary for a cutting tool material to survive the impact and fatigue that can result from aggressive cutting operations such as milling or interrupted cutting or when machining workpiece materials containing material inhomogeneities such as hard phases, fibers, or particles. As shown in Table 1, the fracture toughness values of bulk, freestanding CVD diamond are comparable to those of advanced ceramic materials such as silicon nitride. Furthermore, because the microstructure of polycrystalline CVD diamond can provide a crack deflection mechanism [26–28], proper microstructural engineering can yield fracture toughness values exceeding those of single-crystal diamond and approaching values common to cobalt-sintered PCD. Section III.A includes approaches to optimizing the bulk properties of CVD diamond including fracture toughness. 7.

High-Temperature Phase Stability

Black, graphite-like coatings have been observed on diamond surfaces exposed to atomic oxygen at temperatures as low as 625⬚C [24]. However, diamond oxidation occurs at very low rates in air below 800⬚C and generally does not limit the application range of CVD diamond tooling. CVD diamond is thermally stable to temperatures of at least 1200⬚C in vacuum. By contrast, PCD is particularly susceptible to thermal degradation at temperatures above 700⬚C [29]. The cobalt binder phase can catalyze graphite formation at the sintered contacts between the diamond grains. This high-temperature phase instability, which can be induced by excessive cutting temperatures or im-

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proper brazing or grinding procedures, is known to result in a general degradation of the mechanical properties of the PCD cutting tool tip. 8.

Chemical Corrosion Resistance

The chemical reactivity of carbon limits the use of diamond tooling in ferrous metal and superalloy machining. All forms of diamond tooling are at risk of corrosion or graphitization induced by machining iron-, nickel-, and cobalt-containing metals at elevated cutting temperatures [30]. Molten manganese, chromium, and the platinum group of metals are also true solvents for all forms of carbon including diamond [24]. Other metals capable of reacting with diamond include the carbide-forming transition metals titanium, tantalum, tungsten, and zirconium. Even so, diamond’s superlative combination of properties still maintains it as the preferred form of tooling for selected applications such as bimetallic machining of aluminum–cast iron deck faces for automotive engines [5]. With the exception of the metallic interactions just noted and hightemperature oxidizing environments, pure forms of diamond are extremely chemically inert. Unfortunately, the corrosion resistance of CVD diamond is a property that is often overlooked. For example, the metallic constituents of PCD and cemented carbides limit tool lifetime in corrosive polymer machining. Although the corrosion resistance of ceramic cutting tools can offer measurable improvements over traditional tooling, the advent of CVD diamond technology now allows the production of tooling with complex geometry that can offer both corrosion resistance and unmatched abrasive wear resistance. B.

The Critical Combination of Abrasive Wear Resistance and Fracture Toughness

In order to meet new machining requirements for difficult-to-machine materials, improve productivity, and hold high workpiece tolerances, new cutting tool materials must have both suitable fracture toughness and high abrasive wear resistance. The importance of fracture toughness, a measure of the resistance to crack propagation, was discussed in Sec. II.A.6. However, the specific abrasive wear resistance of a CVD diamond tool is very application specific and, therefore, was not discussed in Sec. II.A. Abrasive wear resistance is the result of a complex interaction between the properties and characteristics of the diamond tool, the workpiece material being machined, and the nature of the specific application. Improved abrasive wear resistance allows machinists to maintain tight tolerances with minimal tool or machine adjustments and reduces machine downtime associated with rapid tool wear and frequent tool changes.

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Figure 4 depicts schematically the trade-off between fracture toughness and abrasive wear resistance in cutting tool materials. For example, advanced ceramic cutting tool materials, known to be very hard and resistant to abrasive wear, tend to be lower in fracture toughness. Metallic cutting tools such as high-speed steel, known to be high in fracture toughness, tend to have relatively low resistance to abrasive wear. Although cemented carbide does not have the superior toughness of high-speed steel, it combines an abrasive wear resistance approaching that of ceramic materials and fracture toughness that is sufficient for a wide range of heavy-duty industrial machining needs. In most applications, the exceptional fracture toughness of high-speed steel is not necessary or worth the inherent trade-off in abrasive wear resistance. Figure 4 also shows that ceramic-like CVD and PVD coatings can markedly enhance the abrasive wear resistance of both tungsten carbide and high-speed steel tooling while the critical fracture toughness of the underlying tool substrate is maintained. From the success of hard coatings in the

Figure 4 Abrasive wear resistance and fracture toughness trade-offs for common cutting tool materials.

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cutting tool market, it is clear that the added hardness and wear resistance of diamond-coated tungsten carbide offer a well-balanced fracture toughness-wear resistance combination. The unique combination expected for CVD diamond-coated cutting tools is depicted at the top center of the figure. Because fracture toughness is a bulk mechanical property and the underlying substrate of a diamond-coated carbide tool is tougher than bulk CVD diamond, the diamond-coated carbide concept offers the potential to exceed the fracture toughness of bulk, freestanding CVD diamond. However, as discussed in Sec. III.B of this chapter, the composite properties of a diamondcoated carbide are captured in the tool design only if the adhesion strength exceeds the forces of the application. The abrasive wear resistance of the cobalt-sintered diamond in PCD can offer as much as 100 times greater tool life over cemented carbide [5]. By contrast, as Fig. 4 shows, PCD-tipped cutting tools are usually inferior in fracture toughness to cemented carbides. Fortunately, the fracture toughness of PCD is sufficient to avoid cutting edge chipping in most rigid machining situations. In fact, as the operating speeds and feeds move beyond the material limits of traditional cutting tool materials in aggressive highproductivity operations, the long life and predictable finish advantages of diamond tooling are often amplified.

C.

Application Characteristics That Affect CVD Diamond Cutting Tool Performance

Every cutting tool application is unique, and industrial cutting tools need to be designed for the worst-case scenario within the targeted range of applications. There are many factors that can directly or indirectly affect cutting tool performance. The feasible application range of a CVD diamond cutting tool design may not be clear until a tool is thoroughly tested in the field. As with any cutting tool, success in a specific operation on a specific machine tool does not ensure the same results with the same tool on the same type of machine at a different location. Because of the complexity of machining processes, this section is provided as an overview of the application characteristics that should be factored into the design and manufacturing processes used to produce CVD diamond cutting tools. 1.

Impact of Machine, Fixture, and Operating Conditions on Performance

Factors such as spindle balancing and rigidity, workpiece vibration, or even poor tool handling practices can dictate whether or not a tool will offer

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a performance advantage in a specific application. Clearly, the type of machining operation (e.g., turning, boring, milling, drilling) and machine operating parameters (e.g., cutting speed, cutting feed rate, depth of cut) have a major influence on the nature of the forces on the CVD diamond cutting edge and the diamond-tool interface. For instance, machining operations where the cutting edge is not in constant contact with the workpiece (e.g., interrupted turning, milling, or end milling) generally require more robust design than continuous cutting operations (e.g., turning, boring, drilling). The impact-like forces generated in interrupted operations require good material strength and fracture toughness to minimize the damage of a CVD diamond tip or diamond coating during use. Other important application details include the coolant type (e.g., dry, mist, flood), chip-forming behavior, and efficiency of chip evacuation from the cutting area. Because CVD diamond (like other forms of diamond) is capable of operating at high cutting speeds and feed rates, machine tools with limited ranges of speed and feed can significantly limit the performance potential of diamond. By contrast, the wear resistance of many traditional cutting tool materials can degrade rapidly when machining processes are put into ‘‘fast forward’’ at high speeds and feeds. As a demonstration, Cline [31] and Tanikella et al. [32] have reported the results of end mill machining tests that were performed on SiC-containing ‘‘bisque ceramic’’ that was heat treated (‘‘presintered’’) at temperatures greater than 1200⬚C. The workpiece material and machining conditions were selected in an effort to accelerate the diamond wear mechanism common to abrasive applications such as ‘‘green ceramic’’ (unfired polymer-ceramic compacts) and graphite machining. The results of the machining tests showed the dramatic performance advantage of thin-film CVD diamond-coated end mills at the selected machining conditions. Figure 5a and b show that the uncoated tungsten carbide and TiNcoated tungsten carbide tools failed within 16 cm of machining (two 7.6cm-long passes). The failure was highlighted by excessive abrasive wear, which was enhanced by frictional heating of the tools. The PVD TiN coating offered no clear advantages under these machining conditions. Optical pyrometry of the carbide and TiN-coated carbide tools indicated temperatures exceeding 900⬚C. By contrast, a diamond tool that had already run 80 previous passes was barely warm to the touch after eight sequential passes at the same machining conditions. Freeze-frame images of the 88th pass are shown in Fig. 5c. Both the TiN-coated and uncoated carbide tooling showed a strong sensitivity to density variations in the presintered ceramic workpiece. In the case of one uncoated carbide tool, the excessive wear and overheating reduced the 9.5 mm cutting diameter of a new tool by over 2.5 mm within less than 23 cm of machining. More details of this case study are summarized in Sec. IV.B.2.c.

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Figure 5 Effect of high cutting speeds on various cutting tool materials: sequential freeze-frame images showing presintered ceramic machining using (a) an uncoated tungsten carbide end mill, (b) a TiN-coated carbide end mill, and (c) a CVD diamond-coated end mill. The uncoated and TiN-coated tungsten carbide tools failed within 16 cm of machining due to excessive wear and frictional heating. The diamond-coated tool operated at cutting temperatures at least 500–1000⬚C lower than the uncoated equivalent and was still worthy of continued testing after more than 670 cm of machining. (From Ref. 31.)

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Figure 5

2.

Continued

Impact of Workpiece Material Characteristics on Performance

The relative performance advantage of one tool over another is dependent on the workpiece material and the requirements for finished part quality. The characteristics of the workpiece such as abrasiveness, corrosiveness, and microstructural homogeneity can significantly affect the utility of a diamond tool in machining operations. Although less aggressive applications such as graphite machining will not always differentiate between tools of varying integrity, applications that generate higher, impact-like cutting forces can rapidly differentiate between tools that offer predictable abrasive coating wear and tools that fail unpredictably due to film delamination. The characteristics of diamond tooling are of particular interest in machining composite materials. The unique advantages offered by composites are generally the result of combining two or more dissimilar metallic and/ or nonmetallic materials in an effort to yield combined properties that exceed those of the individual constituents. For instance, glass fiber–reinforced plastics (GFRPs) combine the stiffness of the reinforcing fibers with the lowcost, lightweight characteristics of an otherwise pliable polymer matrix. Other useful composites, such as high-silicon aluminum alloys, metal matrix

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composites (MMCs), and structural aerospace composites, offer advantages ranging from weight reduction to wear resistance and fatigue resistance. By design, the most unique and enabling composites tend to be composed of materials that have diverse properties and, therefore, vastly different machining behavior. The combined results are workpiece materials that can be abrasive, corrosive, and generally difficult to machine with conventional cutting tool materials [2,3,23,33,34]. Table 2 lists some commonly used metallic and nonmetallic composite materials along with their associated machining challenges. Many early efforts to fabricate components from these and other composites using conventional tooling proved to be cost prohibitive due in part to high machining costs. As the industrial demand for innovative composite materials continues to increase, so does the interrelated demand for cutting tools that can endure the challenges of machining these progressive materials. Many of the case studies discussed in Sec. IV are related to this increasingly important class of materials.

D.

Design and Manufacturing Options and Constraints for CVD Diamond

The design and manufacture of diamond-coated cutting tools varies significantly from thick-film, brazed-on CVD-diamond cutting tools. The last step in manufacturing a thin-film, diamond-coated tool is typically the CVD coating process, whereas freestanding CVD diamond wafer fabrication is the first of many steps in the fabrication of a thick-film, brazed-on CVD diamond tool. Many of the process-related advantages of the thin-film CVD diamond coating process are similar to advantages observed with other hard coatings used for cutting tools (see Sec. I.D). On the other hand, the processrelated advantages of the fabrication process for thick-film CVD diamond are more typical of PCD diamond tooling (see Sec. I.C.2). 1.

Approaches to Engineering Thin-Film CVD Diamond-Coated Tools

Today, CVD diamond processes enable direct coating of high-aspect-ratio, complex shapes ranging from specially molded, chip-breaking inserts to the end mill shown in Fig. 3. However, the manufacture of thin-film, CVD diamond-coated cutting tools does not come without unique technical challenges. Most noteworthy are the challenges associated with adhesion of diamond deposits to tungsten carbide—the preferred substrate for diamond

Table 2

Examples of Difficult-to-Machine Composite Materials Example

Examples of use

Machining issues

Related CVD diamond performance case studies

Composite: A390 (18% Si in Al) Matrix: Aluminum Reinforcement: Silicon particles Composite: Duralcan (30% SiC in Al) Matrix: Aluminum Reinforcement: Silicon carbide ceramic particles Composite: 25% cobalt tungsten carbide Matrix: Cobalt-based alloy Reinforcement: sintered tungsten carbide grains Composite: Carbonepoxy Matrix: Epoxy polymer Reinforcement: Highdensity carbon fibers Composite: G10 Matrix: Polymer Reinforcement: Glass fibers

Reduced-weight, wear resistant, temperatureresistant pistons

Although aluminum is generally free-machining, hard silicon particles are extremely abrasive

Thick-film inserts: IV.A.1.a Thick-film rotary tools: IV.A.2 Thin-film inserts: IV.B.1.a, IV.B.1.b

Brake rotors Lightweight structures

Although aluminum is generally free-machining, hard SiC ceramic particles are extremely abrasive

Thick-film inserts: IV.A.1.c Thin-film rotary tools: IV.B.2.c

High-fracture-toughness wear parts

Tungsten carbide sintering results in strong bonding or contiguity between WC grains. The WC grains are very hard. At elevated temperatures, the metal binder can react with the carbon in diamond. Carbon fibers are extremely abrasive; grinding is often preferred over cutting due to excessive tool wear

Thick-film inserts: IV.A.1.d

Glass fibers induce abrasive tool wear; polymer can cause corrosive tool wear

Thin-film rotary tools: IV.B.2.c

Material type Hypereutectic or ‘‘high-silicon’’ aluminum

Metal matrix composites (MMCs)

Cemented tungsten carbide

Structural ‘‘aerospace composites’’

Fiberglassreinforced polymers (FRPs)

Source: Modified from Ref. 2.

Stiff, lightweight support structures for commercial aircraft Strong, lightweight sporting goods Lightweight, insulative circuit boards Low-cost structural composites

Thin-film rotary tools: IV.B.2.c

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coating commercialization. Many early efforts to introduce diamond-coated carbide cutting tools into the aluminum machining market failed or were significantly delayed because of lack of adhesion treatment technologies that could reproducibly yield WC-Co surfaces worthy of CVD diamond processing and subsequent use. Many early development efforts in the CVD diamond cutting tool industry involved the use of advanced ceramic materials as interim substrate solutions because the chemical compatibility and thermal expansion mismatch were more favorable for diamond coating. A variety of substrate materials including SiAlON, binder-less tungsten carbide and, more commonly, silicon nitride and silicon carbide were employed [23]. Although diamond-coated ceramic tools do have utility in selected applications, the inferior fracture toughness of diamond-coated ceramic inserts and end mills generally limited their use to nonmetallic machining operations such as those involving graphite, polymers, green ceramics, and nonmetallic composite materials. a. Interfacial Integrity. Figure 6 contrasts the failure modes of a ‘‘bad’’ tool (Fig. 6a) that has failed by unpredictable, catastrophic film delamination related to poor interfacial adhesion and a ‘‘good’’ tool (Fig. 6b) that has failed by predictable abrasive wear. The relative utility of these two tools is clear. If the diamond adhesion is not suitable for the application, the desired coating properties simply are not captured in the tool design. As discussed in Sec. III.B in detail, proper diamond-coated WC-Co cutting tool design requires strict attention to both the coating properties and the substrate surface properties. b. Morphology and Surface Roughness Characteristics. Today, most thin-film CVD diamond cutting tools are made from well-faceted CVD diamond deposits because of the higher abrasive wear resistance typically offered by coarse-grained diamond. However, relatively smooth, more lubricious, microcrystalline diamond coatings are commercially available for applications where workpiece surface finish is more critical. Most diamondcoated tools are presently marketed in an as-deposited state with no postdeposition finishing. Depending on the interfacial roughness introduced by adhesion treatment, coating thickness, and the morphological features of the coating, the surface roughness and edge blunting of some diamond-coated tools can limit their use to intermediate finishing and roughing applications. The morphological features of CVD diamond are discussed in more detail in Sec. III.A. c. Postdeposition Finishing Options. Postdeposition finishing techniques can be applied to modify the generally rough, matte finish of diamond-coated products. Diamond-coated ceramic tools with mirror-finished

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Figure 6 Contrasting failure modes of CVD diamond coatings: SEM images contrasting the failure mode of two different diamond-coated tool designs after aluminum metalcutting tests. (a) A tool that failed catastrophically due to insufficient coating adhesion. A metallic buildup of aluminum is evident in the delaminated zone on the tool tip where the adhesion-treated carbide was exposed. (b) A tool that offered a suitable level of adhesion for the application and therefore maintained the slow, predictable wear characteristics desired in a diamond-coated component. As reviewed in Sec. III.B, the diamond/substrate interface characteristics have a significant influence on the nature of tool failure. (From Norton Diamond Film/Saint Gobain Industrial Ceramics, Inc.)

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rake faces similar to PCD tools have been produced in the industry.* Oles et al. [23] have reported the success of a CVD diamond buffing technique in reducing insert surface roughness for the flank face of a diamond-coated carbide insert. Turning tests in A390 (18% Si-Al) showed that the buffed flank surfaces substantially improved the workpiece surface finish. However, the turned component finish of the buffed tools was still inferior to the finish generated by finish-ground PCD tools tested in the same study. Kanda et al. [17] have reported progress in grinding rotary tools to enhance cutting edge characteristics and resulting workpiece surface finish. Although the general tendency of the industry is toward smoother surfaces that mimic the finish ground characteristics of PCD and cemented carbide tools, Oles et al. [23] have also reported a ‘‘microscopic chip-breaking’’ advantage of diamond-coated cemented carbide inserts. Milling and turning studies of low-silicon and high-silicon alloys showed the advantages of diamond facets on the chip-forming rake surface in creating a ‘‘highly stressed chip that is more readily broken.’’ Metallic chips in the shape of small ‘‘sixes’’ and ‘‘nines’’ were reported to be more desirable than continuous stringers or coils that are common to smooth rake-face tools such as PCD. As CVD diamond technology advances, it is likely that the use of polishing, grinding, or other finishing techniques for CVD diamond-coated tooling will become more prevalent. Increases in CVD diamond cutting tool demand will provide justification for tailoring film properties such as thickness and surface roughness to specific applications. Such justification is critical to the presence of CVD diamond in the market because it will undoubtedly lead to an expansion in application range for diamond-coated products. 2.

Approaches to Engineering Thick-Film CVD Diamond Tools

a. Design and Manufacture of Thick-Film Tips. The primary technical challenge in the manufacture of freestanding thick-film CVD diamond cutting tool tips is attaining a throughput of freestanding diamond material having the dimensional and mechanical characteristics needed for downstream processes and ultimate use [35]. This is commonly approached through the manufacture of large-area, crack-free, CVD diamond discs of the necessary thickness with minimal thickness variation and minimal bow. Attaining CVD diamond wafers of this quality is exceptionally difficult due to the unique mechanical properties of diamond and the tendency for these *Mirror finish observed on diamond-coated silicon carbide cutting tools once produced by DeBeers.

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properties to vary measurably with changes in deposition conditions such as temperature and gas chemistry. Clearly, factors such as CVD diamond reactor type, the associated diamond deposition area, deposition rate, and vacuum process control capabilities are critical to success in freestanding diamond production. Although this issue has been discussed in various forums [35], many of the details of the industrial methods used to generate large freestanding diamond discs are presently treated as trade secrets and will not be discussed in this text. Regardless of the challenges, pure CVD diamond wafers for mechanical applications have been commercially manufactured in the thickness range of 150 to over 1000 ␮m with diameters up to 175 mm (see Fig. 2a).* By comparison, commercial high-temperature, highpressure PCD manufacture is presently limited to disc sizes of about 74 mm. Cutting CVD diamond components from freestanding CVD diamond wafers is presently done using laser technology as opposed to the electric discharge machining (EDM) ‘‘wire cutting’’ common to the PCD industry. Pure CVD diamond wafers contain no metallic binders and, therefore, do not afford the conductive properties needed in an EDM workpiece. The general acceptance of EDM wire techniques for diamond tool fabrication coupled with the present lack of the necessary laser technology at cutting tool fabricator sites is a significant barrier to commercialization of thick-film diamond tooling. b. Attachment Techniques for CVD Diamond Tips. Most freestanding, thick-film CVD diamond used for cutting tool applications is approximately 0.5-mm-thick polished diamond. The pure diamond can be attached to the tool body using a high-temperature inert vacuum braze (normally >850⬚C). The use of a high-temperature braze ensures good chemical bonding and excellent braze strength. Commercially available forms of freestanding CVD diamond cutting tool tips are generally made from well-faceted deposits that may have crystal sizes exceeding 50 ␮m. The surface roughness of the thick-film, freestanding diamond is usually removed by diamond finishing techniques in an effort to mimic the desirable characteristics of PCD. In most commercial thick-film CVD cutting tool applications, the relatively smooth nucleation surface is used as the cutting surface and the rough, faceted face becomes part of a vacuum-brazed interface typically bonded to tungsten carbide. A flank-face view of a finish-ground CVD diamond cutting tool tip is shown in Fig. 7. Commercially available thickfilm cutting tool tips offer superior wear resistance, which is typical of coarse-grained thin-film diamond deposits, coupled with mirror finish (commonly <0.5 ␮m R a) polished rake faces and finish-ground flank faces at*Comment refers to Norton Diamond Film’s thick-film product range prior to business closure.

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Figure 7 Flank-face electron microscope view of a freestanding CVD diamond cutting tool after use in a machining operation. The bright white region along the cutting edge contains the abrasive wear scar. As the 100⫻ image depicts, the faceted coarse-grained ‘‘growth’’ face of the CVD diamond tip is incorporated into the vacuum braze layer of the tool (see lower horizontal feature). The polished, fine-grained, ‘‘nucleation’’ face of the diamond is used as the rake face of the tool (see top, dark region above the U-shaped cutting edge). To the naked eye, the rake face of this tool actually has a black mirror finish. (From Ref. 1.)

tained by industrial finishing and grinding techniques, respectively. This unique combination enables thick-film cutting tool tips to generate superior workpiece finish relative to CVD diamond coatings and most other alternative cutting tool technologies. c. CVD Diamond Grinding Challenges. Good cutting edge grinding techniques can yield CVD diamond edge quality similar, if not superior, to that attainable by most or all PCD grades. However, CVD diamond’s erosion resistance often requires more fabrication time and cost to ensure good edge quality. According to a representative of the diamond fabrication industry (T. Drury, J&M Diamond Tool, personal communication, 2000) [1] it takes 10 to 20% longer to grind a CVD diamond tool with an edge quality comparable to that of PCD tooling. Diamond superabrasive wheels are normally used to grind CVD diamond. As with PCD fabrication, toolmakers have the option of using vitrified bonded, resin-bonded, and metal-bonded diamond wheels. Aggressive grinding of CVD diamond can induce flaws that sacrifice the mechanical behavior and cutting action of the cutting edge. When proper

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grinding techniques are employed, the strong nonmetallic bonding of the CVD diamond crystallites minimizes grain pullout on the cutting edge of thick-film CVD diamond tips. Most toolmakers claim that reduction in grinding wheel feed rates can yield CVD diamond edge finishes superior to what PCD can offer. Once the CVD diamond edge quality is attained through proper fabrication techniques, the binder-less construction of CVD diamond offers a continuous polycrystalline cutting edge that lacks the soft binder phase inherently present in metal-sintered PCD and cemented carbides.

III.

OPTIMIZING MECHANICAL PERFORMANCE OF CVD DIAMOND CUTTING TOOLS

Because abrasive wear and mechanical failure mechanisms control the wear life of cutting tools in most applications, optimization of the mechanical properties of CVD diamond cutting tools is essential to maximizing performance. Fortunately, CVD diamond process parameters can be adjusted and monitored in an effort to modify and reproduce desirable material properties and physical characteristics of the deposits. This section contains discussions of the issues and challenges of attaining good mechanical performance of CVD diamond tools. Section III.A contains approaches to engineering surface structure and the bulk mechanical properties of both thin-film and thickfilm CVD diamond deposits. Section III.B will be focused on the fundamentals of the thin-film diamond adhesion and includes specific approaches that have been taken to overcome adhesion to tungsten carbide cutting tools. A.

Optimizing the Surface and Bulk Structure of CVD Diamond Deposits

1.

CVD Diamond Morphology and Defect Structure

One of the most recognizable physical characteristics of CVD diamond deposits grown under different process conditions is the microstructure or morphology of the individual diamond crystals. As shown in Fig. 8, diamond film morphology may range from coarse-grained (diameter >1 ␮m), faceted crystallines to fine-grained (diameter <0.1 ␮m), ‘‘microcrystalline’’ structures. The properties of the diamond film and associated performance can vary widely depending on the selected morphology and application details. Because of the organic nature of CVD diamond synthesis from carbonhydrogen gas mixtures, diamond deposits produced under typical CVD diamond growth conditions may contain small fractions of nondiamond or non-sp3 bonded carbon. Fine-grained deposits (typically grown with higher

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Figure 8 Examples of CVD diamond morphology. Depending on the needs of the application, the morphology of CVD diamond deposits can range from coarse (diameter >1 ␮m) faceted crystallites to fine-grained (diameter <0.1 ␮m) or ‘‘microcrystalline’’ structures. The SEM micrograph in (a) shows the free surface of a coarse-grained diamond film. Note the misorientation of grains relative to each other and the high density of twin defects observed at the surface. The SEM micrograph in (b) shows the free surface of a microcrystalline diamond film. The average grain size for this film is on the order of 100–200 nm. (From Ref. 28.)

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carbon content gas mixtures) generally contain higher amounts of non-sp3 carbon than coarse-grained deposits. In addition to nondiamond carbon defect structure, lattice defects such as vacancies, dislocations, and/or twin planes may also be incorporated into the films. Microporosity in the form of fissures and voids has also been reported in thick-film diamond [35]. High-resolution electron microscopy has been used to resolve the fine structure of lattice defects in films and results have been correlated with growth conditions and mechanisms [36,37]. The resulting influence of defects on the material properties has been determined to be a function of the defect type and density [35,38–42]. 2.

Structural Analysis of CVD Diamond by Raman Spectroscopy

Raman spectroscopy has been demonstrated to be one of the most versatile techniques used to characterize the structural properties of synthetic diamond. Graphite, sp2-bonded amorphous carbon, diamond, and other forms of carbons have strong and easily identifiable Raman spectra. In diamond materials, the primary diamond peak exhibits changes in width that have been related to the degree of structural order, and small shifts in the wavenumber position of the primary diamond peak have been correlated with the stress state in the diamond. Nondiamond carbon has a distinctly different Raman signature that is more intense than the diamond spectrum, allowing the detection of very small amounts of ‘‘graphitic’’ material in CVD diamond films [43]. Many early CVD diamond references refer to the relative amount of non-sp3 carbon versus sp3 carbon in a deposit as a measure of CVD diamond ‘‘quality,’’ where the quality was loosely defined by the percentage of nondiamond carbon and the density of defects incorporated in the deposit [44]. This definition assumes that the ideal ‘‘highest quality’’ Raman characteristic for polycrystalline CVD diamond is one that mimics the perfect singlecrystal diamond—minimal defect structure with a sharp, narrow signature Raman peak at 1332 cm⫺1. In applications such as freestanding optics, this definition may apply. However, in most predominantly mechanical applications, the best performing material often has intergranular and intragranular defect structures that yield Raman spectra quite different from those of a pristine single-crystal. That is, the use of the highest crystalline quality CVD diamond is not necessarily the best overall solution for mechanical applications of diamond. The Raman spectrum of the coarse-grained (‘‘higher quality’’) diamond film depicted in Fig. 8a is presented in Fig. 9. The Raman results show a sharp primary diamond band located at about 1332 cm⫺1 and a low-intensity,

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Figure 9 Raman spectra for a coarse-grained diamond coating: Raman spectrum of coarse-grained diamond film used for thin-film cutting tool applications. Note the sharp primary diamond band located at about 1332 ⌬cm⫺1. This primary diamond band displays a full width at half of the maximum intensity (FWHM) of a