SEMICONDUCTORS & SEMIMETALS V38, Volume 38 (Semiconductors and Semimetals)

Imperfections in IIIjV Materials SEMICONDUCTORS AND SEMIMETALS Volume 38 Semiconductors and Semimetals A Treatise Ed...

Author: EICKE R. WEBER

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Imperfections in IIIjV Materials SEMICONDUCTORS AND SEMIMETALS Volume 38

Semiconductors and Semimetals A Treatise

Edited by R. K . Wiliardson CONSULTING PHYSICIST SPOKANE, WASHINGTON

Albert C. Beer CONSULTING PHYSICIST COLUMBUS, OHIO

Eicke R. Weber DEPARTMENT OF MATERIALS SCIENCE AND MINERAL ENGINEERING UNIVERSITY OF CALIFORNIA AT BERKELEY BERKELEY, CALIFORNIA

Imperfections in III/V Materials SEMICONDUCTORS AND SEMIMETALS Volume 38

Volume Editor

EICKE R. WEBER DEPARTMENT OF MATERIALS SCIENCE AND MINERAL ENGINEERING UNIVERSITY OF CALIFORNIA AT BERKELEY BERKELEY, CALIFORNIA

W ACADEMIC PRESS, I N C . Harcourt Brace Jovanovich, Publishers

Boston Sun Diego New York London Sydney Tokyo Toronto

This book

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printed on acid-free paper.

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Copyright 0 1993 by Academic Press, Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means. electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher.

ACADEMIC PRESS, INC. 1250 Sixth Avenue. San Diego, CA 92101 United Kingdom edition published by ACADEMIC PRESS LIMITED 24-28 Oval Road. London NWI 7DX

The Library of Congress has catalogued this serial title as follows: Semiconductors and semimetals. - Vol. 1 -New

York: Academic Press. 1966-

v.: ill.: 24 cm Irregular. Each vol. has also a distinctive title. Edited by R. K. Willardson, Albert C. Beer, and Eicke R. Weber ISSN 0080-8784 = Semiconductors and semimetals

I. Semiconductors - Collecied works. 2. Semimetals - Collected works. I. Willardson, Robert K. 11. Beer, Albert C. 111. Weber, Eicke R. QC6 l0.9.S4 621.385'2 -dc19 85-642319 AACR2 MARC-S Library of Congress ISBN 0-17-752138-0 (v. 38)

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This volume is dedicated to the memory of Michael Schluter, who has contributed so much to the theory of defects in semiconductors, and whose sudden passing away this fall leaves a gap that will be dificult to close.

E. Weber

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Contents LISTOF CONTRIBUTORS . . . PREFACE. . . . . . . .

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xi

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xiii

Chapter 1 Density-Functional Theory of sp-Bonded Defects in III/V Semiconductors

Udo Scherz and Matthias Schefler I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2 I1. Thermodynamics of Defects in Semiconductors . . . . . . . . . . . . . 5 111. Ab-lnitio Calculation of the Electronic Ground State and of Atomic Vibrations . 13 IV. Methods and Techniques. . . . . . . . . . . . . . . . . . . . . 20 V . Electronic Structures and Concentrations of Native Defects . . . . . . . . 23 VI. An Intrinsic Metastability of Antisite and Antisite-like Defects . . . . . . . 37 VII. The EL2 Defect . . . . . . . . . . . . . . . . . . . . . . . . 42 VIII. The DX Centers . . . . . . . . . . . . . . . . . . . . . . . . 50 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . 54 References . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Chapter 2 EL2 Defect in GaAs Maria Kaminska and Eicke R . Weber I. Introduction . . . . . . . . . . . . . . . . I1. Properties of EL2 Defect . . . . . . . . . . . . 111. Arsenic Antisite Defect in GaAs . . . . . . . . IV. Energy Levels of EL2 Defect . . . . . . . . . V . Models of EL2 Defect . . . . . . . . . . . . . VI. Conclusions . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . .

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CONTENTS

Chapter 3 Defects Relevant for Compensation in Semi-insulating GaAs David C . took I . Introduction . . . . . . . . . . . . . . . . . . . . I1. Compensation in Bulk GaAs . . . . . . . . . . . . . Ill . The Calculation of Compensation . . . . . . . . . . . IV. Known Defects in GaAs . . . . . . . . . . . . . . . . V . The As-Precipitate Model for Compensation . . . . . . . . VLSummary . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . .

. . . . . 91 . . . . . . 92 . . . . . . 98 . . . . . 104 . . . . . . 113 . . . . . 114 . . . . . 114

Chapter 4 Local Vibrational Made Spectroscopy of Defects in III/V Compounds

R . C . Newman I. Introduction . . . . . . . . . . . . . . . . . 1. L o c a l M Vibrational Mode Spectroscopy . . . . . 111. Oxygen Impurities . . . . . . . . . . . . . . . IV . Beryllium Impurities . . . . . . . . . . . . . . V . Carbon Impurities . . . . . . . . . . . . . . . V1 . Boron Impurities . . . . . . . . . . . . . . . VII . Silicon Impurities . . . . . . . . . . . . . . . VIII . Hydrogen Passivation of Shallow Impurities . . . . . IX. Radiation Damage . . . . . . . . . . . . . . . X . Conclusions . . . . . . . . . . . . . . . . . Note . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . .

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. 133 . 136 . 138 . 141 . 147 . . 161 . 167

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180 181 181 181

Chapter 5 Transition Metals in III/V Compounds Andrzej M . Hennel I . Introduction . . . . . . . . . . . . . . . . I1. General Properties of Transition Metal Impunties . . I11. 3d" Transition Metals . . . . . . . . . . . . . IV. 4d" and 5d" Transition Metals . . . . . . . . . V . Semi-insulating TM-Doped I I I i y Materials . . . . Appendices . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . .

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. 194 . . 217 . . 218 . 221 . 228

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CONTENTS

Chapter 6 DX and Related Defects in Semiconductors Kevin J . Malloy and Ken Khachaturyan I. Introduction . . . . . . . . . . . . . . . I1. Electrical Properties . . . . . . . . . . . . 111. Optical Properties . . . . . . . . . . . . . IV. ModelsofDX . . . . . . . . . . . . . . V. Microscopic Structure of the DX Center . . . . VI. Magnetic Properties of DX:The Negative4 Issue. VII. Technology and DX . . . . . . . . . . . . VIII. Summary . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . References . . . . . . . . . . . . . . . .

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235 243 256 266 . 267 . 274 280 284 285 285

Chapter 7 Dislocations in III/V Compounds

K Swaminathan and Andrew S . Jordan I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . I1. Dislocation Types and Structures . . . . . . . . . . . . . . . . . I11. Mechanical Properties. . . . . . . . . . . . . . . . . . . . . . IV . Dislocation Generation and Reduction during Growth of Bulk Crystals . . . V . Dislocations and Device Performance . . . . . . . . . . . . . . . Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . .

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. 310 . 321 335 336

Chapter 8 Deep Level Defects in the Epitaxial III/V Materials Krzysztof W Nauka I. Introduction . . . . . . . . . . . . . . . I1. Observation of Deep States in Epitaxial Layers . . I11. Epitaxial Binaries . . . . . . . . . . . . . IV. Epitaxial Ternaries and Quaternaries . . . . . V. Quantum Wells, Superlattices. and Interfaces . . VI . Deep Levels in Structurally Disordered I I I P Layers VII. Conclusion . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . .

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. 365 . 376 . 381 389 389

CONTENTS

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Chapter 9 Structural Defects in Epitaxial III/V Layers Zuzanna Liliental- Weber. Hyunchul Sohn. and Jack Washburn I . Introduction . . . . . . . . . . . . . . . . . . . . I1 . Homoepitaxy . . . . . . . . . . . . . . . . . . . . 111. Heteroepitaxy . . . . . . . . . . . . . . . . . . . IV . Methods to Decrease the Defest Density in the Epitaxial Layers . V . Conclusions . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . .

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. 397 . 399 . 407 . . 430 . 442 . 443 . 443

Chapter 10 Defects io Metal/III/V Heterostructures William E . Spicer I . Introduction . . . . . . . . . . . . . . . . . . . . . . . I1. Movement of the Fermi Level and Departures from GaAs Stoichiometry . 111. A Model to Explain Fermi Level Moment . . . . . . . . . . . IV . GaAs/Insulator Interfaces . . . . . . . . . . . . . . . . . . V . Conclusions and Discussion. . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .

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449

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INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

493

CONTENTS OF VOLUMES LN THIS sWES . . . . . . . . . . . . . . . . . . 499

List of Contributors Numbers in parentheses indicate the pages on which the authors’ contributions begin.

ANDRZEJM. HENNEL(189) Znstitute of Experimental Physics, Warsaw University, Hoza 69, 00-681 Warsaw, Poland ANDREWS. JORDAN (293) AT&T Bell Laboratories, Murray Hill, New Jersey 07974 MARIAKAMINSKA (59) Institute of Experimental Physics, Warsaw University, Hoza 69, 00-681 Warsaw, Poland KEN KHACHATURYAN (235) Los Alamos National Laboratory, Los Alamos, New Mexico 87545 ZUZANNALILIENTAL-WEBER (397) Center for Advanced Materials, Lawrence Berkeley Laboratory 62-203, 1 Cyclotron Road, Berkeley, California 94 720 DAVIDC. LQOK (91) University Research Center, Wright State University, Dayton, Ohio 45435 KEVINJ. MALLOY(235) Center for High Technology Materials and Department of Electrical Engineering and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87131 KRZYZTOF W. NAUKA (343) Hewlett-Packard Company, 3500 Deer Creek Road, Palo Alto, California 94304-1392 R. C. NEWMAN (1 17) Interdisciplinary Research Centre for Semiconductor Materials, The Blackett Laboratory, Imperial College of Science, Technology and Medicine, Prince Consort Road, London SW72B2, United Kingdom MATTHIAS SCHEFFLER (1) Fritz-Haber Institut der Max-Planck-Gesellschaft, Abteilung Theorie, Faradayweg 4-6, 0-1000 Berlin 33, Germany UDO SCHERZ(1) Fachbereich Physik, Technische Universitat Berlin, Hardenbergstrape 36, 0-1000 Berlin 12, Germany HYUNCHULSOHN(397) Department of Materials Science and Mineral Engineering, University of California, Berkeley, California 94720 WILLIAM E. SPICER(449) Solid State Electronics Laboratory, Department of Electrical Engineering, Stanford University, Stanford, California 94305 V. SWAMINATHAN (293) A T&T Bell Laboratories, Solid State Technology Center, 9999 Hamilton Blvd., Room 2M-230, Breinigsville, PA 18031 JACK WASHBURN (397) Center for Advanced Materials, Lawrence Berkeley Laboratory 62-203, 1 Cyclotron Road, Berkeley, California 94720 EICKER. WEBER(59) Department of Materials Science and Mineral Engineering and Center of Advanced Materials, Lawrence Berkeley Laboratory, 382 Hearst Mining Building, University of California, Berkeley, CA 94720 Xi

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Preface

Research emphasis in the physics and materials science of semiconductors has long focused on understanding perfect materials and structures. However, over the last decade a general recognition has developed of the decisive role of imperfections in semiconductors, and especially in III/V materials, fueled by the widespread appreciation of the relevance of lattice defects during processing and operation of semiconductor devices. The result has been impressive progress in our fundamental understanding of imperfections in semiconductors, based on the availability of experimental methods which allow deep insight into the microscopic and electronic structure of defects, and on the availability of sufficient computing power to enable us to perform realistic model calculations. In some key cases such calculations turned out to be crucial in the interpretation of experimental results, as the reader will find in several places in this volume. Many controversial debates have arisen in this field which center around details of certain lattice defects, such as the so-called DX-centres in AlGaAs or the EL2 defect in GaAs. Such details are fully appreciated only by a rather small contingent of the scientific community who specialize in a very specific topic, such as the EL2 defect. For most scientists in the field, and most direct users of semiconductor materials who are, e.g., concerned with the design and processing of devices, these debates were frequently more confusing than enlightening. This volume is intended to summarize the results of the ongoing basic research on some of the key imperfections in III/V materials and to make this knowledge available to a wide range of scientists, engineers, and advanced students. Thus the contributions of this volume shad be of interest to researchers who already work in the field or consider contributing to it in the future, to engineers who want to utilize the research results and the understanding of the nature and properties -of imperfections in III/V materials achieved to date, and to graduate students who are interested in learning the methods and recent results for the study of defects in III/V materials. The chapters herein were written by specialists in their respective fields whose personal judgments unavoidably influence the material. Many of the

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PREFACE

chapters address topics that were very controversial. Some of these topics are no longer debated; others are still under intense scrutiny. The authors have made an effort to present all relevant arguments in the different controversies touched upon in the text, so that the reader can judge independently. The book is anchored with a chapter (Chapter 1) on state-of-the-art density-functional calculations of defects in III/V materials. This computational technique permits, for the first time, the derivation of meaningful total energies of defects, even in low-symmetry configurations, in addition to valuable information on the defects’ electronic structure. The two main examples discussed in this chapter, the EL2 defect in GaAs and DX and related centers in III/V compounds and alloys, are presented from the experimental point of view in Chapters 2 and 6. Chapter 3 summarizes our knowledge of defects relevant to compensation in semi-insulating GaAs. A great wealth of information on defects in III/V materials stems from local vibrational mode spectroscopy, and Chapter 4 discusses in detail several examples of defects that could only be identified with this very powerful technique. Transition metal impurities are a distinct class of very important and very well understood defects in III/V materials, and Chapter 5 is devoted to this topic. Other deep level defects, many not yet well identified, are found specifically in III/V thin films, and Chapter 8 contains a comprehensive discussion of our present knowledge of those imperfections. Extended defects play a very important role in the function of devices based on III/V technology. Chapter 7 summarizes our knowledge on extended defects in bulk crystals, and Chapter 9 on those defects in thin films. Defects at heterointerfaces can be very important in Fermi level pinning, which can dominate the carrier transport across such interfaces. A detailed discussion of these defects can be found in Chapter 10. Publication of such a volume in a rapidly developing area is subject to the danger that some of the material presented and conclusions reached might be looked upon differently in the light of new experimental and theoretical results that will be published after the volume is in the hands of the reader. This danger is unavoidable as long as books are prepared as printed volumes rather than as constantly updated electronic files. However, in keeping with the tradition of this series, the editor tried to ensure that this volume contains enough material of long-standing value to make it an important resource in the ykars to come. The editor expresses his gratefulness to the contributors and the staff of Academic Press who made this treatise possible. Eicke R. Weber Berkeley December 1992

SEMICONDUCTORS AND SEMIMETALS. VOL. 38

CHAPTER 1

Density-Functional Theory of sp-Bonded Defects in III/V Semiconductors Udo Scherz FACHBEREICH PHYSIK. TECHNISCHE UNNERSITAT BERLIN BWLIN.GWMANY

Matthias Schefler FRITZ-HABER-INSTITUTDER MAX-PLANCK-GESELLSCHAFI

BERLIN. GERMANY

I. INTRODUCTION.

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. . 11. THERMODYNAMICS OF DEFECTS IN SEMICONDUCTORS . 1. Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . 2. Defect Concentration and Gibbs Free Energy of Defect Formation . . . . . 3. Defect Pairs and the Law of Mass Action . . . . . . . . . . . . . . 111. Ab-lnitio CALCULATION OF THE ELECTRONIC GROUNDSTATE AND OF ATOMIC VIBRATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 4. Density-Functional Theory . . . . . . . . . . . . . . . . . 5 . Vibrations . . . . . . . . . . . . . . . . . . . . . . IV . METHODS AND TECHNIQW . . . . . . . . . . . . . . . . . .. . . . 6. Introduction . . . . . . . . . . . . . . . . . . . . . . 7. Pseudopotentials . . . . . . . . . . . . . . . . . . . . 8. Supercell Methods . . . . . . . . . . . . . . . . . . . . 9 . Green-Function Methods . . . . . . . . . . . . . . . . . . . v. ELECTRONIC sTRUCTURE'3 AND CbNCENTRATIONS OF NATIVE DEFECTS . . . . . 10. Electronic Structure of Intrinsic Defects . . . . . . . . . . . . 11. Natiue-Defect Reactions . . . . . . . . . . . . . . . . . . VI . AN INTRINSIC METASTABILITY OF ANTISITE AND ANTISITE-LIKE DEFECTS . . VII. THEEL2 DEFECT. . . . . . . . . . . . . . . . . . . . . . . 12. Introduction . . . . . . . . . . . . . . . . . . . . . . 13. The Pansition to the Metastable Configuration . . . . . . . . . . 14. Comparison of the Theoretical Results to the Experimental EL2 Properties

. . . . . . . . . . . . . . . . . . . . . VIII . THEDX CENTERS 15. Introduction . . . . . . . . . . . . . . . . . . . . . . 16. Theoretical Results for the Si Donor in GaAs under Pressure . . . . ACKNOWLEDGMENT . . . . . . . . . . . . . . . . . . . . . mRENcEs

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Copyright 0 1993 by Academic Press. Inc. All rights of reproduction in any form reserved. ISBN 0-12-7521384

2

UDOSCHFRZAND MAITHIASSCHEFFLER

I. Introduction The requirements of semiconductor technology for accurate control of defect concentrations, concentration profiles, defect electronic structure, diffusion properties, formation and reaction energies, and atomic structures at interfaces has stimulated extensive experimental and theoretical research. Several exciting new phenomena have been discovered throughout these investigations, as for example the “negative U” property of the vacancy in silicon (Baraff et al., 1979, 1980; Watkins and Troxell, 1980), i.e., an effective electron-electron attraction; and the EL2 (Martin and Makram-Ebeid, 1986; Dabrowski and Scheffler, 1988% 1989a; Chadi and Chang, 1988a) and D X (Chadi and Chang, 1988b; Zhang and Chadi, 1990; Dabrowski et al., 1990; Dabrowski and Scheffler, 1992) metastabilities, which demonstrate the capability of the III/V crystal to stabilize defects in different atomic configurations (Scheffler, 1989; Caldas et al., 1990; Dabrowski and Scheffler, 1992). These and many more examples, as well as the discussions and controversiesin the process of unveiling the underlying physics, show that the basic understanding of many-particle effects in condensed-matter science, and in particular for low-symmetry polyatomic aggregates, as for example defects in semiconductors, is still rather limited. The derivation of density-functional theory (DFT) (Hohenberg and Kohn, 1964; Kohn and Sham, 1965; Levy, 1982), together with the local-density approximation (LDA) for the exchange-correlation functional (Dreizler and Gross, 1990, Lundqvist and March, 1983; Ceperley and Alder, 1980; Perdew and Zunger, 1981) has played a significant role in improving this situation, and DFT-LDA will certainly still play an important role in the coming years. This theory describes the electronic ground state and contains all manyelectron effects of the nonrelativistic interacting many-body systems of constant and weakly varying densities. For very inhomogeneous densities and for highly localized electron states (as, for example, in free atoms), the DFT-LDA is not a reasonably defined approximation for the treatment of exchange and correlation. This criticism, although certainly valid in principle, has not stopped theoreticians from applying this approach to calculate structural and elastic properties of polyatomic systems. The demonstrated success of the theory (e.g., Moruzzi et al., 1978; Cohen, 1985) is in fact overwhelming, and no seuere breakdown of the theory has been reported so far (see Section 111.4 for more details). We like to emphasize at this point that an accurate evaluation of the DFT-LDA electron density and total energy is usually very difficult and requires sophisticated methods as well as care and experience. Often the numerical inaccuracy may be higher than the errors due to the LDA. For many defect studies an accuracy with errors below 0.1 eV for the relevant total-energy diferences is needed even for a qualitative de-

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDED DEFECTS

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scription as 0.1 eV is the typical order of magnitude for energy barriers and energy differences between atomic configurations. Therefore higher inaccuracies could give rise to a significantly different geometry and electronic structure. An important deficiency of the present state of the theory concerns excitation properties, as, for example, optical absorption or emission. DFTLDA is only designed for ground state properties. In order to handle excitations it is important to calculate the electron self energy (Sham and Kohn, 1966; Hedin and Lundqvist, 1969), which describes the modification of the exchange and correlation energy and the finite lifetime of the excitation (e.g., due to plasmon or electron-hole excitations). Furthermore, transition matrix elements can play an important role. A tractable and at the same time reliable approach for these purposes has not been developed so far. Therefore, only (semi) empirical calculations either neglecting the self-energy or taking a guessed ansatz (usually fitted to experiments) are used. Localized defects in semiconductors present a particular challenge for the theory. Powerful methods and techniques to handle the ground state have been developed over the last 10 years, and more developments and improvements are underway. To date, no general theoretical approach exists that is suited for a reliable description of all possible defect candidates. In fact, a thorough investigation of point defects, including the local lattice distortions, is still a most demanding task. As a consequence, defect complexes (of more than two partners) and highly distorted transition-metal impurities have not been investigated in detail. The calculation of the ground-state total energy and electron density, which are the key quantities of DFT-LDA, can be used to understand the electronic and atomic structure of defects, In addition, for temperaturedependent properties such as defect concentrations in thermodynamic equilibrium, it is possible to calculate thermodynamic potentials (the Gibbs free energy, for example) from the partition function of a canonical ensemble. Difficulties may arise because in many (maybe most) practical situations, thermodynamic equilibrium is not attained. For example, at or below room temperature, chemical reactions in the bulk may not be in equilibrium with the surface and with the crystal environment. Then it is often assumed that a “partial equilibrium” exists and that thermodynamics can be applied only to certain defect reactions. Such thermodynamic treatment has been done only recently by means of first-principle calculations (Scheffler, 1988; Biernacki and Scheffler, 1989; King-Smith et al., 1989). For defects it was found (Scheffler, 1988; Biernacki et al., 1989) that entropy differences of different defect configurations can reach values of about 3k,, where kB is the Boltzmann constant. At T = 1,OOO K, this entropy corresponds to 0.26 eV, which for many reactions may be of significant importance.

4

U w SCHFXZAND MATIWAS SCHEFFLER

In this chapter we describe the basic concepts as well as the results of DFTLDA calculations of sp-bonded defects in I I I P zincblende-structure semiconductors. We mainly concentrate on structural and elastic properties and discuss the formation energes, stabilities, and defect reactions. Electronic levels and optical properties are discussed with less emphasis, because they are less reliable in the theory than the ground state electron density, the total energy, energy barriers, and forces (see Part HI). We will assume throughout this chapter that the concentration of defects is low, so that their statistics is that of independent particles. Thus, when N , is the number of defects and 2N, = N,,, + N, the number of perfect crystal nuclei (cations and anions), the defect concentration is [D]

ND

= -<<

1.

N c

This definition of the defect concentration will be used throughout this chapter. From [D] the number of defects per cubic centimeter is obtained by multiplying [D] by 4/Q, where R is the volume in cubic centimeters of the conventional unit cell of the host crystal, which for a zincblende lattice contains four primitive unit cells. For GaAs, for example, we have 4/R = 2.2- lo2’ crn-j. Most examples presented in this chapter are defects in GaAs. This is done because GaAs is the mostly studied material and because the quafitatioe properties of these examples and the conclusions are valid for other III/V compounds as well. Therefore, we feel that it is convenient to use GaAs practically as a synonym for a III/V compound and G a and As as synonyms for a group-I11 crystal atom and a group-V crystal atom, respectively. The remaining paper is organized as follows. In Part I1 we summarize the basic thermodynamic relations that are important for calculations of defect reactions and concentrations. In Part 111 we discuss some basic aspects of the density-functional theory and the local-density approximation for the exchange-correlation functional. We will not give a derivation of the theory because this can be found in the clearly written original papers (Hohenberg and Kohn, 1964, Kohn and Sham, 1965; Levy, 1982), as well as in greater detail in the books by Dreizler and Gross (1990) and Lundqvist and March (1983). We will present, however, a short description of the exchangecorrelation interaction, and we will give some hints as to which cases require the LDA to be treated with special caution. Part IV then sketches the two main routes taken at present to evaluate defect properties: the self-consistent Green-function method and the supercell approach. Parts V-VIII describe results of recent calculations. We concentrate on sp-bonded defects, leaving out the first-row elements as well as transition-metal impurities. As men-

1. DENSITY-FUNCTIONAL THEORYOF SP-BONDED DEFECTS

5

tioned earlier, special attention will be paid to formation energies, structural properties, and metastabilities. Part V summarizes calculations of the electronic structure and of the concentration of simple, intrinsic point defects in GaAs. Part VI gives a general description of antisite and antisite-like centers in GaAs and InP, and Part VII continues this discussion with respect to the EL2 defect and its metastability. In Part VIII we discuss the properties of the substitutional donor Si in GaAs, which exhibits a shallow-deep structural transition, and we relate these results to experimental data of D X centers.

11. Thermodynamics of Defects in Semiconductors 1. BASICCONCEPTS The quantum mechanical system of a solid consisting of N , electrons and N nuclei is described by the many-body Hamiltonian

with

Here (ri} denotes all position vectors of the electrons (rl, r2,. . .,r N e ) ) and (R,} denotes the positions vectors of all nuclei (R,,R,, . . . ,RN).The kinetic energy operators of the electrons TEand nuclei T' are given by

and

and the Coulomb repulsion of the electrons VE-E and of the nuclei V1-' is

6

UDO SCHERZ AND

MATTHIASSCWEFFLER

and

where e is the electron charge, the charge of the I th nucleus is - Z,e, and E~ is the permittivity of free space. The attractive interaction between the electrons and the nuclei may be written in the form

where V, is the potential energy of an electron due to the nucleus I: e2 Z, V,(r-Rr) = -- 4m0 Ir - R,I '

(9)

In many cases it may be advantageous to use the frozen-core approximation, in which the strongly bound electrons in closed shells are treated together with the nuclei as rigid ions. This approach often increases the numerical accuracy especially when applied together with the pseudopotential concept (see Section IV.7). In this case N , is the number of valence electrons only and V, in Eqs. (8) and (9) denotes the pseudopotential of the ion I. The eigenvalue problem of the Hamiltonian H of Eq. (2) is solved by using the Born-Oppenheimer approximation. One then neglects the electronphonon coupling, which implies that the states of the Hamiltonian of the electron system H E of Eq. (3) are calculated separately in a first step by considering the coordinates of the nuclei as parameters. Using the densityfunctional theory, described in Section 111.4, the lowest eigenvalue of H E is calculated, which gives the ground-state total energy EE'({ R,]) as a function of the positions of the nuclei and which is called the Born-Oppenheimer totalenergy surface. In the second step the vibrational energy spectrum is calculated at a certain point in configuration space, {R:}. Typically, {R:} corresponds to the relevant minimum of the Born-Oppenheimer surface or is very close to it. E$({RF)) is then calculated as the eigenvalues of the vibrational Hamiltonian Hvib= T'({R,))

+ E:l({RI])--E~'({R~}).

The eigenvalues of the Hamiltonian H of Eq. (2) are given by

(10)

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDED DEFECTS

7

In order to apply this for the calculation of the Gibbs free energy of the solid, we may introduce the volume V as the volume occupied by the atoms at their positions {RY}. We use the canonical ensemble and write the partition function in the form

Zl(T, K {RY}) = D&exp{

3 1exp { -%}, T kBT

(12)

kB

where we have neglected the summation over the excited electronic states. This is a reasonable approximation unless the difference between the lowest excited electronic energy and the ground-state energy is not large compared with kBTIn Eq. (12) the volume dependence of Z1 has been noted explicitly. The degeneracy D& of the electronic ground-state energy E$ of the considered geometry is the spin degeneracy in case of any stable or metastable atomic configuration, and because of the Jahn-Teller theorem there is no orbital degeneracy, kB is the Boltzmann constant, and T the temperature. The geometrical configurational degeneracy will be considered in Section 11.2. To find the Helmholtz free energy and other properties of the thermodynamic equilibrium of the solid, we restrict the just-outlined theory to those atomic positions {RY} that are close to the equilibrium values defining stable or metastable states. The Helmholtz free energy of a crystal containing only one defect is then given by

with

and

=

7[%+

kBTIn (1 -exp

{-

s})] .

Here mi(K {RY}) denote the vibrational frequencies of the solid in the quasi-

Urn S c m z AND MATTHIASSCHEFFLER

8

harmonic approximation,' which have to be summed up (Born and Huang, 1954). For a finite crystal with periodic boundary conditions there are 3N vibrational modes. From the Helmholtz free energy it is possible to derive the entropy S, and the pressure p by

and

Solving the equation of state Eq. (18) for the volume V, = V,(T p, (RY)),we can calculate the Gibbs free energy

Under the condition of given temperature T and pressure p , the equilibrium volume and the equilibrium positions of the nuclei are determined by

2. DEFECTCONCENTRATION AND GIBBS FREEENERGY OF DEFECT FORMATION

We will now consider the thermodynamic quantities that describe a semiconductor crystal containing one type of N , noninteracting defects. This implies that we neglect defect-defect interactions, for example by Coulomb interaction, long-range lattice relaxation, and others. Let the partition function 2, of Eq. (12) describe a crystal containing one defect only, and let x N , be the number of equivalent positions of the defect with respect to translational and point symmetry of the perfect crystal. For a tetrahedral site, x is equal to one.' Then, for a crystal containing N , << E N , defects, the

'

We

1 0 take

USE the term quasi-harmonicapproximation because the described approach allows us into account that the dynamical rnatnx and thus also the frequencies w , vary with the

atomic positions For a group IV semiconductor z would be equal to two for a tetrahedral site, because both atoms per unit cell are identical.

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDED DEFECTS

9

partition function is given by

where the configurational degeneracy of the positions of the defects has been taken into account and 2, is given by Eq. (12). The Helmholtz free energy of such a crystal is then

Equations (13)-(19) also define the Gibbs free energy of the pe8ect crystal with 2N, atoms. Note that the number of atoms of the crystal with the defect may be different from 2N,. To find the change of the Gibbs free energy due to the incorporation of one defect, it may be necessary to calculate the Gibbs free energy of some free atoms that enter or leave the crystal. A defect D"' is formed by the exchange of atoms A,, A,, ... and electrons e- between a perfect crystal, which we denote by 0, and a reservoir. This is described by a chemical reaction of the form

where vi is the number of neutral atoms Ai involved in the reaction and 1 is the charge state of the defect. We now consider different charge states and treat differently charged defects as different defects. This also takes into account that differently charged defects typically have a different geometry. A special example of Eq. (23) is the formation of a 1-charged substitutional atom X at a Ga site in GaAs. This is described by the reaction

X g a e O + X - Ga - le-.

(24)

The reaction Eq. (24) is understood in such a way that a substitutional defect Xga is created inside a perfect crystal and that the atom X enters the defect region whereas the Ga atom leaves this region. The meaning of the words "enter" and "leave" will be specified later, when we describe the defect concentrations and chemical potentials. The change of Gibbs free energy of the system due to the incorporation of ND defects is then

10

U w SCHERZ AND MAT~UAS SCHEFFLER r

1

It consists of a configurational part and contributions describing the defectinduced changes of Helmholtz free energy F , - Fp', volume V, - Vpc, and atomic contributions. Here G(Ai) denotes the ground state energy of the nucleus (or rigid ion) and the electrons of atom Ai. In case of thermodynamic equilibrium and assuming 1 << ND,the change of the Gibbs free energy due to the creation of one defect is

= -k,Tln

(3

2 +po(D),

where we have used the approximation of Stirling. The so-called standard term po(D)can be written in the form po(D)= - kBTIn D& 4- €;I(

V,, {R:))- E;l*Pc(Vpc, (R,P"))

+Fvib(7;V,, {R~>)-FVib@"(7; V p c ,{RF>)+p(Vl - V p " ) -

(27)

1vic(Ai), i

where {RPfJ and (R:} denote the equilibrium positions of the atoms of the perfect crystal and of the crystal containing one defect, respectively. We have assumed that the ground state of the perfect semiconductor crystal is non degenerate. When the system is in thermodynamic equilibrium at a given temperature T and pressure p , the Gibbs free energy necessary to create a defect according to Eq. (23) must be equal to the change of energy due to the environment, and we have =

i

vip(Ai)- IE,,

where E , is the Fermi energy and p(Ai)denotes the chemical potential of the reservoir for atom Ai. The term "reservoir" implies that energies and entropies of the atoms do not depend on the defect concentration. In the same

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDED DEFECTS

11

sense the Fermi energy acts as a reservoir for electrons or holes, if the concentration of the defect is small compared to the background doping. From Eqs. (26) and (28) we then obtain the defect concentration

The numerator in the exponential is often called the Gibbs free energy of defect formation. We see that it depends on the reservoirs of the atoms and of the electrons. For the preceding example of a Ga-site substitutional defect (see Eq. (24)), we obtain

Here p0(X('))is given by Eq. (27), and the atomic chemical potentials p ( X ) and p(Ga) are determined by the chemical state in which the atoms X and Ga are bound in the initial or final state of the chemical reaction outside or at the surface of the crystal. Typically, p ( X ) and p(Ga) can be controlled by the environmental conditions (partial pressure). To give one example: Ga may end up in a Ga-metal crystal or it may, if the crystal is held in As, gas, form together with +As, a new GaAs unit cell. These two extreme cases imply that the Ga chemical potential p(Ga) can be modified over a range of 2 eV, which can have a significant effect on the defect concentration (see Eq. (30)). We close this section with the remark that defects can also be formed without any atoms leaving or entering the crystal. In such cases neighboring or distant defect pairs are created (e.g., a Frenkel pair or an antisite-antisite pair) independent of reservoirs. The reactions are discussed in the next section.

3. DEFECT PAIRSAND

THE

LAWOF MASSACTION

In Sections 11.1 and 11.2 we considered crystals containing one type of noninteracting defects only. This approach, however, can be used as well to determine the concentration of pairs of point defects and higher-order complexes. In this section we consider the chemical reactions between defects forming a defect-defect pair. If all possible defects are in thermodynamic equilibrium with the conditions determined by the crystal environment and by the crystal bulk and surface, then there is also thermodynamic equilibrium

U w SCHERZ AND MAITHIASSCHEFFLER

12

with respect to all reactions of the defects with each other. However, often the full thermodynamic equilibrium may not be attained, because the temperature may be too low so that certain reactions are kinetically hindered; this implies that some of the defects are frozen in metastable configurations. Equilibrium thermodynamics may then still be applied, but should be restricted to only certain defect reactions. The resulting state is usually called a "partial equilibrium." We now discuss defect-defect reactions, concentrating on the formation of defect pairs, Let us consider a reaction of a defect A with charge state i and a defect B with charge state j to produce a defect pair AB with charge state I:

The corresponding law of mass action follows from Eq. (29) and reads

- a(AB'')) exp [A")][BC"] - cr(A"))a(B")) [A B"']

{ -"). kB

T

where the concentration [A")] of a defect A"' is defined by Eq. (1)and tl is the number of equivalent positions of the defect per primitive unit cell of the crystal. The Gibbs free energy of pair binding is Ap

+po(B"') -(I

= P'(A'~))

- i - j ) E F- po(AB")),

(33)

where po(A"))and po(B"') are the standard terms of the Gibbs free energy of defect formation (see Eq. (27)). Again we assume that the Fermi energy is independent of the reaction. Note that the reaction energy A p is independent of the chemical potentials of the reservoirs p(Ai), since according to Eq. (31) no atoms leave or enter the crystal. The chemical reaction Eq. (31) may also be used in the special case of the annihilation of two defects, which may occur if a Ga antisite approaches an As antisite or if a Ga interstitial approaches a Ga vacancy. The reverse of the last reaction is the formation of a distant (i.e., noninteracting) Frenkel pair, which for the cation in GaAs reads

Here i denotes a specific interstitial site. The law of mass action gives

1. DENSITY-FUNCTIONAL THEORYOF SP-BONDEDDEFECTS

13

In general, the concentration of Ga vacancies (and that of Ga interstitials)will depend also on other reactions involving these defects. However, if reaction (34) dominates or if there exists a partial equilibrium for this reaction, we have [VgL] = [Gaf)], and the concentration of vacancies is determined by

Note the factor 2 in the denominator of the exponential, which increases the vacancy concentration significantly. It is simply due to the fact that reaction (34) does not involve atomic reservoirs and that two defects are created simultaneously. Analogous equations to (34) and (36) hold for the simultaneous creation of a distant antisite pair, and for this case the law of mass action reads [As$J[Ga!&] = a(AssJa(GaiL) exp

+

+ + j)EF

po(As&) ,uo(Gaii) (i kB T

Further details for the defect reactions are discussed in Part V.

111. Ab-Znitio Calculation of the Electronic Ground State and of Atomic Vibrations 4. DENSITY-FUNCTIONAL THEORY Modern ab-initio calculations of ground-state properties of solids are typically based on the density-functional theory of Hohenberg, Kohn, and Sham (Hohenberg and Kohn, 1964; Kohn and Sham, 1965; Levy, 1982; Dreizler and Gross, 1990). The basic theorem states that the ground-state energy E f of the many-electron Hamiltonian HE(see Eq. (3))is a functional of the electron density n(r) and has its minimum at the exact ground-state electron density. The equations that follow are given for nonmagnetic systems, but the extension to spin polarization is straightforward. In fact, other extensions such as to relativistic effects, excited states, and timedependent phenomena have also been discussed in the literature (see Dreizler and Gross, 1990, for more details). They are, however, not important to the problems addressed in this chapter. The variational property of the totalenergy functional with respect to the electron density, together with the assumption that any physically meaningful electron density of the interacting many-electron problem can be represented by a density of noninteracting

14

Urn SCHERZ AND MATTHIAS SCHEFFLER

fermions, leads to the Kohn-Sham equation (Kohn and Sham, 1965; Levy, 1982):

The Hartree potential is given by

and the exchange-correlation potential is defined by

where E x ,In] denotes the exchange and correlation functional. Equation (38) is a single-particle equation and can be solved by “standard techniques” (see Section IV). The electron density is given by the eigensolutions of the KohnSham equation (38):

where n,is the occupancy of the ith orbital. Typically n,is one for states below EF and zero otherwise. If defect levels coincide with the Fermi energy, fractional occupancy numbers of the highest occupied states are also possible. Since both potentials in Eqs. (39) and (40) are functionals of the electron density, the Kohn-Sham equation, together with Eq. (39)-(41), has to be solved self-consistently. The total energy is

This expression is in principle exact. However, in practice one approximation is necessary: Although E,,[n] is a uniuersal functional, i-e., there is only one functional that describes all systems, its general form is not known. In fact, it is not clear whether a simple, closed mathematical expression exists for E,,[n]. Only for the interacting many-electron system of constant electron

1. DENSITY-FUNCTIONAL THEQRY OF SP-BONDED DEFECTS

15

densities has the exchange-correlation energy per particle, <:A(n), been calculated by Ceperley and Alder (1980) using the quantum Monte Carlo method. The corresponding functional

E::*[n]

=

[

n(r)cf;,D*(n(r))dz

(43)

is called the local-density approximation of the exchange-correlation functional. It is exact for many-electron systems of constant density, but for inhomogeneous systems (where Vn(r) # 0) it is of course an approximation. Ex, should describe all quantum-mechanical many-body effects: It should correct the self-interaction of the particle with itself, which is contained in the Hartree potential (see Eqs. (39) and (42)), it should take care of the Pauli principle, and it should describe the corrections that arise because the kinetic energy of noninteracting particles (the first term in Eq. (42)) neglects the Coulomb-interaction-induced correlation of the particle motion. The exchange and correlation functional Ex,[n] may be written in the form

where n&

with

r’) is the density of the exchange-correlation hole

s

nxc(r,r’)dz’ =

-1

and where g(r, r’) = g(r’,r) denotes the density-density pair correlation function. It can be shown that only the part of nxcdepending on Ir-r’l and r contributes to E,,[n]. From these properties it follows that when g(r,r’) is replaced by gLDA,part of the errors introduced by this approximation cancel when evaluating Ex, (Gunnarsson and Lundquist, 1976; Fahy et al., 1990). Almost all density-functional theory calculations performed so far have used the local-density approximation (Eq. (43)) or an approximation closely related to it. Experience has shown that this approach gives reliable totalenergy surfaces, and thus structural, elastic, and vibrational properties are generally described remarkably well. For very inhomogeneous systems, as for example free atoms, the error due to the LDA can be quite significant (i.e., several electron volts). Consequently, calculated cohesive energies (i.e., the

16

Urn SCHERZ AND MATTHIAS SCHEFFLER

difference of the total energy per atom of the crystal and of the free atom) can be wrong by about 1 eV (see, for example, Farid and Needs, 1992). It is generally believed that the error for energy diflerences of different geometries in solid-state systems (perfect crystals, surfaces and defects) is much lower. Experience supports this optimistic hope. The most severe problems of DFTLDA calculations for solids reported so far concern magnetic systems. To be precise, this refers to the LSDA (local spin-density approximation). The calculations give a nonmagnetic fcc ground state of iron instead of the ferromagnetic bcc crystal (see Leung et al., 1991, and references therein). Furthermore, the calculated T + 0 ground states of metal oxides (e.g., the high- T, superconductors) are nonmagnetic, whereas experiments show that they are ferromagnetic. We believe that these problems sound worse than they really are. It is important to note that the variational property of DFT holds for all ground states of different symmetry-group representations (including spin). However, the LDA may introduce different errors for each of them. Therefore it is to be expected that in systems with nearly degenerate ground states the ordering of these ground states can be wrong. To give an example, the calculated energy difference between the nonmagnetic fcc-Fe and the ferromagnetic bcc-Fe phase is GO.1 eV per atom. Comparing this theoretical result with experimental data, we have to conclude that the LSDA inaccuracy is of the order of 0.1 eV. The iron example thus shows that a small quantitative error can produce an important qualitative change of the physical properties. This should be taken as a warning to be cautious in interpreting DFT-LDA results for cases where nearly degenerate ground states occur. With respect to defects in III/V compounds, the most severe difficulty of the DFT-LDA approach concerns electronic properties, in particular the calculated band gaps of semiconductors. These band gaps of the DFT-LDA single-particle spectrum are usually much smaller than the experimental (optical) band gaps. In fact, the band topology (i.e., the gaps at r, L, and X)is also often wrong. The reason is that for the correct functional 6E,,[n]/Gn will have a discontinuity when the number of electrons is changed (Perdew and Levy, 1983; Sham and Schliiter, 1983), and this discontinuity is not described properly by the LDA functional. To calculate the band gap, the ground-state total energies for the N,, the N , - 1 and the N, + 1 electron systems are needed. Although for perfect crystals the electron densities for the N,, N,- 1, and N , + 1 systems are practically identical, the true exchange-correlation functional has to be sensitive to the differences. In particular, the quantummechanical many-body effects of the added electron (the N , + 1 state, which contains a conduction-band electron) differ significantly from the corresponding interactions in the N, and N,- 1 states. Obviously, the correct description of these differences by a density functional requires a quite complicated functional form. DFT-LDA apparently is a good method for

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDED DEFECTS

17

systems with a given number of electrons, but it is too rough to describe the differences that occur when the number of electrons is changed and significantly different orbitals get populated. State-of-the-art calculations of the band gap and related quantities therefore do not use the density-functional approach but calculate the selfenergy X(r, r', o)to first order in the screened Coulomb interaction (Hedin, 1965). In the actual calculations the Green function and the inverse dielectric function are evaluated from single-particle energies and wave-functions of DFT-LDA calculations (see Godby et al., 1988, and Hybertsen and Louie, 1986). Thus, it is assumed that the quasiparticle and DFT-LDA wave function are very similar. It is interesting to note that although the band gaps of DFT-LDA calculations are typically much too small, the hydrostatic deformation potentials (i.e., the derivative of the r, L, and X band gaps with pressure) are in close agreement with measured values; see, for example, Fiorentini (1992). Because defect levels are largely affected by band edges, in particular if these have a high density of states, a wrong band gap and gap topology can induce significant problems for defect calculations. In Section VIII we will come back to this point. Deep defects in semiconductors may exist in different charge states. A precondition for this is that at least one defect level is in the band gap. Let us therefore define what we call a defect level. By this we mean the energy to thermally remove an electron from (or to add one to) a localized orbital. The donor level is E(

+/O) = ,UO(D'O)) - p0(D'+')),

(47)

which is the difference in the Gibbs free energy of a crystal containing one neutral defect D(') and a crystal containing one positive charged defect D(+l). As can be seen from Eq. (27), &(+lo) follows from the differences of the ground-state total energy E;'({R;}), of the vibrational part of the Helmholtz free energy, and of the volume work. A corresponding definition holds for the acceptor level. If we neglect the vibrational and volume terms, we may use the Slater-Janak transition-state theorem (Slater, 1974; Janak, 1978). This gives

where EFc(+) is the (positive) Franck-Condon shift, which is due to lattice relaxation as a consequence of the change of the charge of the defect. Here E ( N ,-9 is the highest occupied single-particle eigenvalue of a self-consistent DFT calculation for a system with N , - i electrons, calculated at the equilibrium geometry of the N,-electron system. Because of electron-electron interactions this eigenvalue differs (for localized orbitals) from that obtained

18

U w SCHERZAND MAITHIAS SCHEFFLER

from calculations with N , electrons. The difference,

is positive, and for deep defects U is usually of the order of 0.3 eV. U is called the on-site Hubbard correlation energy. If the same defect orbital can also accept an electron, we get

The transition-state eigenvalue @VC ++) is calculated at the equilibrium geometry of the N,-electron system. Often the values of the Franck-Condon shifts EFC(+) (Eq. (48))and of EFc(-) (Eq. (50))for different charge states are about the same, but this is not valid in general. For deep defects the FranckCondon shift, which is a positive number, can be significant. As a consequence the level difference

can even become negative for deep defects. This is what is called a negative U system. As a result of Ueff< 0, the acceptor level is below the donor level, which means that the N,-electron system is not stable. Then, with increasing Fermi energy the system will go from the N , - 1 state directly to the N , + 1 state, thus capturing two electrons simultaneously. While the single-particle eigenvalues as well as the transition-state eigenvalues are subject to similar DFT-LDA problems as the band gap, we note that the calculated FranckCondon shift, because this is an elastic energy, agrees with experimental results. Equations (48) and (50) give the levels with respect to the energy zero of the calculation. However, usually donor levels are referred to the bottom of the conduction band and acceptor levels are referred to the top of the valence = zCB-E( +/0) and band. This requires us to redefine the levels by Eacceplor - E(O/-) - cyB. For deep-level defects, the distinction between donors and acceptors is only of limited value. We will therefore not follow this description, but we will refer all levels to the top of the valence band which we take as our energy zero.

5. VIBRATIONS Within the adiabatic approximation for the electrons, the dynamics of the nuclei is described by the Hamiltonian of Eq. (lo), where E:' is the total energy of the ground state of the electronic Hamiltonian of Eq. (3).

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDED DEFECTS

19

In order to study the vibrational properties of the Hamiltonian of Eq. (lo), it is usually sufficient to apply the quasi-harmonic approximation.' The vibrational frequencies m iare then determined by det(D - Mu?) = 0,

(52)

where M is the matrix of atomic masses and D is the dynamical matrix

Here {RY} are atomic positions at or close to the stable (or metastable) geometry. From EG'({RY}) and D({RY}) we obtain the Gibbs free energy (Eq.(19)), and the stable or metastable geometry at given pressure and temperature then follows from Eq. (20). The dynamical-matrix elements may be obtained from many selfconsistent total energy calculations performed in the neighborhood of the equilibrium geometry. Similarly, an ab-initio molecular dynamics calculation, using the approach of Car and Parrinello (1985),could be performed (Blochl et al., 1990). These two "direct approaches" require an enormous amount of computer power. Instead, Schemer and Scherz (1986) and Biernacki et al. (1989) (see also Schemer and Dabrowski, 1988; Biernacki and Schemer, 1989) adopted a different approach using a semi-empirical valence-force model, the parameters of which (i.e., approximate equilibrium geometry and force constants) are calculated from first principles. Thus, the main purpose of the valence-forcemodel was to obtain numerically accurate second derivatives of the total energy, which are needed for the dynamical matrix (Eq. (53)). An even more efficient and more accurate approach, which allows us to evaluate the dynamical matrix directly without the intermediate step of a valence-force model, would be the so-called perturbed density-functional theory of Baroni et al. (1987) and Gonze and Vigneron (1989) (see also Fleszar and Gonze, 1990). In each of the previously mentioned examples it is necessary to calculate total energies as well as total-energy derivatives. If an appropriate basis set is used, the in principle exact Hellmann-Feynman theorem can be applied also in practice (Schemer et al., 1982, 1985) in order to calculate forces on the atoms. Either the forces then determine the motion of the particles (in a molecular dynamics study) (Car and Parrinello, 1985; Blochl et al., 1990), or the derivatives of the forces give the components of the dynamical matrix (Bachelet et al., 1986; Schemer and Scherz, 1986; Schemer and Dabrowski, 1988; Biernacki et al., 1989). These different methods have been applied to calculate the vibrational entropy of the vacancy in silicon (see Eqs. (16) and (17)). All studies give a

20

U r n SCHERZ AND MAITHIASSCHEFFLER

result of about 3-4k,. For other defects no calculations exist, but it is generally believed that comparable values (between 1 and 5kB) would be obtained.

IV. Metbods and Techniques 6. INTRODUCTION

The evaluation of Eqs. (38)-(42) requires complicated methods and techniques. This is in particular so for low-symmetry systems, as for example defects in crystals, where Bloch’s theorem is not valid. Such methods and techniques have been developed only during the last years (see Bernholc et al., 1978,1980 Baraff and Schliiter, 1978,1979,1984; Scheffler, 1982; Scheffler et al., 1982; Gunnarsson et al., 1983; Car et al., 1984, 1985; Bar-Yam and Joannopoulos, 1984; Beeler et al., 1985a, 1985b, 1990; Bachelet et al., 1986; Scheffler and Dabrowski, 1988; Scheffler, 1989; Overhof et al., 1991). To date the applicability of these methods and techniques is still limited to special systems, and new ideas and improvements of the theory are still important. Several controllable approximations are necessary in an actual firstprinciples calculation. If carefully applied, they will not significantly affect the results for n(r) and E$({R:}), but they cause certain numerical inaccuracies. The most accurate method developed so far is the self-consistent pseudopotential Green-function method (Bernholc et al., 1978; Baraff and Schliiter, 1978,1979, 1984; Schemer, 1982; Scheffler et al., 1982 and 1985) which, if used together with first-principles, norm-conserving pseudopotentials (Hamann et al., 1979; Kerker, 1980; Bachelet et al., 1982;Gonze et al., 1990, 1991), gives a reliable description of ground-state properties of sp-bonded systems. In the LMTO (linear muffin-tin orbital) Green-function method (Gunnorsson et al., 1983; Beeler et al., 1985a, 1985b, 1990; Overhof et al., 1991), the approximation of spherical potentials is introduced. Because of the variational principle in DFT, this is usually not a severe approximation, but it does not allow the evaluation of defect-induced lattice distortions. Cluster methods suffer from more severe (sometimes uncontrollable) problems: They impose artificial boundary conditions to the wave-functions, and they localize the wave-functions and charge densities to the size of the cluster, which can cause a wrong description of covalent binding. The super-cell approach also suffers from these problems of cluster approximations, but the imposed artificial periodicity usually represents a far less severe approximation. Furthermore, with modern techniques it is now possible to take a cell size of more than 50 atoms. This enables us a systematic test of cell-size-induced inaccuracies. Because of the high complexity of first-principles methods, there is always a

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDEDDmCD

21

risk that some aspects may be overlooked in the calculations. It is therefore good to know if two independent groups, hopefully using different techniques, arrived at the same theoretical results. In Section IV.7, we give a short sketch of the pseudopotential concept. The alternative, i.e., the LMTO theory, is not discussed, because it has not been developed yet to the same level of applicability to treat total-energy surfaces and lattice distortions. We like to mention, however, that for defects in silicon the LMTO method has been applied to interesting problems of defect science (Beeler et al., 1985a,b, 1990), and recently even hyperfine fields have been calculated by Overhof et al. (1991). For the future we expect further exciting developments. In Section IV.8, we outline the supercell method, which represents a conceptually simple theoretical approach to calculate defect properties but which has its clear limitations. These are that the low defect concentration of the true crystal (typically < 1:lo5)is modeled by a concentration of > 1:lo2. This induces quite strong defect-defect interactions, which may complicate the physics that the investigation aims to understand. The best, but more sophisticated, approach is the Green-function method. It describes the concentration limit where only one defect is present in the macroscopic crystal. Thus, no artificial defect-defect interactions are created. Without going into details, the basic ideas of the Green-function method are described in Section IV.9. 7. PSEUDOPOTENTIALS

Because of the localized nature of the atomic core electrons, these states do not contribute significantly to the chemical binding. It is therefore possible and convenient to introduce the frozen-core approximation in which the core electrons are treated together with the nucleus as a rigid spherically symmetric charge distribution. This implies the replacement of the potentials of the nuclei (Eq. (9)), which enter Eqs. (8) and (38), by potentials of the frozencore ions, and of Ex,[n] and ox, [n] by Ex, +n:E!3 and uxc[aal+naE'3. Here::;n is the core electron density of an atomic calculation, and densityfunctional theory is then applied tothe valence electrons, nvsl, only. The pseudopotential theory takes an additional step (see, for example, Cohen, 1985, and references therein) in that it also removes the oscillations of the valence-electron wave functions in the core region, which are caused by the orthogonality to the core states. This is achieved by modifying

[$.,

22

U w S c m z AND MAT~HIAS SCHEFFLER

in the region close to the nucleus in an appropriate way that does not affect the valence-electron wave functions in the chemically important regions but that makes them smooth in the core region. This approach therefore allows an accurate representation of the pseudopotentials in terms of quite simple and numerically advantageous basis sets, such as plane waves or Gaussians. An important step in the development of pseudopotential theory was to realize the condition of norm-conservation (Hamann et al., 1979; Kerker, 1980). It implies that ionic pseudopotentials, which are derived from freeatom calculations, give a correct description of the scattering properties not only at the energy of the atomic eigenstates, but also in a rather wide energy range around it. This is an important condition for using free-atom derived pseudopotentials (often called ab-initio pseudopotentials) in different chemical environments. One disadvantage implied by the norm-conservation is that these pseudopotentials become nonlocal operators: They act differently on states with different angular momentum quantum numbers. As a result, such calculations consume much more computer time than those with local pseudopotentials. This is, however, not a severe problem, in particular as nowadays separable ab-initio pseudopotentials are constructed (Kleinman and Bylander, 1982; Gonze et al., 1990,1991) that remove this disadvantage. The ab-initio pseudopotential concept has been very successful in computational condensed-matter physics, and many new developments still appear (Blochl, 1990; Vanderbilt, 1990) in order to achieve even smoother potentials, which make calculations more efficient.

8. SUPERCELL METHODS

Probably the most simple and still quite accurate ab-initio method to calculate defect properties in a parameter-free way is given by the supercell approach. This approach uses “standard bandstructure methods of a perfect crystal, where Bloch’s theorem holds. These may, for example, be the pseudopotential plane wave, or the LMTO method. The supercell is a large unit cell (typically between 16 and 128 atoms) that may represent the perfect crystal or contains one defect. Obviously, one thus describes a lattice of defects, maybe better termed an alloy than a dilute defect system. If the cell is small (say, 16 atoms) the defect-defect interaction can be quite significant. For example, a defect level in the crystal band gap can then become a defect band with a dispersion of more than 1 eV. This defect-defect interaction is an artifact of the method. Often it may not be important for defect geometries and local lattice distortions, but sometimes it may. Therefore, a careful analysis of results is most important, and different cell sizes ought to be investigated.

1. DENSITY-FUNCTIONAL THEORYOF SP-BONDED DEFECTS

23

9. GREEN-FUNCTION METHODS The best way to handle the difference with respect to the translational symmetry between the perfect crystal and a crystal containing a defect is the Green-function technique. In density-functional theory the Kohn-Sham operator (see Eq. (38)) can be written as a sum of the Kohn-Sham operator of the perfect crystal, ho, and a potential A V induced by the defect h = ho + A K The Green operators Go = (e-h0)-' and G = (~--h)-' are then related by the Dyson equation

G = (1 -G0AV)-'Go

(55)

Surveys of the defect Green-function method are given by Pantelides (1978), Scheffler (1982), and Schluter (1987). There are two main reasons why this method has been used so extensively. First, the Green function of the perfect crystal, Go(&),can be calculated taking advantage of Bloch's theorem and using standard band structure methods. Second, the Dyson equation (Eq.(55)), which gives the properties of the defect, can be calculated from small matrices if atomic-like orbitals are used as basis functions, which are localized at the defect and at a number of neighbors of the defect site.

V. Electronic Structures and Concentrations of Native Defects Native or intrinsic defects are imperfections of the perfect crystal that do not involve impurity atoms and that are in fact unavoidable in principle. However, their concentration can be controlled by the temperature, pressure and by the environment (partial pressure) of the crystal. The growth of crystals under conditions of controlled non-stoichiometry leads to different native defect concentrations. In this section we describe the electronic properties, as well as the formation energies, of vacancies, antisites, and self-interstitials. We restrict this discussion to tetrahedral geometries. Consequently, wave functions and point group. In the case of energy levels are labeled according to the vacancies, the relaxation of the nearest neighbors with respect to their perfect crystal positions may change the symmetry of the defect. A possible change of this relaxation due to the change of the charge of the defect has been discussed in Section 111.4. In the case of Ga and As interstitials in GaAs, we place the defects at the tetrahedral interstitial sites. These results are meant as a guideline. We like to emphasize, however, that we do not expect that these geometries correspond to the true stable positions of self-interstitials. In fact,

U w SCHERZAND MATTHIAS SCHEFFLER

24

similarly to self-interstitials in silicon, we expect that a split-bonded geometry is likely to have a more favorable energy; the energy difference to the herediscussed & site may be as large as 1.5 to 2eV. 10. ELECTRONIC STRUCTURE OF INTRINSICDEFECTS

We start with a discussion of the cation and anion vacancy, These are important defects per se, but an understanding of their electronic structure is also important for substitutional impurities and antisites. A substitutional defect is formed by filling a vacancy with a defect atom. Qualitatively, the electronic structure of substitutional centers then results from the interaction of the atomic orbitals of the defect atom with the localized states of the vacancy. If an atom is removed from its lattice site, there are four dangling orbitals (41,42,43and (p4) of the nearest neighbors pointing towards the vacant site. These four orbitals will form a fully symmetric (4, (6, 43 44) linear combination, which belongs to the a, representation of the & point group, and threefold degenerate linear combinations (4, - c $ ~- 43 $J, (dl 4, - 4 ~ (p4), ~ and (- 4, 4, - 43+44) having t 2 symmetry. This t , level has higher energy than the a, level because the signs in the corresponding wave functions alternating give it a higher kinetic energy. Figures 1 and 2 show the single-particle energies and squared wave functions of the Ga and

+

+ + + +

+

I

14.5

I

FIG. 1. Energy level diagram and contour plots of the two important states of the neutral Cia vacancy in GaAs. Displayed are the electron densities of the t 2 bound state (top) and the resonance (bottom) along the (110)crystal plane. Units are bohr-3.

(I,

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDEDDEFECTS

It* I

25

10.0

8.0

I

la, FIG. 2. Same as Fig. 1 but for the As vacancy in GaAs.

As vacancies in GaAs. In the case of the neutral cation vacancy there are three electrons missing, so that the t , level is occupied by three electrons (see Fig. 1). The corresponding energy level is close to the top of the valence band, and the calculations show that the Ga vacancy should be observable in the charge states Vkt), V&), Vd2,-), and Vk:-), depending on the position of the Fermi level (Bachelet et al., 1981; Baraff and Schluter, 1985b; Laasonen et al., 1992) and therefore acts as a triple acceptor. The important orbitals of the As vacancy are shown in Fig. 2. For the neutral center five valence electrons have been removed together with the As core. As a consequence there is only one electron occupying the t , level, which is close to the bottom of the conduction band. The calculation shows that the tetrahedral As vacancy acts as a donor and is in the single positive charge state for all positions of the Fermi level. Recently Laasonen et al. (1992) found large lattice relaxations for the negatively charged defects V';) and V'i-). Their calculations gave a 17% inward symmetry-conserving (breathing) relaxation, and a similar symmetry-breakingdistortion for both charge states. This is in contrast to the rather small lattice relaxations calculated for the Ga vacancy and for V,:) and Vit) (Scheffler and Scherz, 1986; Laasonen et al., 1992). The reason for the large Jahn-Teller distortion of Vi;) and VA:-) is that when electrons are added to the neutral As vacancy, they form Ga-Ga bonds, thus reducing the symmetry so that the spatialdegenerate t2 level is split, which leads to a lowering of the total energy. Starting from the energy levels and wave functions of the Ga vacancy (see Fig. 1) and of an As atom, one can qualitatively understand the energy-level

26

U w SCHERZAND MA’ITHIAS SCHEFFLER Go-VACANCY

w

%-ANTISITE

AS-ATOM

T

FIG. 3. Single-particle energies and interaction of a neutral cation vacancy in a III/V compound (left) and a free anion atom (right) that result in an anion-antisite defect (middle).

structure of the As antisite AsGa.Figure 3 shows how the splitting of the energy levels due to the interacting states leads to an a, state in the band gap. This state is occupied with two electrons for the neutral defect, and the As antisite thus is a double donor. The corresponding energy-level structures of the As vacancy and the neutral Ga antisite are shown in Fig. 4. Comparing this with Fig. 3 we see that the Ga,, levels are shifted to higher energies. This is because the energy levels of both the As vacancy and the free Ga atom are higher than the corresponding levels of the Ga vacancy and the free As atom. As a consequence, the Ga antisite has the antibonding a, level in the conduction band, whereas the bonding t , level is in the band gap. According to the calculations of Bara5 and Schluter (1985b), the Ga antisite acts as a double acceptor. With respect to the physics depicted in Fig. 3, the single-particleeigenvalue &(aI)of different antisite-like defects (e.g., PGa,AsGa, and Sb,,) in GaAs &-VACANCY

Go,-ANTISITE

Go-ATOM

FIG. 4. Single-particle energies and interaction of a neutral anion vacancy in a III/V compound (left) and a free cation atom (right) that result in a cation-antisite defect (middle).

1. DENSITY-FUNCTIONAL THEQRY OF SP-BONDED DEFECTS

27

should, if lattice relaxation is neglected, follow the trend of the atomic s-orbital energy (Hjalmarson et al., 1980).Since the donor transition involves a population change in this a, eigenvalue,we expect electronic levels to move with the atomic number of the group V defect atom towards higher energies (i.e., closer to the conduction band). This is indeed the trend found in calculations for unrelaxed tetrahedral antisites, i.e., when all host atoms remain at their perfect-crystal positions (see the E ( +/O) results in parentheses in Table I). When a substitutional defect is created, the neighboring atoms relax from their perfect crystal sites. Caldas et al. (1990) calculated the breathing relaxation of the neutral anion antisites, and their results are shown in Table I. It can be seen that the relaxation increases the anion-anion bond length (except for I n P : P ~ ~which ) , shows a small relaxation inwards; see A Q in Table I). The relaxation corresponds to a decrease of energies of the occupied a, donor levels and an increase of the optical excitation energy E,, which corresponds to the excitation att! + sit:; see Table I. Both effects are the TABLE I CALCULATED FRANCK-CONDON SHIFTSEFc, DONORLEVELSE ( +/O) WITH RFSPECTTO THE TOP OF THE VALmCE BAND,A CHARACTERISTIC OPTICAL EXCITATION ENERGYE,, AND RELAXATION ENERGIESEre,FOR DIFFERENT ANION-ANTISITE DEFECTS IN THE TETRAHEDRAL ATOMICCONFIGURATION INGaAs AND InP“

ErCi (ev)

AQ

(ev)

1.16

0.20

0.10

0.42

0.12

1.71

0.27

0.01

-0.03

0.00

0.01

0.48

0.14

Eo

P GaAs

InP

As

0.05 0.03

Sb

0.04

P

0.10

As

0.09

Sb

0.08

0.71 (0.88) 0.81 (1.05) 0.95 (1.55) 0.95 (0.78) 1.3 (1.2) 1.3 (1.6)

.w 0.97

(4

(1

(0.91) 1.03 (0.31) 1.50 (1.36) 1.32 (1.20) 0.77 (0.72)

“Electronic levels E ( +/O) defined by Eq. (47)are calculated from total-energy differences using two special k points. Ere,denotes the energy gained by the breathing relaxation of the first four atomic neighbors for the neutral defect, and AQ gives the distance each atom moves. Results in parentheses are obtained by keeping the atoms at perfect crystal positions.

28

Urn SCHERZ AND MATTHIAS SCHEFFLER

largest for Sbg:, which also shows an increase of localization due to the relaxation (see the two lower contour plots in Fig. 5). If one of the two a, electrons is removed, the bonds between the defect atom and its neighbors are strengthened because of the antibonding character of the deeplevel wave function (see Fig. 5 ) and because the electrostatic interaction between the negatively charged neighbors (anions) and the positively charged antisite will attract the neighbors closer to the defect atom. The dependence of the relaxation of the four nearest neighbors on the charge state of the defect gives rise to moderate Franck-Condon shifts (EFCin Table I). As expected from this discussion, the shifts are bigger for defects in more ionic InP than for defects in less ionic GaAs. It should be noted that the effect of long-range relaxation has not been considered in these calculations. In contrast to the vacancies and antisites, very little is known about selfinterstitials from the experimental point of view. Though interstitial point defects are certainly created by electron irradiation in similar amounts as vacancies, no isolated interstitials have been identified for far by EPR, DLTS, or other methods. A number of calculations for self-interstitials have been performed at the two positions of tetrahedral point symmetry: T,, where the

FIG. 5. Neutral anion-antisite-like defects in GaAs: Squared single-particlewave function of the filled a, state for the unrelaxed defects P,. [upper left panel labeled P(u)], As,, [upper right panel, As@)], and Sb,. [lower left panel, Sb(u)], and for the relaxed Sb,, [lower right panel, Sqr)]. We show the (1 10) plane. Contour lines are in units of bohrC3;the distance between the contour lines is 0.6 for P,, and 0.3 for A%, and Sboa. (After Caldas et al., 1990.)

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDED DEFECTS

29

defect atom has four anions as nearest neighbors, and T,, where the defect atom has four cations as nearest neighbors. For both these tetrahedral positions we do not expect a strong covalent bond because the neighbor atoms are already bonded most favorably with the rest of the crystal. The valence orbitals of the interstitial atom indeed hybridize only weakly with the crystal states. They give rise to eigenfunctions of symmetry a1 and t 2 , the occupation of which depends on the position of the corresponding energy eigenvalues with respect to the Fermi energy. Results of self-consistent supercell calculations are shown in Fig. 6 for the As interstitial and in Fig. 7 for the Ga interstitial in the tetrahedral coordination. It is very probable that the As interstitials are unstable with respect to Jahn-Teller distortions and that the donor levels are then driven out of the gap when the As interstitial moves from the high-symmetry tetrahedral to a lower-symmetry equilibrium position. Similar distortions may also occur for the Ga interstitials, which may be the reason these defects have not been observed by EPR.

M’

AS-ATOM

’..

-‘P

a,

7 *.‘ t ‘,.

‘-S

FIG. 6. Single-particleenergies of the tetrahedral As-interstitialsin GaAs. Top: at the T.site (i.e., nearest neighbors are As) in the single positive charge state. Bottom: at the T, site (i.e., nearest neighbors are Ga) in the neutral charge state.

30

U w SCHERZAND MATIWAS SCHEFFLER Gar

t, , -----

Gar

t*

GO-ATOM

--.___ -P

Ga-ATOM

------

P

-.-----

-,a

FIG. 7. Single-particleenergies of the tetrahedral Cia-interstitialsin GaAs. Top: at the T, site (i.e.,nearest neighbors are As) in the single positive charge state. Bottom: at the T, site (i.e., nearest neighbors are Ga) in the single positive charge state.

1 1. NATIVE-DEFECT REACTIONS

In this section we consider all tetrahedral point defects of a GaAs crystal, which we denote by V,,, V,,, GaAs,AsGa, GaTa,GaTC,As,., and AsTc. In thermodynamic equilibrium the number of these defects is determined by Eq. (29). The formation energies of the defects (see the numerator of the exponential in Eq. (29)),which depend on the chemical potentials, and which directly determine the concentration of the defects, are shown in Fig. 8 for the ,V,

in GaAs

1

0

5

1 .o

Fermi Energy (ev)

1.5

1. DENSITY-FUNCTIONAL THE~RY OF SP-BONDED DEFECTS ,V,

in GaAs I

I

0

31

.5

1 .o

1.5

Ferrni Energy (eV)

AsGo in GaAs I

0

.5 1 .o Fermi Energy (eV)

1.5

GaAs in GaAs I

0

.5

1 .o

1.5

Ferrni Energy (eV)

FIG. 8. Formation energies of the two vacancies (a, b) and the two antisites(c,d) in GaAs as a function of the Fermi energy E,; see the numerator of Eq. (29). Shown are the two limiting cases for a crystal in an As-rich environment and in a Ga-rich environment (see text).

32

Urn SCHERZ AND MATTHIAS SCHEFFLER

four substitutional native defects and in Fig. 9 for the interstitials. All these calculations (Heinemann and Scheffler, 1991) were performed using the supercell method with a 54-atom cell, a plane wave basis with E,,, = 8 Rydberg, and two special k points for the k-integrations. Lattice relaxations have been neglected. They would lower the energies by 0.10.5 eV, if we restrict relaxations to the tetrahedral symmetry. The figures show how strongly the formation energy changes with the atomic and electron chemical potentials. In order to describe the two extreme cases for the chemical environment, let us consider a GaAs crystal in thermodynamic equilibrium with an AsZgas, which is the extreme As-rich condition (see Scheffler and Dabrowski, 1988). If the chemical potential of an isolated As atom is taken to be zero, the chemical potential of the As atom in an As, gas then is half the As, molecular binding energy. We therefore have p(As) = - 2.0 eV. The chemical potential of Ga then is p(Ga) = - 4.8 eV; this follows from the energy needed to remove one unit cell of GaAs (the cohesive energy), which equals 6.8eV and a gain of 2.0eV per As atom from the formation of As,. These energies are approximate values of the corresponding Gibbs free energies which also include the entropy of the molecular gas and GaAs unit cells. If, on the other hand, a GaAs crystal has droplets of Ga metal at the surface, the Ga chemical potential is given by the Ga-metal cohesive energy, which gives p(Ga) = - 2.8 eV. The As chemical potential is then obtained from the energy needed to remove one GaAs unit cell, 6.8 eV, reduced by the Ga-metal cohesive energy to give AAs) = -4.0 eV. The cohesive energies are experimental values after Weast (1986). From this discussion it follows that, depending on the partial pressure and chemical composition of the environment, the chemical potentials of the Ga and As atoms may be set within the ranges -4.8 eV < p(Ga) < -2.8 eV, - 2.0 eV

2 p(As) 2

-4.0

eV,

where the numbers on the left refer to the As-rich and the numbers on the right to the Ga-rich extreme conditions, as discussed. These two extreme cases for the chemical potentials, together with the calculated standard term p o (see Eq. (27), give us two limiting cases for the defect formation energy according to the numerator of the exponential function of Eq. (29). The results for the eight intrinsic point defects in GaAs in tetrahedral coordination are shown in Figs. 8 and 9. Under the assumption that the defect concentration is not too large so that the defects can be treated as independent, these formation energies directly give the defect concentration (see Eq. (29)). It can be seen that the formation energies of the antisites are

1. DENSITY-FUNCTIONAL THEORYOF SP-BONDEDDEFECTS As;

0

,

Asi 10

in GaAs, As neighbors

.5 1 .o Fermi Energy (eV)

1.5

in GaAs, Ga neighbors I

h

2 9

v

x $ 8 C W

c 7

.+

p

LL

0

.5

1 .o

1.5

Ferrni Energy (eV)

Gai

in GaAs I

I

0

.5 1 .o Fermi Energy (eV)

1.5

FIG.9. Same as Fig. 8, but for the two As interstitials(a, b) and the two Ga interstitials(c) in GaAs in both tetrahedral sites T.and T, in GaAs.

33

34

Urn SCHERZ AND MATTHIAS SCHEFFLER

more influenced by the environment (4 eV) than in the case of the vacancies or self-interstitials (2 eV). The charge states of the defects were determined from the position of the corresponding transition states. For example, the transition state for the Ga vacancy was calculated to be N O / - ) = 0.29 eV above the valence band. Therefore, the Ga vacancy is neutral when the Fermi energy is below that value and negatively charged when the Fermi energy is raised above that value. Considering only the substitutional point defects of Fig. 8, we expect from these results that under As-rich conditions in p-type material, the As antisite is the dominating defect, whereas in n-type GaAs the formation energy of the Ga vacancy is lower than for the As antisite. The concentrations of the As vacancy and Ga antisite are much smaller in As-rich environment and at thermal equilibrium. Under Ga-rich conditions the results of Fig. 8 imply that the Ga antisites dominate over the As vacancies for all positions of the Fermi level, and the formation energies differ most for n-type material. It is interesting that for n-type material grown under Ga-rich conditions, there are more Ga vacancies than As vacancies. The reason for this is that in n-type material the Ga vacancy exists in the triple negative charge state, whereas the As vacancy is in the single positive charge state. Under Ga-rich conditions the As antisites are largely suppressed. Concerning the interstitials (see Fig. 9), we find that their formation energies in GaAs for the two different tetrahedral interstitial sites are very similar because in both cases there are no covalent bonds formed and because the ionicity of GaAs is not large. The concentration of the As interstitials should be very small under all conditions. Although Fig. 9 shows only results for tetrahedral centers, we tend to conclude that isolated As interstitials will be also unfavorable in other geometries. We do not, however, rule out an important role for them in defect complexes. Ga interstitials may be present in GaAs in some relevant concentration, at least in p-type material. In fact, we find comparable concentrations of Ga interstitials and As vacancies under Ga-rich conditions for all positions of the Fermi level. The point defects may also form bound defect pairs (see Baraff and Schliiter, 1986) and complexes of defects. Their concentrations can be calculated in the same way as for the point defects using Eq. (29). Obviously, the relative concentration of the bound pair and of the isolated defects is independent of the environment. It is given by the law ofmass action, Eq. (32). Native defects are related to a deviation from stoichiometry, and it is important to understand which of them dominates for given chemical potentials of the cations and anions outside the crystal. We describe the deviation from stoichiometry of a crystal Gal -,As, by

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDED DEFECTS

35

It then follows NAs

X = NGa

+ NAs

(58)

'

where NGa and NA, are the numbers of cations and anions, respectively. For

x =& we have the perfect crystal stoichiometry. In the case of only small

concentrations of the defects, and assuming that the crystal contains no impurities on lattice sites (that means that we disregard the doping here), the deviation from stoichiometry is approximately given by the sum over all possible types of native independent defects in their different charges states D(') (see Eq. (29)):

where we have used Eqs. (28) and (29), and we have MD = --$ for V,, AsTc, and AS,, M, = 3 for VA,, GaTc,and Ga,, MD = - 1 for AsGa, and MD = 1 for GaAs.According to Eq. (29), the deviation from stoichiometry depends on the chemical potentials of the reservoirs of the atoms and electrons. In practical cases a deviation from stoichiometry can be due to impurities and all different types of native defects, i.e., point defects, defect pairs, defect complexes, and other types of disorder such as precipitates that also depend on the history of the growing and annealing process. In order to find the dominating native point defects in thermodynamic equilibrium, which give the main contribution to Eq. (59), one has to consider the nine basic reactions between the native point defects (Kroger, 1964): V$i+ Vz)+GaAs+(i +j)e- e 0 (Schottky)

+

+ j)e - e 0 Ga$)+Asy)-GaAs +(i + j)e- s o V$! + Gay)+ (i + j)e - ==0 Gag: + 2V$J +GaAs +(i + 2j)e e 0 AsgL Gag! + ( i

-

Gag:

+ 2Asv)-GaAs +(i + 2j)e- s 0

(antisite-antisite) (interstitial-interstitial) (Frenkel)

(60)

(antisite-vacancy) (antisite-interstitial).

They have to be completed by interchanging Ga and As, and T can be one of the two interstitial sites T, or T,. The energies of all these reactions do not depend on the environment. They can be obtained from Figs. 8 and 9, taking for example the results for the As-rich case. We will only show a figure for one case, namely for the simultaneous creation of the two antisites, which is the

U r n SCHERZ

36

AND

MATTHIAS SCHEFFLER

reverse of the second equation of Eq. (60).The reaction energy is given by

+

+ +j ) E F ,

(61)

A p = po(As&) p0(Ga!&) (i

and it is shown in Fig. 10. We see that the simultaneous creation of an As antisite and a Ga antisite is more likely in n-type GaAs than in crystals having the Fermi energy in the middle of the energy gap. Furthermore, we can use Fig. 10 in the following way: If, for example, the concentration of the As antisite and the reaction energy of Eq. (61)are known, then the law of mass action, Eq. (37), corresponding to the second reaction of Eq. (60) can be used to determine the concentration of the Ga antisite. All other reactions can be obtained from linear combinations of the reactions of Eq. (60), and the reaction energies are determined similarly to Eq. (61) with the help of Figs. 8 and 9. We close this section by emphasizing that a direct comparison of these theoretical results with experimental observations may often be difficult. This is largely because real crystals also contain defect complexes, precipitates, and dislocations. Furthermore, and in particular, we remind the reader that our discussion of defect concentrations relied on the assumption that the defects considered are present in low concentrations. Thus, defect-defect interactions should be negligible, and the Fermi level should be treatable as given by a reservoir determined by background doping and independent of the charge state and concentration of the considered defects. This is an idealization of growing and annealing processes in which the incorporation of donors and acceptors as well as the defect mobilities must also be taken

'

Distant Antisite pair in GaAs 7.0

1

0

.2

.4

.6

.8

1.0

'

1.2

1.4

Fermi Energy (eV)

FIG. 10. Reaction energy of the simultaneous creation of an As antisite and a Ga antisite.

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDED DEFECTS

37

into account; see Wenzl et al. (1992). A number of models related to growth conditions, where the preceding assumptions are likely not to be valid, have been proposed to estimate the order of native defect concentrations from experimental data (see, for example, Sajovec et al., 1990, and Wenzl et al., 1990a, 1990b, 1991).

VI. An Intrinsic Metastability of Antisite and Antisite-like Defects In the previous section we simply assumed that a defect is stable in one and only one local geometry. This assumption is appropriate for many situations. However, we had also seen that the nature of defects can be changed without changing the crystal stoichiometry (e.g., a Ga vacancy plus an As interstitial can be transformed into an As antisite). The controlling factor of the reactions noted in Eq. (60) and of their combinations was the “electron reservoir,” i.e., the Fermi energy. In this section we discuss an additional mechanism that changes the nature of a defect, where the changes are, however, due to a local atomic rearrangement. This is what is usually called a defect metastability. Optically and thermally inducible structural transitions of defects have been known for several years (see, for example, van Kooten et al., 1984; Chantre and Bois, 1985; Watkins, 1989; Caldas et al., 1990). Because all upto-date unambiguously identified metastable defects are complexes, where the metastability is understood in terms of a rearrangement of one of the constituents, it was interesting when in 1988 theoretical studies predicted (Chadi and Chang, 1988a; Dabrowski and Schemer, 1988a, 1989a) a metastable behavior also for simple substitutional defects. Because no direct experimental proof of this predicted effect exists so far, it is understandable that this new type of metastability is not generally accepted. We believe, however, that the explanation of the general mechanism is well developed and that it is in fact quite plausible. We also note that significant indirect experimental evidence for this new effect exists. In this part we describe the theoretically predicted properties of this new type of defect metastability. We show that it should play some role for antisite and antisite-like centers in practically all III/V compounds, and we explain the effect as a consequence of the capability of group V atoms to form sp3 hybrids (tetrahedral geometry) as well as more or less pure p bonds like those in ASH,. In Part VII we then concentrate on the As antisite in GaAs and relate the theoretical predictions to experimental data. An anion antisite (or antisite-like defect) in a III/V compound is created when a group-V atom substitutes a group411 atom of the host. The

UDO SCHERZ AND MAITHIASSCHEFFLER

38

properties of these tetrahedrally symmetric defects were discussed in Section V, and it was explained that these centers give a deep bound state of the A, representation, and above it a state of the T2representation (see Figs. 3 and 5) that is usually within the conduction band. Caldas et a f . (1990) studied several anion antisite-like defects (P, As, and Sb) in GaAs and in InP. It was found that all these defects possess in the neutral charge state a metastable minimum in the total-energy surface, with the defect atom displaced along the [111] axis, roughly halfway between the substitutional site and the closest tetrahedral interstitial site (T,).Figure 11 shows how the geometry and the valence electron density change upon moving the defect atom from the substitutional tetrahedral position to the displaced positions, which may be described as a vacancy-interstitial pair e l 1 1 Direction ~

If-

( 1 10) Plane

STABLE

BARRIER

METASTABLE

FIG. 11. Metastability of the As-antisite defect. Top: atomic structure. Bottom: the electron density in the (1 10)plane. Large circles represent As nuclei. Small circles represent Ga nuclei. The left-hand side shows the fundamental state, where the arsenic defect atom is bound to four nearest neighbors [only two are in the displayed (1 10)plane]. The middle panel shows the barrier region. The picture on the right-hand side corresponds to the metastable situation (the V,,As, defect pair). Here the arsenic defect is bound to three arsenic neighbors [only one of them is in the (1 10)plane]. The solid "dangling b o n d in the top right-hand picture indicates the vacancy state, which is responsible for the barrier between the metastable and the fundamental configuration. (After Dabrowski and Scheftler, 1988b.)

1. DENSITY-FUNCTIONAL THEORY OF SP-BONDED DEFECTS

39

(labeled I/-Z pair hereafter). We like to emphasize that the interstitial component of the pair should not be identified with the tetrahedral interstitial that was discussed in Section V: The tetrahedral interstitial position corresponds to nearly twice the displacement as that found in the calculations, and it would have a significantly higher total energy as well as a different electronic structure. In fact, the qualitative origin of the metastability is the capability of the defect atom to form a quadruple as well as a triple bond. The latter is not the case for a tetrahedral interstitial. In Fig. 12 we show the corresponding electronic structure and the totalenergy curves. The displacement of the antisite atom lowers the local symmetry to C3u, and the single-particle t , state splits: tZ(ZJ-+2a, (C3,,)+ e(C,,). The single-particle ~ i ( C 3 "states ) of the displaced antisite with energies above the valence band are labeled la, and 2 4 . With respect to the many-electron wave functions, we note that the lowest-energy mean-field configurations of the A, representation are then (la:2a4, (lai2a9, and (lay2a:), which may interact to yield three non-paramagnetic states (S = 0) that we label as ' A , , 'A;, and 'A:*. In Fig. 12a we depict the dependence of the total energies on the displacement Q of the defect atom for these three states. We also show in a schematic form the typical behavior of the singleparticle eigenvalues (Fig. 12c). For small displacements Q, the energy of the ground state exhibits a parabolic behavior around the minimum at the

DISPLACEMENT

DISPLACEMENT (A)

I OM

DISPLACEMENT

DISPIACEMENT (A)

FIG. 12. Single-particle energies (bottom) and total energies for the ground and excited electronic configurations (top) as a function of the displacement of the defect atom along the [11 11 axis. Left: schematicdescription.Right: results of calculations for InP:P:. (After Caldas et al., 1990.)

40

UDOSCHERZAND MAITHIASSCHEFFLER

substitutional site and is dominated by the configuration (lai2a3. With larger displacement, the eigenvalue difference ~ ( 2 a ,-E( ) la,) decreases, and the interaction between these two states as well as with other vacancy-like states increases. This results in a localization of the occupied a, state into a dangling bond at the crystal atom left behind, pointing into the direction of the evolving vacancy. In contrast, the wavefunction of the unoccupied a, state is localized at the displaced defect atom. Because the occupied vacancylike a, state is antibonding with respect to the interstitial atom, the total energy of the system decreases with further increasing displacement of the interstitial until a metastable position is reached at Q M . The usual way to picture this configuration interaction is shown in Fig. 12a, where to the right of QB the dominant configuration of the ground state is ascribed to the configuration (layh:). Figures 12b and 12d show the results for the system InP: 4x3. In the calculations shown in Fig. 12b and 12d, the crystal atoms were kept at their perfect crystal positions. When the four neighbors of the defect are allowed to relax, only the details of the described picture change, but the qualitative behavior remains the same. The internal optical excitation energy E , of the tetrahedral antisite (Fig. 12) is not much affected (see Table I in Part V), while the donor levels shift slightly to lower energy. The barrier height EB= E , -EM decreases (see Fig. 12 and Table 11). An interesting result is that in the metastable configuration QM the donor levels of the six studied defects shift into the valence band. The GaAs:SbG, center is particularly interesting because here the lattice relaxation results in qualitative changes of the defect properties. The unrelaxed SbG, follows the chemical trends described in Section V, but it is an extreme case: At the substitutional site its a, single-particleeigenvalue is very high, the wave function of this state is quite delocalized (Fig.5), and the optical excitation energy E, is very small (TableI). The difference in size between the impurity (Sb) and the removed atom (Ga) makes the V-Z geometry energetically more favorable than the substitutional geometry, i.e., EM 0 (Table 11). However, after the lattice relaxes, the situation is changed. The most prominent changes occur in the substitutional configuration, where the Sb atom was squeezed between its four neighbors: These neighbors relax outwards by about 0.3 A, which gives a gain of 1.7 eV. The a, wave function becomes more localized, and the E ( + / O ) electronic level shifts down in energy to 0.95 eV above the valence-band top. The calculated internal optical excitation energy E, increases with the lattice relaxation to about 1 eV, which is a typical value for anion antisites in GaAs (Table I). Smaller changes are observed in the V-1 configuration, where the system gains about 0.8eV

-=

1. DENSITY-FUNCTIONAL THEQRY OF SP-BONDED DEFECTS

41

TABLE I1 CALCULATED BARRIWHEIGHTSE , AND METASTABLE ENERGIES EM FOR DIFFERENT ANION-ANTISITE DEFECTS IN THE VACANCY-INTERS~TIAL PAIRV-1 ATOMICCONFIGURATION IN GaAs AND InP"

' E , is the barrier from the stable substitutional to the V-1 configuration,

EMis the energy difference between the substitutional and V-I geometries, while QM gives the distance from the substitutional site to the V-I site (see Fig. 12a). Values in parentheses correspond to unrelaxed atomic positions. All results refer to neutral defects.

relaxation energy. Because of this difference in the relaxation energy in the substitutional and in the V-Z geometries, the former becomes stable, while the latter is now metastable-as is the result found for the other anion antisites. The discussed electronic structure (see Fig. 12) indicates the possibility of an optically inducible structural transition. If the system, initially at the geometry (Q = 0 in Fig. 12), is excited from the ground state to the excited state 'A:, it will lower its energy by a displacement of the defect atom in the 11111direction. For an observable structural transition the excited state 'A: at Q = 0 has to be above the local maximum of 'Al (at Q = QB,i.e., E, > Ew). If this condition is fulfilled the defect will, with a certain probability, end up at the V-Z configuration, where, if the temperature is low, it will be frozen in. For GaAs, Caldas et al. (1990) concluded from their calculations that the mentioned condition holds for the As and P antisites, while it does not for the Sb antisite. Hence, for Sb the transition is very unlikely (Baumler et al., 1989a, 1989b).

42

U r n S c m z AND MAITHIASSCHEFFLER

VII.

Tbe EL2 Defect

12. INTRODUCTION As a special example of the metastability discussed in Part VI we will now discuss the calculated properties of the As-antisite in GaAs. In particular we will relate these calculated properties of As,, to experimentally known properties of the famous EL2 center in GaAs. The EL2 defect is the dominant deep donor in undoped GaAs crystals grown under As-rich conditions. Of particular interest is the physicochemical identification of EL2 and the understanding of its unusual metastability: At low temperatures, illumination with white light (precisely ho 2 1.18 eV) makes the deep EL2 level disappear, and then the defect can be no longer detected (Martin, 1981; Martin and Makram-Ebeid, 1986), except under application of hydrostatic pressure Baj et al. (1991). Heating the sample to T > 140K brings the defect and its deep level back in full concentration. Further details of this metastability are discussed in Chapter 2 of this book, and the most characteristic ones are summarized by Dabrowski and Schemer 1989a. Most of the microscopic models for EL2 that are discussed in the literature are complexes where the metastability is understood in terms of a rearrangement of one of the constituents. Because EL2 is accepted as not being impurity-related (Martin and Makram-Ebeid, 1986; Weber and Omling, 1985), these models are built from native defects. The most often discussed models for EL2 are aggregates of several AsGa defects (Frank, 1986; Figielski and Wosinski, 1987),complexes of AsGawith vacancies (Wagner and Van Vechten, 1987; Baraff and Schluter, 1985a),and the distant AsG,-Asi pair (von Bardeleben et al., 1985, 1986; Bourgoin et al., 1988; Meyer et al., 1986, 1987; Meyer, 1988; Delerue et al., 1987; Baraff and Schliiter, 1987; Baraff and Lannoo, 1988).In the last few years the distant AsG,-As~ pair has attracted a particular attention. Von Bardeleben et a). (1985, 1986)proposed the pair on the basis of systematic thermal deep-level transient spectroscopy (DLTS) studies, which strongly indicated the existence of an Asi in the EL2 formation process. This AsGa-Asi pair model was strengthened by electron-nuclear double-resonance (ENDOR) studies by Meyer et al. (1986, 1987) and Meyer (1988), who concluded that the ENDOR data are due to a distant AsG,-As~ pair, that the defect symmetry is CJvrand that the As, sits in the [lll] direction directly coupling to the AsGa at a separation of 4.88 A. Theoretical work by Baraff and Schluter (1987), Baraff and Lannoo (1988), and Caldas and Fazzio (1989) gave support for this AsGa-Asi-pairmodel, and Delerue et al. (1987)explained the pair’s metastable geometry in terms of a displaced Asi. All these theoretical studies were based on semiempirical, parametrized calculations. Based on self-consistent total-energy calculations, Dabrowski and Schemer (1988a, 1988b, 1989a and 1989b) questioned some details of the ENDOR

1. DENSITY-FUNCTIONAL THFDRYOF SP-BONDED DEFECTS

43

analysis. In particular, it was found that a distant pair of the type proposed by the ENDOR analysis is practically unbound. This makes it an unlikely candidate for the dominant defect in GaAs. Last but not least, it was pointed out that such a pair should have a shallow level close to the conduction band, which seems to be in conflict with what is presently known about the EL2 center. It was pointed out, however, that the AsGa may well pair with other centers and that an Asi may also be part of a complex. The position of the Asi would then be quite different to that assumed in the ENDOR analysis of Meyer et al. (1986, 1987). Whatever the nature of the complex including the AsGa (and even leaving it open whether such a complex really exists), we believe that there is no indication that it affects the nature of the EL2 metastability. The symmetry of the EL2 defect in the charge state, showing the characteristic EL2 absorption and the interesting metastability, was directly investigated by absorption studies under uniaxial pressure. These experiments, by Kaminska et al. (1985), Kaminska (1987), Kuszko et al. (1986), Bergmann et al. (1988), Trautmann et al. (unpublished), and Nissen et al. (1900, 1991), give no indication of a complex defect, but show tetrahedral symmetry. Up to now, the suggestion of Kaminska et al. that EL2 has tetrahedral symmetry and that it is identical to the isolated AsGa antisite was not generally accepted (see, for example, Mochizuki and Ikoma, 1987; Levinson and Kefalas, 1987; Baraff et al., 1988) because a simple HuangRhys picture together with the assumption that the defect couples only to a single-phonon mode was inconsistent with the experimental line shape (Martin and Makram-Ebeid, 1986), and because it was questioned that “optical absorption at the isolated antisite can produce the observed metastability” (see, for example, Baraff and Schliiter, 1987; von Bardeleben et al., 1985, 1986; Krambrock et al., 1992). This short discussion shows the difficulty and active controversy about the EL2 center, of which even the most basic property, namely its symmetry, is not generally agreed on. TO THE METASTABLE CONFIGURATION 13. THE TRANSITION

Chadi and Chang (1988a) and Dabrowski and Scheffler (1988a, 1989a) suggested independently that the EL2 metastability is due to the AsGae VG, - Asi structural transition, which we already discussed in Section VI. For the neutral tetrahedral AsGa we have an excited state aft:, which can be reached from the ground state by optical absorption. This state is orbitally degenerate, and as a consequence the system is unstable with respect to a symmetry lowering Jahn-Teller distortion. Dabrowski and Scheffler (1988a, 1989a) found the Jahn-Teller force for the [lll] displacement to be about

U r n S c m z AND MAITHIASSCHEFFLER

44

twice as large as those for the [1001and [l lo] displacements. Thus, the JahnTeller effect will move the central atom in the [111) direction towards the nearest tetrahedral interstitial site. This lowers the symmetry of the defect to C,, and results in a splitting of the t,(T,) state (bottom of Fig. 12) into a lower a,(CJv)state and higher e(C,,) state. Of these two, only the a, state is occupied (with one electron), which is the reason for the Jahn-Teller energy gain. In the C,, point group, the electronic configuration of the excited state is now labeled as la:2ai (see Part VI for the details of this notation). Figure 13 displays the single-particle energies of the la,, 2a,, and e states (top), as well as the three total-energy curves obtained for the three electronic configurations la:2ay (labeled F, which stands for fundamental), l a ~ 2 a ~ (labeled E, which stands for excited), and lay2a: (labeled M, which stands for metastable). This figure should be taken in a semiquantitative way. It shows results of parameter-free calculations, but only one atom is moved, and all others are kept at their perfect-crystal positions. When this constraint is removed, the total energy decreases, but the general picture will not change. h

5

DISPLACEMENT ALONG [ l 1 11 (Z) 10 20 30 40 50 60 70

0 1.6

c,

6 z

1.4 1.2

W

1.0

& a

a

.B .6

d z

m

.4 I

h

>

5

'

'

'

'

'

'

'

'

'

,

'

7

'

'

' I

'

' I

1.2

1.0

0

.5

1.o

1.5

DISPLACEMENT ALONG [ l 1 11

(A)

FIG. 13. Single-particle energies with respect to the valence band edge (top), and total energies of the S = 0 ground states (curves F and M) as functions of the position of the arsenic defect atom (bottom).Zero displacement refers to the tetrahedral As-antisite configuration.The total-energy curve labeled E is an electronic excited state with electronic configuration lai2aj. In these calculations all neighbors of the displaced arsenic atom were kept at their perfect-crystal positions (see text). (After Dabrowski and Schemer, 1988a.)

1. DENSITY-FUNCTIONAL THEORYOF SP-BONDEDDEFECTS

45

The Jahn-Teller theorem predicts that the E total-energy decreases when the symmetry is reduced, i.e., when the AsGa atom is displaced from its central position. This effect can be seen in the E total energy curve of Fig. 13, bottom. The geometry at the minimum of the E total energy curve may play a role in a non-Franck-Condon excitation, and Dabrowski and Scheffler (1988a, 1989a) therefore predicted a zero-phonon line at about 0.1-0.2 eV below the main peak (Fig. 13, bottom). It is most likely that the excited system "falls back" from the E curve down to the F curve, the ground-state total energy. Then the system ends again as a tetrahedral AsG,, antisite. However, Fig. 13 shows that the 2a, single-electron level decreases in energy very rapidly and therefore starts to mix with the la, state. This allows for another electronic configuration, namely lay2af. Thus, once excited to the E curve, the system has a certain probability of changing to the A4 curve. Then the arsenic defect atom will end a considerable distance (about 1.4 A) from its initial central gallium site. We refer to this metastable atomic configuration as the gallium-vacancy-arsenic-interstitial pair, denoted by I/-I. The As interstitial is about 1 A away from the tetrahedral interstitial site. It is therefore chemically bound to only three arsenic atoms (Scheffler, 1989; Dabrowski and Scheffler, 1992). The transition to the metastable state competes with two other possible processes, namely the ionization of the excited state (where the excited electron of the AsGa goes to the conduction band) and the deexcitation ( 1 4 2 4 + laf2a;) at smaller distortions. These two processes will bring the arsenic defect atom back to the fundamental configuration, i.e., to the tetrahedral AsGa antisite. Because of these competitors it is obvious that the probability of the metastable transition is small and that it should be sensitive to local stress and other perturbations. It also depends sensitively on the conduction-band structure. As the arsenic defect atom leaves the gallium site, its bond with one arsenic neighbor that is left behind is stretched, and it almost breaks when the defect enters the barrier region. This is shown in Fig. 11. The barrier of the structural transition is reached when the arsenic atom passes through the (111) plane of three As neighbors. In the metastable configuration, the arsenic defect atom (now an interstitial) binds to these three atoms (see Fig. ll), similarly to the bonding in crystalline grey arsenic. In the vacancy region there is one broken bond, which is filled with two electrons. The electronic structure of the vacancy-interstitial pair found in the selfconsistent calculations (top of Fig. 13 at 1.4A displacement) can be summarized qualitatively in terms of a simple tight-binding picture. The leftand right-hand parts of Fig. 14 show schematically the electronic structure of the isolated gallium vacancy and of an C,,-site isolated arsenic interstitial. The vacancy with tetrahedral symmetry has a t 2 state close to the valenceband edge; in the neutral charge state this level (which can hold up to six

46

U w SCHERZAND MATTHIAS SCHEFFLER Go-VACANCY

V,

As, PAIR (C,

(Td)

As-INTERSTITIAL

"1

(C,

3

e

. .

a, -:...

,,'

,,'

I ---- .

.-'

I . . .

0,

FIG. 14. Schematic summary of the electronic structure of the metastable configuration, i.e., of the as^'' defect pair (middle), which can be understood in terms of a Ga vacancy (left) interacting with a C,,-site As-interstitial (right).(After Dabrowski and Schemer, 1988b.)

electrons) is filled with three electrons. Furthermore, the vacancy has an a,resonant state in the valence band. The arsenic interstitial at a C3, symmetry site has an a, level in the lower and an e level in the upper half of the band gap. For the neutral interstitial, the a, state is filled with two electrons and the e state is filled with one electron. When the two systems interact (the middle part of Fig. 14), the e(C3,) component of the vacancy tZ(TJ level and the interstitial e(V,,) state form a bonding and an antibonding level that both disappear from the gap. The interaction of the t , and a, states of the vacancy with the interstitial a, states is slightly more complicated, but also follows qualitatively the tight-binding picture (see Fig. 14). The five electrons of the neutral gallium vacancy and the three electrons of the neutral arsenic interstitial will fill the three energetically lowest levels of the pair. From the wave-function character of the occupied states, we may label the pair Vd; 'As! + I . The self-consistent calculations of Dabrowski and Schemer (1988a, 1989a) give the result that the empty a, and e states of the pair are close to the conduction-band edge, i.e., the corresponding acceptor levels should be degenerate with the conduction band. The highest filled state (labeled 2a, in Fig. 13) is close to the valence-band edge, i.e., the corresponding electronic e(O/ +) level should be degenerate or almost degenerate with the valence band; it has vacancy dangling-bond character and the wavefunction is very localized. Also, the Green-function calculations by Ziegler et al. (1993) confirm this energy level structure showing that the acceptor levels are indeed close to the conduction band and that the 2a, state is in the valence band. The constrained calculations of Dabrowski and Schemer (1988a, 1989a),shown in Fig. 13, give a barrier for the neutral ground state of 0.92eV between the minimum of the metastable configuration (the &,Asi

1. DENSITY-FUNC~ONAL THEORY OF SP-BONDED DEFECTS

47

pair) and the fundamental configuration (the AsGa antisite). This value decreases to about 0.4eV when the atoms of the cell are allowed to relax. Figure 13 shows that the fourfold-coordinated AsGa antisite and the metastable configuration with the threefold-coordinated Asi have very similar total energy. On the basis of the arguments presented, this result is indeed plausible for a group-V element. The origin of the barrier between the two configurations is, however, not immediately obvious. It may be understood by the fact that the covalent radius of an As atom is 1.2 A. Therefore, the As, is too “thick” to pass easily through the (111) plane of the three As atoms. This argument is, however, not complete and cannot explain why for other charge states the barrier will in fact disappear (see the next subsection). The main reason for the barrier is the filled vacancy-like dangling bond shown schematically in Fig. 11. This state is antibonding with respect to the arsenic interstitial, and its energy (the 2 4 level in Fig. 13) increases when the As interstitial is moved from the metastable configuration toward the vacancy. The occupied vacancy dangling orbital therefore contributes to the repulsion between the constituents of the metastable pair (Dabrowski and Scheffler, 1992). It is now clear that the barrier will change if one electron is removed from this level. The ground-state total energy for the positively charged center with one electron at the Fermi level is given by

Eo is the neutral-charge-state total energy, i.e., the F and M curves of Fig. 13; +/O) is the transition state of the highest occupied single-particle level; and EFis the Fermi level, to which the electron is transferred. Dabrowski and Scheffler (1988a, 1989a) obtained that the barrier is significantly reduced for the E+ total energy, compared to EO, namely by 0.4eV. Thus, the barrier practically vanishes when one electron is removed from the vacancy-like dangling orbital of the VGUAsi pair, which implies that a positive-charged AsGa should not exhibit metastable behavior. This result suggests that a transition from the metastable V-Z to the stable AsGa configuration may be induced by a (temporary) hole capture at the V-1 pair. A second possibility of the VG,Asi + AsGaregeneration is that an electron is (temporarily) captured in the la, level of the metastable system. This corresponds to a temporary, negative charge state of the VGIGaAsj pair. The total energy is given by E(

E- = Eo - E(O/-)

+ EF.

(63)

The transition-state energy E ( O / - ) is related to the occupation change in the

48

U w Scmxz AND MA’ITHIASSCHEFFLEX

la, state of the metastable configuration in Fig. 13. The calculations of Dabrowski and Schemer (1988a, 1989a) predict that the E- total-energy curve is very flat. Thus, the barrier is close to zero, but there are no strong forces pulling the Asi to the vacancy. Still, because the density of states at the bottom of the GaAs conduction band is very small, the negative charge state may live sufficiently long, and this electron-induced regeneration may be a likely regeneration channel. 14. COMPARISON OF THE THEORETICAL RESULTS TO THE EXPERIMENTAL EL2 PROPERTIES

A careful discussion of the EL2 center requires us to take a variety of different properties into account. Dabrowski and Scheffler (1988% 1989a) therefore compiled a detailed list of the most important “experimentally established properites of EL2” and compared these experimental properties with their theoretical results of the AsGae VG,Asi defect. We will not repeat this detailed discussion here but refer the interested reader to the original publication. We just summarize that the comparison of the theoretical results for the isolated arsenic antisite and the AsGa;t VGaAsi metastability (see Section VII.13) to the list of measured properties of the EL2 defect reveals clear similarities. Both defects have basically the same electronic structure: They are double donors and give rise to two deep levels in the forbidden gap. Both defects are not paramagnetic when in the neutral charge state, show the midgap level, exhibit the metastability, and do not have a level in the upper part of the gap. In addition, both centers have the same pressure dependence of the transition state in the stable state (Ziegler and Scherz, 1992). The internal excitation of both centers is practically identical; the theoretical value of the Franck-Condon transitions at an AsGa of 0.97eV agrees well (within the expected accuracy of a parameter-free DFT-LDA calculation) with the EL2 absorption main peak at 1.18eV. The zero-phonon line in the experiments (0.14eV below the main peak) may be compared to the theoretical result of 0.13eV. However, we note that it is not yet clear if the experimental zero-phonon line is indeed a transition to the [1111-displaced arsenic defect atom. As discussed in Section V11.13, optical excitation of the AsGa can induce a structural transition via the intermediate total-energy curve labeled E in Fig. 13. The mechanism implies that the probability of this bleaching effect should be sensitive to the quality of the crystal. This is indeed known experimentally. For the positive charge state of the AsGa antisite, in particular, theory and experiment tell that this is not quenchable directly, but only after the As&;+,’ is transformed to an A$:. The theoretical barrier height for thermal recovery (i.e., for the VG,AS~+ASG~ transition), calculated as 0.4eV, is close to the

1. DENSITY-FUNCTIONAL THEORYOF SP-BONDEDDEFECTS

49

experimental value of 0.34 eV. Also, the regeneration conditions are the same in the calculations and in experiments with EL2: There is a purely thermal process and an electron-induced (“Auger-like”) regeneration process. The electron-induced deexcitation of EL2 can be understood in the just-discussed theory in the following way: It starts with a thermally activated capture of a conduction-band electron in the la, resonant state of the VGaAsi pair. This capture is then followed by relaxation in the Asi to the fundamental configuration, where the captured electron is released. The third channel of regeneration of the fundamental atomic configuration, namely the holeinduced deexcitation, is expected to have a very small cross-section (Dabrowski and Scheffler, 1988a, 1989a). Indeed, such a process has not yet been observed for EL2. Combined EPR-DLTS studies of von Bardeleben et al. (1986) indicated that EL2 is destroyed if the sample is heated to 850°C and rapidly cooled afterwards, but it can be regenerated by 130°C annealing. This result can be qualitatively explained as follows: At high temperatures the AsGa e VGaAsi system dissociates into a gallium vacancy and an arsenic interstitial. Rapid cooling hinders the reverse process, and additional annealing at intermediate temperatures would be necessary to allow for the diffusion of the Asi and the association reaction VGa+ Asi 4 AsGa. Again, as in many EL2-related experiments, the results of von Bardeleben et al. (1986) have not been fully reproduced by other researchers. Lagowski et al. (1986) and Lagowski (private communication) report different temperatures, namely 1,050”C (instead of 850°C) and 850°C (instead of 130°C).This demonstrates the high complexity of EL2 investigations: Experimental results seem to depend strongly on the sample and on the crystal environment. For a more general discussion of how the crystal F e d level (i.e., the electron chemical potential) and the gas in the crystal environment (the atomic chemical potential) can influence defect reactions and formation energies, we refer to Section 11.3 and Part V. The just-described calculations show that the neutral arsenic antisite exhibits, under optical excitation, an intrinsic metastability. The metastable transition is started by a Jahn-Teller effect,as speculated earlier by Scheffler et al. (1984) and Bachelet and Scheffler (1985). The good agreement between the calculated barrier (0.4 eV) and the experimental barrier suggests that the AsGa antisite and EL2 are identical defects. However, the uncertainty in the calculations was estimated as k0.2 eV. Therefore, we cannot positively rule out the possibility that another nearby (but weakly interacting) defect is in fact necessary to adjust the energy barrier to the 0.34 eV observed for EL2. Nevertheless, based on a detailed comparison with many experimental properties, we identify the basic mechanism of the EL2 metastability as that of the AsGaantisite.

50

U w SCHERZAND M ~ r n a SCHEFFLER ~s VIII. The DX Centers

15. INTRODUCTION In this part we discuss again a defect metastability of the type described in Part VI. In particular we consider the Si donor in GaAs. Although the basic mechanism (ie., the sp3 e s p 2 bonding and the nature of the barrier) is the same as before, some interesting additional aspects are identified. From a comparison with experimental results we relate these theoretical findings to experimental results of D X centers. Substitutional groupIV Ga-site and group-VI As-site impurities in Gal -.AI,As with low A1 concentration (x < 0.22) are shallow donors. However, when x exceeds 0.22, or when the sample is put under high hydrostatic pressure, or when the sample is heavily doped, these defects are modified and become deep centers. Then they are called DX centers. For basic research the most exciting properties of D X centers are related to this pressure (or composition, or Fermi-level) inducible transition. Similarly to the discussion on the identification and explanation of EL2 presented in the previous part, for DX there is also no general consensus about its microscopic structure and its metastability mechanism. However, correspondingly with the previous part, we will argue that the metastability is due to a structural change between the tetrahedral donor geometry and a vacancy-interstitial pair geometry (compare Part VI).

16. THEORETICAL RESULTSFOR

m Si DONOR

IN

GaAs

UNDER

PRESSURE

In this section we summarize results of density-functional-theory calculations of Dabrowski and Scheffler (1992). The main approximations in these studies were to replace the k-summation of the 54-atom super-cell by the r point and to neglect lattice relaxations. Unfortunately the theoretical results are now more sensitive to these approximations than was found for the defects discussed in Parts VI and VII. This is largely because DX centers exhibit a shallow +deep transition and because the results are more sensitive to the details of the conduction band. Tests had been performed also for other k-point sets and for some relaxed geometries, so that it was possible to roughly estimate how an improved calculation would modify the results. In order to investigate the pressure dependence, calculations were performed for different lattice constants. To ease the comparison with experimental results, Dabrowski and Scheffler (1992) decided to adjust the theoretical pressure scale by adding to their direct theoretical result a constant value of 3 1 kbar so that the T-X crossing occurs at the experimentally observed pressure. In Fig.

1. DENSITY-FUNCTIONAL THEQRY OF SP-BONDED DEFECTS 0.8

-5 *E:z w

51

0.8

-5 -

0.6

$

0.4

@

W

0.2

0.6

0.4 0.2

0.0

0.0 PRESSURE (kbar)

PRESSURE (kbar)

FIG. 15. Calculated (Dabrowski and Schemer, 1992) (left) and measured (Lang et al., 1979; Landoldt-Bornstein, 1982) (right) pressure dependenciesof the GaAs conduction band minima, of the DX level, labeled as E ( + / - ) [full dots and solid line], and of the deep level of the tetrahedral Si,,, labeled as ESi,,( +/O) [open dots and dashed line]. The zero of the theoretical pressure scale is adjusted such that the T-X crossingpoint is at 40kbar. For the calculateddefect levels lattice relaxation is neglected. We also note that the defect levels suffer from the r-point approximation of the k summation. Improving on this it was estimated that the e(+/-) line would shift up by about 0.3eV and the ~sj,( /0) line would shift up by about 0.4eV.

+

15 we show their results for the conduction band edges and for two Si defect levels, which we will discuss in more detail later. The pressure dependencies of the conduction band are reproduced very well by the theory, but the absolute gaps are too small, which is a typical result for converged DFT-LDA calculations (compare Section 111.4). In Fig. 16 we show the calculated total-energy curves for GaAs:Si, with the Si impurity atom displaced in the same way as the other impurities in Figs. 11,12, and 13. The results of Fig. 16 were obtained with the host atoms frozen at their perfect crystal positions. Lattice relaxations lower the energies, but this does not affect any of the following conclusions. At first we discuss the curve corresponding to the negatively charged defect labeled [D(-' -e-(EF)], where the electron is at the Fermi level. We see in Fig. 16 that the minimum of this curve is at a displaced configuration, where the defect symmetry is C3". Here the defect should be called a vacancy-interstitial (V-1) pair. As in Parts VI and VII above, we emphasize that the Si-interstitial is not at the tetrahedral interstitial site of the lattice but closer to three As atoms. The bonding with these As atoms can be described as largely sp2-like. We note that only for the negatively charged Si defect the V-Z pair geometry has a lower energy than the substitutional, tetrahedral geometry. The mechanism that keeps the impurity at the interstitial site is essentially due to the lughest occupied state of the defect. For the V-Z pair, this state is a single As dangling orbital, indicated in the geometry-plot of Fig. 11 (top right) by the thick black line. It interacts only weakly with the Si interstitial. When the Si atom is

52

UDOSCHERZ AND MAITHIAS SCHEFFLER DISPLACEMENT

0.0

0

0.5

1.0

20

40

DISPLACEMENT

(A) 1.5

60

(X)

FIG. 16. Calculated total energy for GaAs:Si as a function of the Si position (Dabrowski and Scheffler, 1992). Zero displacement corresponds to the tetrahedral SiG. defect. 100% displacement would correspond to the nearest tetrahedral interstitial position, which would be the corner of the cube shown in Fig. 11. Three different charge states are shown. The Fermi level is taken at the minimum of the conduction band, which is at r. The lattice constant underlying these calculations is n = 5.68 k which corresponds to a pressure of - 5 kbar in Fig. 15. The main approximations that may d e c t some quantitative results are the neglect of lattice relaxations and the replacement of the k summation by the r-point.

pushed towards the vacant site, this orbital, as well as the Si-centered orbitals, is compressed, which increases the electron kinetic energy. Thus, when these orbitals are filled with electrons, and this is the case for D(-),we get a barrier. Along the same argument we also understand that when the highest occupied state of D(-)is emptied, as is the case for the neutral or positively charged defect, the barrier should decrease or even vanish. In Fig. 16 we see indeed that for the neutral system the total-energy curve differs significantly from that of the negatively charged center. For D'O) the stable geometry would be at the tetrahedral position (zero displacement). However, at the V-Z pair configuration we can still identify a local minimum. The barrier from this local minimum to the global minimum of D'O) is, however, much smaller than that of the [D(-)- e-(EF)] curve. We find that the calculated barrier heights depend sensitively on the k summation. Improving on the r-point approximation, Dabrowski and Scheffler (1992) estimated that the theoretical barriers for D'O) and [D(-) - e-(EF)] for a V-Z + Si,, path would be about 0.1 and 0.5 eV, respectively. The main effects of a change in the lattice constant are changes in the conduction band structure. Assuming that we have n-type conditions, this translates into a change of the Fermi level. As a consequence we obtain a (to first order) rigid shift of the [D'+)+ e-(EF)] and the ED(-)- e-(EF)] curves relatively to the D(*)curve. The calculations also imply that the structural

1. DENSITY-FUNCTIONAL THEORY OF

BONDED DEFECTS

53

transition from the C,, to the & geometry can be also induced without pressure but by changing the Fermi level. If the Fermi level is high, the absolute minimum of the three curves shown in Fig. 16 will be that of the [D(-) - e-(EF)] curve. Thus, the negatively charged defect with its V-Z geometry will be stabilized. If the Fermi level is low, the [D(+)+ e-(E,)] curve shifts to lower energy and the [D(-) - e-(E,)] curve shifts to higher energy. Then the minimum of all three possible charge states is that of the positively charged Si substitutional. In Fig. 17 this discussion is summarized in a plot that shows the Fermi-level dependence of the different charge states. This figure also shows the theoretical level positions: The tetrahedral, substitutional Si has transition-state levels ES;,,( + / O ) = E,, + 0.1 eV and Q J O / - ) = E , + 0.3 eV. Thus, at the lattice constant taken for the calculations in Figs. 16 and 17, both “levels” are resonances in the conduction band. For the V-Z pair configuration, the results E ~ - I ( O / - ) = E,, - 0.5 eV are obtained. As we are dealing here with transitions between a mainly valenceband derived state (the highest occupied state of the V-Z geometry is essentially an As dangling orbital (Dabrowski and Scheffler, 1988a, 1989a, 1989b; Scheffler, 1989) and the conduction band, these transition-state energies, when compared to experimental ionization energies, may be subject to errors similar to those of the perfect crystal band gap. Figure 17 shows that the ground state for low Fermi energy is that of D(+)(SiGa),and that the ground state for high Fermi energy is that of D(-)(V-Z). The transition from D(+)(Si,,) to D(-)(V-Z) is direct, i.e., without passing through the neutral configuration. This is what is called a negatioe U behavior: In thermal equilibrium, there is either no electron in the defect-induced level, or there are

0’50

$-

1 -

\

D‘(Sio.)

- e-(Ep)

\

I

-0.50

-0.2

0.0

0.2

0.4

FERMI ENERGY (eV)

FIG. 17. Calculated total energies of the single positive, neutral, and single negative charged substitutional GaAs:S&, and of the single negative charged V-I pair as a function of the Fermi level, after Dabrowski and Scheffler (1992). E , = 0 is the bottom of the conduction band. The lattice constant underlying these calculations is a = 5.68 A, which corresponds to a pressure of - 5 kbar in Fig. 15. The main approximations that may affect some quantitative results are the neglect of lattice relaxations and the replacement of the k summation by the r-point.

54

UDO SCHERZ AND MATTHIASSCHEFFLER

two electrons. The coulombic electron-electron repulsion, which typically implies that energy levels shift to higher energy when the occupation is increased, is more than compensated by the large lattice relaxation, i.e., by the displacement of the Si atom from the substitutional to the V-Z pair configuration. The pressure dependence of the energy of the crossing point of the D(+)(Si,,) and D(-)(V-Z) lines of Fig. 17 is shown in Fig. 15 as the full line, labeled E ( + / - ) . Figure 15 also shows the pressure dependence of the “normal” Si,, donor level, ESi,,( + /O), as the dashed line. Dabrowski and Scheffler (1992) compiled a list of the experimentally established properties of the Si D X center, and compared these properties to the properties implied by the theoretical results for the tetrahedral Si donor and the V-Z pair. We will not repeat this discussion here, but we summarize that most of the experimental results are indeed consistent with the Si,,$ V-I model. However, the situation appears to be less clear than for the EL2 center. This is largely because most experiments were done for AlGaAs alloys for which the experimental analysis appears to be more complicated. On the other hand, the calculations were performed mainly for pure GaAs (Chadi and Chang, 1988% 19886 Dabrowski et al., 1990; Dabrowski and Schefler, 1992); only recently they were extended to alloys (Zhang, 1991). Although the detailed calculations reported in Figs. 15-17 were concerned with cation-site donors, where the metastability is due to a displacement of the defect atom, we note that the same type of process can also occur for anion-site donors (Chadi and Chang, 1988a, 1988b). Here, however, the nearest neighbor cation moves. Several experimental results are directly explained by the calculations. However, some questions remain that call for more accurate experiments as well as for more accurate calculations. The most severe disagreement between experiments and the properties of the V-Z model comes from susceptibility measurements, which seem to indicate that D X centers are paramagnetic (Katchaturyan et al., 1989). However, this result is not confirmed by EPR and in fact it has been questioned by other studies (Katsumuto et al., 1990). Paramagnetism of the ground stare of DX centers would be in conflict with the V-Z model. A more detailed experimental and theoretical study of these points should help to finally confirm, to reject, or to refine the model.

Acknowledgment The authors are grateful to J. Dabrowski and C. Ziegler for their critical reading of the manuscript.

1. DENSITY-FUNCTIONAL THF~ORY OF SP-BONDED DEFECTS

55

REFERENCES

Bachelet, G. B., and Scheffler, M. (1985). Proc. 17th Intl. Conf. Phys. Semiconductors (Chadi, J. D., and Harrison, W. A., eds), p. 755. Bachelet, G. B., Bard, G. A., and Schliiter, M. (1981). Phys. Reu. B 24, 915. Bachelet, G. B., Hamann, D. R., and Schliiter, M. (1982). Phys. Rev. B 26,4199. Bachelet, G. B., Jacucci, G., Car, R., and Parrinello, M. (1986). Proc. 18th Intl. Con$ Phys. Semiconductors, p. 801. Baj, M., Dreszer, P., and Babinski, A. (1991). Phys. Reo. B 43,2070. Bar-Yam, Y.,and Joannopoulos, J. D. (1984). Phys. Reo. Lett. 52, 1129; Phys. Reo. B 30, 1844. Baraff, G. A., and Lannoo, M. (1988). Revue Phys. Appl. 23, 817. Baraff, G. A., and Schliiter, M. (1978). Phys. Rev. Lett. 41, 892. Baraff, G. A,, and Schliiter, M. (1979). Phys. Rev. B 19,4965. Baraff, G. A., and Schliiter, M. (1984). Phys. Reo. B 30, 1853. Baraff, G. A., and Schliiter, M. (1985a). Phys. Reo. Lett. 55,2340. Baraff, G. A., and Schliiter, M. (1985b). Phys. Rev. Lett. 55, 1327. Baraff, G. A., and Schliiter, M. (1986). Phys. Reo. B 33, 7346. Baraff, G. A., and Schliiter, M. (1987). Phys. Reo. B 35, 6154. Bard, G. A., Kane, E. O., and Schliiter, M. (1979). Phys. Rev. Lett. 43,956. Bard, G. A., Kane, E. O., and Schliiter, M. (1980). Phys. Rev. B 21, 3583. Baraff, G. A., Lannoo, M., and Schliiter, M. (1988). “Defects in Electronic Materials,” Mater. Res. SOC.Symp. Proc. No. 104 (Stavola, M., Pearton, S.J., and Davies, G., eds.), p. 375. MRS, Pittsburgh. Baroni, S., Gianozzi, P., and Testa, A. (1987). Phys. Rev. Lett. 58, 1861. Baumler, M., Schneider, J., Kaufmann, U., Mitchel, W. C., and Yu, P. W. (1989a). Phys. Rev. B 39, 6253.

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SEMICONDUCTORS AND SEMIMETALS, VOL. 38

CHAPTER 2

EL2 Defect in GaAs Maria Kaminska INSTITUTE OP E x P @ R m . & L PHYSICS

WARSAW UNIWRSIN WARSAW,POLAND

Eicke R. Weber DEPARTMENT OF

MATERIALS SCIENCE

MINE~UL ENGNEFRINGAND CENTER LAWRENCEBERKELFYLABORATORY

AND

FOR

ADVANCED MATERIAIS

U~RstTY OF CALIFORNIA. BWKELEY

I. INTRODUCTION . .

. . . . . . . . . . . . . . . . . . . 1. Conditions of EL2 Creation . . . . . . . . 2. Electrical Properties of EL2 Defect . . . . . 3. Optical Properties of EL2 Defect . . . . . . 4. Metastable Property of the EL2 Defect . . . . 111. ARSENIC ANTBITE DEFECT IN GaAs . . . . . . 5. EPR Studies of Arsenic Antisite Defect . . . . 6. ODENDOR Studies of Arsenic Antisite Defect . Iv. ENERGY LEVELSOF EL2 DEFECT . . . . . . . OF EL2 DEFECT . . . . . . . . . . . V. MODELS

. . . . . . . . . 59 . . . . . . . . . . 60 . . . . . . . . . . 60 . . . . . . . . . . 63 . . . . . . . . . . 64 . . . . . . . . . . 68 . . . . . . . . . . 72 . . . . . . . . . . 72 . . . . . . . . . . 74 . . . . . . . . . . 75 . . . . . . . . . 77 7. Isolated Arsenic Antisite Defect as a Model of EL2. . . . . . . . . . . 77 8. Complex of Defects as a Model of EL2 . . . . . . . . . . . . . . . 78 9. EL2Family . . . . . . . . . . . . . . . . . . . . . . . . 80 VI.C~NCLLJSIONS. . . . . . . . . . . . . . . . . . . . . . . . . 83 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . 85 11. PROPERTIES OF EL2 DEFECT..

. . . . . . . . . . .

I. Introduction The most important task for studies of imperfections in crystals is to determine defect nature. This is a fascinating problem for physicists that also influences materials applications. Through identification of a defect it is possible to control its concentration, within thermodynamiclimits, as well as to understand defect behaviour during growth and crystal processing. So far there is no one definite way to identify a defect. Instead, many experimental 59 Copyright 0 1993 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-7521380

60

M.KAMINSKA AND E. R. WEBER

techniques are used to characterize defect parameters. However, in most cases such information is not sufficient to determine defect nature. In 1977 the general classification of defects: electron (Martin et al., 1977) and hole traps (Mitonneau et al., 1977) in GaAs grown by different bulk and epitaxial techniques was made. The defects were named ELI, EL2,. . . ,EL17 for electron traps and HL1, HL2,. . . ,HL12 for hole traps. After more than 10 years of extensive studies of GaAs in many laboratories all over the world, there is a relatively wide knowledge of the most important of these defects, EL2. However, even in the case of EL2, a common agreement about its detailed microscopic structure has not yet been reached. It is widely believed that EL2 is related to the arsenic antisite defect, but whether it is an isolated antisite or a complex of an antisite with another point defect is still a controversial issue. For other defects, only a few parameters, such as energy position in the GaAs energy gap or carrier emission cross-section, are determined, and their origins are still far from resolved. The EL2 defect is the dominant defect in melt-grown GaAs. It is commonly present in concentrations of 1-2 x 10l6cm-3, both in liquid encapsulated Czochralski (LEC)- and Bridgman-grown crystals (if the free electron concentration is smaller than 1-2 x 10'' ~ m - as~ shown , by Lagowski et al., 1982b-see Part 11). EL2 is also present in concentrations around 10i4cm-3 in vapor phase epitaxy (VPE) GaAs. However, it is not observed in liquid phase epitaxy (LPE) GaAs layers or in molecular beam epitaxy (MBE) GaAs grown at regular temperatures of 550-650°C. Recently, an EL2-like defect in concentrations as high as 10'9-1020cm-3 has been found in MBE GaAs grown at low temperatures between 190 and 300°C (Kaminska et al., 1991a). This material will be referred to as low-temperature (LT) GaAs. EL2 basically controls the electrical and optical properties of GaAs, and its existence makes it possible to achieve thermally stable semi-insulating (SI) GaAs-the key material in integrated circuit technology. In the following paragraphs the results of characterization of a wide range of EL2 properties by transport, capacitance, optical and electron paramagnetic resonance (EPR) techniques will be presented, followed by a review of the competing models of the EL2 defect. In conclusion, both the commonly accepted and the controversial features of the nature of EL2 will be discussed.

11. Properties of EL2 Defect 1. CONDITIONS OF EL2 CREATION

The EL2 defect in GaAs is created under arsenic-rich conditions. Its concentration can be controlled to some extent by stoichiometry change

2. EL2 DEFECT IN GaAs

61

during crystal growth. The studies of the correlation of EL2 concentration with the variation of stoichiometry were performed on GaAs crystals grown by different techniques: LEC (Holmes et al., 1982a, 1982b), Bridgman (Lagowski et al., 1982b) and metal-organic vapour phase epitaxy (MOVPE) (Miller et al., 1977; Battacharya et al., 1980; Wagner et al., 1980a; Samuelson et al., 1981; and Watanabe et al., 1981).In all these cases EL2 concentration increased with As/Ga stoichiometry ratio. However, for the particular type (melt-grown or epitaxial) of GaAs, the change of EL2 concentration with stoichiometry variation did not exceed an order of magnitude for the range of As/Ga ratio in which monocrystalline GaAs could be grown. The only exception was LT GaAs, which could be grown highly off-stoichiometricwith arsenic up to 1.5% more than Ga. The deviation from stoichiometry in LT GaAs increased with decreased growth temperature, and for strongly As-rich layers, EL2 concentration up to a few times 1020cm-3 was observed. Changes of growth temperature led to EL2 concentration variation in the broad range from above 10'' cm-3 to below the detection limit, which was 1Ol8 cmW3(Kaminska et al., 1991a). Strong changes in EL2 concentration, of orders of magnitude, were observed for intentionally doped bulk GaAs crystals with different amounts of shallow donors-Fig. 1 (Lagowski et al., 1982a, 1982b; Kaminska et al., 1982; and Yuanxi et al., 1983). For a broad range of free electron concentration, the EL2 concentration remained nearly constant (- 10l6cmV3)and then dropped rapidly to below 10'3cm-3 (detection limit) when the free electron concentration exceeded 2 x lo" cmP3. To explain this effect, the interaction of gallium vacancies VG,with arsenic atoms (either in the form of substitional AsAsor interstitial Asi atoms), leading to the creation of a defect related to arsenic antisite AsGa was postulated (Lagowski et al., 1982b, and Kaminska, 1985). Lagowski et al. (1982b) were the first to link EL2 with an

FIG. 1. Experimental (points) and theoretical (solid curve) dependenceof EL2 concentration on room-temperature free electron concentration n. From the theoretical fit it was obtained that the arsenic antisite defect was created at about 1,050 K by means of arsenic atom migration and recombination with a gallium vacancy (Lagowski et al., 1982b).

62

M.KAMINSKA AND E. R. WEBER

arsenic antisite defect. AsGahas a double donor character, and according to the mass-action law its creation could be strongly suppressed by intentional doping with shallow donors. The theoretical analysis of the change of the EL2 concentration with free electron concentration based on equations of mass-action led to the two-step model of EL2 creation in bulk GaAs (Lagowski et al., 1982b):

(i) the creation of gallium vacancies under As-rich conditions (during GaAs solidification at about 1,250"C); (ii) the migration of As atoms and their interaction with gallium vacancies, leading to the creation of antisite arsenic related defects (during post solidification cooling-around 800OC). The temperature of EL2 creation as well as annihilation were further studied by Lagowski et al. (1986)and Haga et al. (1988)using heat treatment of GaAs under a protecting As gas atmosphere. In some bulk GaAs crystals, EL2 concentration could be increased by annealing at 700-8WC, whereas in other crystals it stayed nearly constant under these conditions. On the other hand, all bulk GaAs that had been annealed at 1,200"C and rapidly cooled was almost free from EL2 centers (see Fig.2). Such EL2-free specimens showed EL2 presence again after further annealing between 600 and 900°C. These data indicated clearly that EL2 creation in bulk GaAs takes place around 800°C during both GaAs growth (during cooling after solidification) and post-growth heat treatment. EL2 defects in as-grown bulk GaAs can be annihilated by annealing above 1,ooo"C. In as-grown LT MBE GaAs layers, most of the EL2 defect could be annealed above 350°C (Kaminska et al., 1991a).The creation mechanism of EL2 defect in LT M B E GaAs seems to be different from that in bulk GaAs.

- Y P

He-GoAs

3 0 . 0 L , '

'

200

I

\ I41

' " ' ' ' 400 600 do0 1000 1200 TEMPERATURE I *C) '

'

FIG. 2. Change in the concentration of EL2 defects in liquid encapsulated Czochralski (LEC) and Horizontal Bridgmann (HB) GaAs under annealing (Haga et al., 1988).

2. EL2 DEFECT IN GaAs

63

Its concentration is very high and far from thermal equilibrium (most probably because of the lack of enough thermal energy for migration of host atoms introduced during growth into not proper sites). 2. ELECTRICAL PROPERTIES OF EL2 DEFECT

The EL2 defect has deep donor character. Mircea et al. (1976) showed that EL2 is electrically neutral when occupied by electrons and positively charged after relasing electrons. EL2 thermal energy was determined to be 0.75eV below the bottom of GaAs conduction band E, using Hall effect measurements (Henry and Lang, 1977). This means that the EL2 ground state of configuration EL2O/+ is roughly placed in the middle of the GaAs energy gap (EL2'" represents EL2 in the neutral charge state when the EC-0.75eV level is occupied and in a singly positive charge state after giving up an electron). EL2 thermal energy can also be obtained by deep level transient spectroscopy (DLTS) measurements. A typical DLTS spectrum of GaAs is shown in Fig. 3. Thermal ionization of the EL2 defect in a DLTS experiment is observed at slightly above room temperature. EL2 activation energy, EA, obtained from various published DLTS measurements oscillates around 0.825 eV (Martin et al., 1977). The seemingly most accurate value comes from Lagowski et al. (1984a), E , = 815 f 2 meV. According to Henry and Lang (1977) and Mitonneau et al. (1979), the electron-capture cross-section of the EL2 defect is strongly temperature-dependent. Therefore, in order to obtain EL2 thermal energy, EA must be corrected by subtracting about 70 meV, which leads to agreement with the value obtained from Hall effect measurements.

t a

0.08

0 -.0200 0 4 L Temperature 1°C 1

FIG. 3. DLTS spectrum of bulk as-grown GaAs, showing typical peak of EL2 defect.

64

M. KAMINSKA AND E. R. WEBER

The EL2 capture cross-section was (1.2 0.1) x 1013cm2 (Lagowski et al., 1984a).

PROPERTIES 3. OPTICAL

OF

determined

as

B=

EL2 DEFECT

EL2 optical cross-sections, both for photoionization to the conduction band (EL2' + EL2' + e in the conduction band) a;, and for electron capture from the valence band (EL2' + e in the valence band -+ EL2')a$ were determined by Bois and Chantre (1980) in arbitrary numbers by means of photocapacitance measurements, and are presented in Fig. 4. 0." starts at about 0.75 eV, which corresponds to electron optical transition to the r point of the GaAs conduction band. The changes of the slope seen for the 0." curve at about 1 eV and 1.3 eV were attributed to electron photoionization from EL2 to the conduction band in the region of the X and L points of the Brillouin zone in addition to simple photoionization to the point (Bois and Chantre, 1980). Silverberg et al. (1988) obtained the values for B." and a,"in absolute numbers at T = 78 and 295 K. From their data for T = 78 K the value of 0." at 1.2eV is about 1.3 x 10I6 cm2 and the value of B: at 1.0eV is about 0.4 x 10I6cm2. The near infrared absorption spectrum related to EL2 in neutral charge state was first published by Martin (1981)-Fig. 5. Later, the connection between this spectrum and the EL2 defect was supported by DLTS measurements (Skowronski et al., 1986). Namely, it was shown that the intensity of the absorption scales with EL2 concentration, obtained from DLTS. The absorption spectrum characteristic of n-type and SI GaAs consisted of three bands with energy thresholds at about 0.8 eV, 1.0 eV, and 1.3 eV-Fig. 5; its shape was similar to a:-Fig. 4. In 1983 it was found that

0.6

0.8

1.0 1.2 Energy lev1

1L

16

FIG. 4. Spectral dependence of optical cross-section 0." and 0," explained in the insert (Bois and Chantre, 1980).

2. EL2 DEFECT IN GaAs

65

Photon Energy (eV1

FIG. 5. EL2 absorption and photocurrent spectra with intracenter absorption spectrum separated.The shape of the EL2 absorption spectrum was first published by Martin (1981), and the fine structure shown in the insert by Kaminska et al. (1983).

the central part of the absorption spectrum begins with the zero phonon line (ZPL) at 1.039eV and a few of its replicas, mainly with a phonon of 11meV energy (Kaminska et al., 1983)-Fig. 5, insert. The comparison of the EL2 optical absorption spectrum with the corresponding photocapacitance (Bois and Chantre, 1980) and photocurrent (Kaminska et al., 1983)spectra showed that the central part of the three spectra is distinctly weaker for the last two. It was then possible to separate the absorption spectrum in the energy range 1.0-1.3 eV and attribute it to EL2 intracenter transitions (Kaminska et al., 1983)-Fig. 4. The rest of the absorption spectrum corresponds to EL2 photoionization to the conduction band. It begins with photoionization to the r point of the GaAs Brillouin zone at about 0.8eV and is followed by transitions to the L and X points starting from 1.0 and 1.3eV energy, respectively. The measurements of the 1.039 eV ZPL performed in magnetic field and under uniaxial stress (Kaminska et al., 1985) were the key optical experiment in the investigations of EL2 nature. Because of its importance, they were repeated independently by Bergman et al. (1988) and by Trautman et al. (1990), indicating the same number of stress-split spectral components as reported by Kaminska et al. (1985)and correcting the error made in the figure description regarding two symmetries in the polarization selection rules for (110) stress orientation. The results of an uniaxial stress experiment led to the identification of EL2O ground and excited terms in the intracenter absorption process as 'A, and 'Tz, respectively (Kaminska et al., 1985).This means that the EL.2' ground state of energy position in the middle of the GaAs gap has 'A, symmetry and the excited state, resonant with the conduction band and placed at 1.04eV above the ground state, has 'T, symmetry. The T, representation is triply degenerated, and levels belonging to such represen-

66

M. KAMINSKA AND E. R. WEBER

tation cannot exist in lower symmetry than & (tetrahedral). This indicates that EL2 must be a point defect with & point symmetry, and should therefore have a tetrahedral neighbourhood. Together with the technological data presented in Section 11.1, the results of the uniaxial stress experiment strongly indicated that the isolated arsenic antisite defect is the origin of EL2. The further discussion of this problem together with other proposed models of EL2 will be presented in Part V. EL2 luminescence properties are not yet well established. Many authors (Yu, 1979, 1982, 1984b; Yu and Walters, 1982; Yu et al., 1982; Leyral and Guillot, 1982; Leyral et al., 1982; Mircea-Roussel and Makram-Ebeid, 1981; Shanabrook et al., 1983; Samuelson et al., 1984; Tajima, 1982, 1984, 1985a, 1985b, 1985c, 1986; Tajima et al., 1986a, 1986b;and Kikuta et al., 1983)have reported a luminescence spectrum for SI GaAs crystals with Gaussian shape and peak position changing in the energy range 0.62-0.68 eV. Tajima et al. (1986a)showed that this luminescenceindeed consists of two bands peaked at 0.63eV and 0.67eV that could be separated by excitation with light of different energies-see Fig. 6. The 0.63 eV luminescencecould be excited with light of energy higher than 1.4 eV, whereas the 0.67 eV band appeared for excitation with light from the energy range 0.8-1.4 eV. The excitation spectrum of 0.67eV luminescence is shown in Fig. 7. It involves two bands peaked at about 1.0 and 1.3eV (Tajima et al., 1986a). Tajima (1986) also found that the 0.67 eV luminescence starts with fine structure consisting of a zero-phonon line at 0.758 eV and its replicas with 11 meV phonon-Fig. 8. Because a phonon of such energy is not characteristic of the GaAs host

0.5 0.6 0.7 0.8 0.9 Photon Energy (eV) FIG. 6. Photoluminescence spectra of undoped SI LEC GaAs as a function of excitation photon energy (Tajima ei al., 1986a).

2. EL2 DEFECT IN GaAs I

!

1

'

1

*

I

,

I

'

I

67

,

I

T1L.2 K

0.6

I

,

I

1.0 1.2 1.4 Photon Energy I eV I

0.8

,

I

1.6

FIG.7. 0.67 eV photoluminescenceand photoluminescenceexcitation spectra of GaAs. For exciting light of 0.8-1.4 eV energy, a 0.67 eV luminescence band was observed, whereas 0.63 eV luminescence appeared for exciting light of energy higher than 1.4 eV (Tajima et al., 1986a).

3

m , , , , . , , , , ,

0 h

c

ul

4

C

0 .-

.-3

E

W

0.68 0.72

0.76 0.80

Photon Energy (eV ) FIG. 8. Spectrum of vibrational structure of 0.67 eV luminescence band (Tajima, 1986).

lattice, and because it appeared in the EL2 intracenter absorption spectrum (Kaminska et al., 1983), it is possible that 11 meV is a local phonon characteristic for EL2 and 0.67 eV luminescence is related to EL2. However, no other support for this relation exists. Tajima (1986) and Tajima et al. (1986a) linked 0.67 eV luminescence to an electron transition from the EL2 level to the GaAs valence band. We think rather that this luminescence is related to the intracenter transition of EL2 in the singly ionized charged state. It will be further discussed in Part IV. Several authors (Yu et al., 1982; Tajima, 1982; Kikuta et al., 1983; Windscheif et al., 1983; and Yu, 1984a)also attributed another luminescence observed in SI GaAs with a maximum at about 0.8eV energy to the EL2 defect. However, no suggestion about a link to any specific transition was given. Moreover, there is no proof that this luminescenceis related to the EL2 defect.

M. KMNSKA

68

AND

E. R. WEBER

For n-type GaAs, Tajima et al. (1986b) observed a luminescence spectrum with the maximum varying in the energy range 0.61-0.68 eV depending on the crystal. However, for T = 77K the maximum of the band was always around 0.63 eV. They attributed this luminescence to deexcitation of an electron from the conduction band to the EL2 level. Again, there is no proof that this luminescence is related to EL2.

4. METASTABLE PROPERTY OF THE EL2 DEFECT EL2 metastability is often called the fingerprint of this defect. It is indeed recognized as the most characteristic feature of EL2, occurring at low temperatures under the influence of illumination with light of 1.0-1.3 eV energy (Leyral et al., 1982; Bois and Vincent, 1977; Vincent et al., 1982). The studies of EL2 metastability allowed a precise determination of the excitation spectrum for the process of EL2 transition to its metastable state EL2M (Leyral et al., 1982; Vincent et al., 1982; Skowronski et al., 1985; Kuszko and Kaminska, 1986). It turned out that the excitation spectrum is identical to the EL2 intracenter absorption spectrum (Fig. 9), including its fine structure. That proves that the EL2 intracenter transition ' A , -,IT, is the first step toward the metastable configuration. EL2 metastability can be observed in photocurrent (Lin et al., 1976), photocapacitance (Vincent and Bois, 1978; Mitonneau and Mircea, 1979; Omling et al., 1984), absorption (Martin, 1981), and luminescence (Yu, 1984b; Leyral and Guillot, 1982; Leyral et al., 1982; Tajima, 1985a) measurements through the quenching of the respective spectra-for example, see absorption quenching in Fig. 10. The first report about the extraordinary feature of GaAs crystals, which was the quenching of

-VI

5

-m

I .-

-lnh-xmkrAbrorptm

-

C

OLwMcrCrmc

- -2

Flm(ocopaclbrr.

c

- .-

u .c

-

01

u

s

._

-; c

'

n

.<

2. EL2 DEFECT IN GaAs

69

Energy (eV) FIG. 10. Optical absorption spectra for the same undoped SI GaAs crystal. Curve a: after cooling in the dark; curves b and c: after white light illumination for one and 10 minutes, respectively (Martin, 1981).

the photocurrent spectrum as a result of illumination, appeared in 1976 (Lin et al., 1976), even before the introduction of the EL2 name. The first detailed description of a photocapacitance transient corresponding to ionization and EL2 defect transition to its metastable state was given by Bois and Vincent (1977). In Fig. 11 such photocapacitance changes under illumination with 1.06pm light are shown. The photocapacitance changes, its initial fast rise and subsequent slow decrease almost to the initial value without further light sensitivity, show that electrons from the EL2 ground state freeze at the EL2 metastable state and cannot be further ionized to the conduction band. It is well established that the EL2 transition from its neutral ground state

Time (s) FIG. 11. Photocapacitance quenching in GaAs at 77 K versus time after a direct electric pulse under 1.17 eV illumination (Bois and Vincent, 1977).

70

M. KAMINSKA AND E. R. WEBER

to the metastable state occurs without change of the defect charge state (Skowronski et al., 1985; Bray et al., 1986). Therefore, the EL2 defect is neutral when in the metastable state (i.e., the EL2Mo'+ level is occupied). On the other hand, no optical absorption spectrum characteristic of the EL2 metastable state has been found. It is thus impossible to determine the energy position of the EL2 metastable state within the GaAs band structure. Usually it is placed in the upper part of the GaAs energy gap (Bois and Vincent, 1977; Vincent et al., 1982; Chantre et al., 1981). The return from the metastable to the ground state takes place with the thermally activated rate r determined independently by Mittoneau and Mircea (1979): I

= 8 x 10" exp(-0.34 eV/kT)s-'

and by Vincent et al. (1982): r = 2 x 10" exp(-0.3 eV/kT)s-'.

Mittoneau and Mircea (1979) also showed that EL2 recovery from its metastable state is accelerated by the presence of free electrons. They proposed two mechanisms for the transition to ground state: (i) thermal deexcitation through the barrier of about 0.3 eV; (ii) "Auger-like" deexcitation. The full formula for the rate of EL2 recovery from its metastable state can in general be written as r = 2 x 10' exp( -0.3 eV/kT) s -

+ 1.9 x 1014nu, exp(-0.107

eV/kT) s- l ,

where n is the free electron concentration in cm-3 and u, is the thermal electron rate in cm/s for temperature 7: Studies of EL2 recovery from its metastable state were also carried out by means of absorption measurements (Trautman et al., 1987). The kinetics of thermally activated recovery of EL2 absorption was observed after prior quenching of the spectrum (see Fig. 12). As can be seen in Fig. 12, the recovery process depends on the number of free electrons and it occurs typically at about 130 K for SI GaAs and about 60 K for n-type GaAs. The analysis of the kinetics of EL2 recovery for different n-type and SI GaAs crystals fixes the rate of EL2 recovery as r = 1.7 x 101zexp(-0.36eV/kT)s-1+ 1 . 6 10-9nexp(-0.085eV/kT)s-1. ~

2. EL2 DEFECT IN GaAs Time

-

71

1

Temperature ( K 1

FIG. 12. Thermally activated recovery of EL2 absorption taken at 1.17eV for n-type and SI GaAs after previous quenching by illumination with 1 pm light at T = 10 K (Trautman et al., 1987).

(n x 10l6

In SI GaAs when the number of free electrons is small, the second part of this formula can be neglected, and the recovery occurs mainly through a barrier of about 0.3 eV height (this corresponds to a 130 K recovery temperature). In ntype GaAs the second part of the formula becomes important; it describes the shift of the recovery process to lower temperatures. The full formula for I obtained by means of absorption recovery measurements is consistent with the Mittoneau and Mircea (1979) model of the two mechanisms participating in EL2 recovery and, within experimental error, agrees with the values of parameters describing the recovery rate obtained by them. It seems that the recent hydrostatic pressure experiment (Baj and Dreszer, 1989), and, one hopes, future such experiments, can provide new information about the nature of so called “Auger-like’’ deexcitation, an EL2 recovery mechanism, which has never been precisely characterized. Optical absorption measurements under hydrostatic pressure showed the existence of another charge state EL2M-1’ in the metastable configuration a small distance above the bottom of the GaAs conduction band. Probably this level, EL2M-”, when occupied with an electron, accelerates EL2 recovery, and its action is described by the second part of the formula for the EL2 recovery rate. The EL2M-’’ should then have a smaller barrier for transition to the EL2 normal state (about 0.1 ev) than EL2M01+,for which it is about 0.3 eV. Baj and Dreszer (1989) showed also that at hydrostatic pressure above 0.3 GPa, the EL2M-/’ state enters the GaAs energy gap, which enables the capture of an extra electron by EL2. In recent years, more data have emerged on optical regeneration of EL2 from its metastable configuration, as well as on the well-known purely thermal recovery of EL2 discussed earlier. Early on it was thought that EL2 in the metastable state is optically inactive and that recovery can be achieved only through thermal excitation. However, photoinduced EL2 recovery by

72

M. KAMINSKA AND E. R. WEBEX

differentexperimental techniques has been reported recently: photoluminescence (Tajima, 1984), photoconductivity (Nojima, 1985a, 1985b; Nojima et af.,1987; Jimenez et al., 1989; and Alvarez et af., 1989), photocapacitance (Mochizuki and Ikoma, 1985), absorption (Fischer, 1987; Parker and Bray, 1988; Tajima et al., 1988; Fischer and Manasreh, 1989; Manasreh and Fischer, 1989) and EPR (von Bardeleben et al., 1987). These studies have established that the optical recovery of EL2 in the metastable state can be induced. However, it is difficult to draw any common conclusion from these data. Even basic features of the optical recovery process, such as the spectral dependence or the number of recovered centers, differ from paper to paper. It seems that the process is temperature-dependent, and since different studies were performed at different temperatures from that of liquid helium to above 100K, comparison is difficult. Generally, at helium temperatures only a few percent of the EL2 centers could be optically recovered but the efficiency of this process increases with temperature. Further studies are necessary to provide an understanding of the process of EL2 photoinduced recovery and to decide if it is due to the creation of free electrons by illumination, which as discussed earlier accelerate the recovery process, or if it is connected with any particular transition within the EL2 defect. It is notable that the optical recovery is much more efficient under hydrostatic pressure, especially above 0.3 GPa, when 100%of the EL2 centers can be recovered even at helium temperatures (Baj and Dreszer, 1989). Also, the effective recovery of an EL2-like defect at helium temperatures was observed in LT-GaAs (Kurpiewski et al., 1991). Very recently, the optical recovery of EL2 was directly confirmed for semi-insulating GaAs, using above-bandgap illumination (Khachaturyan et al., 1992).

In. Arsenic Antisite Defect in GaAs 5. EPR

STUDIESOF ARSENICANTISITEDEFECT

The first report of an arsenic antisite defect in as-grown SI GaAs was made in 1980, when the characteristic four-line spectrum was observed in an EPR experiment (Wagner et ai., 1980bFFig. 13. The four isotropic lines were interpreted as originating from the electron hyperfine interaction with the central nucleus of spin: I = $. The defect was identified as a positively charged arsenic antisite (singly ionized arsenic atom with three electrons in the bonds) on the basis of the shape of the EPR spectrum, its line intensity, and the value of spectrum parameters (arsenic nucleus spin: I = 3). In the EPR spectrum, only the hyperfine interaction with the nucleus of arsenic is resolved, whereas individual lines of superhyperfine interaction with ligands are not seen. That is because of the low super-hyperfine splitting

2. EL2 DEFECT IN GaAs

I

I

I

I

lo00

2000

3000

73

I

I

I

Loo0 5000 Magnetic Field t Gauss)

FIG. 13. EPR spectrum due to the arsenic antisite defect (Weber and Omling, 1985).

in comparison with the width of its components. Therefore, it is not possible to discern in a simple way arsenic antisite defects with different ligand surroundings. However, on the basis of parameters describing the EPR spectrum and by comparing them with analogous data for P-P, (phosphorus antisite with four phosphorus ligands) and P-P, (phosphorus antisite with three phosphorus ligands) defects in Gap, it was concluded that the EPR signal originates from the As-As, defect (Goswami et al., 1981). This means that at least the first coordinate zone of the antisite defect is a tetrahedron consisting of four arsenic atoms. One of the most important questions for EPR investigations of the arsenic antisite defect was whether that center has any connection with the EL2 defect. Based on a wide range of different studies (described briefly in the following), it was proven that in as-grown GaAs, EL2 is identical with the arsenic antisite observed by EPR. However, one should remember that the DLTS peak above room temperature (Fig. 3), as well as the characteristic infrared absorption band shown in Fig. 5, is related to the neutral charge state (three arsenic valence electrons participating in GaAs bonds and two electrons present at the center), whereas the EPR signal corresponds to the singly ionized charge state of the arsenic antisite defect (three arsenic valence electrons participating in GaAs bonds and one unpaired electron present at the center). The first suggestion as to the identity of EL2 and the arsenic antisite defect observed by means of EPR was made by Weber et al. (1982) on the basis of a photo-EPR experiment on plastically deformed GaAs. Plastic deformation leads to a substantial increase in arsenic antisite-related defects, and therefore the EPR signal is bigger than in as-grown crystals and thus is more easily studied. The photo-EPR experiment showed that the arsenic antisite defect possessed two energy levels: As;:' at 0.52 eV and AsgP at 0.75 eV above the valence band. The latter level was identified with the +

M. KAMINSKA AND E. R. WEBER

74

EL2OJ midgap level. However, since this experiment was performed on plastically deformed GaAs, further studies were made on as-grown crystals in order to support the connection of EL2 and the EPR quadruplet signal. In 1984 the correlation of EPR line intensity with the concentration of carbon acceptor in as-grown GaAs was recognized (Elliott et al., 1984). This suggested that the arsenic antisite defect observed in EPR had a compensation character; on the other hand, it was well known that EL2 is the main compensating center for shallow acceptors in undoped GaAs. The next argument for the identity of EL2 with the arsenic antisite defect observed in EPR came from experiments in which it was found that the EPR signal after illumination of crystals with 1 pm light at helium temperature had a metastable character (Baumler et al., 1985).The EPR signal was recovered on heating the sample to about 140K, which correlated with the metastable properties of EL2 in SI GaAs. The photo-EPR experiment reported by Baumler et al. (1985) made on as-grown GaAs confirmed the energy positions of the two charge states of arsenic antisites as proposed by Weber et al. (1982) from the experiments performed on plastically deformed crystals. The very last word in the matter of relations between EL2 and the arsenic antisite defect observed by means of EPR was given by Hoinkis et al. (1989). The systematic studies performed on a great variety of GaAs crystals by different techniques led to the conclusion that EL2 has two energy levels, gives rise to the ZPL in the neutral charge state, and gives rise to the EPR quadruplet, MCD (magnetic circular dichroism), and ODENDOR (optically detected electron-nuclear resonance) signals in the singly ionized state (MCD and ODENDOR experiments are discussed in the next paragraph). The transfer of EL2 to its metastable state is connected with the disappearance of all these manifestations. The question about the identity of EL2 and EPRdetected arsenic antisite was answered positively and, it is to be hoped, definitely. +

6. ODENDOR STUDIESOF ARSENICANTISITEDEFECT

The super-hyperfine interaction of many defects with ligands can be observed by means of the electron-nuclear double resonance (ENDOR) technique, which provides information about the close neighbourhood of the defect. Unfortunately, ENDOR cannot be used on GaAs because of a very low signal-to-noise ratio. On the other hand, the magnetic resonance technique connected with optical detection (specifically, optically detected ENDOR, that is, ODENDOR) is extremely valuable for investigations of arsenic antisite microscopic structure in GaAs crystals. This technique was applied successfully to GaAs by Spaeth (1986). Optical detection methods are

2. EL2 DEFECT IN GaAs

75

Enerqy IeV1

Wavelength 1 nm)

FIG. 14. Integrated magnetic circular dichroism of as-grown SI GaAs and its decomposition into two Gaussian bands (Meyer et al., 1984).

based on the effect of the magnetic circular dichroism (MCD) of the absorption spectrum. For GaAs two absorption bands with peak positions at 1.05eV and 1.29 eV were found (see Fig. 14) and ascribed to As& defect intracenter transitions (Meyer et al., 1984). As mentioned in Section 111.5, it was verified in different studies that the defect observed by ODENDOR spectroscopy is the same as the AsGacenter seen by EPR, DLTS, and optical absorption measurements (Hoinkis et al., 1989, and Hofmann et al., 1986). The angular dependence of ODENDOR lines showed a complicated structure, but most lines could be explained by taking into account interactions of the arsenic antisite with four neighbouring arsenic atoms. However, for high radio frequency, some extra lines were observed coming from (111)-directed interactions within the same defect center. Based on the fit to these extra lines, it was proposed that the EL2 defect is an arsenic antisite complex with arsenic interstitial located on the (111) direction but outside the closest interstitial location with respect to the antisite atom (Hofmann et al., 1986, and Spaeth, 1986). This is in obvious contradiction to the conclusion coming from the previously described uniaxial stress experiment performed on the EL2 ZPL (Kaminska et al., 1985) which supports the isolated arsenic antisite model. Models of EL2 and all contradictions will be discussed later in Part V.

IV. Energy Levels of EL2 Defect

As pointed out earlier, the results of electrical (Henry and Lang, 1977), capacitance (Lagowski et al., 1984a),optical (Kaminska et al., 1985)and EPR (Weber et al., 1982) measurements allowed the determination of the energy levels of EL2. The EL2'/+(As:r) level is placed at 0.75 eV below the bottom of the GaAs conduction band, and EL+/++(As;:+ +) at about 0.52 eV above the top of the valence band. Combining the results of DLTS (Lagowski et al., 1984a) and optical (Kaminska et al., 1985)experiments, it is possible to place

76

M.KAMINSKA AND E. R. WEBER

EL2 +'

\

FIG. 15.

\\\\'\'IT

V.B.

Energy levels of the EL2 defect in the neutral charge state within the GaAs band

structure.

the energy levels of the EL2 defect in its neutral state within the GaAs band structure, as seen in Fig. 15. On the other hand, from photo-EPR (Weber et al., 1982) and integrated MCD (Meyer et al. 1986) spectra, the energy position of As& defect levels can be determined. The thermal energy of excited levels in respect to the ground one must be taken as the low energy thresholds of the separated bands of the integrated MCD spectrum. This means that two excited As;, states are about 0.8 eV and 1.15eV above the ground one. On the other hand the excitation spectrum of EL2 0.67 eV luminescence (Fig. 7) is very similar to the integrated MCD spectrum (Fig. 14). Therefore, we believe that 0.67 eV luminescence is excited through As:, excited states and 0.67 eV luminescence corresponds to the intracenter transitions within the As& defect. The energy 0.76 eV of the 0.67 eV luminescence ZPL (Tajima, 1986) can be then regarded as the energy distance between As;, ground and the first excited states. This energy distance is determined with greater accuracy than if taken from 0.8eV threshold of the integrated MCD curve. Figure 16 shows the energy levels of the As;, defect.

I

\\\\\\\\\\\\

V.B

FIG. 16. Energy levels of the arsenic antisite defect in the singly positive charge state within the GaAs band structure.

2. EL2 DEFECT IN GaAs

77

Up to now, no experiment could determine the energy position of the EL2 metastable state, EL2Mo‘+. As mentioned in Section 11.4, this state was usually placed in the upper part of the GaAs energy gap (Bois and Vincent, 1977; Vincent et al., 1982; Chantre et al., 1981). From experiments studying the return of the EL2 defect from its metastable to the ground state, the value of the thermal barrier between the metastable and the ground state was determined to be about 0.3 eV (Vincent et al., 1982; Mitonneau and Mircea, 1979). By means of recent hydrostatic pressure experiments, the position of the EL2M-I’ charge state was found to be about 16 meV above the bottom of the conduction band (Baj and Dreszer, 1989).

V. Models of EL2 Defect

Studies of the dependence of EL2 concentration on stoichiometry and on doping level with shallow donors (Lagowski et al., 1982b), as well as the results of EPR measurements (Weber et al., 1982),provided strong evidence that EL2 contains AS,. However, there is still controversy as to whether EL2 is the isolated AsGaitself or a complex of two or more defects, one of which is the AsGa. Furthermore, there are obvious differences between properties of centers giving the same characteristic EPR quadruplet signal (Weber and Omling, 1985), indicating the existence of a “family” of arsenic antisiterelated defects. The arguments in favour of different models of EL2, as well as the meaning of the EL2 family, are presented next.

AS A MODEL OF EL2 7. IWLATED ARSENICANTISITEDEFECT

The piezoabsorption and Zeeman effect measurements carried out by Kaminska et al. (1985) on the ZPL of EL2 intracenter transitions yielded the symmetry of EL2 ground and excited levels as ‘ A , and T,, respectively. That indicated point symmetry of EL2. On the other hand, the technological (Lagowski et al., 1982b) and EPR (Weber et al., 1982) data showed that the arsenic antisite is involved in the formation of EL2. It could therefore be concluded that EL2 is an isolated arsenic antisite (Kaminska, 1985).One can, however, suppose that outside the first coordination zone, which makes the main contribution to the local field, there occurs disorder having a weak interaction with the arsenic antisite and unnoticed in the uniaxial stress experiment. That possibility was excluded by means of very high-resolution absorption measurements performed in the energy region of EL2 intracenter absorption ZPL (Kuszko et al. 1988).No additional structure resulting from

’

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M. KAMINSKAAND E. R. WEBER

possible complexing of the arsenic antisite was observed. Therefore, all together the optical studies strongly support the model of EL2 as an isolated arsenic antisite. For many years, the real challenge to the model of EL2 as a point defect of arsenic antisite was its metastability. In early EL2 studies it was thought that an isolated defect in a covalent crystal such as GaAs is too simple to give rise to metastability. Initial theoretical calculations supported this point of view, showing that there was no large lattice relaxation of AsGa and that the breathing distortion at the AS,, was less than 1% (Bachelet and Scheffler, 1985, and Scheffler et al., 1985). The breakthrough in this matter was made by Baranowski et al. (1986), Dabrowski and Scheffler (1988), and Chadi and Chang (1988). They explained the EL2 transition to its metastable configuration as the photodissociation of AsGa instead of symmetric lattice relaxation. The idea was that under illumination an arsenic antisite atom moves from an antisite position in the (1 1 1 ) direction toward an interstitial position. Using modern pseudopotential calculations in which the motion of the extra arsenic atom can be followed, Dabrowski and Scheffler (1988) and, independently, Chadi and Chang (1988) showed that there is a metastable minimum of energy at about midway between the Ga site (occupied by an As atom when EL2 is in the normal state) and the arsenic interstitial position. Therefore, EL2 metastability can be explained in terms of an isolated arsenic antisite model with the assumption that under illumination, nonsymmetric movement of the antisite arsenic atom in the (1 1 1) direction occurs. The pseudopotential calculation also supported the idea that arose from the experimental studies of Skowronski et al. (1985) and Kuszko and Kaminska (1986), that the first step in achieving metastability was the EL2 intracenter transition ' A , 3 ' T 2 .From the fit to the data of uniaxial stress experiment, the 'T, state was found to be coupled with T Jahn-Teller mode (Kaminska et al., 1985), leading to a slight movement of the extra arsenic atom in the ( 1 11) direction after intracenter transition. This movement in the ( 1 11) direction is much more pronounced when the metastable configuration is achieved. 8. COMPLEX OF DEFECTS AS

A

MODELOF EL2

Several models of the EL2 defect as a complex have been proposed. In most of them the arsenic antisite is associated with another defect, such as an arsenic vacancy, VA, (Lagowski et al., 1983), a second arsenic antisite AsG, (Figielski et al., 1985), clusters of other arsenic atoms (Ikoma et al., 1984), or arsenic interstitial Asi (von Bardeleben et al., 1985). Theoretical calculations showed that the AsGa-YAs model could not be taken seriously since (1) the

2. EL2 DEFECT IN GaAs

79

EPR spectrum should be that of V’, instead of AsGa (Baraff and Schluter, 1985, 1986) and (2) rearrangement of the AsGa-VAAscomplex to a gallium vacancy in n-type GaAs should occur (Figielski et al., 1985; Ikoma et al., 1984; and von Bardeleben et al., 1985), which contradicts experimental data. On the other hand, the model of two arsenic antisites was not consistent with polarization rules for the splitting of the ZPL coming from EL2 intracenter absorption (Bergman et af., 1988, and Figielski and Wosinski, 1987). The “complex” EL2 model, which is still seriously considered by some researchers, is a pair of arsenic antisite with an arsenic interstitial. Bardeleben et al. (1985)were the first to propose this model, when by means of EPR and DLTS measurements they found two types of arsenic antisite defect in electron-irradiated GaAs. One of them was identified with EL2 because of its characteristic photoquenching behaviour (metastability),and the other was stable under photoexcitation. As shown by DLTS, after 850°C thermal treatment (10 minutes) followed by a quench, EL2-like centers partially annealed, whereas the remaining defects showed no more metastability. Further long annealing (about 60 minutes) around 100°C restored metastable properties of the defects. To explain such behaviour, von Bardeleben et al. (1986a) and Stievenard et al. (1986) postulated that the EL2 ground state corresponds to the complex of an arsenic antisite with an arsenic interstitial in the second neighbour position, trapped by the strain field of AsGa The effect of 850°C thermal treatment was explained as the breaking of the AsGa + As, complex into an AsGaisolated defect that remained in its position and an Asi atom that moved away. The complex could be restored by long annealing around l W C , during which the migration of the Asi atom toward the AsGa defect was possible. In this model, EL2 transition from a stable to a metastable configuration was explained as the change of the position of Asi from the AsGa second neighbour to the first neighbour one. However, this model does not explain certain experimental results. First of all are the results of optical measurements. Since some uncontrolled outdiffusion in the region close to the surface of an annealed sample always occurs, it seems that DLTS results of succeeding steps of thermal annealing should be verified by means of absorption measurements. (One must remember that the effects observed by DLTS refer to a region about 1 pm from the sample surface, whereas absorption refers to bulk properties.) As reported by Baranowski et al. (1986), SI GaAs samples covered with Si,N, were heated up to 850°C and then rapidly cooled to room temperature. The EL2 infrared absorption spectrum, including its fine structure at 10 K, absorption quenching after 1 pm illumination, and thermally activated process of absorption recovery up to room temperature, was investigated. In contrast to the DLTS data, no differences in EL2 optical properties before and after annealing were observed. At the same time, the DLTS data of von

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Bardeleben et al. (1985) were not fully reproduced by other research groups. As already mentioned in Section 11.1, Lagowski et al. (1986)as well as Haga et al. (1988) reported EL2 destruction above 1,ooo"C and its regeneration around 800°C. Nevertheless, the first theoretical semiempirical calculations by Baraff and Schluter (1987),Baraff and Lannoo (1988),and Caldas and Fazzio (1989) gave support to the AsGa-Asi complex model of EL2. Simultaneously, Delerue et al. (1987) explained metastability in this model as displacement of Asi. However, more recent self-consistent total energy calculations (Dabrowski and Scheffler, 1988, 1989) showed that the distant pair AsG,-Asi was practically unbound. Moreover, such a pair should have a shallow level close to the conduction band, which is in obvious conflict with the role of EL2 as a compensating deep center in SI GaAs. It seems that the AsGa-Asi model of EL2 does not fully explain EL2 properties. On the other hand, the AsGa-Asi model of EL2 is consistent with the explanation of ODENDOR lines (Spaeth, 1986)as discussed in Section 111.6.ODENDOR results indicated that a singly ionized arsenic antisite defect is weakly coupled with another defect placed on the (1 1 1) direction, which was ascribed to an arsenic interstitial. More work seems necessary in order to either support or reject the AsG,-As~ model of EL2.

9. EL2 FAMILY

Taniguchi and Ikoma (1983) were the first to point out the differences between midgap levels in LEC GaAs. They compared wafers coming from the seed and tail parts of the same ingot by DLTS. In the sample cut close to the seed, a level with activation energy 0.75 eV and electron-capture cross-section 2.4 x cm2 was found, whereas the sample cut from the tail part showed the presence of a level with activation energy 0.82 eV and electron-capture cross-section 3 x cm2. The tail level had practically the same parameters as the midgap defect in Bridgman-grown GaAs. As shown by DLTS, this defect is the only mid-gap defect in Bridgman-grown GaAs except for the specific case of intentionally heavy doped material with Ga,03, when another level (probably due to oxygen) is present (Lagowski et al., 1984a). A peculiar point was that all GaAs mid-gap levels in LEC and Bridgman crystals showed the same metastable properties characteristic of EL2 (Ikoma er al., 1984, and Taniguchi and Ikoma, 1984). Simultaneously, photocapacitance kinetics connected with defect transitions to the metastable state were nonexponential (Taniguchi et al., 1986, and Mochizuki and Ikoma, 1985). On the basis of these data Taniguchi and Ikoma (1983) postulated the existence of a whole family of mid-gap levels (so called EL2 family) in GaAs

2. EL2 DEFECT IN GaAs

81

instead of a single level. As suggested by Ikoma and Mochizuki (1985), the arsenic aggregates of different size (Ikoma et al., 1981) could be responsible for the origin of different mid-gap levels. However, in bulk as-grown GaAs, the presence of an EL2 family is not detected by optical absorption measurements. Both LEC and Bridgmangrown crystals show identically shaped infrared absorption bands and accompanying fine structures (Kaminska, 1985),although the fine structure in particular should be very sensitive to differences within an EL2 family. In addition, several papers appeared questioning the accuracy of defect parameters obtained by DLTS. It was shown that the method of surface treatment (Hasegawa et al., 1986), high ratio of deep level concentration to uncompensated shallow donor concentration (Skowronskiet al., 1986),poor quality of Schottky diode with too high reverse bias current (Lagowski et al., 1984b) and high electric field in the range of Schottky diode (Makram-Ebeid and Lanoo, 1982)could cause a shift and broadening of DLTS peaks and lead to a nonexponential capacitance transient. This can result in erroneous determination of deep-level parameters. Therefore the idea of an EL2 family existing in as-grown bulk GaAs and consisting of defects with different parameters as determined from DLTS measurements is questionable. On the other hand, there are unquestionable differences between the properties of arsenic antisite-related defects present in as-grown bulk GaAs and those of such defects introduced in plastically deformed GaAs or GaAs irradiated with electrons or neutrons. After the first observation of a characteristic EPR quadruplet signal ascribed to the arsenic antisite-related defect by Wagner et al. (1980b) in as-grown GaAs, many other papers appeared presenting the same four-line EPR spectrum for plastically deformed GaAs (Weber et al., 1982;Weber and Schneider, 1983; Wosinski et al., 1983; Omling et al., 1986; and Suezawa and Sumino, 1986), electronirradiated GaAs (Goswamiet al., 1981;Kennedy et al., 1981; Beall et al., 1985; von Bardeleben and Bourgoin, 1985; von Bardeleben et al., 1985, 1986a, 1986b, 1986c, and Goltzene et al., 1985a) and neutron-irradiated GaAs (Woerner et al., 1982; Schneider and Kaufmann, 1982; Goltzene et al., 1984a, 1984b, 1984c, 1984d, 1985a, 1985b, 1986; Beall et al., 1986; and Wosik et al., 1986)-Fig. 13. The concentration of arsenic antisite-related defects was in plastically deformed crystals (Omling et shown to increase up to 10’’ al., 1986).In electron-irradiated material it reaches an 8 x lo” cm-’ value for 4 x 10l8 doses (Goswami et al., 1981), and in neutron-irradiated GaAs for doses above 10l8 cm-2 (Beall et al., 1986). it grows up to lo’* Although the position and the shape of the four lines in the EPR spectrum was the same for all GaAs crystals mentioned above, there was a basic difference in metastable properties. In as-grown GaAs, the EPR spectrum as well as the characteristic absorption band of the EL2 defect disappeared after

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M. KAMINSKA AND E. R. WEBER

illumination at low temperatures as described in Section 11.3. Such was not the case in plastically deformed GaAs, where only a small part of the infrared absorption was quenchable (Omling et al., 1986) (see Fig. 17), and in electronirradiated GaAs where partial quenching of the EPR quadruplet signal was observed (von Bardeleben et aL, 1985). In neutron-irradiated GaAs no metastability of the EPR signal and near infrared absorption was detected (Wosik et af., 1986). Arsenic antisite defects also differ in annealing temperature. In as-grown GaAs, EL2 is stable up to about 850°C (Makram-Ebeid et al., 1982). However, the clear annealing steps of arsenic antisite defects produced by plastic deformation at about 500°C (Weber and Schneider, 1983) and at about 450°C for neutron-irradiated GaAs (Woerner et al., 1982) were observed. One more important difference between arsenic antisite defects in as-grown and deformed or irradiated GaAs, namely temperature dependence of EPR signal (related to the spin-lattice relaxation time), was studied carefully by Hoinkis and Weber (1989). They correlated the temperature dependence of the EPR signal with the metastable property of the AsGa defect and distinguished two classes of centers: (i) with metastable property and longer spin-lattice relaxation time and (ii) with shorter spin-lattice relaxation time and lack of metastability. A local stress field tends to shorten spin-lattice relaxation time. Therefore, Hoinkis and Weber (1989) suggested the existence of a class of similar arsenic antisite-related defects that are exposed to differing local stress fields. High local stress present in neutronirradiated GaAs is correlated with the lack of metastability of the arsenic

0.6

0.8 1.0 1.2 l.L Photon Energy (eV)

FIG. 17. Near-infrared absorption of different plastically deformed GaAs crystals before and after illumination with white light (Omling et al., 1986).The strength of deformation is indicated on the figure.

2. EL2 DEFECT IN GaAs

83

antisite defect in such crystals. On the other hand, EL2 in as-grown GaAs with relatively low local stress does possess the metastable property. In plastically deformed GaAs both kinds of antisite arsenic, with and without the metastable property, can be present in similar concentrations (the ratio between the two kinds of centers depends on the deformation strain experienced by the crystals). In the same spirit one can understand the properties of arsenic antisite defects observed in LT MBE GaAs. Because of low growth temperature, such crystals can be strongly arsenic rich; their lattice parameter differsby 0.1% from bulk GaAs (Kaminska et al., 1989),and one can expect high local stress fields higher than in as-grown GaAs. It is therefore not surprising that arsenic antisite defects in LT MBE GaAs crystals show only partial quenching, as shown by Kaminska et al. (1991b) and Kurpiewski et al. (1991), indicating that some defects possess metastability and some do not. In conclusion, it seems that differences between EL2 defects in as-grown bulk GaAs are negligible (if any), but there is noticeable variation in the properties of arsenic antisite-related defects in GaAs crystals with different local stress fields.

VI. Conclusions

In conclusion, the features of the EL2 model that are accepted by most researchers are presented. They are followed by a short discussion of points of the EL2 model that are still controversial. The association between EL2 and AsGais not questioned. It was confirmed by: (1) technological experiments-creation of EL2 under As-rich conditions and annihilation by intentional heavy shallow donor doping (Lagowski et al., 1982b);and (2) EPR measurements-identification of the AsGa quadruplet signal (Wagner et al., 1980b) and identical energy levels and quenching behaviour of AsGa as EL2 defect (Weber et al., 1982, and Baumler et al., 1984).

The closest neighburhood of the arsenic antisite in the EL2 defect is a tetrahedron formed by four arsenic atoms. That conclusion comes from the uniaxial stress and Zeeman effect measurements carried out on EL2 intracenter absorption ZPL (Kaminska et al., 1985). They indicated T, as EL2 point symmetry. Also, the value of parameters describing the EPR spectrum of AsGa in as-grown GaAs agrees well with the value expected for the As-As,

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defect (Goswami et al., 1981). The ODENDOR pattern also supports this statement (Meyer et al., 1987). It is strongly probable that tbe EL2 defect in its metastable configuration distingmisbes the (111) direction. However, it was found that the 'A, T2EL2 intracenter transition is the first step in achieving its metastable state (Skowronski et al., 1985; Kuszko and Kaminska, 1986), and the T2state is coupled with the t Jahn-Teller mode (Kaminska et al., 1985). This means a slight movement of the arsenic antisite atom in the (111) direction after the intracenter transition. The pseudopotential calculation (Dabrowski and Scheffler, 1988; Chadi and Chang, 1988) suggested that the movement in the (1 11) direction is increased when the EL2 metastable configuration is being achieved. Very recently, Trautman and Baranowski (1992) experimentally confirmed the trigonal symmetry of EL2 in the metastable state. In the EL2 model there is still no agreement as to whether it is an isolated arsenic antisite or a complex involving the arsenic antisite defect. The isolated arsenic antisite model was suggested based on an uniaxial stress experiment carried out on ZPL of EL2 intracenter absorption (Kaminska et al., 1985). The last few years have brought more theoretical support for this pointdefect, rather than a complex-defect, model (Dabrowski and Scheffler, 1988; Chadi and Chang, 1988; Baraff, 1989a, 1989b; and Kaxiras and Pandey, 1989). However, the results of ODENDOR measurements (Meyer et al., 1987) are in conflict with the EL2 model as an isolated arsenic antisite defect. An interesting suggestion solving this discrepancy was given by Dabrowski and Scheffler (1989): They stressed that the optical absorption was due to the neutral charge state of the EL2 defect, whereas the ODENDOR experiment probed the singly ionized arsenic antisite. Therefore, it cannot be excluded that As;, and As& have a different local environment and that EL2' may be a point defect, whereas EL2' may be a complex (e.g., AsGa together with an acceptor). However, there is no doubt that further studies are necessary in order to determine the precise nature of EL2 defect. In both competitive models of the EL2 defect, isolated AsGaas well as complex of AS,, with Asi, the EL2 metastable configuration is ascribed to atomic movement. It is worth mentioning here the very recent experimental results that support this point of view. An x-ray rocking curve experiment showed the difference in full width of the rocking curve before and after illumination of GaAs at low temperatures (Kowalski and Leszczynski, 1991). This effect disappeared after the sample was warmed above 110 K. Such an observation seems to be the very first straightforward experimental evidence of a strong lattice relaxation induced by the EL2 transition to its metastable configuration.

'

2. EL2 DEFECT IN GaAs

85

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Kuszko, W., and Kaminska, M. (1986). Acta Phys. Pol. A 69,427. Kuszko, W., Jezewski, M., Baranowski, J. M., and Kaminska, M. (1988). Appl. Phys. Lett. 53, 2558. Lagowski, J., Parsey, J. M., Kaminska, M., Wada, K., and Gatos, H. C. (1982a). Proc. of 2nd Con$ on Semi-insulating 111-V Materials, Evian 1982, p. 154 (ed. Makram-Ebeid, S., and Tuck, B.). Shiva Publishing Ltd., Nantwick, U.K. Lagowski, J., Gatos, H. C., Parsey, J. M., Wada, K., Kaminska, M., and Walukiewicz,W. (1982b). Appl. Phys. Lett. 40, 342. Lagowski, J., Kaminska, M., Parsey, J. M., Gatos, H. C., and Walukiewicz, W. (1983). Proc. Int. Conf. on GaAs and Related Compounds, Albequerque, New Mexico 1982, Inst. Phys. Conf. Ser. 65, 41. Lagowski, J., Lin, D. G., Aoyama, T., and Gatos, H. C. (1984a). Appl. Phys. Lett. 44,336. Lagowski, J., Lin, D. G., Gatos, H. C., Parsey, J. M., and Kaminska, M. (1984b). Appl. Phys. Lett. 45, 89. Lagowski, J., Gatos, H. C., Kang, C. H., Skowronski, M., KO, K. Y.,and Lin, D. G. (1986). Appl. Phys. Lett. 49, 892. Leyral, P., and Guillot, G. (1982a). Proc. of 2nd Conf. on Semi-insulating 111-V Materials, Evian 1982, p. 166 (ed. Makram-Ebeid, S., and Tuck, B.). Shiva Publishing Ltd., Nantwick, U.K. Leyral, P., Vincent, G., Nouailhat, A., and Guillot, G. (1982b). Solid St. Comm. 42, 67. Lin, A. L., Omelianovski, E., and Bube, R. H. (1976). J. Appl. Phys. 47, 1852. Makram-Ebeid, S., and Lanoo, M. (1982). Phys. Reo. B 25, 6406. Makram-Ebeid, S., Gautard, D., Devillard, P., and Martin, G. M. (1982).ApplPhys. Lett. 40,161. Manasreh, M. O., and Fischer, D. W. (1989). Phys. Reo. B 40,11756. Martin, G. M. (1981). Appl. Phys. Lett. 39, 747. Martin, G. M., Mitonneau, A., and Mircea, A. (1977). Electron. Lett. 13, 191. Meyer, B. K., Spaeth, J. M., and Scheffler, M. (1984). Phys. Reo. Lett. 52, 851. Meyer, B. K., Hofmann, D. M., Niklas, J. R., and Spaeth, J. M. (1987). Phys. Rev. B 36, 1332. Miller, D. M., Olsen, G. H., and Ettenberg, M. (1977). Appl. Phys. Lett. 31, 538. Mircea, A., Mitonneau, A., Hollan, L., and Briere, A. (1976). Appl. Phys. 11, 153. Mircea-Roussel, A., and Makram-Ebeid, S. (1981). Appl. Phys. Lett. 38, 1007. Mitonneau, A., and Mircea, A. (1979). Solid St. Commun. 30,157. Mitonneau, A,, Martin, G. M., and Mircea, A. (1977). Electron. Lett. 13, 666. Mitonneau, A,, Mircea, A., Martin, G. M., and Pons, D. (1979). Phys. Rev. Appl. 14, 853. Mochizuki, Y.,and Ikoma, T. (1985). Jpn. J. Appl. Phys. 24, L895. Nojima, S. (1985a). J. Appl. Phys. 57, 620. Nojima, S. (1985b). J. Appl. Phys. 58, 3485. Nojima, S., Asahi, H., and Ikoma, T. J. (1987). Appl. Phys. 61, 1073. Omling, P., Samuelson, L., and Grimmeis, H. C. (1984). Phys. Rev. B 29,4534. Omling, P., Weber, E. R., and Samuelson, L. (1986). Phys. Reo. I3 33, 5880. Parker, J. C., and Bray, R. (1988). Phys. Rev. B 37, 6368. Samuelson, L., Omling, P., Titze, H., and Grimmeis, H. C. (1981). J. Cryst. Growth 55, 164. Samuelson, L., Omling, P., and Grimmeis, H. C. (1984). Appl. Phys. Lett. 45, 521. Schemer, M., Beeler, F., Jepsen, O., Gunnarsson, O., Andersen, 0. K., and Bachelet, G. B. (1985). Proc. of the 13th Intern. Conf. on Defects in Semiconductors, Coronado. California 1984, p. 45 (ed.Kimerling, L. C., and Parsey, J. M.), vol. 14a. The Metallurgical Society of the AIME, Warrendale, Pennsylvania. Schneider, J., and Kaufmann, U. (1982). Solid St. Comm. 44,285. Shanabrook, B. V.,Klein, P. B., Swiggard, E. M., and Bishop, S.G. (1983). J. Appl. Phys. 54,336. Silverberg, P., Omling, P., and Samuelson, L.(1988). Appl. Phys. Lett. 52, 1689. Skowronski, M., Lagowski, J., and Gatos, H. C. (1985). Phys. Reo. B 32,4264.

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SEMICONDUCTORS AND SEMIMETALS, VOL. 38

CHAPTER 3

Defects Relevant for Compensation in Semi-insulating GaAs David C . Look UNlVERSITY RESEARCH CENTER

WRIGHTSTATEUNIWRSITY DAYTON. OHIO

I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . COMPENSATION IN BULKGaAs . . . . . . . . . . . . . . . . . . .

11.

1. Impurities

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91 92 93

2. Stoichiometry Considerations . . . . . . . . . . . . . . . . . . 96 111. THECALCULATION OF COMPENSATION . . . . . . . . . . . . . . . . 98 104 IV. KNOWNDEFECTS IN GaAs . . . . . . . . . . . . . . . . . . . . 3. Methods of Defect Identification . . . . . . . . . . . . . . . . . 104

. . . . . . . . . . V. THE AS-PRECIPITATE MODELFOR CoMPENSAnON . VI. S ~ M A R Y .. . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . 4. Defects Relevant for Compensation 5. The Efects of Thermal Peatment .

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105 110 113 114 114

I. Introduction Completely pure and defect-free GaAs, at 296K, would have equal electron n and hole p concentrations of 1.47 x lo6 ~ m - mobilities ~ , f i n and p p of 8,000 and 400 cm2/V-s, respectively, and thus a resistivity of 5.05 x lo8Rcm (Blakemore, 1982). If, on the other hand, we could add small concentrations of impurities or defects sufficient to drop the Fermi level E , a little, such that n = 3.29 x lo5 cm-3 and p = 6.57 x lo6 cmV3,without altering the mobilities significantly,then the maximum possible 296 K resistivity in GaAs (at these mobilities), namely 2.37 x lo9 R-cm, would be attained. A remarkable, and certainly very important, property of GaAs is that these extremely high resistivities may indeed be closely approached by doping with the deep acceptor Cr (Look, 1977), or by growing the material under conditions such 91 Copyright 0 1993 by Academic Press, Inc. All rights of reproductlon in any form reserved. ISBN 0-12-752138-0

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that the deep donor defect EL2 (see Chapter 2 of this volume) dominates the shallower impurities. By “compensation” in semi-insulating (SI) GaAs, we mean the process by which the bound electrons and holes of shallow donors and acceptors are transferred to the deep level (EL2 or Cr) where thermal excitation to the conduction or valence bands is improbable. In this work, “shallow” will refer to any center shallower than EL2 or Cr, which includes almost all other centers. We will be mainly concerned with donor and acceptor defects, as opposed to impurities, since that is what this volume is about. As late as five years ago, this chapter would have been much simpler to write, since it was commonly assumed before that time that the only defect of any importance in compensation considerations was EL2. However, with the advent of increasingly pure materials, it has become clear that even shallow defects must now be included in any realistic compensation model (Look, 1988).Moreover, high-temperature processing, which is necessary to improve material uniformity or to make devices, can cause important modifications in the types and numbers of these shallow defects, and can thus drastically affect the resistivity. We will attempt to summarize what is known about these phenomena at this time.

11. Compensation in Bulk GaAs

In this chapter we will be concerned with defects occurring in as-grown GaAs, as opposed to defects created by particle irradiation (see Chapter 5 of this volume), deformation, or other nonthermal processes. It must be immediately pointed out, however, that to understand the defects in as-grown material, it is exceedingly fruitful to compare them with defects produced by the other methods, especially particle irradiation, and even more specifically, electron irradiation. The reason is that electron irradiation, at energies of a few hundred kilo-electron volts and higher, produces simple defects, mainly vacancies and interstitials (Pons and Bourgoin, 1985), and it is necessary to understand the simple defects before the more complex defects can be elucidated. Furthermore, we are somewhat fortunate in that the complex defects often have some of their energy levels close to those of their simple constituents. For example, it is thought that divacancies and even larger clusters of vacancies can introduce some levels in the energy gap similar to those of isolated vacancies (Jaros and Brand, 1976; Sankey and Dow, 1981), and the same holds true for vacancy-impurity pairs (Shen and Myles, 1987). Thus, from a compensation point of view, it is important to understand the simple point defects so that correlations with the grown-in defects (which are usually more complex) can be carried out.

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We will also restrict our discussion in this chapter to relatively small defects, i.e., we will not consider precipitates and dislocations. The reason is twofold: (1) dislocations will be discussed in Chapter 8 of this volume; and (2) there is no firm evidence that either dislocations or precipitates inherently affect the electrical properties of GaAs, especially SI GaAs. The explanation of this fact is that they are probably neutral in most circumstances, i.e., they do not behave like large concentrations of donors or acceptors (see, however, Vignaud and Farvacque, 1990). Of course, it must be allowed that dislocations, especially, can have secondary effects on the GaAs electrical properties in that they can “getter” (attract) point defects and impurities which themselves may be electrically active. For example, there is strong evidence that arsenic atoms, in As-rich GaAs, move preferentially into the neighborhoods of dislocations, increasing the AsGa (EL2?) and possibly As, concentrations (Miyazawa and Wada, 1986; Lee et al., 1988; Suchet et al., 1988). Thus, without further evidence, we will take the point of view that dislocations may affect the concentrations of existing species of point defects and small complexes,but do not themselves constitute electrically active defects of a significant nature.

1. IMPURITIES To understand how defects might be formed in S1 GaAs, we must consider how the material is grown. This subject has been reviewed recently by several authors (AuCoin and Savage, 1985; Parsey, 1988) and so will be only briefly discussed here. There are primarily five methods used to grow bulk GaAs at the present time: (1) horizontal Bridgman (HB); (2) horizontal gradient freeze (HGF); (3) vertical gradient freeze (VGF); (4) low-pressure liquidencapsulated Czochralski (LP-LEC); and (5) high-pressure liquidencapsulated Czochralski (HP-LEC). Of these five, the latter three, VGF, LPLEC, and HP-LEC, produce most of the semi-insulating GaAs today, with the HP-LEC technique probably being dominant. Diagrams of the HP-LEC process are presented in Figs. 1 and 2. Figure 1 shows a typical experimental set-up for in-situ compounding of Ga and As metals to produce polycrystalline GaAs. The starting materials are (99.9999 +%) pure, and As loss is inhibited by the molten B,O, cap and about 60 atm. of high purity nitrogen gas. When the reaction of the Ga and As is complete, then single-crystal growth can proceed immediately if a single-crystal seed is lowered into the melt, as shown in Fig. 2. Again, the B z 0 3 encapsulant and high-pressure inert gas are employed to minimize As loss during the crystal growth. Usually, the crucible holding the

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I

Rf coil

Graphite Susceptor

BN Support

Ta Thermocouple Well R-Rh Thermocouple

FIG.1. Apparatus for high-pressure in-situ compounding of GaAs. (From AuCoin and Savage, 1985. Reproduced by permission of Howard W. Sams and Co., Inc.)

melt is lined with pyrolytic boron nitride (PBN) in order to avoid Si contamination, which is a problem with the less expensive quartz crucibles. Typical impurity concentrations for a completed crystal are given in Table I. As might be expected, however, since there is graphite (C), BN, N,, and B,O, in the vicinity of the growing crystal, the concentrations of C and B depend strongly on the detailed growth conditions. For example, the concentration of B can easily vary by two orders of magnitude, depending on the initial water content in the B,O, (Ta et al., 1982).Fortunately, B normally goes on a Ga site, especially in the usual As-rich LEC material (Alt and Maier, 1991),and since it is isoelectronic with Ga, no direct electrical activity results. (However, there is some evidence for the indirect effects of B on the electrical properties.) It might appear that we should also worry about N and 0 as potential contaminants. In fact, up until about 1979,it was assumed that 0 was the dominant deep donor in GaAs. Shortly thereafter, however, it was realized that EL2 assumed this role (Huber et al., 1979),and it has never been clear since then whether 0 plays any role at all. Recently, localizedvibrational mode (LVM) spectra of an O-related center with a two-electron transition at E , - 0.57eV have been seen in purposely O-doped GaAs (Schneider et al., 1989; Alt, 1989; Skowronski et al., 1990; Neild et al., 1991),

3. DEFECTS RELEVANTFOR

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95

Seed crystal Crystal

Susceptor

FIG. 2. Liquid-encapsulated Czochralski pulling technique. (From AuCoin and Savage, 1985. Reproduced by permission of Howard W.Sams and Co., Inc.)

TABLE I TYPICAL IMPURITYAND EL2 LEVELS IN LEC GaAs

Species Si S

Se Sn Te B Mg Cr Mn Fe C EL2

Usual Electrical Activity

Concentration (cm - 3,

Technique

SD SD SD SD SD N SA DA DA DA SA DD

5 x 1014 2 x 1015 7 x 10'2 8 x loi4 6 x 1013 4 x 1014 3 x 1014 3 x 1014 9 x 1014 2 x 1015 3 x 1015 1.2 x 1OI6

SIMS SIMS SIMS SIMS SIMS SIMS SIMS SIMS SIMS SIMS LVM Absorption

SD = shallow donor, SA = shallow DA = deep acceptor, N = neutral.

acceptor,

D D = deep

donor,

%

D. C . LOOK

but there are no reports of significant concentrations (21 x 1015cmP3)in undoped, LEC material. Similarly, although N may go in the lattice in some form, it does not appear to be important from a compensation point of view. In summary, the impurities of most concern for compensation in SI GaAs are S and Si, as shallow donors, and C and Fe, as shallow (with respect to EL2) acceptors. To obtain SI GaAs, as will be seen later, it is necessary that the shallow acceptors N , dominate the shallow donors ND,i.e., NA3 N D . Since the impurity donor and acceptor concentrations are of the order of low-10I5 cm-3, from Table I, it is clear that we will have to include any electrically active defects of this concentration range in our compensation model. Thus, the goal of this chapter is to identify defects that are known to sometimes exist in the 1015-cm-3concentration range, or higher.

2. STOICHIOMETRY CONSIDERATIONS The growth of the GaAs crystal, as it freezes out from the melt, can be modeled by a phase diagram (AuCoin and Savage, 1985; Hurle, 1988)such as that shown in Fig. 3. Here the solidus region is greatly exaggerated, because, in actuality, at its widest extent the stoichiometry probably deviates less than lo-* from the value 0.5. Although the solidus narrows considerably for temperatures below the maximum phase extent point, still it is possible for a higher nonstoichiometry to be “frozen in” if the crystal is cooled rapidly. The stoichiometry of the melt has a great effect on the resistivity of HPLEC crystals, as is shown in Fig. 4 (Holmes et al., 1982). On the As-rich side,

I

Solid W u b i l i

LIQUID

500

GaAs + As

3. DEFECTS RELEVANTFOR

COMPENSATION IN SEMI-INSULATING

GaAs

97

1o9

108 10’ 108

E

P lo5

C

1

t

p-TYPE

I I

SEMI-INSULATING

‘1

‘I. I

Critical As lxmlpiiion

..4

Stoichimeflc Commition

0.42

0.44

0.46

0.48

0.50

0.52

0.54

Arsenic Atom Fraction in Melt

FIG.4. The resistivity in LEC GaAs as a function of the As fraction in the melt. (From Holmes et al., 1982. Reproduced by permission of the American Institute of Physics) the resistivity is determined by the deep donor EL2, as long as the shallow acceptor concentration N,, is greater than the shallow donor concentration N,. It is now generally acknowledged that EL2 is a pure defect, either isolated AsGa, or a complex involving AsGa,such as AsG,-Asi (see Chapter 2 for a detailed discussion of EL2). Also, there is evidence that EL2 is a double donor (Weber et al., 1982; Omling et al., 1988), with the first donor level (EL2O/+)at about E,-0.75 eV (at T=O), and the second ( E L 2 + / + +at ) about E , + 0.52eV. The second level (EL2””) is not important in the compensation picture for SI GaAs. In Ga-rich material the dominant level is an acceptor, most likely a double acceptor, with the first acceptor level ( A - ” ) at about E , + 0.077 eV, and the second ( A - - ’ - ) at about E , + 0.20eV (Yu et al., 1982; Moore et al., 1984). Although the identity of A is more uncertain than that of EL2, still there is good evidence that it is a pure defect and that it may well be the isolated GaAs,or a defect complex involving GaAs. It is interesting that in As-rich material the concentration of EL2 is nearly always within a factor of 2 of 1 x 10l6 cm-3, and the same can be said for the concentration of A in Ga-rich material. These concentrations are normally higher than those of the electrically active impurities (see Table I), so that Asrich material is semi-insulating(as long as N,, > N,) and Ga-rich material is p-type, because of either A or carbon impurity. Thus, growers of SI GaAs usually begin with an As-rich melt and try to keep N,, very low in order to achieve high resistivity (Holmes et a)., 1982). In the earlier material, natural

98

D. C . LOOK

carbon contamination was sufficient to ensure that N A , 3 NDs;however, in recent years there are many examples in which even the carbon is well under the lOI5cm-3 level of concentration. For example, a recent data sheet on a boule supplied to this laboratory by a major commercial crystal grower had [C) < 4 x 1014and [S] = 8 x 1014 cm1113, i.e., N , k NAs.What then are the dominant NA, and ND, in these cases? We will later show that there are defects other than EL2 in the 10'5cm-3 concentration range, and that these also must be considered in the compensation. First, however, we will discuss the mechanism of compensation in more detail.

111. The Calculation of Compensation

To produce SI GaAs, we must have the proper mix of shallow donors, shallow acceptors, and EL2 in order to ensure that the free electron and hole concentrations, n and p , are low. In the nondegenerate (Boltzmann) limit, which certainly holds for SI GaAs, n and p can be written

where eG is the band gap and gF is the Fermi level, written with respect to the valence band to keep all energies positive; k is Boltzmann's constant; and N, and N , are the effective conduction-band and valence-band densities of states, given (for T > 100 K) by Blakemore (1982): N,

= 8.63 x

10137-3'2[ l - 1.93 x 10-4T-4.19 x 10-'T2],

(3)

To have both n and p as small as possible, we want eF N 4 2 , or near midgap. The exact cFis determined from the change balance equation, since the total sample must be neutral:

where k denotes a particular center. Here it is implicitly assumed that all of the centers N A , and N,, are either neutral or singly charged for all cFwithin the band gap. In fact, as already discussed, there is strong evidence that this condition is not true for either EL2 or A; i.e., we believe EL2 is a double

3. DEFECTS RELEVANTFOR COMPENSATION IN SEMI-INSULATING GaAs

99

donor (0, +, and 2 + charge states), and A is a double acceptor (0, -, and 2 charge states). Even higher complexities can be imagined; e.g., the arsenic interstitial Gai, with As neighbors, may have four charge states (0, + , 2 +, and 3+) producing three transitions within the band gap (Baraff and Schluter, 1985). Thus, we need a more general formalism in order to handle centers of any complexity. A completely general charge-balance equation is as follows (Look, 1982; Look, 1989): c =e,, +c,, =P

+

1

(dDk-I)nkh,

(6)

k,L = O,m

where k denotes a particular center and k r n =

Nk

gkd'm' -eXP([Ekdm - Ekl'm' -(t'- el)+]/k T ) 1 L',m' z d,rn gktm

+ 1

(7)

Note that nkcm,lNk is the occupancy factor of the t'rnth state of center k. Here the restriction on the summation index means that el # t' and rn' # m, at the same time. In Eq. (6), t',k is the maximum number of donor transitions that a given center may have, and t A k is the maximum number of acceptor transitions, all within the band gap, of course. For example, if the EL2 center is a double donor and has no acceptor levels, then t?Dk = 2, lAk = 0, and t' would range from 0 to 2. The index m allows excited states to be included, within each charge state t'. The energies cum are total energies, not transition energies; the latter are defined by EL = E[ - ~ c - 1 , where E,, is considered to be at the valence band edge. Conversely, the total energies are simply sums of the transition energies; i.e., EL = El

+ E,-1+

EL-2

+ ... + El.

(8)

As an illustrative yet practical example of the application of Eqs. (6) and (7), we consider the AsGa center, which presumably is EL2, or is a primary component of EL2. We will assume that the two extra electrons that As brings to the lattice site when replacing Ga are in an s-like state, i.e., with only the twofold spin degeneracy. This situation is illustrated in Fig. 5; from data in the literature (Weber et al., 1982), the single-donor transition (O/+) is at EC-O.75eV, or Ev+0.77eV (if EG= 1.52eV at T=O), and the double-donor transition (+/2+), at Ev + 0.52eV. Thus, El = 0.52eV and E z = 0.77eV, whereas the total energies are = El = 0.52 eV and E~ = E z + El = 1.29 eV. The state degeneracies are also shown in Fig. 5, and the whole situation is outlined in Table 11.

100

D. C . LOOK

/

E2 = 0.77

I

I

I

I I I

I

'&lo= 0.52

I /

I /

I

- &Ew=O -=t

I El =0.52

i

900'4

910'1

I I I &,---L -L 1El = 0 . 0 2 3 Pz I I I .

p+,p-

s 1 - L

A L L

FIG. 5 . A schematic of the various energies (in electron volts) and degeneracies involved in the descriptions of As,, and Ch. The open circles denote holes, and the solid circles, electrons.

We use these data to derive the charge balance equation for a simple compensation model consisting only of EL2 (assumed to be AsGaor an AsGalike structure), Si,,, and CAs.The relevant electron structure for SiGacan be represented schematically by the lower two levels of the AsGa structure, as shown in Fig. 5. Theoretically, the third level would apply also, but the assumption is that the two-electron state of Si,, has a very high energy, due to electron-electron repulsion (Look, 1982), and that it therefore has a small probability of occupation and need not be considered. For CAs,the schematic structure is assumed to be that shown on the right-hand side of Fig. 5. We can now apply Eq. (6),suppressing the index m:

TABLE I1 A SUMMARY OF THE Aka(EL2?) CHARGE AND ENERGY CONF~GURATION ASSUMINGTHATONLYTHE GROUND STATESARE PORTAN ANT'

Center

e

As,, e,=2

2

Charge 0

Total Energy

Degeneracy

cZ0= 1.29 eV

920=1

Transition Energy

Transition Notation

Transition Designation

E , =cZ0 -eI0 =0.77 eV

(O/+)

Single donor

El =cl0 -coo =0.52 eV

(+/2+)

Double donor

E , = ~ ~ ~ - c ~ ~ =eV 1.51

(O/+1

Single donor

( -/O)

Single acceptor

du=O L

s

SiG,

e,=

1

+1

=0.52 eV

910=2

0 1

+2 0

eo0=O

goo = 1 910=2

0 1

+1 -1

cl0= 1.51 eV

1

Cu=0

CAS

eD, =o Cu= 1

0

Eoo=O

cI0=0.025 eV EO0 = 0

goo = 1 910 = 1 El =el0-coo = 0.025 eV 900=4

~

“I.e., rn

= 0 for each C.

Also included are a shallow donor (say, Si) and a shallow acceptor (say, C). All energies are at T=O, and E,(T = 0)= 1.52 eV.

102

D. C. LOOK

Then, by letting e0 = 0, Eq. (9) can finally be written 2NEL2

n=p+ 1

+

+

91 92 - exp[-El +e,]/kT+ - e x p [ - ~ ~ + 2 ~ , ] / k T

90

90 NEL2

1

+ - exp[El -EF]/kT+ 90

91

1

91 +exp[-E1

go

92

-

exp[el--E2+EF]/kT

91

++]/kT

1

90 +exp[E,-E,]/kT

91

The numerical values for the various energies and degeneracies are listed in Table 11. However, as a further simplification, we note that for actual semiinsulating material, E , = 0.7 eV. Therefore,

so that Eq. (10) reduces to

Equation (1 1) is just the familiar simple form of the charge-balance equation, with transition energies (Es) substituted for total energies ( E S ) . In fact, we almost could have written down Eq. (1 1) by inspection. However, we could not have written Eq. (10) by inspection, and that is why it is worthwhile to go

3. DEFECTS RELEVANTFOR COMPENSATION IN SEMI-INSULATING GaAs

103

through the exercise of applying Eqs. (6) and (7), which make it possible to solve, in a straightforward manner, any system, with any number of centers, of any complexity. Equation (10) (or Eq. (11)) may now be solved by substituting Eqs. (1) and (2) for n and p , respectively, and solving for eF.However, it is illuminating to find the solution by a graphical method, i.e., by using the so-called Shockley diagrams (Shockley, 1950). To apply this method, we transpose the last term on the right-hand side (RHS)of Eq. (10) to the LHS, in order to put all the negative charges on the LHS, and the positive charges on the RHS. Equation (10) then becomes

and the various terms are plotted as a function of EF in Fig. 6. Here we assume concentrations Nsi = 1 x lo”, N,,, = 4 x 1015, and NELZ= 1 x loi6cmP3,

FIG.6. A Shockley diagram at 296 K illustratingthe various positive and negative charges in the system as a function of Fermi level. The equilibrium Fermi level is found from the intersection of the curves for total positive charge and total negative charge, respectively. Note that a doubling of [EL21 changes the equilibrium Fermi level very little.

and room-temperature (296 K) energy values: eG= 1.424 eV, E ~ ~ 0 .~ 5 eV, 2~ eEL2,2 = 1.29 eV (Duncan and Westphal, 1987, found that EEL,2 E,-0.65 eV at 296K, so e2=0.52+(1.424-0.65)= 1.29eV), eSi,,= 1.418eV, and E ~ ~ =, 0.026 + ~ eV. Although some of these numbers may be open to dispute, the concept can still be illustrated. The total negative charges (LHS) are shown by the square points in Fig. 6, and the total positive changes, by the circular points. The intersection is the equilibrium value of eF,which is near mid-gap for the concentrations shown and does not change much even if N,,, is doubled (see triangular points in Fig. 6). In fact, the equilibrium eF does not change significantly as long as Nsi N,,, < NEL2;however, if N,,, falls below N s i , then the intersection will jump to near the conduction band, while if N,,, exceeds NEt2,but is less than 2N,,,, the intersection will fall to near eEL2,‘c 0.5 eV. The latter condition almost never happens, because usually N E L 2> 1016cm-3 and very seldom is N,,, this large. Thus, this simple diagram helps us understand why temperature-dependent Hall-effect measurements rarely show an activation energy of 0.52 eV, even though such a situation is entirely possible theoretically. The Si/C/EL2 compensation model presented here has been in vogue for several years, and still is the most accepted model for SI GaAs. However, it has recently been realized that the concentrations of Si and C are, in some cases, lower than the concentrations of known defects, most of which are shailower than EL2 and thus can swing the eFintersection by large amounts. We will consider some of these defects in the next section.

-=

IV. Known Defects in GaAs

3. METHODS OF DEFECT IDENTIFICATION

Many impurity levels have been positively identified in GaAs and other semiconductors, because the presence of impurities can often be confirmed by analytical techniques. A positive identification of defects is, of course, much more difficult, so that only the As antisite defect AsGa has been identified (by EPR) with any degree of certainty (Wagner et al., 1980).(Even the well-known EL2, while acknowledged to be a pure defect by most workers in the field, may be an isolated defect [AsGJ or a complex defect.) However, sometimes defect $fingerprints can be found even though the detailed nature of the defect itself may not be known. For example, irradiation with 1 MeV electrons is known from DLTS (deep-level transient spectroscopy) measurements to produce electron traps with energy fingerprints at E , - 0.15 eV and E,-0.29eV (Pons and Bourgoin, 1985), and these results are confirmed with Hall-effect measurements (Look and Sizelove, 1987). These centers can be

,

~

3. DEFECTSRELEVANTFOR

COMPENSATION IN

SEMI-INSULATING GaAs

105

produced at fairly high concentrations in pure epitaxial GaAs layers, so that it is certain that they are defects, not associated with any impurity; however, their detailed identities are, as yet, uncertain. Even in as-grown material, a pure defect can sometimes be identified by showing that its concentration is larger than the concentrations of any impurities in the sample (Look et al., 1982). Again, Hall-effect or DLTS measurements can determine the concentration of the defect quite accurately,and then a broad analytical tool, such as spark-source mass spectroscopy,can be used to assign upper limits to most of the known impurities. Some of the impurities, such as C and 0, may require other methods to determine their concentrations. In this way, several defects have been fingerprinted, but not necessarily positively identified.

4.

DEFECTSRELEVANT FOR COMPENSATION

The accumulated literature of DLTS, PICTS (photon-induced current transient spectroscopy), and TSC (thermally stimulated current) measurements reveals literally hundreds of electron and hole traps (Neumark and Kosai, 1983),some of which undoubtedly are defects. However, most of these traps have concentrations << 101scm-3, and thus are not important, in general, for compensation in SI GaAs, for which it is known that [C], at least, is usually greater than lo1’ ~ m - Of ~ .course, [EL23 is usually greater than 1016crr-3, but as we saw from the Shockley-diagram analysis, it is the shallower levels that can produce large swings in E ~ Thus, . we need to look for centers that are often observed at concentrations > 1 0 ” ~ m - in ~ SI GaAs. In a recent analysis (Look, 1988), it was suggested that such defects seem to fall into four groups, or “bands,” near E , - 0.15 eV, E , - 0.4eV, E, - 0.75eV, and E, 0.1 eV. Other studies (Kitagawara et al., 1988; Siege1 et al., 1991; Mitchel et al., 1991) are in general agreement with this picture. The “constituents” of these bands are listed in Table 111, along with the experimental techniques used to observe them and the various preparations of the samples in which they are observed.

+

a. C.15 Band

The most dominant level in 1 MeV electron-irradiated, n-type GaAs occurs at Ec-0.15eV, an electron trap as observed by DLTS (Pons and Bourgoin, 1985), and a donor, as observed by the Hall effect (Look et al., 1982). The “donor” nature is inferred from indirect evidence (Look, 1987a), since a temperature-dependent Hall-effect (TDH) measurement cannot distinguish between a donor and an acceptor from the fit to Eq. (6) alone (Look, 1987b). The production rate z is about 2 defects/cm3 for each 1 MeV electron/cm2

106

D. C . LWK TABLE 111 HIGH-CONCENTRATION DEFECTSOBSERVEDIN GaAs”

Energy

Type of Sample

Method of Observation

E , - 0.13 to 0.14eV Ec - 0.15 to 0.20eV E , - 0.35eV (EL6) E , - 0.42 eV E, - 0.82 eV (EL2) E , - 0.76 eV (EL2) EV 0.01 to 0.06eV Ev + 0.07 to 0.1 1 eV

AG, AN, IR AG, IR AG, AN AG, AN AG, AN AG, AN AN AG, AN, IR

Hall-effect, DLTS Hall-effect DLTS Hall-effect DLTS Hall-effect Hall-effect Hall-effect, PL, DLTS

Designation

C.15 band C.4 band

c.75 V.l band

+

”“AG” as-grown; “ A N = annealed; “IR”

irradiated.

(i.e., z 2: 2 cm- ’), independent of the carrier concentration or doping. Furthermore, it can be produced in quantities much higher than the initial donor and acceptor concentrations (which are easy to measure in pure, n-type GaAs by the TDH technique). Thus, this center is not complexed with any impurity. One other level, a donor at EC-0.045eV is produced at about the same rate, although it is more difficult to observe. There is fairly good evidence that these two levels constitute two states of the As vacancy V,,, or possibly the Frenkel pair V,,-As, (Pons and Bourgoin, 1985). Now, the E , - 0.15eV level, or something close to it, has also been observed by many workers in as-grown and annealed bulk LEC and HB samples, at concentrations as high as 10’6cm-3 (Look et al., 1982). At such concentrations, these centers must be considered in any compensation model. Originally they were attributed to oxygen, since they tended to be observed in 0-doped crystals. However, it is now believed that 0 plays a very limited direct role in as-grown GaAs, but that it inhibits Si doping (which can come from the quartz crucibles), and this causes eF to drop to the next dominant donor (the 0.15eV center). (Recently, firm fingerprints of 0 in GaAs have been established by local vibrational mode [LVM] absorption [Ah, 1989; Schneider ef al., 1989; Skowronski et al., 1990; Neild et al., 19911, but the concentrations are not significant in undoped material.) Some of the defects constituting the C. 15 band in as-grown GaAs have been shown to be pure defects by comparison with analytical results (Look et al., 1982).Although no firm evidence exists, it seems reasonable to believe that the 0.15 eV defects in as-grown material are related to the 0.15 eV defects in irradiated material. Note that they could not be identical because the 0.15 eV defects, as well as most of the other defects in irradiated GaAs, anneal out at

3. DEFECTS RELEVANT FOR COMPENSATION IN SEMI-INSULATING GaAs 107

temperatures below 3WC, whereas the defects in as-grown GaAs are stable even at much higher temperatures. Thus, the present evidence suggests that VAs-like donor defects at E, - 0.15 eV can exist in appreciable concentrations in SI GaAs. The observed spread in energy, 0.13-0.20eV, may be due to different configurations or complexes of this basic defect. One complex, which has been theoretically studied in some detail, is VASAsGa,which can be created from the nearestneighbor hop of an As atom to a gallium vacancy VGa (Baraff and Schluter, 1986), or from the interaction of mobile VA, and AsGa during the hightemperature crystal growth. Other VA, complexes that have been proposed involve impurities, such as VA,-O, VAsZnGa, and VAsBGa;it is possible that all of these V,, complexes, as well as the isolated VA, itself, have a dominant energy level near E, - 0.15 eV.

b. C.4 Band In addition to the E, - 0.15 eV band, another level at E, - 0.42 eV is commonly observed in both HB and LEC GaAs, at concentrations high enough to pin eF (Look et al., 1983; Fornari and Dozsa, 1988; Young et al., 1988). Along with EL2, it also was originally attributed to 0, but since then has been shown to be a pure defect. However, unlike the Ec-0.15eV band, which can vary from 0.13 to 0.20 eV in the TDH experiment, the 0.42 eV level is fixed to within 0.01 eV by nearly all observers; thus, it is likely a relatively simple defect without a large number of variations. Thresholds near 0.4eV are also commonly seen in photoconductivity (PC) (Arikan et al., 1980; Jimenez et al., 1984) and photocapacitance (PCAP) spectra (Vasudev and Bube, 1978), and an emission peak with an activation energy near 0.4 eV is nearly always observed in SI GaAs by PICTS (Teh et al., 1987). Recently, it has been shown to be more prevalant in regions with high dislocation density (Young et al., 1988)that are also known to be As-rich in SI GaAs (Cullis et al., 1980); thus, As, or AsGa in some form would seem to be likely candidates. Other speculation has centered on the divacancy VA,-V,,, although it is hard to imagine much VGain As-rich regions. The 0.42 eV center is almost certainly a donor since, as an acceptor, it could not pin cFwithout the further condition that ND, > NAs,which is highly unlikely in present-day LEC GaAs from impurity concentrations alone. In light of the observations of the 0.42 eV level by TDH, PICTS, PC, and PCAP measurements, it would also be expected to appear in DLTS spectra. Indeed, there is a DLTS level at 0.42 eV, EL5, which has been seen in vaporphase epitaxial (VPE) material (Martin et al., 1977), and at high concennear the surface in annealed HB and LEC material trations (> 1015 (Kuzuhara and Nozaki, 1986b).However, it does not seem to appear at high

10s

D. C. LOOK

concentrations in as-grown material, or even in the bulk regions of annealed material. In fact, the only DLTS center (besides EL2) that does exceed l O ’ ’ ~ m - ~quite often in as-grown GaAs is EL6, at EC-0.35eV (Kitagawara et al., 1988; Fang et al., 1987; Auret et al., 1986). This center has also been tentatively attributed to the defect V,,-V‘, (Fang et al., 1987), but there is no firm evidence as yet. More will be said about EL6 later in connection with annealing experiments, but we can summarize our compensation model so far as follows: two DLTS centers, EL2 at E, - 0.82 eV and EL6 at E, - 0.35 eV, and three TDH levels, at E, - 0.15eV, E, - 0.42 eV, and E, - 0.75 eV, commonly exist at concentrations > loi5cm-3 in SI GaAs. The E, - 0.75 eV TDH center is well-known as EL2; however, is the E, - 0.42eV TDH center related to either EL5 or EL6? These questions are still open. c. C.75 Band

The dominant member of the C.75 band is certainly EL2, which is extensively discussed in Chapter 2 of this volume. This defect is nearly always found within the concentration range 1.0 k 0.5 x 10l6~ r n in - ~undoped, SI GaAs grown by the LEC method, and around the low end of this range in VGF material (Look et al., 1989).The overall purity of these materials is such that only B is sometimes found in greater concentrations than EL2, and B is mainly substitutional for Ga and thus neutral. Therefore, EL2 is the most important of the defects and impurities involved in the compensation of undoped, SI GaAs, and indeed is the only mid-gap center known to be capable of rendering undoped material semi-insulating. (Other deep centers, such as EL0 and other members of the EL2 “family,” have been proposed as possible compensating centers, but to date there is no firm evidence that any of them exist in high enough concentrations to be important.) As with the 0.42 eV center, but unlike the 0.15eV band, the EL2 energy (presumably O/ +) is nearly always within 0.01 eV of E, - 0.75eV, as measured by TDH, or E, - 0.82 eV, as measured by DLTS. Therefore, EL2 probably has a single fixed structure most of the time, and any variations either do not differ by more than 0.01 eV in energy, or are present in much lower concentrations than the main structure.

d.

V.1 Band

There is abundant evidence that one or more native acceptor defects in the energy range Ev+O.l+O.l eV can exist and be stable in high concentrations in GaAs:(l) A hole trap, HO, at Ev+0.06eV, has been seen in p-type electronirradiated material (Pons and Bourgoin, 1985);(2) an acceptor, thought to be near E , + 0.1 eV, is produced at very high rates (- 5 cm-’) in 1 MeV electron-

3. DEFECTS RELEVANT FOR COMPENSATION IN SEMI-INSULATING GaAs 109

irradiated n-type GaAs (Look and Sizelove, 1987); (3) an acceptor at EV+0.15eV, in concentrations > l O " ~ m - ~ has , been thoroughly investigated in 885°C-annealed (and quenched) LEC GaAs (Boncek and Rode, 1988); (4) an acceptor, probably within 0.05 eV of the valence band and of concentration > 10l6~ m - is~ produced , in 950°C-annealed (and quenched) HB material (Asom et al., 1988);and (5) an acceptor level at E, +0.07eV has been observed by photoluminescence (PL) in 950°C-annealed(and quenched) LEC GaAs (Yu et al., 1987). In most of these cases, the evidence that the acceptors are not associated with any impurity is very strong. Another center, a double acceptor with levels at E, 0.077 and E , + 0.23 eV, respectively, has been observed by PL, TDH, and DLTS in Ga-rich LEC GaAs, and is thought to be the gallium antisite, GaAs(Yu et al., 1982).(Note, however, that the stoichiometry of SI GaAs is usually As-rich.) Theoretical studies suggest that three defects, VG,, GaAs,and VGaGaAs,are all expected to have energy levels reasonably close to the value E, + 0.1 eV (Baraff and Schluter, 1985, 1986). Thus, from the experimental and theoretical evidence we believe that VGa- and GaA,-like defects exist and are important for compensation in electron-irradiated and ingot-annealed GaAs samples. There is a high likelihood that one or more of these defects is important for compensation in SI GaAs, because many workers have observed semi-insulating behavior in samples with [C] in the low 1014cm-3range (Look et al., 1986). Then, since the condition NAs > ND, must hold, either ND, S 1014cm-3, or NAs is made up of acceptors other than C. The latter possibility is more likely, since the defects at Ec - 0.15 and Ec - 0.42 eV would be included here in the ND,, and they are often in the 10'5-1016 range. Furthermore, no other acceptor impurities (i.e., other than C) are commonly found in SI GaAs. Thus, we believe that acceptor defects are important.

+

e. Defects Observed by EPR Perhaps the only defect that has been positively identified in GaAs is the As antisite, As&, which has been thoroughly investigated (Wagner et al., 1980) by electron paramagnetic resonance (EPR). Many of the properties of AsGa, including the mid-gap energy level, mimic the properties of EL2; indeed, there is fairly good evidence that EL2 = AsG,, even though controversy still exists (see Chapter 2). However, in recent years the EPR technique has been used to identify several other centers in as-grown, SI GaAs: FR1, FR2, and FR3 (Kaufmann et al., 1986) and BE1 (Hoinkis and Weber, 1988). The FR2 and FR 3 centers are thought possibly to be acceptors associated with boron (BAS and BG,-GaA,, respectively) since they are ubiquitous in SI, LEC GaAs, which usually (but not always) contains significant quantities of B. With respect to their energy levels, it is notable that all four of the EPR defects

110

D. C . LOOK

appear in SI GaAs only when illuminated, and thus are probably not mid-gap centers. (Mid-gap centers would be expected to have two charge states existing simultaneously in SI GaAs, with one of them being EPR-active.) In fact, very recently the (-/0) level of FR1 was fixed at approximately E , 0.27eV (Hendorfer and Kaufmann, 1991).The centers FR1 and BE1 are likely the same, and BE1 has been seen in estimated concentrations of 10’7-10’8 cm-3 in material annealed at 1,200”Cand then quenched this fact indicates that BE1 is a pure defect. In as-grown GaAs, [BE11 is closer to ~ m - which ~ , makes it potentially important in the compensation picture, depending on its donor/acceptor nature and energy levels.

+

5. THEEFFECTSOF THERMAL TREATMENT

In the mid-l980s, a noticeable improvement in the overall quality of undoped, SI GaAs took place with the advent of whole-boule annealing, typically an 850-950°C anneal for 5-20 hours (Rumsby et al., 1984).For the materials of that time, which were usually As-rich, the main effect of the annealing was an increase in the homogeneity of EL2 and the electrical parameters (i.e., less pronounced “W” or “M” patterns), although the dislocation-density pattern was largely unchanged. A little later, however, it was found in near-stoichiometric materials that very large resistivity changes could be produced by simple heat treatments, and that the final resistivity depended critically on the cooling rate (Ford et al., 1986).(Actually, such effects on a smaller scale had been discovered much earlier, but had not evoked a great deal of interest at that time [Woodall and Woods, 19663.)It is quite clear now that changes in defect, not impurity, concentrations are the dominant factor in these large resistivity changes, and that at least some of the defects are members of the bands listed in Table 111. These phenomena are discussed next. a. Role of C.15 and C.4 Bands in Annealing Phenomena

In experiments on undoped, near-stoichiometric GaAs ingots it was shown (Ford et al., 1986;Look et al., 1986)that a 5-h, 950°Canneal in an evacuated quartz ampoule produced uniform, semi-insulating material ( p > lo7a-cm) if the ingot was “fast-cooled” (FC),i.e., pulled rapidly from the furnace, but produced uniform conducting material (n-type, p 1 a-cm) if “slow-cooled” (SC),i.e., cooled in a furnace that was simply turned off. It was further shown that the dominant center in the SC material was a donor at E,-0.13 eV, and in the FC material, EL2. The SC and FC processes are completely reversible, any number of times, and the process affects the bulk, not just the surface.

-

3. DEFECTS RELEVANT FOR COMPENSATION IN SEMI-INSULATING GaAs

111

These basic differences between slow cooling and fast cooling have been confirmed by many different groups (Nakamura et al., 1988; Inada et al., 1989; Reichlmaier et al., 1988), and the picture that seems to have emerged is that at least some of the donors in the C.15 and C.4 bands, including EL6, are created at moderate annealing temperatures (say, 400-600°C) (Ogawa, 1986; Kitagawara et al., 1988; Auret et al., 1986), and then destroyed at higher temperatures (say, 700°C) (Kuzuhara and Nozaki, 1986a; Kitagawara et al., 1986, 1988; Auret et al., 1986). Thus, during a slow cool from high temperature, these centers are initially absent but are created as the temperature decreases, while a fast cool does not leave enough time for creation. Note that a complex defect such as AsGaVAs would seem to be a likely candidate for this process in that existing AsG, and VA,could move and find each other in the 500°C range, or the "hopping" reaction VGa --* VA,ASG, could take place; then, at higher temperatures, the AsGaV,, complex could break apart, with the VA, perhaps annihilating with As, or forming VGaGaAs acceptors by the hopping reaction VA,--* VGaGaAs.Another complex that could participate in the reversibility phenomenon would be VAsVGa,which has been suggested as a candidate for EL6. Again, this complex could be stable at moderate temperatures, and then break apart at the higher annealing temperatures. The mechanism of large resistivity change due to an EC-0.13eV center or another of the C.15 group, is well illustrated by the Shockley diagram of Fig. 7. Note that, depending on the existing NA,-ND, concentration, a small concentration change in a C.15 center can greatly swing the Fermi level and thus the resistivity. The same is true of a C.4 center, although the Fermi level swing is not as great. The key to producing a large cF swing is having ND, rise above NAs,because then the deep donor EL2 is ineffective in producing semiinsulating material. b. Role of C.75 Band

In the electrical-reversibility experiments carried out at 950"C, the EL2 concentration changed very little, certainly not enough to swing cF significantly (Look et al., 1986). In fact, to effect a large change in eF, [EL21 must drop very close to, or below, NAs-NDs. It has been shown that EL2 can be reduced to very low levels by annealing for several hours at very high temperatures, about 1,200"C, and can then be largely restored by annealing at 800°C (Lagowski et al., 1986). The presumed model here is that AsG, (EL2 itself, or a component thereof) becomes unstable at 1,2Oo"C,but that at lower temperatures EL2 is formed from migrating gallium vacancies: V,, + AsA, + V,, + AsG,. However, an 800°C anneal increases EL2 significantly only if it was very low to begin with, which does not apply to most of

I12

0

02

04

06

08

10

12

14

&F (ev) FIG. 7. A Shockley diagram at 296 K illustrating how a small change in the concentration of the 0.15 eV center can shift the Fermi level greatly.

the present-day whole-boule-annealing processes (see also Suemitsu et al., 1991). In short, the C.75 band appears to play a rather limited role in compensation changes caused by the usual whole-boule annealing. c.

Role of V . l Band

As discussed before, at least three acceptors, at E , + 0.07 eV, E , + 0.15eV, and E, + 0.03 eV (or less), have been found to increase in concentration as a result of a high-temperature (885-95OOC) anneal and quench. The latter two have been measured in concentrations > 10l6cm-3 so that their importance in the compensation picture is unequivocal. Their possible identities, such as V,,, GaAs,and VGGaGaAsr have been discussed before; however, note that these acceptor defects, whatever they are, must be stable at k 90O0C, and thus they differfrom the donor defects of the C.15 and C.4bands. More work needs to be done to determine the detailed properties of the relevant acceptor defects.

3. DEFECTS RELEVANT FOR COMPENSATION IN SEMI-INSULATING GaAs 113

V. The Asprecipitate Model for Compensation

Because present-day, SI, LEC GaAs is As-rich, it often contains As precipitates. It is possible that these precipitates are sometimes metallic in nature, and thus act as Schottky barriers, which are known to pin eFat about E , - 0.8 eV in n-type GaAs and Ev - 0.6 eV in p-type GaAs, i.e., near midgap. Each metallic precipitate of radius ro would accumulate from the surrounding region a charge Q given by Gauss’s law: Q = 4rmOAV,

(13)

where A V is the difference between the Fermi level at the metallic surface, given above, and that in the bulk. Warren et al. (1990)have proposed that if ro is large enough, and the number of precipitates N , is high enough, then all of the sample would be depleted of free charge, and eF would be near mid-gap. Look (1991) has also analyzed this model in some detail. Let r, be the radius of depleted material around each precipitate. Then charge balance requires that 4.n

- (r:

3

- ri)eNl;\

= Q,

where N& = NEL2-(NAs - ND,),and the fraction f of depleted material is just

Martin et al. (1990) have summarized a variety of studies on precipitate formation in SI, LEC, GaAs. By choosing the maximum ro (l,OOOA), maximum N , (lo9 cm-3), minimum N i & (1 x 10” cm-3), and maximum AV (0.7 V), from their data, we still get f < 0.001. Thus, As-precipitates cannot account for the semi-insulating nature of most present-day GaAs. Furthermore, the standard model (Eq. (10))can be basically verified by other means, since n, N,,,, Nsi, and N,,, can all be determined by independent experiments. Actually, the model of Warren et al. was originally proposed to explain the semi-insulating nature of molecular-beam epitaxial (MBE) GaAs grown at a very low temperature, 200°C and then annealed at 600°C. Such material can have N, as large as lo1’ ~ m - with ~ , ro N 30w. Further discussion of the As-precipitate model as applied to MBE material can be found in the listed references (Warren et al., 1990; Look, 1991).

114

D. C . LOOK

VI. Summary

We have demonstrated that several defect centers, at energies near E , - 0.15, E , - 0.4, and E , + 0.1 eV, are important in the SIGaAs compensation picture. The dominant center is of course the deep donor EL2 (AsGa?),but smaller concentration changes in these other centers can swing the resistivity more, because they are shallower. Some of these centers are also involved in the large, and often reversible, resistivity changes observed in thermally annealed GaAs. Thus, it is important to discover their identities and the conditions under which they appear or disappear. We can hope that much effort will be directed toward these ends in the future.

REFERENCES Alt, H. Ch. (1989). Appl. Phys. Lett. 54, 1445. Alt. H. Ch., and Maier, M. (1991). Semicond. Sci. Technol. 6, 343. Arikan, M. C.. Hatch, C. B., and Ridley, B. K. (1980). J. Phys. C: Solid St. Phys. 13, 635. Asom, M. T., Parsey, J. M.,Jr., Kimerling, L. C., Sauer, R., and Thiel, F. A. (1988). Appl. Phys. Lett. 52, 1472. AuCoin, T. R.,and Savage, R. 0. (1985). Gallium Arsenide Technology (D. Ferry, ed.), p. 47. Howard W. Sams, Indianapolis. Auret, F. D., Leitch, A. W. R., and Vermaak, J. S. (1986). J. Appl. Phys. 59, 158. BaraB, G. A., and Schluter, M. (1985). Phys. Rec. Lett. 55, 2340. BaraB, G. A,, and Schluter, M. (1986). Phys. Rec. B 33, 7346. Blakemore, J. S. (1982). J. Appl. Phys. 53, R123. Boncek, R. K., and Rode, D. L. (1988). J. Appl. Phys. 64,6315. Cullis, A. G., Augustus, P. D., and Stirland, D. J. (1980). J . Appl. Phys. 51, 2556. Duncan, W. M., and Westphal, G. H.(1987).GaAs and Related Compounds (W. T. Lindley, ed.), p. 39. Inst. of Phys. Conf. Ser. No. 83. IOP, Bristol. Fang, 2.-Q., Schlesinger, T. E., and Milnes, A. G. (1987). J . Appl. Phys. 61, 5047. Ford, W., Mathur, G., Look, D., and Yu, P. W. (1986). Semi-insulating IrljV Materials, Hakone, 1986 (H.Kukimoto and S. Miyazawa, eds.), p. 227. Ohmsha, Tokyo. Fornari, R., and Dozsa, L. (1988). Phys. Stat. Sol. (a) 105, 521. Hendorfer, G. and Kaufrnann, U. (1991). Phys. Rev. B 43, 14569. Hoinkis, M., and Weber. E. R. (1988). Semi-insulating I I I j V Materials, Malmo, 2988 (G. Grossman and L. Ledebo, eds.), p. 43. Adam Hilger, Bristol. Hoimes, D. E., Chen, R.T., Elliott, K. R., and Kirkpatrick, C. G. (1982). Appl. Phys. Lett. 40,46. Huber, A. M.,Linh, N. T., Debrun, J. C., Valladon, M., Martin, G. M., Mitonneau, A,, and Mircea, A. (1979). J . Appl. Phys. 50, 4022. Hurle, D. T. J. (1988). Semi-insulating l l l / V Materials, Malmo. 1988 (G. Grossman and L. Ledebo, eds.), p. 11. Adam Hilger, Bristol. Inada, T., Otoki, Y.,Ohatu, K., Taharasako, S., and Kuma, S. (1989). J . Crystal Growth 96, 327. Jaros, M., and Brand, S. (1976). Phys. Rea. B 14, 4494. Jimenez, J., Gonzalez, M. A., DeSaja, J. A., and Bonnafe, 1. (1984). J. Materials Sci. 19, 1207. Kaufmann, U., Baeumler, M., Windscheif, J., and Wilkening, W. (1986). Appl. Phys. Lett. 49, 1254.

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Kitagawara, Y., Noto, N., Takahashi, T., and Takenaka, T. (1986). Semi-insulating ZZZ/V Materials, Hakone, 1986 (H. Kukimoto and S. Miyazawa, eds.), p. 273. Ohmsha, Tokyo. Kitagawara, Y., Noto, N., Takahashi, T., and Takenaka, T. (1988). Appl. Phys. Lett. 52, 221. Kuzuhara, M., and Nozaki, T. (1986a). J. Appl. Phys. 59, 3131. Kuzuhara, M., and Nozaki, T. (1986b). Semi-insulating ZZI/V Materials, Hakone, 1986 (H. Kukimoto and S. Miyazawa, eds.), p. 291. Ohmsha, Tokyo. Lagowski, J., Gatos, H. C., Kang, C. H., Skowronski, M., KO,K. Y., and Lin, D. G. (1986).Appl. Phys. Lett. 49, 892. Lee, B., Gronsky, R., and Bourret, E. D. (1988). J. Appl. Phys. 64, 114. Look, D. C. (1977). J. Appl. Phys. 48, 5141. Look, D. C. (1982). Phys. Rev. B 25,2920. Look, D. C. (1987a). Solid State Commun. 64, 805. Look, D. C. (1987b).J. Appl. Phys. 62, 3998. Look, D. C. (1988).Semi-insulating ZZZ/V Materials, Malmo, 1988 (G. Grossman and L. Ledebo, eds.), p. 1. Adam Hilger, Bristol. Look, D. C. (1989).Electrical Characterization of GaAs Materials and Deoices, Chapter 1. Wiley, New York. Look, D. C. (1991). J. Appl. Phys. 70, 3148. Look, D. C., and Sizelove, J. R. (1987). J. Appl. Phys. 62, 3660. Look, D. C., Walters, D. C., and Meyer, J. R. (1982). Solid State Commun. 42, 745. Look, D. C., Chaudhuri, S., and Sizelove, J. R. (1983). Appl. Phys. Lett. 42, 829. Look, D. C., Yu, P. W., Theis, W. M., Ford, W., Mathur, G., Sizelove, J. R., Lee, D. H., and Li, S. S. (1986). Appl. Phys. Lett. 49, 1083. Look, D. C., Walters, D. C., Mier, M. G., Sewell, J. S., Sizelove, J. S., Akselrad, A,, and Clemans, J. E. (1989). J. Appl. Phys. 66, lo00 (1989). Martin, G. M., Mitonneau, A., and Mircea, A. (1977). Electronics Lett. 13, 191. Martin, S., Suchet, P., and Martin, G. M. (1990). Semi-insulating III/ V Materials, Toronto, 1990 (A. Milnes and C. J. Miner, eds.), p. 1. Adam Hilger, Bristol. Mitchel, W. C., Brown, G. J., Rea, L. S., and Smith, S. R. (1992). J. Appl. Phys. 71,246. Miyazawa, S., and Wada, K. (1986). Appl. Phys. Lett. 48, 905. Moore, W. J., Shanabrook, B. V., and Kennedy, T. A. (1984). Semi-insulating ZIZ/V Materials, Kah-nee-ta, 1984 (D. C. Look and J. S. Blakemore, eds.), p. 453. Shiva, Nantwich, U.K. Nakamura, Y., Ohtsuki, Y., and Kikuta, T. (1988). Japan J. Appl. Phys. 27, L1148. Neild, S. T., Skowronski, M., and Lagowski, J. (1991). Appl. Phys. Lett. 58, 859. Neumark, G. F., and Kosai, K. (1983). Semiconductors and Semimetals, Vol. 19 (R. K. Willardson and A. C. Beer, eds.), p. 1. Academic Press, New York. Ogawa, 0. (1986). Semi-insulating ZIZIV Materials, Hakone, 1986 (H. Kukimoto and S. Miyazawa, eds.), p. 237. Ohmsha, Tokyo. Omling, P., Silverberg, P., and Samuelson, L. (1988). Phys. Rev. B. 38, 3606. Parsey, J. M., Jr. (1988). Semi-insulating IIZ/V Materials, Malmo, 1988 (G. Grossman and L. Ledebo, eds.), p. 405. Adam Hilger, Bristol. Pons, D., and Bourgoin, J. C. (1985). J. Phys. C: Solid State Phys. 18, 3839. Reichlmaier, S., Lohnert, K., and Baumgartner, M. (1988). Japan. J. Appl. Phys. 12, 2329. Rumsby, D., Grant, I., Brozel, M. R., Foulkes, E. J., and Ware, R. M. (1984).Semi-insulating IIZ/V Materials, Kah-nee-ta, 1984 (D. C . Look and J. S. Blakemore, eds.), p. 165. Shiva, Nantwich, U. K. Sankey, 0. F., and Dow, J. D. (1981). Appl. Phys. Lett. 38, 685. Schneider, J., Dischler, B., Seelewind, H., Mooney, P. M., Lagowski, J., Matsui, M., Beard, D. R., and Newman, R. C. (1989). Appl. Phys. Lett. 54, 1442. Shen, Y.-T., and Myles, C. W. (1987). Appl. Phys. Lett. 51, 2034.

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Shockley, W. (1950). Efectrons and Holes in Semiconductors, p. 467. Van Nostrand, New York. Siegel. W., Kuhnel, G., Schneider, H.A., Witte, H.,and Flade, T. (1991). J . Appl. Phys. 69, 2245. Skowronski, M., Neild, S. T., and Kremer, R. E. (1990). Appl. Phys. Lett. 57, 902. Suchet, P., Duseaux, M., Schiller, C., and Martin, G. M. (1988). Semi-insulating ZZZ/V Materials, Malmo. 1988 (G.Grossman and L. Ledebo, eds.), p. 483. Adam Hilger, Bristol. Suemitsu, M., Terada, K., Nishijima, M., and Miyamoto, N. (1991). J. Appl. Phys. 70, 2594. Ta, L. B., Hobgood, H.M., and Thomas, R. N. (1982). Appl. Phys. Lett. 41, 1091. Teh, C. K., Tin, C. C., and Weichman, F. L. (1987). Can. J. Phys. 65, 945. Vasudev, P. K., and Bube, R. H.(1978). Solid-State Electronics 21, 1095. Appl. Phys. 67, 281. Vignaud, D., and Farvacque, J. L. (1990). .I. Wagner, R. J., Krebs, J. J., Stauss, G. H.,and White, A. M. (1980). Solid State Commun. 36, 15. Warren, A. C., Woodall, J. M., Freeouf, J. L., Grischkowsky, D., Melloch, M. R.,and Otsuka, N. (1990). Appl. Phys. Lett. 57, 1331. Weber, E. R.,Ennen, H., Kaufmann, U., Windschief, J., Schneider, J., and Wosinski, T. (1982). Appl. Phys. LRtt. 53, 6140. Woodall, J. M., and Woods, J. F. (1966). Solid State Commun. 4, 33. Young, M. L., Hope, D. A. O., and Brozel, M. R.(1988). Semicond. Sci. Technol. 3, 292. Yu,P. W., Mitchel, W. C., Mier, M. G., Li, S. S., and Wang, W. L. (1982).Appl. Phys. Lett. 41,532. Yu, P. W., Look, D. C., and Ford, W. (1987). J. Appl. Phys. 62, 2960.

SEMICONDUCTORS AND SEMIMETALS. VOL. 38

CHAPTER 4

Local Vibrational Mode Spectroscopy of Defects in III/V Compounds R . C. Newman INTERDISCIPLINARY RFSEARCHCENTRE FOR SEMICONDUCTOR

MATERIALS

BLACKEITLABORATORY IMPERIALCOLLEGE OF SCIENCE,TECHNOLOGY AND MEDICINE LONDON. UNITED KINGDOM THE

I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . 118 11. LOCALIZED VIBRATIONAL MODESPECTROSCOPY . . . . . . . . . . . . . 121 1. Vibrational Modes of Isolated Impurities . . . . . . . . . . . . . . 121 126 2. Impurity Complexes . . . . . . . . . . . . . . . . . . . . . 3. The Effect of Temperature and Strain . . . . . . . . . . . . . . . 127 4. Electrically Active Impurities . . . . . . . . . . . . . . . . . . 128 5. Calibration of LVM Absorption Strength . . . . . . . . . . . . . . 130 6. Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . 132 111. OXYGEN IMPURITIES . . . . . . . . . . . . . . . . . . . . . . . 133 IV . BERYLLIUM IMPURITIES . . . . . . . . . . . . . . . . . . . . . . 136 V . CARBONIMPURITIES . . . . . . . . . . . . . . . . . . . . . . . 138 VI . BORONIMPURITIES . . . . . . . . . . . . . . . . . . . . . . . 141 VII . SILICON IMPURITIES . . . . . . . . . . . . . . . . . . . . . . . 147 7 . BridgmanGaAs . . . . . . . . . . . . . . . . . . . . . . . 147 8. Liquid-Phase Epitaxial GaAs . . . . . . . . . . . . . . . . . . 149 9. MBE and MOCVD GaAs . . . . . . . . . . . . . . . . . . . 149 10. Calibration Data for LVM Line Strengths . . . . . . . . . . . . . 151 11 . Effect ofthe Fermi Level on Dopant Site Occupation . . . . . . . . . . 152 12. MBE Material Grown at Low Temperatures . . . . . . . . . . . . . 153 155 13. Silicon DX Centers . . . . . . . . . . . . . . . . . . . . . 14. Delta-Doping . . . . . . . . . . . . . . . . . . . . . . . 159 15. LEC Czochralski GaAs . . . . . . . . . . . . . . . . . . . . 160 16. Ion-Implanted Silicon . . . . . . . . . . . . . . . . . . . . . 161 VIII . HYDROGENPASSIVATION OF SHALLOW IMPURITIES. . . . . . . . . . . . 161 17. Acceptor Impurities Occupying Ga-Lattice Sites . . . . . . . . . . . 162 18. Donor Impurities Occupying Ga-Lattice Sites . . . . . . . . . . . . 164 19. Anharmonic Effects . . . . . . . . . . . . . . . . . . . . . 166 20. A Comparison with BASDejects and Si DX Centers . . . . . . . . . . 167 IX. RADIATION DAMAGE . . . . . . . . . . . . . . . . . . . . . . 167 21. Defects on the Group V Sublattice . . . . . . . . . . . . . . . . 168 22. Defects on the Gallium Sublattice . . . . . . . . . . . . . . . . . 174 23. Site Switching oflmpurities during Annealing oflrradiated GaAs . . . . . 179 180 24. Final Remarks . . . . . . . . . . . . . . . . . . . . . . .

117

Copyright Q 1993 by Academic Press. Inc. All rights of reproduction in any form reserved. ISBN 0-12-752138-0

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R. C . NEWMAN

X. CONCLUSIONS. . . . . . . . . . . . . . . . . . . . . . . . .

180 .181 181 REFERMCFS . . . . . . . . . . . . . . . . . . . . . . . . . 181

NOTE. . . . . . . . . . . . . . . . . . . . . . . . . . . ACKNOWLEDGMEN~S . . . . . . . . . . . . . . . . . . . . . .

I. Introduction Impurity elements of the first three rows of the periodic table (see Table I) are of great importance in determining the properties of GaAs. They may be present as deliberately added dopants in bulk or epitaxial material, or they may be incorporated as inadvertent contamination, such as boron in liquid TABLE I LIGHTIMPURITIES IN GaAs Impurity

Comments

Hydrogen

Grown-in impurity in some LEC crystals; introduced by proton implantation or hydrogen plasma treatments; forms complexes with other impurities and defects and passivates their electrical activity. An interesting amphoteric impurity: Li, is a donor, while Li,, is an acceptor. Li ditfusion can lead to the electrical compensation of either n- or p-type asgrown GaAs. A common shallow acceptor used to grow ptype molecular beam epitaxial (MBE)material. Can be present as an isoelectronic impurity B,, or an impurity antisite defect B,, depending on the stoichiometry of the material. Residual acceptor contaminant, as C,,, in most material; could be preferred shallow acceptor since it has a low diffusion coefficient and it is stable with respect to high-temperature treatments. Little is known, but N,, may be an isoelectronic trap with the electronic level lying in the conduction band at atmospheric pressure. Present in low concentrations as either a bonded interstitial, or an off-center substitutional atom, OAs. Little-used shallow acceptor. Isoelectronic impurity, used in higher concentrations to produce AI,Ga, -,As alloys. The most commonly used shallow donor impurity; it is amphoteric and may be present as S i , as well as S&; it forms complexes with native defects that act as deep acceptors in highly doped n-type material. Isoelectronic impurity, used in higher concentrations to produce GaP,As, --x alloys. Little-used shallow donor.

Lithium

Beryllium Boron Carbon

Nitrogen Oxygen Magnesium Aluminum Silicon

Phosphorus Sulfur

“Helium, fluorine, sodium and chlorine impurities have not been listed since their properties have not been documented.

119

4. DEFECTS IN III/V COMPOUNDS

encapsulated Czochralski (LEC) crystals where boric oxide is used as the encapsulant. The lattice location of an impurity atom will be indicated by a subscript added to the chemical symbol for the atom. Thus, an aluminum atom occupying a gallium lattice site will be written as AlG,, while an interstitial atom, such as gallium, will be written as Gai. The two types of vacancy will be designated by VG, and VAs. As indicated in Table I, some impurities are “simple,” such as beryllium, which is always present as BeG,, but others, including boron, may occupy either gallium or arsenic lattice sites. In the later discussion we shall refer to BAScenters as impurity antisite defects, because of the expected close relation to native GaAsdefects. The relative concentrations of Baa and BAS,or Si,, and Si,, in silicon-doped GaAs, may change as a result of material processing, such as heat treatments. In addition, pairing of impurities with native defects can occur. These reactions are quite likely to resemble those found in other III/V compounds such as Gap, and consequently it is sometimes useful to make intercomparisons. Ideally, the electrical properties of any impurity or defect should be correlated with the local atomic structure, although isoelectronic impurities such as AlG, or PAS do not give rise to electrical activity. Hall and Shubnikov de Haas (SdH) measurements yield values for the carrier concentration [n] and the mobility p, but provide no spectroscopic information. Far infrared (IR) and photoluminescence (PL) spectroscopy do give such information, but the interpretation in terms of assignments to particular impurities is often difficult or impossible, particularly in highly doped material (see Hamilton, 1989). Likewise, deep-level transient spectroscopy (DLTS) is very sensitive, but provides no direct information about the chemical identity of the center giving a particular signal. In addition, chemical analyses made by secondary ion mass spectrography (SIMS) or radioactivation techniques lead only to values of the total concentrations of various impurities, and not to the distributions amongst the possible sites that may be occupied. Thus, the interpretation of [n] and p at the atomic level is far from straightforward, even if possible contributions from intrinsic defects are ignored. For silicon, the most-studied semiconductor material, the shortcomings just outlined for electrically active centers have been largely overcome by examining crystals by the electron paramagnetic resonance (EPR) technique. Where appropriate, these measurements have been supplemented by electron nuclear double resonance (ENDOR) measurements, leading in many cases to complete and unambiguous models of impurities, defects, and their complexes, since nuclei with a nonzero spin (including ”Si with Z = have been identified and located with respect to some reference point of the defect. The success of these techniques for silicon was due in large measure to the fact

4)

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R. C . NEWMAN

that the EPR linewidths are relatively small (- 1-10 gauss) because only "Si has a nonzero nuclear spin, and it is only 4.7% abundant. When GaAs crystals became available, corresponding information was sought using these same techniques. However, it rapidly became clear that EPR linewidths were considerably larger (100-400 gauss) (Schneider, 1989), and only a limited number of defect centers were identified (all the host lattice nuclei have spins with I = 8. The increased linewidths automatically limit the sensitivity of conventional measurements to defect concentrations in the range 1 0 I 6 ~ r n - ~overlapping , spectra are not easily separated, hyperfine and superhyperfine structure is lost, and sometimes the angular variation of a nonisotropic spectrum is too small to be detected. EPR linewidths of defects in GaP (Kaufmann et a!., 1976; Kennedy and Wilsey, 1979) are smaller than those in GaAs, providing opportunities for intercomparisons, but it may not always be clear that the same generic defect is being considered. This procedure is of limited value, and furthermore the ENDOR technique may not provide complete information. For example, for MnGa impurities in Gap, all the superhyperfine interactions with the surrounding Ga atoms are detected (van Engelen and Sie, 1979; van Engelen, 1980), but no interactions with the phosphorus nuclei (31P 100% abundant, 1 = f). Similarly, for the EL2 defect in GaAs, all the "As (loo%, I = 4) nuclei are detected, but no Ga nuclei (69Ga, 60%, I = $ and "Ga, 40%, I = 3) (Spaeth et d.,1985).It is clear that another microscopic technique is required to reveal the local atomic structure to supplement other types of measurements. A technique that satisfies many of the requirements for defects involving impurities of low atomic mass is localized vibrational mode (LVM) spectroscopy (Newman, 1969, 1973; Spitzer, 1971; Barker and Severs, 1975).This technique had been successful in revealing the properties of centers in silicon crystals containing oxygen, carbon, and boron impurities, defects such as Ci and Bi atoms displaced by high-energy irradiation, complexes of more than one atom such as C,-Oi or Ci-Oi pairs, complexes involving a heavy atom such as B,-As, or B,-Sb, pairs, or finally complexes involving vacancies such as Oi-V pairs. The technique is most valuable when it is combined with others (see, for example, Davies, 1989) to yield a more complete picture, and when calibrations of absorption cross-sections have been established. The scope for applying this method to GaAs is much greater, since all the elements listed in Table I would be expected to give LVMs. Briefly, the mass of the impurity has to be significantly lower than those of the host lattice so that nonpropagating vibrational modes occur at frequencies greater than the maximum lattice frequency. These modes are usually detected by infrared (IR) absorption spectroscopy, but Raman scattering can also be used (Hon et al., 1970). The absorption line is identified by isotopic substitution of the

4. DEFECTS IN III/V COMPOUNDS

121

impurity, while the number and identity of its nearest neighbors can be determined by Fourier transform infrared (FTIR) measurements, which reveal fine structure when there are mixed host lattice isotopes, i.e., 69Ga (60%) and 71Ga (40%). If alternatively the impurity has all 75As (100%) neighbors, no fine structure is produced, and a single sharp line is found. It should already be clear that the LVM technique has features in common with EPR and ENDOR. The identification of the central impurity by isotopic substitution is equivalent in some sense to an identification of a hyperfine interaction, while the structure arising from the near neighbors would correspond in the same way to superhyperfine interactions. The LVM technique has a sensitivity as good as, or better than, conventional EPR applied to GaAs, while it is not necessary for defects to be paramagnetic. An overview of the LVM technique is presented in Section 11, to provide the necessary background for the following discussion. Most of the individual impurities listed in Table I are discussed in Sections 111-VIII, and it is shown how information may be obtained about such diverse topics as crystal perfection, D X centers, impurity antisite defects, &doping, hydrogen passivation of impurities, ion implantation, etc. Section IX is devoted to a discussion of radiation damage, produced mainly by 2 MeV electron irradiation, as revealed by LVM spectroscopy used in conjunction with the EPR technique, and published DLTS data. A brief summary is given in Section X.

11. Localized Vibrational Mode Spectroscopy 1. VIBRATIONAL MODESOF ISOLATED IMPURITIES The Reststrahl absorption of pure GaAs is very strong at frequenciesjust below the maximum lattice frequency om,,(-295 cm-' at 4.2 K) (Mooradian and McWhorter, 1967), so that the material is essentially opaque. In addition, there is weaker absorption from two-phonon and higher-order processes (Fig. 1). The two-phonon processes may be divided into two types, namely summation bands, which are of most importance here, and difference bands, which occur at o om,,.The absorption due to the summation processes has a cutoff at 2w,,, and is reduced in strength as the temperature is lowered to 4.2K (see, for example, Cochran et al., 1961). The localized vibrational modes (LVM) of most impurities (Table 11) lie in the spectral region from om,,to 2o,,,. When impurities with a mass greater than 31 amu are present, modified lattice modes involving significant displacements of the impurity lie within the bands of optic or acoustic modes of the perfect crystal. In general, broad infrared absorption features occur at o c om,,with a correspondingly low

-=

122

R. C . NEWMAN

m

a

0

ioo

200

300 400 WAVENUMBERS CM- 1

500

600

FIG. 1. Intrinsic vibrational absorption of GaAs at 4.2 K.

sensitivity for their detection (Barker and Severs, 1975). Only rarely can useful information be obtained if a resonance occurs at very low frequencies where the density of lattice modes is small. As an example, the rotational modes of bonded interstitial oxygen impurities I6O and '*O in silicon crystals lead to sharp resonances near 30 cm- ' with well-resolved isotopic shifts (Bosomworth et al., 1970); there are no equivalent data for GaAs. Substitutional impurities with a mass mimpless than that of the host lattice atom that is replaced (Tables I and 11) give rise to an LVM with an angular frequency oLgiven by

[-

= kimp

1

+

Mimp

-1,

1

XMnn

where kimp is the force constant between the atom and its neighbors, M,, is the mass of the nearest neighbors, and x 2 is a parameter that depends on the local angle bending and bond stretching force constants (Newman, 1973; Leigh and Newman, 1988). The frequency oLis greater than omax, provided kimpis comparable with a perfect lattice force constant. A disturbance at this high frequency cannot propagate, and the mode is localized spatially. Calculations using cluster models, or other techniques, show that Eq. (1) is a good approximation for wLsince the motion of the second nearest neighbors is small and the motion of third neighbors can be ignored (Leigh and Newman, 1982). Large changes in oLwill be produced if the mass of the impurity is changed by isotopic substitution, leading to its positive identification. As an example,

-

4. DEFECTS IN III/V COMPOUNDS

123

TABLE I1 VIBRATXONAL MOD= OF ISOLATEDIMPURITIES IN GaAs Impurity 'H ZH %i,, 'LiG. 9BeGa

v(cm-')

See Section VIII See Section VIII 482 450 482 540 517 628 601

582 561 480 836 790 715,730 679 331 326 322 362 384 379 373 399 389 355 not observed

Reference

Theis and Spitzer (1984) Laithwaite et al. (1975);Nandhra et al. (1988); Murray et al. (1989b) Newman et al. (1972) Collins et al. (1989) Thompson et al. (1973) Morrison et al. (1974); Woodhead et al. (1983); Gledhill et al. (1984) Newman et al. (1972) Theis et al. (1982); Leigh and Newman (1982) Kachare et al. (1973) Akkerman et al. (1976) Schneider et al. (1989) Song et al. (1987) Schneider et al. (1989) Leung et al. (1972)

Lorimor and Spitzer (1966) Spitzer and Allred (1968); Theis and Spitzer (1984); Murray et al. (1989a) Spitzer and Allred (1968); Theis and Spitzer (1984) Leung et al. (1974); Lorimor and Spitzer (1966) Spitzer (1967); Smith et al. (1966)

the infrared absorption due to 12CAs and l3CAS impurities (Newman et d., 1972) is shown superposed on the two-phonon background with the cutoff near 2w,,, = 590 cm - (Fig. 2). The underlying intrinsic absorption, measured for pure GaAs, has to be subtracted from the composite spectrum to reveal weak LVM lines more clearly. However, the incorporation of a high concentration of impurities or defects produced by high-energy electron irradiation (Section V) may shift and broaden the absorption features of a sample relative to the reference, making the spectral subtraction less than perfect. According to Eq. (l),smaller shifts of oLwill occur if the masses of the nearest neighbors are changed. For light impurities occupying gallium lattice

124

WAVENUMBER (cm

l)

Frc. 2. Low-resolution LVM absorption (77 K) from '*C,, and "C,, impurities in GaAs. (Reprintedwith permission from Solid S t . Commun. 10, Newman, R. C., Thompson, F., Hyliands, M., and Peart, R. F; Boron and Carbon Impurities in Gallium Arsenide, Copyright 1972, Pergamon Press PLC.)

sites, isotopic changes cannot occur since 75Asis 100% naturally abundant. However, there are two naturally occurring isotopes of gallium, namely 69Ga (60%)and 7'Ga (a%), and their different statistical combinations give rise to closely spaced lines for impurities occupying arsenic lattice sites. This effect was first noted to explain the greater linewidth of the LVM line of compared with that of '*SiGaunder conditions of low instrumental resolution (Laithwaite and Newman, 1977). Subsequently, the LVM spectrum of l2CAS impurities was resolved into five fine-structure components when Fourier transform spectroscopy (FTIR)became available (Theis et al., 1982, 1983). In fact, nine such components would be expected, since there are two complexes with symmetry (Ch7'Ga, and CAs6'Ga4),each giving one triply degenerate mode, two complexes with C3, symmetry (C,,71Ga369Ga and CAs7 'Ga69Ga3), each giving a nondegenerate longitudinal and a doubly degenerate transverse mode, and one complex (CA,7'Ga,69Ga,) with C,, symmetry, giving three nondegenerate modes (Fig. 3). Cluster calculations have shown that the three highest-frequency components are close together and are unlikely to be resolved experimentally;a similar result is obtained for the three lowest-frequency lines. The calculations (Leigh and Newman, 1982) are in excellent agreement with the observations (Fig. 4). The importance of this result cannot be over-emphasized, because measurements of LVM linewidths, and more particularly the detection of fine structure, provide information about the lattice site of the impurity atom. The

4. DEFECTS IN III/V COMPOUNDS

125

FIG. 3. Results of a cluster calculation showing the fine-structure components of the "CA, LVM line in GaAs due to the neighboring mixed Ga isotopes, with the combinations shown in the lower part of the diagram. The strengths of the nine LVM components are shown by the height of the bars (Murray and Newman, 1989).

1.75

t h

v)

t

z

' 3

>

a

B 4:

1.25

Y

w

s8 a

m 4:

0.75 582.0

582.4 582.8 583.2 WAVENUMBERS I cm-'

FIG. 4. A comparison of the calculated data shown in Fig. 3 with the experimentally resolved structure of the '2C,, LVM line in GaAs (4.2 K; 0.03 cm- resolution). The theoretical bars have been broadened by a Lorentzian function to simulate the measurements (Gledhill et al., 1991).

126

R. C. NEWMAN

pattern shown in Fig. 4 is in effect a fingerprint for a tetrahedral impurity with Ga neighbors. For impurities bonded strongly to only one, two, or three gallium atoms, the fine structure of the LVM line will be different, as discussed in Sections 111 and IX. 2. IMPURITYCOMPLEXES

If a second impurity or a lattice defect is present in a nearest-neighbor site to the light impurity, the separation of the resulting longitudinal mode wII from the doubly degenerate transverse mode wl will depend on the identity of the second impurity. Thus, the second impurity is characterized spectroscopically, even if it has a high mass. Two light impurities may also pair, in which case both of the original LVM lines should split: An example discussed in Sections VI and VII.15 is the SiG,-B,, pair. Second-neighbor donoracceptor pairs have also been observed (Theis and Spitzer, 1984) (Table 111). Such centers have only C,symmetry, and three nondegenerate LVM lines are produced. In principle, information about the symmetry of any complex can be obtained simply by counting the number of LVMs. However, care is needed because some lines may overlap and some modes may fall into the lattice continuum (aL< w,,,) if a lattice bond adjacent to the light impurity is weakened (Section VIII). Further information about the structure of complexes can be obtained from isotopic fine structure in favorable cases. Suppose an arsenic atom were replaced by a heavy impurity that had more than one isotope, and a nearestTABLE 111 LVM DATA FOR SECOND NEIGHBOR IMPURITYPAIRS Pair Defect 28s'

b.-CUGa 28Si,,-zk,, 28Si.y"&,

z8Sica-7Li,, 28Si,,-

v,

28Si,,-9Be,,"

V ( c m - 1)

314, 316, 399 318, 382, 395 314, 319,405 416,480,481 314, 319,405 438,441,454 366.8, 367.5, 397.8 381.1 and 388.2

References Spitzer et al. (1969) Allred et al. (1969) Chen and Spitzer (1980) Theis and Spitzer (1984) Chen and Spitzer (1980) Theis and Spitzer (1984) Ono and Newman (1989) Mohades-Kassai et al. (1989)

"No modes of the paired Be,, were detected, and the third L V M of the paired silicon atom is assumed to lie under the stronger line from 28Sii. (7-2.

4. DEFECTS IN III/V COMPOUNDS

127

A Ge

(I)

5

3

ABUNDANCES8

h7*8

+27

+20 %

WAVENUMBERS (cm-l)

FIG. 5. The structure of the longitudinal LVM of a nearest-neighbor S&,-Ge,, donoracceptorpair in GaAs (4.2K, 0.03 an-' resolution),showing fine structure due to the various Ge isotopes together with a computer simulation (Gledhill et al., 1986).

neighbor pair were formed with a light atom such as SiGa.In the transverse mode, the light impurity would interact with the heavy atom only via a bondbending force constant (to first order), and negligible isotopic splitting would be expected. On the other hand, a strong effect would be expected for the longitudinal mode, where the two impurities vibrate out of phase along a common axis. This model is illustrated by the absorption of Si,,-Ge,, pairs (Gledhill et d., 1986): The transverse mode of the SiGa atom is sharp (-0.4 an-'), whereas the longitudinal mode is broad and the isotopes of the paired germanium atom are resolved (Fig. 5). AND STRAIN 3. THE EFFECTOF TEMPERATURE

Fine structure of the type described can only be observed if the linewidth Am of the LVM is sufficiently small. Am depends upon the lifetime z of the excited state of the oscillator and the amount of strain in the host lattice. z is an intrinsic parameter that depends on the rate at which the excitation decays into lattice phonons via anharmonic terms in the vibrational potential. This is generally more probable for a two-phonon process, when a,,, < wL < 20,,,, than if three phonons are involved. There is also a significant advantage in making measurements at low temperature (4.2 K)

128

R. C. NEWMAN

-

when values of AUI 0.3-0.4 cm-I are found for impurities such as BGa. The strain in the crystal depends upon the concentration of all the point defects, including the impurities under investigation, and line defects (dislocations) that are present. The former defects give rise to a Lorentzian broadening of Am, producing a similar effect to a decrease in T, while the latter give rise to a Gaussian broadening (Stoneham, 1969). The effects of varying the sample temperature and the concentration of point defects are discussed in more detail in Section V. It is worth noting that whereas LVM fine structure is readily observed for most GaAs samples, it has not been resolved in GaP because of residual lattice strains.

4.

ELECTRICALLY ACTIVEIMPURITIES

LVM absorption measurements of Si,, donors cannot be made directly because of the intense associated free carrier absorption. There is no freezeout of the carriers at 4.2 K,but even if there were, as for SiGain Gap, there would be strong photo-ionization absorption that could obscure much weaker LVM lines. To make measurements feasible, samples must be rendered transparent by effectingelectrical compensation. Two methods have been developed involving (a) diffusion or (b) high-energy irradiation. Diffusion of lithium into either n or p-type GaAs leads to autocompensation (Lorimor and Spitzer, 1967; Theis and Spitzer, 1984), since Li,, atoms act as acceptors while Li, atoms act as donors. Alternatively, copper diffusion can be used to compensate n-type material. Both these techniques can be applied to bulk material (Spitzer et al., 1969). A third possibility for compensating thin layers up to 5pm in thickness is to diffuse atomic hydrogen into the material using an rf plasma as the source (Section VIII). All three methods lead to the formation of complexes between the grown-in impurities and the diffusing atoms. Although the resulting complexes, especially those involving hydrogen, are of considerable interest in their own right, it is not possible to deduce the impurity distribution that was present in the as-grown material. The alternative compensation method requires the sample to be irradiated with high-energy (1-2 MeV) electrons at room, or lower, temperatures (Spitzer et d., 1969). The range of the electrons is about 1 mm, and hence 2mm thick samples may be examined by giving equal doses of irradiation on each side. The dose required in units of electrons per square centimeter is close to the grown-in carrier concentration in units of cm-3. The incident electrons displace lattice atoms, and the resulting defects act as electron and/or hole traps. This method was first used to compensate highly doped silicon crystals that were almost compensated during growth by the in-

4. DEFECTS IN III/v COMPOUNDS

129

corporation of both donor and acceptor impurities (Smith and Angress, 1963). However, mobile vacancies and self-interstitials are trapped by the grown-in impurities to form new defects such as Oi-V(Corbett et d.,1961),Ci (Newman and Bean, 1971)and Bi (Tipping and Newman, 1987b),which also show LVM absorption. A vast amount of information about the damage process in silicon has emerged from such measurements over the last 25 years. Similar effects might have been expected in GaAs, but extended irradiations of samples containing Al, Si, Be, or P either have no effect, except for line broadening, or lead to changes that are very small. It has now been shown by the Raman scattering technique that no changes occur during the early stages of the irradiation when the sample is still opaque and absorption measurements cannot be made (Murray et d.,1989a).Thus, the irradiation treatment can be used to determine the grown-in distribution of many impurities. This conclusion is crucially important for the assessment of silicon-doped GaAs that has been used to explore models for b-doping and the DX center (Section VII. 13). However, there are interactions of mobile radiation-induced defects with grown-in carbon and boron impurities; these are discussed in Section IX. Irradiation of GaAs by other high-energy particles, including neutrons, protons, or ions, also leads to electrical compensation. To a good approximation kimp klacti,, for AlG,, BGa,and PASisoelectronic impurities, but kimp is increased in value by some 20% for singly ionized donors occupying Ga-lattice sites or acceptors occupying As-lattice sites (Grimm, 1972). As a consequence, the LVM lines from 28SiGaand 28SiAshave quite close frequencies (Table 11), both higher than that of the lighter 27AlGa. For acceptors occupying Ga-lattice sites, or donors occupying As-lattice sites, the value of kimp is reduced. Thus, M&, has a low LVM frequency, while an LVM initially expected for 32SAsis not detected (Beall et d.,1985a), and it is inferred that the mode occurs in the lattice continuum (Table 11). Similar systematiceffects occur for GaP and the II/VI compounds (Newman, 1973). Presumably, the static charges on the impurities interact with those on the host lattice atoms to shorten the covalent bonds when kimpis increased, and a repulsive interaction extends the bonds when kimpis reduced, implying a net negative charge on As atoms and an equal positive charge on Ga lattice atoms (see de Girocoli et d.,1989).This classification was helpful in assigning modes in early work and has been discussed again recently, in connection with the charge state of BAScenters (Section VI) (Dischler et d., 1989). In electrically compensated samples, donors are in a positive charge state while acceptors are negatively charged. It is necessary to establish what would happen to the LVM frequency when such impurities are neutralized. For a shallow impurity, very little change would be expected because the electron or hole would be in an extended Bohr orbit so that any influence on kimp would be small. However, for an impurity or complex with a deep

-

130

R. C. NEWMAN

electronic level the trapped camer would be more localized and the strength of the bonds would be changed significantly. These expectations for shallow and deep levels are discussed in Sections V and 111, respectively.

5. CALIBRATION OF LVM AFSORPTIONSTRENGTH Once the absorption in an LVM line has been measured, it is often necessary to convert the data into an impurity concentration, but a calibration first has to be established. The LVM integrated absorption is independent of the sample temperature in the harmonic approximation and may be written

where a is the absorption coefficient (cm-I), v is the energy of the LVM in wavenumbers, n = 3.57 is the refractive index of GaAs, and c is the velocity of light. The left-hand side of Eq. (2) is measured, leaving N and q as quantities to be determined. N is the concentration of impurities occupying the lattice site that gives rise to the particular LVM line, e.g., Si,, atoms. The value of N is not always easily determined, since for this example silicon atoms may be present in several different types of site, or complexes (Section VII). The quantity q is called an apparent charge and is defined as the dipole moment per unit displacement in the particular mode. Values of q are usually close to the electron charge e, but the presence of a static charge on an impurity does not necessarily mean that q is large, nor vice versa. For neutral carbon in silicon "C0, q 2Se, whereas for negatively charged boron "B-, also in silicon, q e (Newman, 1973). It is therefore necessary to carry out a calibration for each impurity in each lattice site or complex in every host lattice. Equation (2) has been written for an impurity with Tdsymmetry where there is only one LVM line. If there is a perturbation from an adjacent atom or a lattice defect, more than one line occurs. For a small perturbation from a second neighbor, it is usually satisfactory simply to sum the absorptions in each line to obtain the total integrated absorption. However, for strong interactions, it should not be assumed that q has the same value for each mode because the perturbation will lead to a local redistribution of the electron density. A summary of available data is given in Table IV. It is often convenient to know the concentration that will give an integrated absorption of 1 A common question is to ask, "What is the sensitivity of LVM absorption spectroscopy?" For Ch impurities where the LVM line falls in a region of low

- -

4. DEFECTS IN III/v COMPOUNDS

131

TABLE IV CALIBRATXON DATAAND VALUES OF THE APPARENT CHARGE q TO CONVERTINTIGRATED AWRPTION(IA) OF IMPURITY LVM LINESTO DEFECTCONCENTRATIONS Impurity

Concentrations to Give IA = 1 ( c I l - 3 x 10’6) 5.5 6k 1 3 2.4 (77 K) 3.1-4.1 1.1 0.95 f0.29 0.8 0.2 1.18k0.20 (300 K) 0.92 f 0.20 (77 K) 3.1 k0.4 5.5 Li or Cu diffusion 5.3 10.0 6.0k 1.0 5.0 & 0.4 5.5 6.8 12.7 6.0 5.0 25.3 (acceptory 2.7 (acceptor)’ 19.0 (donor)’ neutral or acceptof

N

Reference

rl

(Units of e)

1.1kO.1 1.2 1.6 1.9 1.7-1.5 2.8 3.0 3.3 2.7 3.1 2.5 2.0

Nandhra et al. (1988) Brozel el al. (1978) Maguire et al. (1985) Brozel et al. (1978) Theis et al. (1983) Hunter et al. (1984) Homma et al. (1985) Brozel et al. (1986) Arai et al. (1988) Brozel et al. (1978) Spitzer and Allred (1968)

2.0 1.4 1.85 2.0 1.9 1.7 1.2 1.8 2.0 0.9 2.8b 1.0

Laithwaite and Newman (1976) Chen et al. (1980) Woodhead et al. (1985) Murray et al. (1989a) Spitzer and Allred (1968b) Laithwaite and Newman (1976) Chen et al. (1980) Woodhead et al. (1985) Murray et al. (1989a) Chen et al. (1980) Murray et al. (1989a) Chen et al. (1980) Ono and Newman (1989)

-

“See text (Section VII.10). bThe calibration data given by Murray et al. (1989a)are in error.

background (two-phonon) absorption (Fig. 2), the detection limit is better than 5 x lOI3 since samples 5 mm in thickness can be used. On the other hand, for 28SiGathe LVM line falls in a spectral region where the twophonon absorption is relatively more intense (Fig. 1).A detection limit closer ~ realistic for a sample 1 mm in thickness (Murray et to 3 x lOI4 ~ m is -then al., 1989a). For epitaxial layers, the sensitivity decreases in proportion to the reduction in thickness of the layer containing the impurity of interest. These

R. C . NEWMAN

132

detection limits are therefore better than that of the EPR technique using standard (non-optical) detection methods for the observation of, say, AsGa defects. 6. RAMANSPECTROSCOPY

So far it has been implied that IR absorption is always used for the spectroscopic measurements of LVMs. The technique has a very high instrumental resolution of 0.03 cm- ' or better, but shortcomings are the requirement for relatively thick samples and the need to compensate samples containing a high concentration of shallow donors or acceptors. The latter disadvantage is overcome by using Raman spectroscopy where the depth of the probing light may be reduced to only 10 nm at a photon energy of 3 eV (krypton laser) (Ramsteiner et al., 1988). The free carrier absorption in this

hwL=3.00eV

n=0.7X 1 0 ' 8 c m - 3

r .-c u) c

-

e,

-c C

m

5 a:

350

400 450 Raman Shift (cm-l)

500

FIG. 6 . Raman scattering from LVMs of silicon impurities in various centers (see Section VII) after subtraction of the multiphonon background (77 K, 5 cn- ' resolution,hv = 3 eV). Note that an increasing concentration of silicon in the samples leads to a reduction in the carrier concentration En] (see also Fig. 15) (Wagner et al., 1989a).

4. DEFECTS IN III/V COMFQUNDS

133

thickness of material is negligible, and the concentration of carriers may be reduced anyway because of surface depletion effects. The scattered light reveals the LVM line superposed on a continuum of scattering produced by multiphonon processes (Fig. 6). It is again necessary to subtract this background obtained from pure GaAs to reveal the LVM lines. Measurements made to date had a low spectral resolution of 5 an-', which does not allow nearest-neighbor fine structure to be resolved. This is not a limitation if the same LVM line has been fully characterized by previous IR absorption measurements, provided adjacent lines are not too closely spaced. A Raman calibration can also be established by comparing the strength of the LVM scattering with an intrinsic multiphonon feature, to eliminate errors caused by variations in the laser power, geometrical factors, etc., but samples with a known impurity concentration have to be used. The Raman technique is more complicated than IR absorption as an absolute measuring process, since the scattering cross-sections depend on the incident photon energy and the sample temperature (Ramsteiner et d.,1988). A principal problem is the occurrence of resonance effects as found for the LVM line of Si,,, the strength of which is greatly increased when there is electronic excitation to the El gap along a (1 11) direction (3 eV excitation), and the sample is held at 77 K. Only under these conditions does the Raman spectrum resemble the IR absorption spectrum. The sensitivity of the technique, using an array detector, is 2 x 10" atom cm-2 for Si,, impurities, corresponding to a high impurity concentration of 2 x 10'' The technique is nondestructive and should be regarded as complementary to IR absorption; it is particularly useful for the investigation of ion-implanted or b-doped material (Section VII).

111. Oxygen Impurities

Bulk GaAs crystals grown by the LEC technique are in contact with liquid boric oxide throughout their growth, and contamination by both boron and oxygen might be expected. Effects due to boron are discussed in Section VI. Undoped (or chromium doped) crystals grown by the Bridgman method often have gallium oxide (Ga203)added to their melts to produce highresistivity material (Gooch et al., 1961). The excess oxygen combines with residual silicon, which may be present as contamination from silica components in the equipment, and the introduction of Si,, donors is thereby prevented or reduced. Again, the crystal might be expected to take up excess oxygen. However, chemical analysis using fast particle radio-activation techniques has shown that the oxygen content of such materialis less than about 5 x lo1' cm-3 (Brozel et al., 1978; Clegg, 1982).Such a concentration is

134

R. C. NEWMAN

close to the detection limit for SIMS, but would be easily detected by DLTS if the oxygen were present in electrically active defects giving rise to deep levels. There has been speculation that certain defects do incorporate oxygen atoms (Sturge, 1962; Lin et al., 1976; Lagowski et al., 1984), and there is a need for correlated DLTS and LVM measurements. So far, only limited LVM data are available. Early measurements showed no detectable 1R absorption due to oxygen in bulk GaAs doped with Ga,O,, but when AsZO3was used as an alternative dopant, an absorption line was found at 836 cm- * (300 K) (Akkerman et al., 1976).It was confirmed that the absorption was due to an LVM of oxygen, since an isotopic analogue was found at 790cm-' in material doped with As,O, enriched with l80The . frequencies of these lines are much higher than that of 582 cm-' for substitutional lZCAs (Table 11),which has a lower mass, suggesting that the oxygen does not occupy a tetrahedral lattice site. It is helpful to recall that bonded interstitial 1 6 0 i impurities in silicon crystals produce an L V M at 1,136cm-' (9pm band at 4,2K), which is likewise a much higher frequency than that of 607 cm-' for substitutional 12C in the same host (see Newman, 1973).The inference is that oxygen atoms may also be present as bonded interstitials in GaAs, bridging one Ga and one As atom (Fig. 7). This structure had been proposed to explain high-frequency vibrational modes of oxygen in GaP (Barker et d., 1973), although samples containing enriched "0 were not examined.

f

169-69

z

0 Ia U

0 m

0

a

I

710

715

720 842 WAVENUMBERS (crn-l)

a45

,

,

,

9

FIG. 7. The L V M of (a) 1 6 0 i in GaAs showing isotopic splitting from the single Ganeighbor, and (b) the otf-eentex l6OAs defect showing isotopic splitting from two Ga-neighbors (4.2 K, 0.03 cm I resolution)(Schneider et al., 1989).

4. DEFECTS IN I I I N COMPOUNDS

135

Recently, the LVM lines in GaAs have been reexamined using highresolution FTIR with the sample held at 4.2 K. They were then resolved into close doublets, with a strength ratio of 60:40 corresponding to the isotopic abundances of 69Gaand 'IGa (Fig. 7) (Schneider et al., 1989).Such a splitting would be expected for the proposed interstitial structure, which has been confirmed by Song et d. (1990b), and the LVM lines were therefore assigned to an antisymmetric mode of vibration of each isotope, analogous to that of the 1,136cm- oxygen mode for l60in silicon. At low temperatures (4.2 K), this latter mode also shows splittings due to the different combinations of the two 28Si(92.3%),"Si (4.7%)or 30Si(3.0%) atoms to which the oxygen atom is bonded. The GaAs crystals examined did not contain measurable concentrations of other impurities, and the likelihood of complex formation was therefore minimal. On the other hand, several high-frequency absorption lines were found in GaP (Barker et d.,1973)and complexes of oxygen paired with other impurities such as silicon were almost certainly present. The concentration of [Oil atoms in the GaAs samples was not determined, and so it is not yet possible to quote a value for q (Eq.(2)). With the assumption that q e, the value of [Oil would have been about ax-3.However, for Ojatoms in silicon, the value of q is close to 4.0e: 3x A corresponding value for GaAs would reduce the estimated value of [Oil by a factor of 16. Determining a meaningful value of q for Oi in GaAs will be extremely demanding because of the low concentrations ( c j [Oil 10l8 in silicon), and also because a fraction of the oxygen is present in other sites, as discussed later. The impression may have been given that most GaAs samples show a weak absorption band from Oi atoms, but this is not so. Out of a large stock of material examined in our laboratory, only three samples showed the line, and there was no obvious correlation with the conditions of crystal growth. An extensive program of work varying the growth conditions in a systematic way is needed for the observations to be understood. An LVM line at 730cm-' and two close lines near 715cm-' have also been detected. FTIR measurements show that all three lines have triplet structures corresponding to the vibrations of a light atom bonded to two gallium neighbors (Fig. 7). It was suggested that the vibrating atom might be an AsGa antisite defect (Song et d., 1987), but later this suggestion was withdrawn and it was speculated that the atom was oxygen (Desnica et I., 1988; Zhong et d.,1988). Subsequentlyit was shown that the 715 cm-' LVM line had an isotopic analog at 679 cm- in GaAs doped with l 8 0 , proving that oxygen was indeed involved (Schneider et d.,1989). Other measurements showed that the three lines arise from a common defect, since illumination of the sample caused correlated and reversible changes in the strengths of the lines (Zhong et al., 1988;Alt, 1989, 1990a;Song et al., 1990a).The implication

-

-

136

R.C . NEWMAN

is that the LVM lines refer to three different charge states of the oxygen defect. The difference in frequency of 15cm-' between the lines at 730 and 715 cm- ' indicates that the center has relatively deep electronic levels. The observations, including recent piezospectroscopic measurements (Song et a/., 1990b) are consistent with those expected for an off-center substitutional oxygen atom bonded to two gallium nearest neighbors, analogous to the A-center (Oi- V pair defect) found in irradiated silicon when an Oi atom captures a mobile vacancy (Watkins and Corbett, 1961). This center gives only two LVM lines. A line at 836 cm- from LOi- V]' (Corbett et a/., 1961)shifts to 884cm-' for [Oi-U- (Bean and Newman, 1971)when the Fermi level cF crosses the known acceptor level at (EC-0.17eV). information about the electrical properties of the center in GaAs has recently been obtained by Alt (1990b), who has shown that it is a negative-U defect. Deep oxygen donors are found in GaP (see Dean, 1986) with concentrations of about 10'6cm-3, but no LVM data have been reported. It is known from PL studies that close donor-acceptor pairs, such as (O,-Zn,& form, and similar complexes would be expected in GaAs. Pairing with carbon, boron, silicon, zinc, or intrinsic defects could explain the observations of yet further weak LVM lines due to oxygen in some GaAs samples (Song et d.,1990a). In summary, recent measurements have shown that oxygen may be present in GaAs in at least two types of center. Comparisons of the observations with those for oxygen in silicon and GaP crystals suggest that the centers involve Oi atoms, and off-center substitutional atoms respectively. The detection of the isotopic fine structure from the Ga neighbors was of crucial importance in allowing models to be proposed.

IV. Beryllium Impurities Beryllium is the favored shallow acceptor impurity for the doping of MBE GaAs and other III/v compound semiconductors. Its LVM absorption was first observed in liquid-phase epitaxial layers of GaAs that had been compensated by 2 MeV electron irradiation (Laithwaite et al., 1975).A single line was found at 482cm-' at 77K corresponding to the 100% abundant 913eGaacceptors. More recently, measurements were repeated on MBE GaAs at 4.2 K with a higher instrumental resolution of 0.1 cm-' (Nandhra et a/., 1988). The linewidth of 0.6cm-' is consistent with that expected for an impurity with four "As nearest neighbors (Fig. 8). Neither type of sample showed any other LVM absorption that could be attributed to Be complexed with intrinsic defects generated by the irradiation. Similar data have also

4. DEFECTS IN III/V COMPOUNDS

137

?

E

s 120 I-

z

Y 5 0 $

90

z 0 I-

60

n.

gCT

30

m

b:

I

I

I

I

476

480

484

WAVE NUMBERS (cm-')

FIG.8. The LVM line of 'Be in GaAs, showing (a) a symmetrical shape in electrically compensatedmaterial and (b) an asymmetric Fano profile in as-grown p-type material (Murray et al., 1989b).

been obtained by Raman scattering (Wagner and Ramsteiner, 1989). An interesting point is that no resonant enhancement of the LVM line occurs at an incident photon energy of 3 eV, as found for the line from Si,, (Sections I1 and VII). A combination of Hall measurements to determine Cp] = [BeGa] in unirradiated material, and LVM absorption data, led to a calibration (Eq. (2)) with q = 1.1 k O.le (Table IV). Calibration data for Raman scattering have also been obtained (Wagner et al., 1991). IR measurements at 4.2 K have been made on MBE samples containing without electrical compensation. These samples [Be] = 3.7 x 10" showed only low transmission because of a strong electronic absorption continuum. No lines corresponding to electronic transitions of the Be acceptors were found, indicating that the doping level was above the metalinsulator transition. The BeG, LVM then appeared as an asymmetric derivative-shaped Fano profile (Fig. 8) superposed on the background. Such effects are well known in the fields of atomic spectroscopy, nuclear physics, etc., and references have been given by Murray et al. (1989b). Theory indicates that there should be a shift in the LVM line position and a broadening due to the electron-phonon coupling (Fano, 1961). The peak of the profile shown in Fig. 8 is indeed slightly shifted by 0.3 cm-' to a lower energy, compared with that of 482.4an-' for compensated material. It is unclear how the Fano profile should be analysed in this context, because the electron irradiation used for compensation of the GaAs would also have led

138

R. C . NEWMAN

to a broadening and small shift of the LVM line (see Section V). An outstanding problem is to understand the origin of the electron-phonon coupling. As the sample is metallic, the electronic wavefunctions would be spread over the whole crystal, whereas the vibrational wavefunctions would be localized around the Be atom and its four nearest neighbors. Thus, the magnitude of the overlap appears to be too small to explain the observations. Raman scattering measurements made on uncompensated GaAs doped with Be failed to reveal Fano effects, in contrast to those observed from silicon highly doped with boron acceptors. Fano anti-resonances, or dips in the electronic absorption continuum, are found close to the positions expected for the LVM absorption lines of loB and I l B in the latter material (Murray et al., 1989b). Further investigation of the electron-phonon interactions is required. In summary, beryllium appears to be a simple impurity in GaAs, as it occupies only Ga lattice sites, but there are difficulties in estimating the strength of the LVM line in material that is not completely compensated. This problem was apparent in estimating the degree of compensation that occurs during hydrogen passivation of Be acceptors (Nandhra et d., 1988) (Section VIII.17).

V. Carbon Impurities

Carbon is an important residual contaminant in semi-insulating (SI) LEC GaAs, and may also be a useful stable acceptor dopant. In SI crystals, carbon acceptors are present in a negative charge state due to the presence of the mid-gap deep donor defect EL2. In weakly p-type material, there is freeze-out of the holes at 4.2 K to give neutral acceptors. Thus, it is possible to make LVM measurements on either 12Ci, or ‘’Cis centers without having to irradiate crystals to effect compensation. A low-resolution spectrum showing the isotopic shift of l3CAS(Fig. 2), together with a high-resolution fingerprint spectrum showing the Ganeighbor isotopic fine structure (Fig. 4), has already been shown. Highresolution spectra for neutral l2CAS centers have also been reported, and it was found that the LVM line was shifted to a lower energy by 0.15 cm-’ at 4.2K (Shanabrook et al., 1984). A small shift is expected for a shallow acceptor due to a weakening of kimp (Eq. (1)) (Section 11.4). There are again confusing aspects of the interpretation. Firstly, an electron-phonon interaction occurs which might lead to a small “Fano shift,” similar to that found for Beca acceptors (Woodhouse et al., 1992).Secondly, the comparison of the

4. DEFECTS IN III/V COMPOUNDS

139

LVM frequencies for the two charge states was not made on two separate samples. Instead, the p-type material was compensated progressively by small doses of electron irradiation that would have led to a shift and broadening of the LVM line due to the introduction of damage (see below). Estimates of the calibration of the strength of the C,, LVM line have changed significantly since the first, made on poor-quality polycrystalline Bridgman material that contained a high concentration of the impurity. However, making reliable measurements of the lower concentrations present in modem SI crystals is also difficult, but a value of q 3e is now considered to be accurate for room temperature measurements;a summary of the data is given in Table IV. The integrated absorption in the line has been reported to decrease by about 30%as the sample temperature was increased from 150 to 300K (Dischler et d., 1989), although the theory for a harmonic oscillator indicates that the net absorption (absorption less the stimulated emission) should be independent of temperature. Anharmonic coupling of the LVM to lattice modes will lead to sidebands as the temperature is increased, similar to vibronic sidebands of an electronic transition (Elliott et al., 1965). This process was suggested subsequently to explain a measured change of about 10% in the calibration for carbon in silicon when the temperature was changed from 77 to 300K (Newman and Smith, 1969). Changes in the lineshape and the linewidth will also occur as T is increased, and the effects are complicated for the CAsLVM line because of the fine structure (Alt, 1988). Consistent estimates of the integrated absorption are therefore difficult to make, especially as the temperature-dependent two-phonon background has to be subtracted from each composite spectrum. A random distribution of point defects can be introduced into GaAs in a controlled way by subjecting samples to progressively higher doses of 2 MeV electron irradiation. The defects lead to (a) a homogeneous strain, or an increase in the GaAs lattice spacing, and (b) an inhomogeneous strain. These strains produce a progressive shift of the LVM frequency to a lower energy, and a Lorentzian broadening of the line, respectively. (Similar effects have been reported by Laithwaite and Newman, 1977, for the LVM lines due to silicon impurities in irradiated GaAs.) The experimental data shown in Figs. 9 and 10 (Gledhill et al., 1989), can be used to assess the structural quality of the GaAs crystal and provide an alternative technique to x-ray analysis using measurements of rocking curves. For comparable measurement times, the two techniques appear to be of a similar sensitivity, if the magnitude of the change in the lattice spacing is related to the change in the LVM frequency via a Griineisen constant. A precise comparison is not possible, since all the lattice defects would contribute to both types of change, but in a way that cannot be quantified adequately. The effects of introducing point defects is similar in this context to raising

-

140

R. C . NEWMAN

FIG.9. The loss of resolution of the fine structure of the LVM line of "C,, in GaAs due to increasing inhomogeneous strain produced by 2 MeV electron irradiation (4.2 K; 0.03 atresolution). (High Resolution FTIR Study of LVMs due to C in GaAs: Measurements of Internal Strains and Structure of the c(1) Lines, by Gledhill et nl., 1989.)

0

5

10x10'7

RADIATION DOSE (e-cm-2)

FIG. 10. Shift in the fine structure peak at 583 cm-' (Fig. 9) from the LVM of "C,, in GaAs produced by the presence of damage defects introduced by 2 MeV electron irradiation at room temperature. Note the onset of saturation of the damage at high doses, indicated by the nonlinearity (High Resolution FTIR Study of LVMs due to C in GaAs: Measurements of Internal Strains and Structure of the C(l) Lines, by Gledhill et al., 1989).

141

4. DEFECTS IN III/V COMPOUNDS

the sample measurement temperature from 4.2 K. Firstly, the thermal expansion of the lattice lowers the LVM frequency, and secondly the lifetime of the first excited state decreases, leading to a Lorentzian broadening (Dischler et d., 1989). Once T is raised sufficiently, there will be significant occupation of the first excited state of the oscillator, and excitation to the next higher state will produce large shifts and broadening due to anharmonic effects. An important point emerges. Although the frequency of a sharp LVM line can be measured for a particular sample with great accuracy (0.001 CII-'), since it is relative to that of the He-Ne laser line used to control the interferometer, there is little meaning in quoting the frequency with this precision, unless the temperature and lattice spacing are also specified to the required accuracy. Since carbon is a group IV element, it might have been expected to show amphoteric behavior, similar to that of silicon (Section VII). However, no LVM line that could be attributed to CGadonors has been identified. The line, if it existed, should be sharp, with a half-width of about 0.3 cm- and its frequency might be expected to be similar to that of CAs,by comparison with the data for silicon impurities (Table 11).

',

VI. Boron Impurities Boron normally occupies Ga-lattice sites in LEC GaAs to give LVM absorption lines from "BGa (80% abundant) and l0BGa(20%) at 517 and 540 cm- respectively. High-resolution spectra show that the linewidths are only 0.3 cm- ',proving that the boron atoms have arsenic nearest neighbors (Collins et d., 1989). Similar data are available for boron in Gap, where Raman measurements were used to show that the boron atoms occupied sites with symmetry (Hon et d., 1970). The level of boron contamination derived from the B,03 encapsulant is greater for GaP crystals compared with GaAs, which in turn is greater than that for InP (Newman et d., 1970), in the same sequence as the melting temperatures of the compounds. When silicon is added to a GaAs melt, the boron concentration in the crystal is considerably greater, and is almost equal to the silicon content (Thompson and Newman, 1972). Heavily borondoped material is also produced if aluminum is added to the melts of either GaAs or Gap, because of a displacement reaction in which elemental boron is released from the encapsulant (Maguire et d.,1985; Woodhead and Newman,

',

1981).

GaAs crystals grown from undoped gallium-rich nonstoichiometric melts show p-type conduction that increases toward the tail end of the crystal,

142

R. C . NEWMAN

where inclusions of Ga metal are sometimes found. Such crystals exhibit IR electronic absorption from a double acceptor with energy levels at (E, + 78 meV) and (E, + 203 meV), respectively. This acceptor can also be detected by electronic and vibrational Raman scattering and DLTS. It is commonly supposed that a gallium antisite (Ga,,) defect, possibly complexed with another defect, is responsible for the observations (for references, see Kaufmann, 1989). If GaAsdefects are present in crystals that contain boron, it could be speculated that B,, impurity antisite defects might also be present, but electronic IR absorption has been detected for only one double acceptor (Addinall et at., 1990). However, once such p-type gallium-rich material has been subjected to a small dose of 2 MeV electron irradiation, sufficient to raise the Fermi level to a position close to E, + 200 meV (Fig. 1I), new LVM lines are observed at 601 and 628cm-', due to "B and loB impurities, respectively (Woodhead et al., 1983; Newman, 1985a). High-resolution FTIR spectra revealed a five-line fine-structure "fingerprint" showing that these boron atoms occupied sites of % symmetry with four Ga nearest neighbors (Fig. 12) (Gledhill et d.,1984; Moore et al., 1985). Two possibilities had to be considered. Either the boron atoms were present

?

-05 z

1.8-

ANNEAL AT 210'C

I-

a

SEm

1.4 - IRRADIATE

4

1OI5 e-FLUENCE I e-cm-*

FIG. 1 1 . The production of the "BAS impurity antisite center by 2 MeV electron irradiation of Cia-rich nonstoichiometricGaAs, showing a welldefined threshold fluence. Annealing for 30 or 60 min reverses the process, which is continued at a lower rate during subsequent irradiation (Newman, 1986).

4. DEFECTS IN III/V COMPOUNDS 1

143

I

I

GaAs

J 60 1

601.5

602

WAVENUMBERS cm-l

FIG. 12. The resolved fine structure of the "BAS LVM line due to the four neighboringmixed gallium isotopes.

as B A S , or they occupied tetrahedral interstitial sites with Ga neighbors. A detailed discussion of this question has been given elsewhere (Newman, 1985a),which led to the conclusion that the defects were BASantisite centers. A central argument was that the frequencies of the isotopic sequences l0BAs, IIBAs,I2CAS, l3CASin GaAs, and 1°Bp, llBp, lZCp,l4CPin GaP were similar to the corresponding sequence 1°B, "B, "C, I3C, 14C found in silicon crystals (Fig. 13), demonstrating that the nature of the bonding of the boron atoms was essentially the same as carbon atoms in each of the three hosts. Thus, boron must occupy substitutional group V sites in GaAs and Gap, since it is well established that carbon is present as a substitutional acceptor, while both boron and carbon are substitutional impurities in silicon. It has been implied that the sequences of LVM frequencies show that the boron is in the single negative charge state according to the classification given in Section 11.4 (see Dischler et d., 1989), but a double negative charge state cannot be ruled out. The BASfine structure pattern (Fig. 12) is slightly different in detail from that of CAs(Fig. 4). The greater overall width can be explained by a reduced

R. C. NEWMAN

144

14 4.5 lc

ISOTOPE MASS (a.m.u.) 13 12 11

,

13c

'B

12c

10 'OB

"7

sr

5

-$

4.0

n

lwx m

fz

W

2> f

3.5

2

Y

3.0

0.07

0.09

0.08

0 .1

M-' (a.m.u.)-I imp

13. Plots of w z versus (mimp)-' for *4C, '%,'*C, 'lB, and loB in GaAs, Gap, and Si hosts. The similarity of the three plots indicates that boron atoms are present as B, impurity antisite defects in GaAs and GaP (Newman, 1985a). FIG.

ratio of the local angle bending to bond stretching force constants (Newman, 1985a), while other small differences could be due to anharmonic effects. Since BASdefects would be expected to be acceptors, it is not clear whether the 78/203 meV levels relate to BAS or GaAsdefects. It could be inferred that BASdefects do not exist in as-grown material, but are produced by the irradiation treatment (Moore et al., 1985). Thus, migrating Gai atoms produced by the displacement of Ga lattice atoms could in principle exchange sites with BGa atoms by the Watkins (1965)replacement reaction, and mobile Bi atoms could then combine with arsenic vacancies (V,, defects), also produced by the irradiation. When it was assumed that an integrated absorption of 1 cm-' in the BASLVM line corresponded to 3 x 10l6defects cm-3 (Table IV), it had to be concluded that the reactions described would have to be essentially 100% efficient. In other words, the introduction rate, defined as the number of centers per cubic centimeter produced per incident 2 MeV electron per square centimeter on the sample, was 1.25 cm-', close to the expected primary displacement rates of 4-5 cm-' for Ga and As lattice atoms (Woodhead et al., 1983). It would be very unusual for the introduction rate to be so high for such a two-stage irradiation damage process, especially when account is taken of the low concentration of BG, atoms that was

4. DEFECTS IN III/V COMPOUNDS

145

present. In addition, the reduction in [BGa] was too small to explain the growth of [BAS](Addinall et al., 1990). There are other difficulties with this radiation damage model. The most direct relates to other electron irradiation experiments carried out on p-type crystals containing a high concentration, [BGa] lo'* grown from a stoichiometric melt doped with aluminum (Maguire et al., 1985). BG, atoms were removed by the treatment, but the process involves the trapping of Asi atoms (Section IX.21.a) to form stable (BG,-Asi) complexes. More importantly, there was NO production of BAS centers. A prerequisite for the formation of these defects in p-type material is that the crystals should have been grown from gallium-rich melts and is unrelated to the concentration of BGa.The threshold dose of irradiation required before the onset of formation of BAScenters (Fig. 11)is also difficultto explain, unless it is ascribed to a shift in the position of E ~ The . overall inference is that the irradiation per se is not the crucial process required for the formation of BAScenters. This conclusion is borne out by the observation of the defects in as-grown nonstoichiometric GaAs that also contained donor impurities that would have raised the position of the Fermi level (Fischer and Yu, 1986; Addinall et al., 1990). The irradiation treatments given to the aluminum-doped material led to no detectable removal of AIG, atoms or formation of AlA, defects; it is not known whether this might occur in nonstoichiometric material. It was later proposed that a BASatom is bistable and would spontaneously move off its lattice site toward a nearest neighbor interstitial site in p-type material (Newman, 1986).The total energy of the system would be lowered by removing BASacceptor states, which would be replaced by states associated with the paired V'As-Bi defects, which might have donor properties. In n-type material, to be discussed later, a lower energy would be achieved by having B A S acceptors present. This proposal of bistability has been investigated recently using first principles calculations (Zhang and Chadi, 1990).According to the theory, the boron atom would move to a new equilibrium position in p-type GaAs, near the plane of three of the original four tetrahedral Ga nearest neighbors. Since the bond along the trigonal C3"axis would be greatly elongated, the vibrational frequency of a longitudinal mode of the boron atom would be low, and would probably fall into the lattice continuum (w c urnax). However, the three remaining bonds would be shortened and strengthened. A new transverse doubly degenerate mode of the displaced B atom should then occur at a higher frequency than that for BAs(TJ (see Section VIII.20). No such mode has been found, although the background intrinsic absorption of GaAs is low in this spectral region (w > 2wmaJ, which should make the detection of such a band relatively simple. Zhang and Chadi (1990) also showed that the Ga, should be similarly bistable, and so the theory does not help in distinguishing the origin of the 78/203 meV energy levels.

-

146

R. C . NEWMAN

This apparent impasse could be removed if it were speculated that the B A S defect actually dissociates in strong p-type material to produce a VA, separated spatially from the Bi atom. The threshold in the irradiation dose (Fig. 1 1 ) would still be explained, together with the observation of stable BAS defects in as-grown GaAs with an elevated Fermi level. However, in our recent work the concentration [BAS]appeared to correlate with the concentrations of the deep electronic levels measured by DLTS, with an implication that GaAsdefects may not be present, or alternatively that they have much deeper energy levels. Further work is required to clarify the interpretation, which has a wider relevance to other bistable, and possibly negative4 centers, including AsGa(Dabrowski and Scheffler, 1988; Chadi and Chang, 1988a; Baraff, 1989), GaAs(Zhang and Chadi, 1990), and D X (see Section V11.13). Strong LVM lines from B A S centers are also observed in heavily doped ntype GaAs following electron irradiation to effect compensation (Thompson et af., 1973). In addition, satellite lines are present and depend on the chemical TABLE V LVM FREQUENCIES (cm-')

OF

B,-vI

AND

B,-Si,,

PAIRS IN

GaAs AND GaP

(MORRISON et a/., 1974) GaAs I1B,-Se, "B,,-Te,, loBA,-Se*, 1oBA5-TeA* "B,,-Si,, loBA,-SiG,

"1

576.4 580.7 601 .0" 605.0" 570.Fb 596.Wb

"2

w3

609.4

621.7 622.6 649.0 649.6

606.5

636.5 633.1 66 1 .O 684.8

-

B"(T*) 602.5 603.3 628.8 629.2 600.9 625.6

601.4 601.4 627.8 627.8 601.4 627.8

625.6 626.8 626.3 653.2 654.7 654.1 627.2 654.7

624.5 624.5 624.5 652.1 652.1 652.1 624.5 652.1

GaP "B,-S,

595.8

IIB,-Se,

599.0

"B,-Te, 'IB,-S, 'OB,-Se, "B,-Te, "B,-S& "B,-S&,

600.8 622.2" 625.4" 627.4" 594.4E.b 620.6a.b

633.3 632.2 628.7 661.3 660.0 656.6 692.7 723.0+

647.6 649.2 649.4 676.1 677.8 678.2

"Calculatedfrequencies assuming w('"B)/o("B)= 1.044: lines at these positions would be masked by stronger lines. *Doublydegenate mode. The values of LT) are close to those of "B,,, loBA,(Td)in Ga,,, and l1BPand 'OB,(q) in Gap.

4. DEFECTS IN III/V COMPOUNDS

147

identity of the donor species. Thus, two lines are found for &,-BAS pairs with C,, symmetry, while three LVM lines are found for TeAs-BA, and SeAs-BAs pairs with C, symmetry. These data are listed in Table V, together with similar results for Gap, where S,-BA, pairs were also observed (Morrison et al., 1974). Our original assignment (Thompson and Newman, 1972) of the silicon pair defects in GaAs to BGa-SiAs pairs is incorrect. The lines listed refer to the perturbations of the LVM of the paired BAS;other satellite lines would be expected around that from Si,, (see Section VII.15). A puzzling feature, which has been noted previously, is that the degree of pairing is much greater than would be expected from the statistics of donoracceptor formation.

VII. Silicon Impurities 7. BRIDGMAN GaAs

Silicon impurities in GaAs are incorporated preferentially on Ga lattice sites to produce n-type material grown by the Bridgman technique. It is necessary to effect electrical compensation before LVM absorption measurements can be made (Section 11.4). In early work this was achieved by diffusing Cu or Li into samples at temperatures in the region of 900°C. LVM spectra then showed lines due to Si-Cu and Si-Li second neighbor donor-acceptor pairs (Table 111), and so some redistribution of Si impurities amongst the possible lattice sites must have occurred (Spitzer, 1971;Murray and Newman, 1989). Consequently, later measurements have made use of high-energy electron irradiation (2 MeV) (Spitzer et al., 1969). In lightly doped n-type material, a single LVM line is observed at 384 cmwith a linewidth of only 0.4cm-', confirming that the silicon atoms (28Si, 92.3% abundance) occupy Ga lattice sites. As the doping level is increased, further lines from the less abundant isotopes 29SiGa(4.7%)and "SiGa (3.0%) are detected at 379 and 373 cm-', respectively. A broader line exhibiting fine structure spread over some 1.5 cm-' also appears at 399 cm-', due to 28SiAs acceptors. The structure due to the various isotopic combinations of the four Ga nearest neighbors is unambiguous, but less well resolved than that for CA, or BASimpurities (Sections V and VI). At the next higher level of doping, two further lines, which are correlated in strength, appear at 393 and 464 cm-'. Doping samples with enriched ,OSi leads to a splitting of the higher-frequency line into four components, while the 393 cm-' line shows a less well resolved isotopic structure at lower frequencies. The two lines are ascribed to the longitudinal and transverse antisymmetric modes of SiGa-SiAsnearestneighbor donor-acceptor pairs. The fine structure of the longitudinal mode

'

148

R. C . NEWMAN

relates to 28SiGa-28SiAs, 28SL;a-30SiAs,3oSi,a-28SiAsand 30SiGa-30SiAs pairs (Theis and Spitzer, 1984). Two further lower-frequency symmetric modes must occur, but have not been detected in absorption, implying that the associated dipole moments are small (Brozel et nl., 1979). At the highest doping levels, whcn the carrier concentration exceeds about 3 x 10l8~ m - ~ , two new overlapping absorption features labeled Si-X and Si-Y are detected at 369 and 367 c n - l . The absorption from such a sample is shown in Fig. 14. Electron irradiation treatments, extended well beyond the dose required to effect compensation, lead to a progressive reduction in the strengths of these features. On subsequent annealing, the lines are regenerated but at different rates, so allowing them to be partially resolved (Brozel et al., 1979). The separation of the lines has also been facilitated by measurements made on heavily doped MBE and MOCVD epitaxial layers, which have shown only SCX to be present (Murray et al., 1989a). Other plastically deformed Bridgman GaAs, subsequently annealed near 70O0C, showed growth of the Si-Y center (On0 and Newman, 1989).This defect gives sharp (A 0.4 ern- l ) lines at 366.8 and 367.5 em- together with a third line at 397.8 cm-I (Table 111) that had not been detected previously because it is usually obscured by the fine structure of the stronger line. The sharpness of the lines indicates that a Sica atom gives the LVMs, and further analysis led to the

-

0

~

l

A

.

,

.

~

,

l

l

l

l

l

10

FIG. 14. LVM absorption spectrum of silicon-doped Bridgman GaAs showing absorption from the various silicon centers discussed in the text. An L V M line from "AI,, present as an inadvertent impurity (Table 11) is also detected (4.2 K, resolution 0.1 cm-') (On0 and Newman, 1989).

4. DEFECTS IN III/V COMPOUNDS

149

conclusion that the defect should be identified with a SiG,-VG, second neighbor pair with C, symmetry. This type of center is well known in II-VI compounds (Schneider, 1967), and its presence in GaAs was invoked in early work to explain a commonly occurring photoluminescence line (Williams and Bebb, 1972). However, further work is required to check the interpretation because the possibility that a fast-diffusing but unknown metal may have been present and formed the pairs cannot be ruled out. The atomic structure of the Si-X center is not well understood, but a recent analysis has suggested that a Si,, atom and a Ga vacancy are likely to be involved (Murray et al., 1989a). Further evidence for the presence of VG, is provided by the fact that Cu diffusion leads to a large reduction in the concentrations of both the Si-X and Si-Y defects (Spitzer et al., 1969). Cu diffuses interstitially and then combines with Ga vacancies to form CU,, acceptors, so that Si,- VG, defects would be converted to siG,-cuG, centers. The mechanism for the conversion of Si-X is not yet clear. In summary, Si atoms may be present in five types of centers. It has already been stated that there is no redistribution of Si atoms in the early stages of the irradiation, as determined from Raman experiments (Section 11.6), but prolonged irradiation leads to a very slow and small increase in the strength of the line from "SiGa and a corresponding reduction in that from %iAS, apart from the effects already discussed for the Si-X and Si-Y centers.

8. LIQUID-PHASE EPITAXIAL GaAs Silicon-doped LPE GaAs may be either n- or p-type, depending upon the are obtained, implying growth conditions. Values of [ p ] up to 3 x 10l8 that the concentration of Si,, acceptors can be greater than that of SiGa donors. LVM spectra of as-grown electrically compensated samples show that the strength of the line from Si,, is comparable to that of the line from Si,, (Spitzer and Panish, 1969; Laithwaite and Newman, 1976).No lines from Si-X or Si-Y have been detected, which is consistent with the interpretation that these centers incorporate V,, defects. LPE GaAs could be Ga-rich or stoichiometric, but certainly not As-rich. A problem with a quantitive analysis of LPE material, several microns in thickness, is that it is electrically inhomogeneous and the site distribution of the silicon, as well as its total concentration, may have spatial variations.

9. MBE AND MOCVD GaAs Layers of silicon-doped epitaxial MBE material ranging in thickness from 1 to 20 pm and grown at a temperature of 550°C on a (100)plane of SI GaAs

150

R. C . NEWMAN

have shown Si LVM spectra very similar to those found for Bridgman samples (Fig. 15), except that Si-Y centers were not detected (Maguire et al., 1987; Murray et al., 1989a). As the doping level was increased the carrier concentration [n] passed through a maximum value of 5.5 x 10l8~ m - ~ , before falling to 4.5 x 10” when the total estimated silicon concenThe LVM spectra of these most highly doped tration reached 3 x 10’’ samples showed a large increase in the strength of the line from Si-X, a reduction in the strength of the SLaline, but no appreciable increase in the strength of the line from SiAS.Chemical analysis of the same material did not reveal any contamination, and it was concluded that the Si-X defect is a deep acceptor, but its energy level is not known. Thus, the limiting value of [n] is

I

M°CVD

,-

Eu

CnlHALL

Y

X 10l8crn-3

2

w

0 LL LL

8 100

“I 6+ 50 a

6 07 u

3.4 2.0

50.---

0

m

a

380 395 410 WAVENUMBERS(crn ‘1

365

MBE

El

I

I

A

v

$

0 “I

rn a

0

1

0.45

1

1

365 380 395 410 WAVENUMBERS(cm-’ )

FIG. 15. LVM spectra for siiicondoped epitaxial layers grown on S1 GaAs substrates by either MOCVD or MBE. Note that the spectral lines are displaced sideways for clarity of presentation (Murray et al., 1989a).

4. DEFECTS IN III/V COMPOUNDS

151

not due primarily to site switching of Si atoms from Ga to As lattice sites. Similar data were obtained for MOCVD material (Fig. 15). Not all silicon-doped MBE layers are n-type. Growth on (111)A, (112)A, and (113)A planes (Okano et al., 1989), terminated by Ga atoms, leads to the formation of p-type layers, but we are currently unaware of reported LVM spectra for such material.

10. CALIBRATIONDATAFOR LVM LINESTRENGTHS The carrier concentrations of samples [n] (prior to irradiation) can be measured by the Hall effect or the SdH method; the total silicon content of samples can be measured by calibrated SIMS, while the integrated absorption in each of the LVM lines can also be measured. It follows that estimates can be made of the apparent charges q (Eq. (2)) for each type of Si defect, if a suitable range of samples is available, with the added assumption that the concentrations of electrically active intrinsic defects present are small. In that case we may write

[nl

= [Si,,]

- [Si,,]

- [Si-X]

f [Si- Yl,

(3)

since SiGa-SiAspairs should be electrically neutral. The f signs have to be determined if no assumptions are made about the electrical behavior of Si- Y defects. The concentrations are related to the LVM integrated absorption according to Eq. (2). The measurements of Chen et al. (1980) and Woodhead et al. (1985) made on Bridgman and LPE samples were not satisfactory for a variety of reasons. The individual calibrations for Si,, and Si,, can only be found if the ratio of the strengths of the two LVM lines can be varied significantly for a range of samples. In practice, this does not occur unless very high doping levels are used, but then absorption from Si-X and Si-Y appears in Bridgman crystals. In addition, it becomes increasingly difficult to measure the strength of the 28SiGaLVM line, because there is negligible transmission at the peak. Alternatively, [SiGaltotcan be determined from measurements of the strengths of the lines from 29SiGaand 30SiGa(Woodhead et al., 1985). However, the strength of the LVM line from Si,, at 399cm-' would have been overestimated, because of the overlapping line from Si- I.: The total integrated absorption (three lines) from Si- Y would likewise have been underestimated (On0 and Newman, 1989). More recent measurements (Murray et al., 1989a) made on a series of relatively thin MBE and MOCVD layers ensured that there was always adequate transmission of the incident radiation, and a spectral resolution of

152

R. C . NEWMAN

0.1 cm- was used. Unfortunately, the ratio of the strengths of the lines from

Si,, and Si, still did not vary a great deal, making it difficult to specify an accurate calibration for SiAs.The analysis was, however, simplified, since SiY defects were not present, but this precluded any information being obtained about the electrical activity of this defect. The results are given in Table IV. This topic has been discussed at some length, as it is necessary to have calibrations of the LVM lines to obtain meaningful data relating to DX centers and &doping. GaAs samples with known silicon concentrations in the different sites allow similar absolute calibration data for Raman scattering measurements to be determined, as discussed in Section 11.6.

1 1. EFFECTOF THE FERMI LEVELON

DOPANT

SITEOCCUPATION

The maximum n-type carrier concentration that can be achieved for normal growth conditions of GaAs is limited to about 5 x lo1*~ m - ~ . Various experiments have been carried out in an attempt to modify this value, because it was not clear whether it was a general limit for all n-type dopants or whether it was specific to silicon. Doubly doping samples with a second donor, which was either tin or a group VI impurity, led to silicon site switching from Ga to As sites, but with no net increase in [n] (Brozel et al., 1980). Doubly doping Bridgman samples with Si and an acceptor increased the concentration of [Si,J, but the material was then partially compensated, leading to a lower value of [n]. The latter work has been extended recently to MBE GaAs grown at 580°C and doubly doped with high concentrations of silicon and beryllium [A, > [SiGJ (Mohades-Kassai et al., 1989). For p-type samples with & (Table VI), lines from S k a donors and BeGaacceptors were observed, together with weak lines attributed to Be,.-S& second neighbor pairs (Table 111). The important points were (a) that [SiJ was estimated to be about 1.8 x 10l9 and (b) that lines from Si,, acceptors, S&-SiAs pairs, Si-X, and Si-Y were not detected (Fig. 16). The absence of the first three of the latter centers was not unexpected as they involve acceptor defects, but the absence of Si-Y strongly suggests that this defect might also be an acceptor or a neutral defect, but not a deep donor. For n-type material grown under the same conditions with [Si,.] > [Be,J, the silicon site distribution was similar to that for other singly doped MBE material and to that found in Bridgman samples. The observation of Si-Y in the Si/& n-type sample would be consistent with its assignment as a deep acceptor. This conclusion would not be unexpected for a SiGa-VGa defect, since the paired gallium vacancy could be a double, or even a triple, deep acceptor.

4. DEFECTS IN III/V COMPOUNDS

153

TABLE VI ANALYSIS OF LVM LINESTRENGTHS TO DETERMINE IMPURITY CONCENTRATIONS FOR MBE SAMPLES DOUBLY DOPEDWITH Si AND Be AND A COMPARISONWITH HALLMEASUREMENTS Impurity Concentrations'

Carrier Concentrations (1018

(1018 m - 3 )

Si,,

Si,,

Si-X

18 29

0 6.8

0 5.0

Be,, 23.5 15

cn-3)

nopt

Cnl

5.5(P)

4.w

244

1.2(n)

"Data for neutral Si&3i, pairs not included. Data in first section derived from calibrations in Table IV (Mohades-Kassai et al., 1989).

FIG. 16. LVM spectra for n- and p-type MBE GaAs layers doubly doped with silicon and beryllium. Small lines at the positions of the arrows are due to Sb,-Be,, second neighbor pairs (Mohades-Kassai et al., 1989).

Overall these observations provide strong evidence that the position of cF has a large effecton the silicon site distribution and leads to the limiting ntype carrier concentration.

GROWNAT 12. MBE MATERIAL

LOW

TEMPERATURES

Silicon-doped GaAs grown by MBE at 400°C has high values of [n],which may exceed 1019cm-3, and a very simple LVM spectrum (Fig. 17). Such

R. C. NEWMAN

154

-z5

6C

48

!-

w

0

36 w 0 0

4

24

l-

a

29

SiGa

LT 12 4

360

380

jiGa-SiAs

intrinsic

1

feature

I

siA~

400

1

420

WAVENUMBER (cm-')

FIG. 17. L V M spectrum of a silicon-doped MBE layer grown at 400°C. Note the absence of theSi-XandSi-Y structuresinspiteofthe highmeasured valueof[n]=l.l3x 1019cm-3(SdH) (4.2K, resolution 0.1 at-')(Eaves et al., 1988).

material has been characterized in several ways (Murray et a)., 1989a). The total silicon content [Sk,J was first estimated from the calibrated flux from the silicon cell on the MBE growth equipment. The value of [Sit,,] was also determined from calibrated SIMS measurements. The value of [n] was found from SdH and Hall measurements. The latter concentration was somewhat lower than the former, but this small difference is expiicable since some carriers would be trapped in D X levels at the high value of [n], even at zero pressure. This effect was more noticeable for other tin-doped GaAs material where [n] 2 x lo" c r ~ (see - ~ Section VII.13). The Si-doped material was then irradiated, and the concentrations of [Si] present as Si,, donors, SiAs acceptors, and SiG,-siA, donor-acceptor pairs were determined using the calibrations discussed in Section VII.10. Thus, [n] (SdH) should be equal to [Si&J-[SiAsJ, while [Sit,,] should be equal to the sum of [Si,,], [Si,,], and [SiGa-SiAs].It is important to note that there were no detectable Si-X or SiY defects present. All these data (Table VII) are self-consistent to within + 107; and show that there was no measurable concentration of silicon in sites where it gave no LVM absorption. These observations are important to the analysis presented in Section VII. 13, but appear to contradict the conclusions of Section VII.11. Consequently, certain samples were annealed for 20 min at 500°C or 6WC, and then

-

4. DEFECTS IN III/v

155

COMPOUNDS

TABLE VII OF DATAFOR SILICON-DOPED GaAs SAMPLE SHOWING DX ANALYSIS BEHAVIOR UNDER HYDROSTATIC PRESSURE

Quantity Measured

Method

Concentration ( x lor8an-3) 11.2 1.2 12.4 13.0 11.3 10.0 14 6

“A small increase should be made for silicon present as SiGa-SiAspairs.

irradiated to obtain new LVM spectra. The heat treatment led a reduction of [Si,J, and the lost donor atoms reappeared as Si,,, SiA,-SiGapairs, and SiX defects. Clearly, diffusion had occurred, to produce a site distribution similar to that found in samples grown at the higher temperatures. Thus, samples grown at 400°C are metastable and would not retain their as-grown properties during device processing at higher temperatures. In addition, deep defects have been detected by DLTS (Blood and Harris, 1984), and it has been pointed out that the stoichiometry may not be well controlled. Defects in MBE GaAs grown at very low temperatures down to 200°C (Smith et al., 1988)have been studied by Kaminska et al. (1989a, 1989b).This material was As-rich, leading to an increase in the lattice parameter, the presence of AsGa antisite defects (Section IX), and other centers that may be VGa. 13. SILICON DX CENTERS In AlGaAs, deep donor levels are present (DX centers). Originally it was proposed that the defects responsible were shallow impurities (donors, D) complexed with an intrinsic but unidentified defect X, leading to the designation DX. X as used in this context should not be confused with the defect in the Si-X center discussed above. The two terminologies are each of long standing but are quite independent, and it is only recently that the two topics have become associated. Subsequently, DX-like behavior was also detected in heavily doped n-type GaAs subjected to a high hydrostatic pressure, showing that the presence of aluminum was not necessary (Mitzuta et al., 1985). The observations were

156

R. C.NEWMAN

related to changes in the band structure that are similar to those produced by the addition of aluminum (Fig. 18). That is, the r minimum rises in energy but at a higher rate than the higher-lying L minimum, while the X-minimum decreases in energy and eventually crosses the r minimum. The DX level appears to lie just below the L minimum. At zero pressure the ground state is shallow and is associated with the r minimum, but above a critical doping level additional carriers go into the DX level. When pressure is applied, the critical doping concentration is reduced, until eventually at high pressures the deep DX state has the lower energy, and all the carriers may be lost. It was then suggested that it was the substitutional impurities themselves that were the DX centers, and that there was no associated intrinsic defect X. For silicon-doped GaAs, LVM spectroscopy can clearly reveal whether or not a defect X is present in a first or second neighbor site. Unfortunately, a similar check cannot be made for group VI donors, since 32SAsdoes not give rise to an LVM (TableII). Consequently, the highly silicon-doped MBE GaAs grown at 400°C described in Section VII.12 was subjected to hydrostatic pressures up to 15 kbar (Eaves et al., 1988). There were reductions in [n], determined by SdH measurements, and an increase in the mobility. When the sample was illuminated with the pressure still applied, [n] returned to its original value at zero pressure, showing that trapped electrons had been released (Fig. 19). To produce this return of carriers, the incident photon energy had to exceed a threshold value of about 1 eV, whereas thermal reactivation requires a much lower energy of about 0.1 eV. The released carriers were not retrapped and

0 0.2 0.4 0.6 0.8 1

(All COMPOSITION ( x )

0

20

40

PRESSURE (kbar)

FIG. 18. Positions of the r, L,and X minima of(a) AlGaAs as a function of composition and (b) GaAs subjected to a hydrostatic pressure. A notional position of the DX-level is shown in (b) just below the L minimum (Maude et al., 1990).

4. DEFECTS IN m/v COMPOUNDS

10

157

-

8 -

-*

t

J- LIGHT I

I

0

5

0, 10 P(kbar)

h I

15

FIG. 19. The variation of [n] (SdH) and the electron mobility p with increasing hydrostatic pressure for the Si-doped MBE GaAs sample shown in Fig. 17. Note the decrease A[n] is 6 x lo'* ~ 3 1 for 1 ~P =~ 15 kbar (Eaves et al., 1988).

caused persistent photoconductivity. This behavior is also typical for DX centers in AlGaAs and can be explained if the defects responsible undergo a large lattice relaxation in changing from the shallow to deep configuration. For the GaAs sample, the maximum measured reduction in [n], -6 x 10" ~ m - due ~ ,to the application of the pressure has to be equal to, or smaller than, the concentration of DX centers present. Since the value of [Si,,] - [Si,,] of 1.0x 1019cm-3 is greater than [DX] at a pressure of 15 kbar, it is numerically possible for Si,, impurities to be identified with DX centers (Table VII). However, no detectable Si,, donors complexed with intrinsic defects were revealed by the LVM spectra (less than 10I8~ m - ~The ). conclusion has to be that the DX center should be identified with the Si,, donors themselves, and hence there is no associated X defect. An alternative possibility is that isolated Si,, donors are compensated at high pressure by bistable intrinsic defects located at sites remote from the chemical donors (third or more distant neighbors). In the latter case, the concentration of bistable defects would have to be comparable with [Si,,] for all samples. Since DX behavior is found in MBE, LPE, and bulk material (see Henning and Ansems, 1987), where variations in stoichiometry are expected, this idea seems unlikely but is not excluded by the high-pressure measurements. The proposed DX behavior of Si,, donors has been attributed to a bistability in their lattice location. The site of T, symmetry corresponds to the

158

R. C. NEWMAN

shallow configuration, but it is proposed that the atom moves along a [l 113 axis towards an interstitial site when it has the deeper electronic level (Fig. 20), and the defect has also been predicted to be negative-U (Chadi and Chang, 1988b). In principle, LVM spectroscopy could be used to verify or discount this model. The modified defect (see also Section VIII) would have C,,, symmetry, with a low longitudinal frequency due to the extension of the bond along the axis, while the transverse mode should have a higher frequency than that of the T, center. It would be necessary to carry out LVM measurements on an unirradiated sample at 4.2 K while it is subjected to a high hydrostatic pressure (perhaps 30 kbar), which should lead to a complete freeze-out of all the carriers. The results of such an experiment have not been reported. Attempts have been made to investigate DX behavior by LVM spectroscopy in silicon-doped AlGaAs, where the aluminum concentration has been limited to a few per cent (5-1073. In the DX configuration, the Si atom is supposed to move towards an interstitial site that has one or more A1 neighbors (Morgan, 1989). Unfortunately, the lines from the silicon donors become very broadened because of the lattice disorder (Murray et al., 1988),

SIMPLE DX DIAGRAM

P=O As

Q-0

0-

per,,

Ga

0Ga(or Al)

As

P'

T,j

Ga C,"

FIG. 20. Proposed model for DX behavior of bistable Si impurities in GaAs subjected to a high hydrostaticpressure. In the deep configuration,P > Pcri,,there should be a modification of the Si,, LVM (see Chadi and Chang, 1988b).

4. DEFECTS IN III/V COMPOUNDS

159

and absorption from discrete centers with one, two, or more A1 second neighbors has not been identified to date. Further work using superlattice structures similar to those used for DLTS measurements may be helpful in this context (Mizuta, 1990).

14. DELTA-DOPING N-type material may also be produced by interspersing sheets of silicon dopant in the GaAs at regular intervals throughout the MBE growth process (Wood et al., 1980). At normal growth temperatures, SIMS measurements show that the silicon atoms, deposited while the Ga flux is shuttered, do not stay in a plane following further growth of GaAs (Beall et al., 1988). There are two effects. First, there is a spreading of the sheet due to diffusion, and secondly there is segregation of the silicon atoms, which tend to move toward the growing surface. As a result, broadened and somewhat asymmetric SIMS profiles are found. These effects are particularly marked at high sheet doping levels of 4 x lOI3 cm-’. However, it has been shown that Si diffusion and segregation do not occur to any significant extent during the growth of layers at 400°C. More importantly to the immediate discussion is the observation of a saturation in the added electron concentration as the amount of dopant in the b-layer is increased (Zrenner et al., 1987). Recently Zrenner and Koch (1988) and Zrenner et al. (1988)proposed that the limit in [n] was due to the presence of DX centers in some of their samples. This possibility can be checked by LVM spectroscopy. An LVM examination of a stack of 100 8-layers each doped to 4 x 1013 atom cm-’at 400°C showed that only some 25-30% of the deposited silicon atoms occupied the various lattice sites in GaAs (similar effects were found for sheet doping levels of 2 x 1013 and 8 x lOI3cm-’) (Beall et al., 1989), explaining the measured limited electrical activity. Because the samples were compensated by electron irradiation, DX centers (see Section VII.13) would have been ionized. SdH measurements (4.2K) made by other workers (Koenraad et al., 1990) on illuminated material containing b-doped layers have shown only a relatively small increase in [n] compared with measurements made on samples kept in the dark, showing that DX behavior was not important in their samples, although [n] was smaller than would be expected from the silicon doping level. On heating our b-doped superlattice to 600°C for 30 min, silicon diffusion occurred as expected, and the total concentration of [Si,,] + [Si,,] + [SiGa- Si,,] + [Si - X] rose to some 75% of the estimated grown-in impurity content. It was concluded that silicon atoms formed electrically inactive

160

R. C. NEWMAN

clusters at the surface during growth, and that these clusters were then buried by the further growth of undoped GaAs. During subsequent heating the clusters acted as sources for silicon to diffuse into the surrounding matrix. Such clustering of silicon atoms had been suggested previously by Zrenner et al. (1987). Related LVM Raman measurements (Wagner et al., 1989b)have also been made on samples grown at 580°C with a single Si &doped layer at different depths below the top surface. The limited penetration of the 3 eV incident photons allowed the depth distribution of the Si,, atoms to be determined. An asymmetric profile was deduced, indicating surface segregation, while the strength of the signal implied that not all the silicon atoms were Ramanactive. In this work it was suggested that the inactive atoms were located on the surface of the GaAs capping the 6-layer if the thickness of this layer were too small. Thus, there is a common conclusion that not all the Si impurities are located in lattice sites. The difference of interpretation about the alternative location, is almost certainly due to the difference in the growth temperatures.

15.

LEC CZOCHRALSKI GaAs

Boron derived from the B 2 0 3 encapsulant may be incorporated into silicon-doped LEC GaAs as Si,,-BAS donor-acceptor nearest-neighbor pairs (Section VI). These complexes are most easily revealed in LVM spectra as satellites on either side of the lines from isolated BASdefects, but there should be satellite lines around the line from the isolated silicon donors. One such line has been observed at 349 cm-' (Morrison et al., 1974).A second LVM of the paired silicon atom is expected, but has not been detected so far. It is likely that it occurs in the spectral region near 400cm-' and is obscured by the stronger line from 28SiAsat 399cm-'. The observation of a Si LVM from the boron complex in GaAs does not prove that a Si,, atom is involved. However, similar silicon complexes with B, centers have been observed in GaP (Table V). In that host, isolated Si,, atoms give rise to an LVM, but isolated Sip atoms do not, because the reduction in mass from that of 32Pis too small. When Si-B complexes are present, a new LVM mode is observed at 427.4 cm- on the low-energy side of the line from Si,, at 464 cm - This new mode must be due to a paired SiG,, in which case the corresponding mode in GaAs also involves a Si,, atom (Morrison et al., 1974).Thus, the defects in GaAs are SiG,-BA, pairs and not siAs--BGapairs. This topic has been included because recently it has been observed that D X behavior in silicon-doped GaAs that also contains boron is different from

',

4. DEFECTS IN III/V COMPOUNDS

161

that when boron is absent (Li et al., 1989). LVM measurements correlated with other types of measurements are needed to understand these new observations. 16. ION-IMPLANTED SILICON A common procedure for fabricating devices is to implant GaAs with silicon, and subsequently to remove the damage by annealing. Implants of 29Siare normally used to avoid contamination from 14N2molecules. The ion energy may be close to 100 keV, and doses in the range 5 x loi4 to loi6 atom cm-2 have been investigated (Wagner and Ramsteiner, 1987; Wagner and Fritzsche, 1988). Such layers examined by LVM Raman scattering showed the normally forbidden TO phonon line in the back scattering geometry from a (100) face, because of residual lattice damage, even after annealing (Wagner, 1988). LVM lines from 29Siwere observed, but as pointed out elsewhere, their relative strengths depend upon the incident photon energy and the sample temperature (see Holtz et al., 1986; Nakamura and Katoda, 1985). In addition, the conditions of the anneal are important in relation to the method used to prevent the loss of arsenic from the implanted surface. Heating samples in a overpressure of arsenic, or while they are capped with a deposited layer of silicon nitride, led to the “usual” distribution of silicon amongst the various lattice sites. However, if the sample is coated with silica, the concentration of the Si-X defect is enhanced and a smaller electrical activation, [n] of the n-type dopant, is found. The difference is explained by the diffusion of Ga atoms, derived from the GaAs, into the capping layer (Wagner et al., 1987), leaving V,, defects in the implanted layer.

VII. Hydrogen Passivation of Shallow Impurities Atomic hydrogen generated in an rf or microwave plasma diffuses to a depth of a few microns into GaAs held at a temperature in the range 150300°C (Pearton et al., 1987). If the crystal is doped with shallow acceptors (Zn,,, Be,,) or shallow donors (Sic,, SnGa),their electrical activity is lost and the centers are said to be passivated. In fact, hydrogen atoms form close pairs with the grown-in impurity, and the LVM frequencies of the hydrogen are characteristic of that impurity, even if it does not itself give rise to LVM absorption. More information can be obtained from complexes with light atoms such as Be,,-H (Nandhra et al., 1988) and SiG,-H (Jalil et al., 1987) and it is reasonable to suppose that the structure of a Be,,-H pair will be the

162

R. C . NEWMAN

same in all essential detail as that of a Zn,,-H pair; similar comments apply to Si,,-H and Sk,-H pairs. A discussion of the LVMs of the paired hydrogen (and deuterium) has been given elsewhere (Chevallier et al., 1990), but subsequent data (Kozuch et al., 1989)for SnGa-H pairs indicate that some relatively minor modifications of the interpretation are necessary.

17. ACCEPTORIMPURITIES OCCUPYING GI-LATTICE SITES

The first shallow passivated acceptor to be examined by LVM spectroscopy in GaAs was zinc (Pajot et al., 1987). Only one hydrogen stretching mode with a high frequency of 2146.9cmI' was found, together with a corresponding deuterium mode at 1549.1cm- '. The ratio (oH/oD) is equal to 1.386, whereas the use of Eq. (l), with x = 1, predicts a larger value of 1.404 if the mass of the atom M,, to which the hydrogen is bonded is 70amu. The atom cannot be identified, as the masses of 65Zn, "Ga, and "As are not distinguishable in this context. No doubly degenerate transverse wagging mode was found, although such a mode is expected as the symmetry of the complex cannot be greater than C3".It is implied that the restoring force for displacements perpendicular to the axis between the hydrogen atom and the atom to which it is bonded is very low, so that the mode occurs in the lattice continuum. Similar measurements made on Be-doped MBE layers (Nandhra et al., 1988) led to the observation of H and D stretching modes at 2037.1 and 1471.2 cm-'. The frequency ratio o H / w D= 1.384 is only marginally different from that for Zk,-H pairs. It was therefore argued that the H-atom is not bonded strongly to the light 9BeGaatom, as the frequency ratio would then have to be smaller than 1.348; rather, it must be bonded to a neighboring As atom. Again, no hydrogen wagging mode was observed. The formation of Be,,-H complexes leads to a reduction in the integrated absorption of the LVM line from isolated BeGa atoms at 482.4cm-' (Section IV). Two new LVM lines of the paired Be would be expected, but only one, attributed to the transverse mode, has been found at 555.7 cm- ' for Be-H and 553.6 cm-' for Be-D. It is inferred that the frequency of the longitudinal mode of the Be is low and falls into the lattice continuum. The observations are explained if the hydrogen atom takes up a bondcentered position (Fig. 21). The Be atom relaxes along the [1111 crystal axis toward the adjacent interstitial site, into the plane of its three remaining As neighbors. The bonds with these atoms are reduced in length and are thereby strengthened, so that the transverse mode of the paired Be atom occurs at a higher frequency than that of the unpaired tetrahedral impurity. The Be-H bond must be weak, as the frequency of the longitudinal mode of the Be is

4. DEFECTS IN III/v

163

COMPOUNDS

AS

FIG.21. The model for a Be,,-H

pair center in GaAs (Nandhra et al., 1988).

low. Thus, the hydrogen atom is bonded primarily to an arsenic atom that was an original neighbor of the Be acceptor. These deductions are in agreement with a recent theoretical model of the complex (Briddon and Jones, 1989,1990,1991) (Table VIII). In summary, the electrical activity of the Be is lost because it forms bonds with only three neighbors, while the hydrogen passivates the bond on the fourth As neighbor. It is inferred that the Zn-H defect has the same structure.

TABLE VIII VIBRATIONAL FREQUENCIB (cn-') OF THE Be-H COMPLEX IN GaAs Mode Be(T,) stretch Be(l-3) wag H(TJ stretch W 3 ) wag

Calculated Frequency (BC)"

Experimental

300 620 2,018 300

N.D.' 550 2,037 N.D.

N

-

"Briddonand Jones (1989, 1990, 1991). bNandhraet al. (1988). 'N.D.-not detected.

Valvob

164

R. C . NEWMAN

18. DONORIMPURITIES OCCUPYING GI-LATTICE SITES LVM data for l19Sn-H pairs have now been reported (Kozuch et al., 1989). For these centers, both longitudinal and transverse modes of the paired hydrogen were found at 1327.8 and 746.6 cm - respectively. A corresponding longitudinal mode from paired deuterium was found at 967.7 cm-': the transverse mode expected near 530cm-' was obscured by the strong twophonon absorption in that spectral region (Fig. 1). The bonding arrangement for Sn,,-H pairs is clearly different from that of the Be-H pairs, since the wagging mode of the hydrogen is at a much higher frequency, and surprisingly the ratio oH/oD for the longitudinal mode is only 1.372. Si-H pairs show a hydrogen longitudinal mode with fine structure due to the presence of the three silicon isotopes (Fig.22) (Pajot et al., 1988). The frequencies are 1717.25 cn-' for 28Si,1716.89 cn-' for 29Si, and 1716.53 cm- ' for 'Si. These observations provide conclusive proof that the H atom is bonded directly to a silicon atom, but the value of x derived from Eq. (1) is

180 -

40cmi

z

-5

STRETCt Si-D

100-

c

z

g

~

Z9S1

200 2

U.

w

00

450-

z s! c

SI-H Si-H STRETCt

a

r

U

%m

250

i

1OOcm

l

<

50

1715.4

1716.4 1717.4 1 7 1 8 . ~ WAVENUMBER (ern.')

FIG. 22. The L V M lines of the H and D stretching modes of Si,,-H pairs in GaAs showing fine structure due to the three naturally occurring silicon isotopes (Pajot et al., 1988).

4. DEFECTS IN III/v

165

COMPOUNDS

TABLE IX VIBRATIONAL FREQUENCIES (cm-') Mode

Calculated Frequency (BC)"

SiFJ SiU-3)

430 339 2,209 639

HF,)

W,)

OF THE

SCH COMPLEX IN GaAs

Calculated Frequency (AB)" <%la.

456 1,813 982

Experimental Valueb N.D.' 410 1,717 896

"Briddon and Jones (1989,1990, 1991). bPajot et al. (1988). 'N.D.-not detected.

close to 2.8. It appears that the hydrogen is bonded to an atom with an equivalent mass of 78 amu, rather than 28 amu, because the motion of the silicon atom is constrained by bonds to its neighbors. The longitudinal mode of Si-D that occurs at 1247.61 cm-' for 28Si-D also shows structure due to the silicon isotopes. Surprisingly, the ratio mH/wD= 1.376 is almost identical with that measured for paired tin donors. Pairing leads to a reduction in the integrated absorption of the LVM line from SiGa(Td),and a new sharp line (Am-0.4 cn-')grows at 409.95 cn-' for Si-H, or 409.45 cm-' for Si-D. As

FIG.23. The model for a Sio,-H pair center in GaAs (Briddon and Jones, (1989, 1990, 1991).

166

R. C . NEWMAN

This line was ascribed to the transverse mode of the paired silicon atom, and since no longitudinal mode has been found it was thought to have a low frequency so that it was also lost in the lattice continuum. This interpretation implies a large lattice relaxation of the Si atom towards three of its neighbors, but it was not possible to distinguish whether the H atom occupies a bondcentered (BC) or an antibonding (AB) location adjacent to the silicon atom. Subsequent calculations by Briddon and Jones (1989, 1990, 1991) have indicated that the AB location has the lower energy, and there is agreement between the estimated and measured LVM frequencies (Table IX).Thus, the silicon atom loses a bond to one As neighbor but remains fourfold coordinated (Fig. 23), while the axial As neighbor is in a trivalent state with two electrons in a lone pair orbital.

19. ANHARMONIC EFFECTS

In our previous analysis (Pajot et al., 1988), it was inferred that a low value of the measured ratio wH/oD for a hydrogen vibration implied that the hydrogen was bonded to an atom with a low mass, as found for Si-H pairs. The analysis is obviously inadequate, since a low value of the ratio has now been measured for Sn-H pairs. So far, the vibrations have been assumed to be harmonic, but it is well documented that anharmonic effects are important because of the low mass and the consequent large amplitude of the hydrogen vibration (Elliott et al., 1965; Newman, 1969). Cubic terms in the vibrational potential have to be treated by second-order perturbation theory, while quartic terms give first-order shifts in the frequency. The analysis for a given mode leads to an expression of the form w = v - B/mimp,

(4)

where w (cm- I ) is the measured energy, v (cm-') is the energy that would be found in the absence of anharmonicity, and B is a constant, the value of which depends on the magnitude of the anharmonicity. The ratio wH/oD and oH are measured quantities, while vH/vD = r can be estimated from the known atomic masses and the value of (Newman, 1990), using Eq. (1). Thus, for H-Sn we have 1327.8 = VH - B, 967.7 = vH/1.408 - B/2, whichleadtovH=1445.3cm-' a n d B - l 1 7 c m - ' . I f r i s t a k e n a s

(5)

(6)

1.405for

4. DEFECTS IN III/V COMPOUNDS

167

Si-H pairs, corresponding to the H being paired with an equivalent mass of 78 amu. (x=2.8), we obtain B = 133 cm-' and vH equal to 1850 cm-'. The same analysis applied to Be-H pairs with r = 1.404(see the earlier discussion) gives B = 100 cm- and v = 2137 cm-'.A similar value of B is again obtained for Zn-H pairs. Thus, all the data can be explained if the longitudinal Hmode is anharmonic and the downward shift in energy is about 100cm-'. This value is comparable with those of -65 cm-' and 75 cm-' found for SiH and As-H bonds in molecules (McKean et al., 1982). Further work is required to investigate these effects, but it is clear that a low value of wH/wD does not necessarily imply that the H atom is bonded to a neighbor with a low mass.

'

20. A

COMPARISON WITH

BASDEFECTS AND si Dx CENTERS

The gross weakening of one Be-As bond for the Be-H pair and the large lattice relaxation correspond rather closely to a proposed structure for a bistable BAS defect (Section VI) in p-type GaAs. Since an LVM for the transverse mode of the Be is predicted and found experimentally for Be-H, it is all the more difficult to understand why a similar mode has not been found for the boron impurity antisite defect. The model for the Si-H center has similarities to the proposed relaxed D X configuration for Si,, (Section VII. 13), since both centers have one weakened Si-As bond. It is implied that the deep DX center should show a highfrequency LVM line in silicon-doped material.

IX. Radiation Damage When GaAs is irradiated with high-energy electrons, host lattice atoms are displaced into adjacent interstitial sites to produce Frenkel pairs VGa-Gaiand VAS-Asi on the two sublattices. V,, and VA, are electron and hole traps, respectively (van Vechten, 1980), while the two interstitial species are likely to be donors. For 2 MeV electron irradiation, this picture is oversimplified, as a proportion of the damage events (- 10%)will lead to double displacementsto form VG,-VA, pairs, or antisite defects, again with adjacent interstitial atoms. To understand the radiation process and the subsequent anneal of the damage, it is necessary for all the defects, and their interactions with each other and with impurities, to be characterized both electrically and structurally. A comprehensive analysis of the available data is beyond the scope of this section, and the discussion is restricted to showing how LVM spec-

168

R. C . NEWMAN

troscopy has helped clarify our understanding of some of the processes. The IR measurements have been combined with EPR studies made on common samples, but DLTS data have been taken from the literature. Comparisons with irradiated GaP have been particularly valuable in relation to both LVM and EPR measurements. We start by describing LVM measurements that prove that mobile group V interstitials are trapped by impurities to form stable pairs. Other LVM lines found in irradiated Gap, but not GaAs, may be due to Gai defects. These data are then used to provide information about the formation of AsG, and P, antisite defects and their complexes. Finally, a brief description is presented of boron and silicon impurity site switching in GaAs during isochronal annealing, with the sequential involvement of arsenic and gallium vacancies. Most discussion relates to defects produced by low doses of electron irradiation. For heavily doped n-type GaAs, a dose (cm-2) numerically equal to [n] (cm - ’) is required to effect electrical compensation. However, free carriers return after a heat treatment close to 200°C, when DLTS measurements indicate that VAs-Asi pairs anneal (Lang, 1977; Pons et al., 1980; Pons and Bourgoin, 1985). If the electron fluence is increased by a factor of 10, similar samples remain transparent after heating up to 500°C, and the effects of annealing up to that temperature can be followed by LVM spectroscopy. For higher-temperature anneals, samples have to be given a further short electron irradiation to recover their IR transmission, but this procedure has not been commonly used. Similar overall comments apply to electron-irradiated Gap.

21. DEFECTSON

THE

GROUPV SUBLATTICE

DLTS measurements show that small doses of irradiation given to n-type GaAs introduce a series of electron and holes traps that were originally ascribed to displaced Ga-atoms (Lang, 1977). Later work showed that the defects were due to As-Frenkel pairs (Pons and Bourgoin, 1981), which remained stable up to about 200°C. Similar behavior has been found in GaP (Lang and Kimerling, 1974). Much less information is available about these defects in high-resistivity or p-type material (Pons and Bourgoin, 1985),and it is possible that not all the defects are stable. It follows that dissociation may occur, releasing mobile group V interstitials and leaving immobile isolated group V vacancies, in both GaAs and Gap. Once mobile Asi atoms are produced, they are selectively trapped by BG, and C, impurities, similar to the trapping of self-interstitials by the same impurities in silicon crystals (Tipping and Newman, 1987a, 1987b; Bean and Newman, 1970).

4. DEFECTS IN III/v COMPOUNDS

a.

169

The BGa-& or B(1) Defect

Irradiation of undoped or p-type LEC GaAs by 2 MeV electrons leads to a reduction in the concentration of isolated BG, impurities. New centers with lower than axial symmetry, previously called B( 1)-centers, are formed and give LVM lines at 763, 641, and 372cm-' for "B(l), and 796, 669, and 387cm-I for 'OB(1) (Thompson et al., 1973; Brozel and Newman, 1978; Collins et al., 1989). Two lines are at much higher frequencies than that of the corresponding BG, defect (Table 11), implying shortened and stronger covalent bonds, similar to those found for oxygen impurities (SectionIII). It is inferred that the B(1)-center incorporates a trapped interstitial atom and that significant rebonding takes place. In our first account of these centers, it was speculated that the interstitial atom was Ga, (Thompson et al., 1973), but subsequent FTIR analysis has shown that the highest- and lowest-frequency LVM lines have widths of only 0.35 and 0.3 cm-' (Collins et al., 1989). The remaining line has a greater width of 0.56 cm-', but a Lorentzian shape (2% Gaussian) with no evidence that it is an unresolved doublet. The lifetime of this particular vibrational state may be shorter than the other two, as its location 269cm-' above the lower state at 372cm-' ("B(1)) is extremely close to the TO mode of 267 cm- for GaAs at the r point. The conclusion is that the complexed boron has only As nearest neighbors, including a trapped Asi atom; a possible model is shown in Fig. 24. B(1)-centers are also formed in highly doped n-type GaAs ([n] 10'8cm-3), but only after a threshold dose of irradiation has been exceeded (Brozel and Newman, 1978). It was concluded that Asi atoms were

'

-

u FIG. 24. Proposed model for the bonded B,,-Asi or B(l) center (Brozel and Newman, 1978).

170

R. C . NEWMAN

not mobile in the early stages of the irradiation, consistent with the stability of Frenkel pairs observed by DLTS. Pons and Bourgoin (1985) have questioned the interpretation of the threshold, but later measurements indicated that it was real (Murray et al., 1987)(see also von Bardeleben et al., 1986). In undoped GaAs, there is no detectable threshold that has to be exceeded (Maguire et al., 1985). The B(1)-center would be electrically active according to the proposed model, but evidence for changes in the charge state has not been obtained from shifts in the LVM frequencies (cf: results for oxygen impurities, Section 111). At high electron doses, the rate of B(l) formation decreases and the centers appear to be destroyed by the capture of further mobile intrinsic defects to give new boron complexes that also show LVM absorption. The kinetics of the annealing of B(1)-centers,which occurs near 200°C are the same as those for the annealing of VA,-AS~ Frenkel pairs (DLTS) (Ozbay et al., 1982), with a lower rate in p-type material compared with n-type. A large reduction in the lattice strain also occurs during this stage, as revealed by high-resolution LVM measurements of the fine structure of the CA,LVM line (Section V) (Gledhill et al., 1990). Since there is regeneration of isolated B,, impurities (Maguire et al., 1986), the paired Asi atoms must have been removed. The combined IR and DLTS data then imply that VA, defects become mobile and recombine with the interstitials. The alternative possibility, that BG,-Asi defects dissociate, would require their binding energy to be equal to the barrier for recombination for the VA,-Asj Frenkel pairs. Production of B(1)anters also occurs in Gap, but only the highestfrequency LVMs have been detected, at 849 and 882cm-' for "B(1) and 'OB(l), respectively. Absorption due to the other modes is assumed to be present but obscured by the intense two-phonon absorption of GaP crystals. In p-type and undoped crystals there is immediate formation of B(1)-centers with electron irradiation, but a larger threshold dose than that found in ntype GaAs has to be exceeded before there is formation of the complexes in heavily doped n-type material. The threshold is greater than 1019 for the most highly doped samples with [n] 1019~ m - The ~ . B(1)-centers anneal in the range 250-300"C (Thompson et al., 1973). Although there are less detailed measurements available (FTIR and annealing kinetics),it is clear that the B(l)-center in GaP must be a BG,-Pi pair by comparison with the B(1)-center in GaAs.

-

b. The Cu-& or C(l) Defect

Irradiation of GaAs by 2 MeV electrons also reduces the concentration of C,, acceptors, giving the LVM line at 582 cm- '. In high-resistivity or p-type

171

4. DEFECTS IN I I I N COMPOUNDS

material, there is immediate growth of a new center labeled C(1),giving LVM lines at 577 and 606 cm-’ with a strength ratio close to 2: 1 (Thompson et al., 1973).The proximity of these lines to that at 582 cm-’ (CAJindicates only a small perturbation of the bonding of the C,, acceptor, similar to that found when Lii atoms pair with boron acceptors in a silicon host (Spitzer and Waldner, 1965), to form centers with C,, symmetry. FTIR measurements show that the higher-frequency C(l) line, which is assigned to the longitudinal mode of a trigonal center, is a close doublet (Fig. 25) because of the strong interaction of the C atom with a single 69Ga or 71Ga atom on the axis. Interactions of the C atom with the three remaining Ga neighbors produce fine-structure features in the doubly degenerate mode. A quartet structure is expected from theoretical modeling (Gledhill et al., 1991),consistent with the observations (Fig.26). This is the first example of a “fingerprint” for an impurity coupled strongly to three Ga neighbors. If the trapped interstitial had been a Ga atom, the longitudinal mode would have been expected to split into four resolved components (the two axial Ga atoms are not equivalent), contrary to the observations. The C(1)-center must therefore be a CA,-Asi pair, as shown in Fig. 27.

3’ (a) Expt.

h

r

k

Y

I-

z w 0 LL

3 LL

3.50

z

P In U

8m 4

3 -.45

605

606

607

WAVENUMBERS (cm-’)

FIG.25. The longitudinal L V M mode of the C(1)-centershowing isotopic splitting due to one axial Ga neighbor.Also shown is a calculated profile with eight components deduced from a cluster calculation (cf:Fig. 4) (Gledhill et nl., 1991).

R. C . NEWMAN

172 3.351

1

WAVENUMBERS (cm-')

FIG. 26. The transverse L V M mode of the C(1)center showing isotopic splitting from three nonaxial Ga atoms (see Fig. 27). There are a total of 12 components in the spectrum (Gledhillet a/., 1991).

Prolonged irradiations destroy C(1)-centers, implying that they capture additional mobile intrinsic defects. This behavior is similar to that found for B(1)-centers, and for interstitial carbon (Chappel and Newman, 1987) and boron (Tipping and Newman, 1987b)centers in silicon crystals. The available evidence indicates that interstitial complexes, once formed, act as nucleation sites for the aggregation of larger self-interstitial clusters. C(1)-centers anneal near 19O"C, a temperature only just, but definitely, lower than that required for the anneal of B(1)-centers (Gledhill et al., 1990) (observed in the same samples), and prior to the stage where there is removal of strain from the crystal when Frenkel pairs recombine. It is therefore inferred that C(l)-centers dissociate. There is an increase in [C,,], but not all the isolated carbon lost in the irradiation is recovered. This result is not surprising if some proportion of C(1)-centers had been converted to larger interstitial clusters. Similar formation of C(1)-centers occurs in irradiated Gap, where the defects give L V M lines at 642 and 599cm-', around the line at 606cm-'

4. DEFECTS IN III/V COMPOUNDS

173

n

FIG. 27. A proposed model of the C,,-Asi or C(l) center in GaAs showing the longitudinal mode w , , and the transverse mode wI of vibration. The carbon atom is assumed to be displaced from its & site towards one axial Ga atom.

from C, (Thompson et al., 1973). The defect is assigned to a C,-Pi pair, and annealing around 170°C leads to the regeneration of C, acceptors (see Lang, 1977, for details of the annealing of DLTS centers). In n-type Gap, a threshold dose of irradiation has to be given to samples before there is formation of C(1)-centers. This dose is the same as that required for the formation of B(1)-centers (measured in the same samples) (Newman and Woodhead, 1984). c.

Destruction of BASDefects in GaAs

The production of BAS centers in Ga-rich p-type GaAs during electron irradiation has been discussed in Section VI. If the irradiation is prolonged, the concentration of these centers reaches a maximum and then decreases much more slowly, but no new LVM lines are produced (Woodhead et al., 1983). In heavily doped n-type Gap, a threshold dose again has to be exceeded before BAS defects are destroyed (Newman and Woodhead, 1984). Since this threshold is the same as that required for the formation of B(l) and C(l) centers, it is implied that BAScenters trap mobile group V interstitials. The boron atoms may then be displaced into interstitial sites by the Watkins replacement reaction (Watkins, 1965). The same type of reaction might also explain the slow loss of SiAscenters found in GaAs after very extended irradiations (see Section VII).

174

R.C . NEWMAN

d. Summary

Group V interstitials are mobile in high-resistivity or p-type GaAs and GaP during 2 MeV electron irradiation at a current density of 15 pA cm-', and they are selectively trapped by B and C, and possibly Si, impurities in the two hosts. In n-type material, mobility only occurs once a threshold dose is exceeded that depends on the initial doping level, and it is implied that this corresponds to a change in charge state of a group V Frenkel pair. V,, defects probably becomes mobile near 20O0C,but there is no evidence for mobility at lower temperatures. Since there is evidence that self-interstitial clusters are formed, not all V,, defects can be lost in the 200°C annealing stage in GaAs, but they will be annihilated over a range of somewhat higher temperatures. This last comment is especially relevant to samples given a large dose of irradiation (including fast neutron irradiations).

SUBLATTICE 22. DEFECTSON THE GALLIUM Pons and Bourgoin (1981) argued that no defects were produced on the Ga sublattice in GaAs. However, EPR measurements that reveal isolated VGa defects in irradiated high-resistivity or p-type GaP (Kennedy and Wilsey, 1978; Hage et al., 1986), but not in n-type material, do not support this view. a.

The Ga(1) Center in GaP

Irradiation of GaP leads to the growth of LVM lines at 419.5 and 424.5 cm-' with a strength ratio of 1: 1.6 (Hayes et al., 1970; Woodhead and Newman, 1982; Gledhill et al., 1981), at a rate corresponding to the introduction of a primary irradiation defect, and certainly unrelated to the presence of any impurity. An additional weaker line is found at 430.5 cm- '. Originally it was supposed that the two former modes were due to the vibrations of a strongly bonded 31Patom, as it was thought that gallium atoms would have too high a mass to give LVMs. However, this argument was questioned, and subsequently it was inferred that a Ga atom was involved, possibly as an antisite defect (Woodhead and Newman, 1982), or as a bonded Ga, atom. Later work showed that the defect (or defects) were only produced after a threshold dose of irradiation in heavily doped n-type Gap, but the critical dose was much smaller than that required to produce BGa-Pi pairs (Fig. 28) (Beall, 1985; Newman, 1985b). It follows that the Ga(1) LVM lines probably refer to a defect involving a displaced Ga atom, and it should be noted that they are produced in irradiations at 77 K. These defects anneal

4. DEFECTS IN III/V COMPOUNDS

0

10

5

Electron Dose

15

20

175

25 ”

f 1 0 1 7 cm-2

FIG. 28. The sequential formation of PP,, Ga(l), PPI, and B(l) centers in heavily doped ntype GaP following successive doses of 2 MeV electron irradiation.The Ga(1) and B(1) centers were measured by IR LVM, while the PP, and PP, concentrations were measured by EPR on the same sample (Beall, 1985; Newman, 1985b). Reprinted with permission, Figure 6 of “13th International Conference on Defects in Semiconductors”,by R. C. Newman, p. 87.

at a temperature close to 250°C, but there is currently no information about the kinetics or the mechanism. The Ga(1) defect is not observed in GaAs, and the modes are presumed to be at a low frequency and lost in the lattice continuum.

b. The V,, Defect in GaP The existence of an EPR spectrum from VG, defects in p-type material has already been mentioned. It is important next to examine the possibility that the defect may be bistable with a possible conversion to a PGa-Vp pair by a single atomic jump of a phosphorus neighbor, analogous to the suggested mechanism of formation of AsGa-VAs pairs in GaAs (Lagowski et al., 1983; Van Vechten, 1984;Baraff and Schluter, 1985). This alternative description of the defect is written as PP3,since the central phosphorus atom has only three phosphorus neighbors. An EPR spectrum with resolved hyperfine and superhyperfine structure corresponding to such a PP3 structure was observed by Kennedy and Wilsey (1979) in irradiated n-type material. There was speculation that the “missing phosphorus neighbor” of a true antisite defect PP4 was another impurity such as sulfur, oxygen, etc. However, a combined LVM and EPR study (Beall et al., 1984b), using either Si- (LVM line at 464cm-’) or sulfur-doped GaP and including chemical analysis of samples, provided

I76

R. C. NEWMAN

convincing evidence that the defect was the modified V,,, by showing that no impurity (Si, S, C, B, 0)could be involved. The inference is that V,, defects in GaP are indeed bistable and appear as PGa-Vp in n-type material. The next important step was the observation of a threshold dose of irradiation required for the formation of PP, defects (in n-type samples). Their EPR signal was first detected as the spectrum from sulfur donors was almost lost (Beall et a!., 1984b Kennedy and Wilsey, 1985). These authors argued that E~ was pinned within 3 kT of the donor level (Ec- 0.107 eV) at this stage of the irradiation, but other work on Te- (and Si-) doped GaP revealed similar behavior, although the donor energy level (JZ-0.093 ev) is different (Beall, 1985). It is necessary in such analysis to take into account inhomogeneities in the grown-in dopant concentration and the damage introduced, since eF will be at different energies relative to the conduction band at different locations. The important point was that the thresholds for PP, and Ga(1) production were very similar (Fig. 28) (Beall, 1985; Newman, 1985b), adding weight to the assignment of the LVM lines to a gallium defect. It could be argued that the two observations relate to the same defect, perhaps a modified Frenkel pair Gai-PGa-Vp, but it would be difficult to effect a correlation, because the PP, spectrum reaches a maximum and then decreases in strength due to a change in charge state (Kennedy and Wilsey, 1985). Such a change would not necessarily modify the LVM Ga(1) spectrum. After a certain dose of irradiation (Fig. 28), the PP, spectrum is lost and instead a new EPR spectrum PP, (Goswami et al., 1981; Kennedy and Wilsey, 1981) is observed to grow and saturate. The structure of this defect is still unknown, but its central phosphorus hyperfine parameter A = 700 x 10-4cm-1 is almost the same as that of the PP, center, 704 x lo-, cm- If the super-hyperfine structure had not been detected, it would not have been possible to distinguish the two centers; this comment is important to the interpretation of EPR measurements made on GaAs. Furthermore, the value of A for PP, was found to increase monotonically up to 850 x lo-, cm-' after extended irradiations to 10'' cm-,(Beall, 1985). This higher value is close to that of A = 966 x l o p 4cm-'for the true antisite defect PP4 (Kaufmann et al., 1976). Finally, we note that the concentration of PP, defects was not increased in our irradiated high-resistivity or p-type GaP samples (Beall, 1985). Thus, there is no evidence that mobile Pi atoms are trapped by V,, defects to produce PP, defects. c.

The V,, and AsGaComplexes in GaAs

-

In irradiated GaAs, a broad EPR line with g 2 (designated as a singlet spectrum) has been variously attributed to V,,, V,,, and clusters of AsAs,

4. DEFECTS IN III/V COMFQUNDS

177

defects. There is no definitive assignment, and the line could be due to a superposition of spectra. As-grown semi-insulating chromium-doped Bridgman GaAs shows an EPR quadruplet structure that was assigned to AsAs, centers (the same notation as that used for Gap), with a central hyperfine parameter A =9OOx lo-, an-' for 75As with I = j (Wagner et al., 1980). This interpretation was subsequently confirmed by optically detected ENDOR (Spaeth et al., 1985). Electron irradiation of SI or p-type GaAs leads to the production of centers that give an indistinguishable EPR spectrum (with linewidths -400 G) detected by conventional means. It was suggested (Kennedy et al., 1981)that mobile Asi atoms combined with VG, to form AsG, defects with a low introduction rate of 0.02cm-' (Beall et al., 1985b). However, ENDOR measurements showed that the defects were antisite complexes, and that they were different in SI LEC GaAs compared with ptype material (Spaeth et al., 1985). This result is consistent with our finding that PP, defects are not produced by irradiation in similarly doped Gap. The concentration of defects giving a quadruplet EPR spectrum is greatly enhanced by plastic deformation (Weber et al., 1982), neutron irradiation (Goswami et al., 1981;Worner et al., 1982),and electron irradiation of highly doped n-type material (Goswami et al., 1981).Again, ENDOR measurements indicate that all these various centers are antisite complexes. The difficulty of interpretation stems from the large linewidth, which precludes the detection of super-hyperfine interactions in EPR spectra. For irradiated n-type GaAs, some parallels can be drawn with GaP for the formation of antisite defects. First, a threshold dose of irradiation has to be given before the defects are observed (Goswami et al., 1981), but then the introduction rate is very high, corresponding to that expected for the production of primary defects. Later work by Spaeth et al. (1985) revealed the growth of a center with a small value of the central hyperfine parameter in the early stages of the irradiation. This observation was followed by more detailed information given by von Bardeleben et al. (1986), who reported a value A = 680k40 x lo-, cm-', which is larger than that found by Spaeth et al. It was argued that the defect responsible was an AsAs, center generated from a V,, defect, which would be analogous to the formation of the PP, center in Gap. It was then again supposed that mobile Asi atoms combined with AsAs, defects to convert them into AsAs, centers. That interpretation is in conflict with the ENDOR data, and would not be consistent with the sequence of defect introductions found in Gap. Thus, the centers should logically be assigned to AsAs, defects. In fact, this was one of the options discussed in some detail by Beall et al. (1985b). They also showed from a combined EPR and LVM study of n-type samples that the defects giving the EPR spectrum were generated just prior to the threshold dose required for

R. C . NEWMAN

I78

-5

I

0

12-

c

-z v)

10-

W X

W i

s

0

0 m 0

m

a

6-

U

0 2

0 Ia

4-

U

I-

z *-

u

2

0

0

0

1

2

3

4

5

ELECTRON DOSE ( l o l a cm-*)

FIG. 29. The production of As,, complexes and B,,-Asi pairs by 2 MeV electron irradiation of n-type GaAs, showing the growth of the former center slightly before the latter (Beall et nl., I984a).

the production of B(l) centers (Fig. 29), i.e., prior to the onset of mobility of Asi atoms (Beall et al., 1984a). This result is in one-to-one correspondence with the measurements made on GaP (Fig. 28). In another combined LVM and EPR investigation, it was shown that the n-type dopant atoms, silicon or sulfur, played no role in the processes, again in agreement with results for GaP (Beall et al., 1985a). If the irradiation of n-type GaAs is extended to very high doses, the concentration of “antisite” complexes reaches a maximum proportional to the initial n-type doping level in the crystal, but it then falls before rising again, corresponding to introduction of defects in high-resistivity samples (Fig. 30). This result led to the conclusion, independent of ENDOR measurements, that either one or both of the centers was an antisite complex, rather than the isolated defect (Beall et al., 1985b). In summary, it has to be concluded that the EPR quadruplet structure is not a fingerprint for the presence of isolated AsGaantisite defects, and there is a large degree of uncertainty about the interpretation of the observations. Comparisons of the EPR and LVM data for GaAs with those for GaP have

4. DEFECTS IN III/V COMPOUNDS

179

ELECTRON DOSE I 1018crn-2

FIG. 30. The production of As,, antisite complexes in two undoped SI GaAs samples, and one heavily doped n-type sample, resulting from 2 MeV electron irradiation (Beall et al., 1985b).

been helpful in making limited progress. It seems likely that V,, defects are consumed in the formation of AsAs, defects, leading to an excess of V,, defects, particularly in n-type material. The latter centers would then be available for defect interactions during subsequent annealing, for which there is evidence, as discussed next.

23. SITE SWITCHING OF IMPURITIES DURING ANNEALINGOF IRRADIATED GaAs

V,, defects as such have played no role in the processes discussed so far, but they must be present, as displaced Asi atoms have been identified. LVM studies of annealing have shed some light on their fate. When irradiated samples are heated above 20O0C, site switching of B,, and Si,, impurities starts to occur, with the generation of isolated B A S and SiAsimpurities. For boron impurities, the process occurs in two stages centered around 300 and 500°C (Maguire et al., 1985), while the 500°C annealing stage is dominant for silicon impurities (Maguire et al., 1986).It is clear that V,, defects have to be available to be occupied. It was presumed that these defects diffuse to the impurities to form pairs in the initial stage. The Be, or Si,, atom then has to make a diffusion jump, and the V,, has to diffuse away. Heating the samples to a higher temperature, near 6oo"C, was presumed to lead to a reversal of the process to give a site distribution similar to that found in the as-grown

180

R. C . NEWMAN

material. It must be emphasized that site switching only occurs in preirradiated samples, and the effects increase with dosage. Particularly marked changes occur in samples irradiated with fast neutrons, and corresponding effects for boron impurities were found in G a P crystals. In a combined LVM and EPR study of the annealing of a no-irradiated LEC GaAs crystal doped with [Si] 4 x 10'' cm-3, there was an increase in the concentration of paramagnetic AsGa centers by a factor of about three around 450"C, with a subsequent reduction near 600°C (Maguire et af., 1986). As the increase started, there was a sharp decrease in the strength of a singlet EPR spectrum near g 2, which implies that it might be due to V,, defects.

-

-

24.

FINAL REMARKS

In summary, LVM studies have provided indirect evidence about the irradiation damage process, via the interaction of the native defects with grown-in impurities. Such information is invaluable in view of the dearth of direct data about lattice vacancies, self-interstitials, etc., but it is unfortunate that nearest-neighbor fine structure has not been found for the Ga(1) LVM lines in Gap.

X.

Conclusions

There is no doubt that LVM spectroscopy has been successful in providing information about the sites occupied by light atoms, and the properties of complexes incorporating these atoms. The measurements are most useful when they are combined with other techniques applied to common samples. The other methods include SIMS, DLTS, EPR, etc., which give complementary information. Many problems remain unsolved, but the LVM method has been illustrated by results relating to D X centers, other bistable defects, 6doping, ion implantation, hydrogen passivation of shallow impurities, and the effects of electron irradiation, etc. The most significant step forward has been the identification of the number and type of nearest neighbors of impurities deduced from the fine structure (or lack of it) produced by the various combinations of 69Ga and 'lGa host lattice atoms in GaAs. These observations have been made possible by the high resolution and low noise of FTIR spectra, but just as importantly by the growth of high-quality, strainfree bulk and epitaxial GaAs crystals. Very recently we have shown that both the infrared and Raman techniques can be used to study silicon donors and beryllium acceptors in MBE InAs and InSb, thereby broadening the scope of LVM spectroscopy even further (Addinall et al., 1991).

4. DEFECTS IN III/V COMFQUNDS

181

Note In Section VII.13, it was stated that an experiment to study the LVM spectrum of highly Si-doped GaAs under a high hydrostatic pressure had not been reported. Since the present manuscript was accepted, such an experiment has been performed (Wolk et al., 1991). Once the pressure exceeded 23 kbar, there was a loss of free carriers from an as-grown Si-doped sample, and a previously unreported LVM line appeared at a lower frequency than that due to normal Si,, shallow donors. The extrapolated energy of the new line at zero pressure was 376k 1.5cm-'. It was argued that this was the transverse E-mode of the silicon DX configuration. This interpretation has been queried by Jones and Oberg (1991), who interpreted the downward shift in frequency by an outward breathing mode displacement resulting from a change in the charge state of the silicon impurity. Such a possibility clearly cannot be ruled out in view of the findings of Dmochowski et al. (1991) that there is a deeper donor level with rl,symmetry associated with Si,, centers.

Acknowledgments The author is greatly indebted to the following colleagues who have made major contributions to this work: R. B. Beall, M. R. Brozel, G. A. Gledhill, N. K. Goswami, K. Laithwaite, R. S. Leigh, J. Maguire, R. S. Morrison, R. Murray, P. S. Nandhra, B. Ozbay, M. J. L. Sangster, F. Thompson, J. E. Whitehouse, and J. Woodhead. The provision of special samples from Plessey Research (Caswell) Ltd., Philips Research Laboratories, RSRE (Malvern), and SERL (Baldock) is greatly acknowledged. D. J. Chadi, R. Jones, and M. Stavola are thanked for communicating their results prior to publication, and J. Dmochowski, R. A. Stradling, and J. Wagner are thanked for helpful discussions. The illustrations were prepared by Mr. N. Powell, while special thanks are due to Miss Nikki Green for preparing the manuscript for publication. The financial support of The Science and Engineering Research Council is also acknowledged.

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Wolk, J. A., Kruger, M. B., Heyman, J. N., Walukiewicz, W., Jeanloz, R., and Halle, E. E. (1991). Phys. Rev. Lett. 66, 774. Wood, C. E. C., Metze, G., Berry, J., and Eastman, L. F. (1980). J . Appl. Phys. 51, 383. Woodhead, J. and Newman, R. C. (1981). J . Phys. C: Solid St. Phys. 14, L345. Woodhead, J., and Newman, R. C. (1982). J. Phys. C: Solid St. Phys. 15, L541. Woodhead, J., Newman, R. C., Grant, I., Rumsby, D., and Ware, R. M. (1983). J . Phys. C: Solid St. Phys. 16, 5523. Woodhead, J., Newman, R.c., Tipping, A. K., Clegg, J. B., Roberts, J. A., and Gale, I. (1985). J . Phys. D: Appl. Phys. 18, 1575. Woodhouse, K., Newman, R. C., Nicklin, R., Bradley, R. R. and Sangster, M. J. L. (1992). J. Cryst. Growth 120, 323. Worner, T., Kaufmann, U., and Schneider, J. (1982). Appl. Phys. Lett. 40,141. Zhang, S. B., and Chadi, J. (1990) Phys. Reo. Lett. 64, 1789. Zhong, X., Jiang, D., Ge, W., and Song, C. (1988). Appl. Phys. Lett. 52, 628. Zrenner, A., and Koch, F. (1988). Properties oflmpurity States in Superlattice Semiconductors (c. Y.Fong, I. P. Batra, and S. Ciraci, eds.). NATO ASI Series 183, 1. Zrenner, A,, Koch, F., and Ploog, K. (1987). Proc. 14th Int. Symp. on GaAs and Related Compoundr. Crete, ins:. Phys. Conz Ser. 91, 171. Zrenner, A., Koch, F., Williams, R. L., Stradling, R. A., Ploog, K., and Weimann, G. (1988). Semicond. Sci. Technol. 3, 1203.

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SEMICONDUCTORS AND SEMIMETALS, VOL. 38

CHAPTER 5

Transition Metals in III/V Compounds Andrzej M . Hennel INSTITUTEOF

EXPERIMENTAL PHYSICS

WARSAWUNIV~RSITY WARSAW, POLAND

I. INTRODUCTION. . . . . . . . . . . . . . . 11. GENERAL PROPERnES OF TRANSITION METAL IMPURITIES . 111. 3d" TRANSITION METALS. . . . . . . . . . . . 1. Conjiguration 3d' . . . . . . . . . . . . . 2. Configuration 3dZ . . . . . . . . . . . . . 3. Configuration 3d3 . . . . . . . . . . . . . 4. Configuration 3d4 . . . . . . . . . . . . . 5. Conjiguration 3d5 . . . . . . . . . . . . . 6. Conjiguration 3d6 . . . . . . . . . . . . . I . Conjiguration 3d' . . . . . . . . . . . . . 8. Conjiguration 3d8 . . . . . . . . . . . . . 9. Conjiguration 3d9 . . . . . . . . . . . . . IV. 4d" AND 5d" TRANSI~ON METALS. . . . . . . . . V. SEMI-INSULATING TM-DOPEDIII/V MATERIALS. . . . APPENDICES . . . . . . . . . . . . . . . . 10. TM Energy Levels. . . . . . . . . . . . . 11. Absorption and Emission T M and RE Spectra . . . REFERENCES . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

.

. . . . . . . . . . .

. . . . . . . . . . . . .

.

. . . .

.

. . .

. .

.

.

. .

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. . . 189 . . . 190 . . . 194 . . . 195 . . . 198 . . . 202 . . . 203 . . . 206 . . . 208 . . . 210 . . . 213 . . . 215 . . . 217 . . . 218 . . . 221 . . . 221 . . . 224 . . ,228

I. Introduction

The history of transition metal (TM) impurities in III/V compounds started in the mid-1960s with three important papers. The first was the presentation by Haisty and Cronin (1964) from Texas Instruments Inc. at the Seventh International Conference on the Physics of Semiconductors in Paris, concerning Hall effect measurements of V, Cr, Mn, Fe, Co, and Ni levels in GaAs crystals. The second was a US patent # 3,344,071 (1967) due to G. R. Cronin concerning the preparation of semiinsulating GaAs crystals by doping with chromium. The third was the paper 189 Copyright 0 1993 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-752138-0

190

A. M. HENNEL

from Stanford University published in Physical Review by Baranowski et al. (1967) presenting the optical spectra of Fe and Co in GaAs and G a P crystals. In the ensuing quarter of a century, these three papers were followed by hundreds of scientific papers and reports. Experimental knowledge of TM impurities in III/V compounds had thus, in the mid-l980s, reached a kind of "critical mass" that started to stimulate improvements in theoretical models. This fact manifests itself in the number of review papers devoted to this subject, Among them, we can find papers concerning all the deep defects in III'V compounds (Neumark and Kosai, 1983; Milnes, 1983);papers devoted exclusively to TM impurities (Kaufmann and Schneider, 1980b, 1982; Masterov, 1984; Clerjaud, 1985, 1986; Schulz, 1986); or even to specific impurities such as Cr in GaAs (Allen, 1986), or Fe in III/V compounds (Bishop, 1986). There is also a book entitled Transition Metal Impurities in semiconductors by Omel'yanovskii and Fistul (1986). However, in spite of its year of publication, this book presents the experimental data only up to 1980. The theoretical models dealing with the electronic structures of TM impurities in semiconductors were presented in review papers by Zunger (1986), by Vogl and Baranowski (1985) and Vogl (1985), and by Bates and Stevens (1987). Several recent theoretical papers (Delerue et al., 1989; Langer er al,, 1988; Hamera er ul., 1989)improved our understanding of fundamental TM properties. This chapter is devoted to the general physical properties of T M impurities (mainly from the 3d" series) in GaAs, Gap, and InP crystals. It covers the experimental situation until early 1991. Because of its brevity, this chapter should be treated as a guide-book to this large field, rather than a collection of all the relevant information collected to date. A description of the most popular experimental techniques may be found in special chapters of the reviews by Clerjaud (1985, 1986)and Hennel(1985), and in the references therein.

11. General Properties of Transition Metal Impurities

TM impurities occupy substitutional, cation sites in III/V compounds. There are some reports of interstitial positions of TM, but none of these is definite, and sometimes new experimental data ruled out such a hypothesis (see, for example, Hage et a f . , 1989). The typical solubility limits are in the ~ exception . ismanganese, which was even used to order of 10'7-10'8 ~ m - An obtain the first diluted magnetic III/V semiconductors GaMnAs and InMnAs (Munekata et ul., 1989). The electronic configurations of external shells of TM elements are 3d"4s2.

5. TRANSITTON METALSIN III/v

COMPOUNDS

191

The only exceptions are chromium and copper, which have configurations 3d54s' and 3dl04s', respectively. The electronic configuration of a TM atom at a cation site in a III/V crystal is thus 3d"-', and the neutral charge state of the impurity may be formally described as Me3+ (in the same manner as GaAs may be formally treated as Ga3 + As3-). TM impurities form many deep levels in III/V crystals, acting as electron and hole traps; the formal charge states observed thus range from Me4+(3d"-') to Me"(3d""). A classification of these traps is performed in the following way: A level intermediate between two charge states-for example, Me3+(3d"- ') and MeZ+(3d")states-is called a Me3+/'+ level (sometimes Me3+/Me2+ level). An empty Me3+"+ level means that all the centers are in the Me3+ state; a filled Me3+''+ level means that they are in the Me2+ state. It should be mentioned that this classification, proposed by J. W. Allen, was established in the 1980s. In earlier papers, a rather misleading terminology ("Me" level" in place of the r'Me3+/2+level") was very often used. In semiconductor terminology, Me4+/3+ is a donor level, Me3+ I 2 + is an acceptor level, and is a double acceptor level. One has to remember that these many electron levels may be located in the gap, as well as in crystal bands. Several authors have demonstrated a phenomenological alignment of TM energy levels within a class of materials (for example, III/V compounds). The question of the choice of an energy reference level is still not settled. The vacuum energy (Ledebo and Ridley, 1982; Zunger, 1986) and the average dangling bond energy (Langer et al., .1988) were proposed. According to recent calculations (Hamera et al., 1989),the two possibilities are more or less equivalent. Therefore, the figures for the various impurities (shown in the next sections) are prepared according to the Langer et al. (1988) scheme, i.e., the energies of the valence band maxima are taken as 0 for Gap, 0.17 eV for InP, and 0.33 eV for GaAs. Comparing the energy distances between the different charge states in free TM ions and TM impurities, one can see about two orders of magnitude reduction (20-50 eV versus 0.4-1.5 eV). This effect is explained by a very weak dependence of a "real" impurity core charge on its formal oxidation charge, as was shown in theoretical calculations (Haldane and Anderson, 1976). It must be clearly stated that the electrons or holes are really trapped by the TM centers, but their charges are redistributed between the surrounding atoms (ligands).This property explains the occurrence of two, three, or even four charge states of several TM impurities in III/V crystals. On the other hand, these formal charge states preserve their spin-related properties. According to Hund's rule, the ground state of each electronic configuration is the highest spin term ' L . If its orbital momentum +

" +

192

A. M. HENNEL

quantum number L is equal to three or more, a term splits in the tetrahedral crystal field of the ligands into 2 s + 1 Lstates ( A l , A , singlets, E doublets, or TI, T, triplets). The lowest-lying state will determine the magnetic properties of a center detected by electron paramagnetic resonance (EPR)measurements. The entire group of states (sometimes together with the nearest atomic terms) is responsible for the optical properties of a center, i.e., for the intracenter absorption and luminescence spectra characteristic of each configuration. The spin-orbit interaction, being about an order of magnitude (or more) weaker than the crystal field, is taken into account as a perturbation, splitting the ”+‘L states. This so-called “weak crystal field limit” model implies that the crystal field is weaker than the electron interaction. This approximation, good for ionic and IIjVI crystals, should be replaced in the case of the III/V compounds by the “strong crystal field limit.” In this chapter, the weak-field classification is used, as it is more popular and easier to use. The correspondence between the strong and weak field levels may be found in many reviews (Schulz, 1986; Zunger. 1986). Interaction with symmetrical and nonsymmetrical (Jahn-Teller effect) lattice vibrations also plays an important role in determining such TM properties as optical and EPR spectra. There are two recent reviews devoted to this subject (Clerjaud, 1988a; Ulrici, 1984). As a result of all these many-electron properties of TM centers, a host material doped with a TM impurity may exhibit completely different properties, depending on additional co-doping with shallow centers. Different locations of the Fermi level in the energy gap may activate different TM charge states, and change the magnetic and optical properties of the crystal. This fact is shown schematically in Fig. 1. In p-type crystals we could observe a hole trap at energy E l , and a broad photoionization band, corresponding to the transitions from the valence band to the Me4+I3+donor level, starting at energy E , (see, for example, Fig. 2). In an SI material, we could observe sharp absorption and luminescence intracenter spectra of the Me3 charge state (see, for example, Figs. 3 and 4). In n-type crystals, the Me3+I2+acceptor level at energy E 2 and the completely new optical spectra of the Me2+ charge state may be detected. All the three crystals could also have different EPR spectra. Finally, we cannot forget about the complexes formed by the TM and other impurities, as well as native defects. Some of them were only observed in EPR measurements; some were identified in optical measurements. Several complexes were proposed as good excuses to explain unclear data. For a few others we have clear pictures (microscopic model, optical spectra, sometimes even energy levels), and these are mentioned in the following sections. +

5. TRANSITION METALSIN III/v

COMPOUNDS

193

ACCEPTOR LEVEL

EG

Me4+ Me3' Me2' FIG. 1. Schematic presentation of TM impurity energy levels in a IIIjV compound. The solid and dashed lines represent the ground and excited states, respectively. The vertical arrows represent intracenter absorption and emission transitions. The slanted arrows represent photoionization band-level transitions.

h

d I S

T

t: t-

z

W H U

LL LL W

0 U

z 0 H

P H O T O N ENERGY tCh-1)

FIG.2. An example of photoionization absorption corresponding to valence band-TM level transition in the case of Mn-doped InP (Lambert et al., 1985a).

194

A. M. HENNEL

CI

'.68 88 Y

B m

0

3

I1

ll

/ '66.!2

'

'.+4 ' :+6

'

;+8 '

:a0

ENERGY

'

:82

.04

.86

.88

[eV]

FIG. 3. An example of intracenter absorption in GaAs, corresponding to the 3 A2 transition of the V3+-(3d2)charge state (Wysmolek ef a/., 1989)

PHOTON ENERGY ( P V )

-

FIG 4. An example of intracenter luminescence in InP, corresponding to the 3T2(3F) 3 A 2 transition of the V3+(3d2)charge state (Skolnick rr ol., 1983a).

111. 3d" Transition Metals

In this part, the general properties of the TM from the iron 3d" series are presented. The different TM charge states are classified according to particular electronic configuration. Thus, information about chromium may

5. TRANSITION METALS IN III/v COMPOUNDS

195

be found in sections on 3d2, 3d3, 3d4, and 3d5 configurations. Detailed information about all the levels mentioned, as well as about absorption and emission ZPLs, may be found in the Appendices, in Tables V-X. 1. CONFIGURATION 3d1 The 3d' electronic configuration may be found in the III/V compounds dopsed with titanium and vanadium, in the case of the Ti3+and V4+ charge states. One could also expect this configuration for the scandium impurity (Sc' charge state). However, there are no conclusive data in the literature concerning this impurity. The only existing information may be found in the papers of Nakagawa and Zukotynski (1975) and Brandt (1987). In III/V compounds, the vanadium V4+(3d') charge state is below the V4+/3+ donor level. This level lies within the GaP and InP energy gaps, as shown by Ulrici et al. (1989) and Deveaud et al. (1986b) (see Fig. 5). The titanium Ti3+(3d1)charge state lies between the Ti4+/3+donor level and the Ti3+/'+ acceptor level in III/V compounds. In GaAs and GaP crystals, both these levels were found in the energy gap (Brandt et a/., 1989; Roura et al., 1987). In the case of InP, only the Ti4+I3+donor level lies in the energy gap (Brandt et al., 1986);the Ti3+/'+ acceptor level is degenerate with the conduction band (see Fig. 6). The free-ion ground term of the d' electronic configuration is the 2D term, which splits into the ground 2E state and the excited 'q state in a tetrahedral crystal field (see Fig. 7). EPR measurements of high-resistivity Ti-doped III/V compounds and ptype V-doped GaP reveal, at low temperatures, isotropic EPR signals of the +

FIG. 5. The energy levels of the vanadium impurity in GaAs, Gap, and InP. The dashed lines represent the levels that are predicted but not yet observed. The energies of the valence band maxima are taken as 0 for Gap, 0.17 eV for InP, and 0.33 eV for GaAs.

1%

A. M. HENNEL

Tic;. 6 . The energy levels of the titanium impurity in GaAs, Gap, and InP. The dashed line represents a level which is predicted but not yet observed. The energies of the valence band maxima are taken as 0 for Gap, 0.17eV for InP, and 0.33 eV for GaAs.

\

b-

FIG. 7. The energy-level scheme for the d' electronic configuration in a tetrahedral crystal field.

ground 2 E state. Their g factors and linewidths are collected in Table I. Absorption bands with the sharp ZPLs corresponding to the ' E => 'T2 optical transitions were observed in the case of the Ti3+ centers in GaAs (Hennel et al., 1986a), G a P (Ulrici et al., 1988),and InP (Brandt et al., 1989), and in the case of the V 4 + centers in G a P (Ulrici et al., 1989) and InP (Clerjaud et al., 1987b). The complementary emission 'T2 * ' E bands were TABLE I PARAMETERS OF THE 3d' EPR SPECTRA I N III/V COMPOUNDS Impurity Ti3-(GaAs) Ti3-(InP) Ti3-(Gap) V4 (Gap)

y-Factor 1.9362i0.0005 I .94k0.02 1.943k0.003 1.960 0.003

A B (mT) 16.5 45

18 21

References Clerjaud et a / . (1987a) Lambert et a / . (1987) Kreissl et al. (1988) Ulrici et al. (1989)

5. TRANSITION METALSIN III/V COMPOUNDS I

--

-

1

-

1

,

566 meV

'E 0.4 U

-

.-e0

c

-

2 a

-

I

I

,

,

I

l

l

,

I

197

I

G a A s : TiH+(3d') T =5K

-

569 meV

v

e

a 0.3

1

I

0.60

Q65

1

1

1

-

0.70

Photon Energy (eV1 FIG. 8. The absorption spectrum of the * E * zTz intracenter transition in the Ti3+(3d') centers in GaAs (Brandt et a[.,1989).

FIG.9. The luminescence spectrum of the 'TZ=-' E intracenter transition in the Ti3+(3d1) centers in GaP (Ulrici et al., 1988).

A. M. HENNEL

198

I-w z

a a

3

0

EI a

-fl

-

-

-

-

I

I

observed only in the case of the Ti3+ centers in GaAs (Ulrici et al., 1986a) and G a P (Ulrici et al., 1988).In all other cases, the absence of any emission bands is caused by the degeneracy of the excited 2T2 state with one of the semiconductor crystal bands. These facts were clearly shown in the photoconductivity and DLOS measurements of Ti-doped InP by Wasik et al. (1989) and Bremond et al. (1986b) (degeneracy with the conduction band), and also in DLOS measurements of V-doped InP by Clerjaud et al. (1987b) (degeneracy with the valence band). Examples of 3d' spectra are shown in Figs. 8-10.

2. CONFIGURATION 3d2 Electronic configuration 3d2 may be found in III/V compounds doped with titanium, vanadium, and chromium, in the case of the Ti2+,V 3 + , and Cr4+ charge states. The chromium Cr4'(3dZ) charge state lies below the Cr4+13 donor level in IIIjV compounds. In GaAs, Gap, and InP crystals, this level lies in the energy gap (Look et al., 1982; Kaufmann and Schneider, 1980a; Bremond et al., 1988).However, in the case of Gap, its exact position is not known yet (see Fig. 11). The vanadium V3+(3d2)charge state is between the V4+I3+ donor level and the V3+12+acceptor level in IIIjV compounds. In G a P crystals, both these levels were found in the energy gap (Ulrici et al., 1987, 1989). In the case of InP, only the V4+13+donor level lies in the energy gap (Deveaud et al., 1986b);the V 3 + " acceptor level is degenerate with the conduction band. In the case of GaAs, only the V 3 c i 2 +acceptor level lies in the energy gap +

+

5.

TRANSITION

GaAs

0.05

METALSIN III/v COMPOUNDS

GaP

199

TnP

c

evt

........ ,

T06lcV

c c

FIG. 11. The energy levels of the chromium impurity in GaAs, Gap, and InP. The dashed lines represent the levels that are predicted but not yet observed. The energies of the valence band maxima are taken as 0 for Gap, 0.17 eV for InP, and 0.33 eV for GaAs.

(Brandt et al., 1985); the V4+/3+ donor level is degenerate with the conduction band (Hennel et al., 1987) (see Fig. 5). The titanium Ti2+(3d2)charge state is above the Ti3+/2+acceptor level in III/V compounds. This level lies in the GaAs and GaP energy gaps (Hennel et al., 1986a; Roura et al., 1987) (see Fig. 6). The free-ion ground term of the d2 electronic configuration is the 3F term, which splits into the ground 3 A 2 state and excited 3T2 and 3T1 states in a tetrahedral crystal field (see Fig. 12). In an analysis of optical spectra, one should also take into account other d2 terms, such as the 'P term and two low-spin ' D and ' G terms located above the ground 3F term. At low temperatures, EPR measurements of high-resistivity V-doped III/V compounds, p-type Cr-doped III/V compounds, and n-type Ti-doped GaP reveal EPR signals from the ground ' A 2 state. Their g factors and linewidths are collected in Table 11.

FIG. 12. The energy-level scheme for the d2 electronic configuration in a tetrahedral crystal field.

200

A. M. HENNEL TABLE I1 PARAMETERS OF THE 3dZ EPR SPECTRA IN IIIjV COMPOUNDS

Impurity TiZ'(GaP) V3-(GaAs) V (Ga P) V3 '(InP) Cr4 '(GaAs) Cr4+(GaPj Cr4+(InPj

g-Factor

AB (mT)

1.952&0.003 1.957 1.963 1.96& 0.02 1.994 0.001 1.986 1.999

20 11.8 10.5 40

References Kreissl et al. (1987) Kaufmann et a/. (1982) Kreissl and Ulrici (1986) Lambert et al. (1985b) Stauss et al. (1980) Kaufmann and Schneider (1980a) Goswami et al. (1980)

11.2 8.5

35

There are no reports in the literature of any Cr4+ internal transitions. In the case of V 3 + centers, several absorption bands with sharp ZPLs are observed between 0.7 and 1.8eV in GaAs, Gap, and InP (Clerjaud et al., 1985a; Ulrici et al., 1987). These bands are attributed to the 3 A 2 * 3T2(3F), 3 A , * 'E('D), 3 A 2 * 3T1(3F), 3 A 2 'A1('G), and 3A2 * 3T1(3P)transitions. The last band is located around 1.75eV and may be observed only in Gap.

CaAs:V

Somi-insulating

I

I

J

, - ,

5000

,

6400

sdoo

,

,

I 1

-

9500

, .

,

, "

.

,

I

,

,

do0

ENERGY km-9

FIG. 13. The absorption spectrum of the ' A , 3Tz(3F),3 A z => 'E('D), 3 A , =-37'1(3F),and 3,423 ' A , ( ' G ) intracenter transitions in the V3+(3d2)centers in GaAs (Clerjaud et al., 1985a).

201

5. TRANSITION METALS IN III/V COMPOUNDS

alcm-'

b

The complementary 3T2(3F) 3A2 emission bands were found in all three compounds (Skolnick et al., 1983a; Aszodi and Kaufmann, 1985). Examples of vanadium spectra are shown in Figs. 3-4 and 13-14. In the case of the Ti2+centers, two broad absorption bands, corresponding to 3A2 3T1(3F)and 3A2+-3T1(3P)optical transitions, were observed at 0.66 eV and 1.01 eV in GaAs by Hennel et al. (1986a) (Fig. 15), and at 0.63 eV and 1.03eV in GaP by Ulrici et al. (1988). These bands were also observed in

I

--

1.0

-

0.9

-

I

I I I GaAt: Ti2'( 3d2) T=5K

I

I

1

-

.c

d

-

0.5

1 0.6

I

1

I

I

0.7 0.8 0.9 1.0 Photon Energy (eV)

-

1 1.1

FIG. 15. The absorption spectrum of the 3Az 3T1(3F)and 3A23 3T1(3P)intracenter transitions in the Ti2+(3d2)centers in GaAs (Hennel et al., 1986a).

202

A. M. HENNEL

photoconductivity or DLOS measurements (Guillot et al., 1986; Roura et al., 1987; Brandt et al., 1989), both excited states being located in the GaAs and => 3 A , emission band was found at GaP conduction bands. The 3T2(3F) 0.43 eV only in G a P crystals (Roura et a/., 1989).

3. CONFIGURATION 3d3

The 3d3 electronic configuration may be found in III/V compounds doped with vanadium and chromium, in the case of the V z + and Cr3+charge states. The chromium Cr3+(3d3)charge state is between the Cr4+I3+donor level and the C r 3 + ” + acceptor level in III/V compounds. Both these levels lie within the GaAs, Gap, and InP energy gaps (Look e f al., 1982; Kaufmann and Schneider, 1980a; Clerjaud et al., 1981; Bremond et a!., 1986a, 1988) (see Fig. 11). The vanadium V2+(3d3)charge state lies above the V3+,’+ acceptor level in III/V compounds. This level lies in the GaAs and G a P energy gaps (Hennel et al., 1987; Ulrici et al., 1987) (see Fig. 5). The free-ion ground term of the d 3 electronic configuration is the 4F term, which splits into a ground 4T1 state and excited “T2 and 4A, states in a tetrahedral crystal field (see Fig. 16). However, the low-spin 2G term, located above the ground 4F term, should also be taken into account. At low temperatures, EPR measurements of high-resistivity Cr-doped GaAs reveal an orthorhombic signal, attributed to the ground 47’1 state suffering a Jahn-Teller distortion, as shown by Krebs and Stauss (1977a) and Stauss and Krebs (1980). There are no conclusive EPR results for Cr3+ centers in other compounds. In the case of the V 2 + centers, an isotropic spectrum with g-factor equal to 3.07-t.0.02, and a linewidth of 57mT, was found in ODESR (optically detected electron spin resonance) measurements of V-doped ri-type GaAs by

FIG 16. The energy-level scheme for the d 3 electronic configuration in a tetrahedral crystal field. There are two possible ground states-either a high-spin 4T,(4F)state, or a low-spin 2E(2C) state (see text).

5. TRANSITION METALSIN III/v COMWUNDS

203

Gorger et al. (1988). The V2+(3d3)spin state deduced from these measurements is +,which corresponds to the 'E('G) ground state. This low-spin state was predicted in the theoretical calculations of Katayama-Yoshida and Zunger (1986) and Caldas et al. (1986) for V2+ centers in GaAs and GaP crystals. Absorption measurements of the V2+ centers reveal a broad, weakly structured spectrum between 0.6 eV and 1.1eV in GaAs (Hennel et al., 1987; Bremond et al., 1989),and between 0.8 eV and 1.1 eV in GaP (Clerjaud et al., 1985a; Ulrici et al., 1987). The GaAs spectrum may also be observed in photoconductivity and DLOS measurements (Hennel et al., 1987; Brkmond et al., 1989).The similarity of the GaAs and GaP absorption spectra leads to some doubts about the results of phonon scattering from V centers in both compounds, currently interpreted in terms of the low-spin model in GaAs, and in terms of the high-spin model in GaP (Butler et al., 1989). The absorption spectrum of the Cr3+(3d3) centers in GaP consists of several features between 1 eV and 1.4 eV (Halliday et al., 1986).The first band, with a very complex ZPL structure, is interpreted as the 4T,(F)*4T2(F) transition. The second broad internal transition, with a maximum at about 1.3 eV, has no definitive interpretation yet. The corresponding 4T2(F)* 4T'(F) luminescence spectrum was also detected (Eaves et al., 1985; Thomas et al., 1987). In Cr-doped InP crystals, absorption and emission spectra with ZPL structures very similar to that in GaP were observed by Barrau et al. (1982b) and Clerjaud et al. (1984) and should probably be interpreted in the same manner as in Gap. In Cr-doped GaAs crystals, similar absorption bands were not observed. The only spectrum interpreted in terms of the Cr3+(3d3)charge state is an emission band at 0.57 eV, observed in GaAs by Deveaud et al. (1984b). The proposed interpretation of this band, as one due to the spin-forbidden 'E(G) 4T1(F)transition, is not fully consistent with the results obtained for Gap. Another possibility is that this band is due to recombination of the Cr2+(3d4) charge state with a hole (Deveaud et al., 1980). The latter interpretation is supported by measurements of the decay time of this luminescence band (Crasemann and Schulz, 1986).

4. CONFIGURATION 3d Electron configuration 3d4 may be found in III/V compounds doped with chromium, in the case of the Cr" charge state. One could also expect this configuration for manganese centers (Mn3 charge state). However, it was shown by Schneider et al. (1987) that a neutral acceptor state of this impurity +

204

A. M. HENNEL

is formed by a delocalized hole weakly coupled to the 3d5 core, and cannot be described in terms of the 3d4 configuration. In III/V compounds the chromium Cr2+(3d4)charge state lies between the Cr3+'2+acceptor level and the Cr2+/' double acceptor level. Both these levels lie only in the G a P energy gap (Kaufmann and Schneider, 1980a; Clerjaud er al., 1981). In GaAs and InP crystals, the Cr2+'l+double acceptor level is degenerate with the conduction band (Hennel and Martinez, 1982) (see Fig. 11). term, The free-ion ground term of the d4 electronic configuration is the which splits into the ground 'T2state and the excited 5 E state in a tetrahedral crystal field (see Fig. 17). At low temperatures, EPR measurements of n-type Cr-doped GaAs and InP crystals reveal a tetragonal signal, attributed to the ground 5T2state suffering a Jahn-Teller distortion (Krebs and Stauss, 1977b; Stauss et al., 1977). Absorption bands with the sharp ZPLs corresponding to 'T2 3 ' E optical transitions were observed in the case of the Cr2+centers in GaAs (Clerjaud et al., 1980; Williams et al., 1982), G a P (Kaufmann and Schneider, 1980b), and InP (Clerjaud el al., 1984). In GaAs and InP crystals, these bands were also observed in photoconductivity and DLOS measurements (Eaves et al., 1981; Bremond et al., 1986a), the excited 5 E state being degenerate with the conduction bands (see Fig. 18). This fact has serious impact on the complementary 5 E* 'T2 emission. In GaAs crystals, this luminescence was observed either by direct excitation within the Cr2+absorption band, or under hydrostatic pressure (Deveaud ef al., 1984b). In the second case, the hydrostatic pressure lifts the E state-conduction band degeneracy around 0.6GPa, and the emission band may be observed under the conventional above-band-gap excitation (Fig. 19). After a further increase of the pressure the intensity of this band reaches a maximum around 2-3GPa, and then quickly decreases between 3 and 5 GPa. In the same pressure region, some new emission features were observed between 0.7 and 0.9eV that are +

FIG. 17. The energy-level scheme for the d 4 electronic configuration in a tetrahedral crystal field.

5. TRANSITION METALS

IN

III/v COMPOUNDS

205

Energy (eV)

FIG.18. DLOS spectra of two chromium levels in InP, measured by Brbmond et al. (1988). The sharp maximum of the left-hand curve corresponds to the 'T2 3 5Eintracenter transition of the Cr2+(3d2)charge state.

....

..

12.15

...........

.. .............. . . . .. .:

..

..

...

..........

. ... . .. ..-....".... .. . . . . ....... . .. . .. . . . . . . .".11 ....,"............. ... .... . . .... .. ... ... . ..... ... 11.5

.

.. :.:

05

0.6

0.7

0.8

I

ENERGY (eV)

FIG.19. The hydrostatic pressure-induced luminescence spectrum of the ' E 3 'T2 intracenter transitions in the CrZC(3d4)centers in GaAs (Deveaud et al., 1984b). The applied pressures are indicated in the figure in kilobars (1GPa = 10 kbar).

206

A. M. HENNEL

connected with a crossing of the excited 5 E state with a low spin state (either * A , or jT1)(Zigone et al., 1986). In SI Cr-doped GaAs, additional luminescence bands, with very rich ZPL structures, were observed around 0.8 eV (see, for example, Barrau et al., 1982a). The presence of these bands was correlated with the presence of specific donors, such as Te (Deveaud et al., 1984a) or Se (Fujiwara et al., 1986a);arsenic vacancies (Fujiwara et al., 1984),or isoelectronic In impurities (Fujiwara et al., 1986b). All these bands are interpreted as internal Cr2+(3d4) transitions for symmetry lower than tetrahedral, i.e., in Cr-Te, Cr-Se, CrVAS, and Cr- V,,-In complexes. Observation of these bands implies that excited states of CrZ+(3d4)are in the GaAs energy gap in such complexes (Deveaud et al., 1984a). It should also be noted that neither in InP crystals (where the 5 E state is located about 0.3 eV above the bottom of the conduction band), nor in G a P crystals (where the ' E state lies in the gap), was the ' E * 5Tz emission observed.

5. CONFIGURATION 3d5 The 3d5 electronic configuration may be found in III/V compounds doped with chromium, manganese, and iron, in the case of the Cr+, MnZ+,and Fe3' charge states. The chromium Cr1+(3d5)charge state exists only in G a P crystals, above the C r 2 + ' l double acceptor level (Clerjaud et al., 1981). This level is in the GaAs conduction band and may be activated either under hydrostatic pressure (Hennel and Martinez, 1982), or by very high doping with donors (Guimaraes et a/., 1985) (Fig. 11). The manganese MnZ+(3d5)charge state lies above the Mn-related acceptor level in GaAs, Gap, and InP crystals (Chapman and Hutchinson, 1967; Abagyan et al., 1975; Takanohashi et al., 1988). The iron Fe3+(3d5)charge state is below the Fe3+"+ acceptor level in III/V compounds. This level lies in the GaAs, Gap, and TnP energy gaps (Lang and Logan, 1975; Brehme, 1986; Juhl et al., 1987) (see Fig. 20). The free-ion ground term of the d 5 electronic configuration is the 6S term. This term does not split in a tetrahedral crystal field, and in Tdgroup notation is called the 6Al state. In analyses of optical spectra, one should also take into account the 4G term, located above the ground 'S term. EPR measurements of high-resistivity Fe- and Mn-doped III/V compounds, and n-type Cr-doped Gap, reveal spectra attributed to the ' A , state. Their g factors and linewidths are collected in Table 111. EPR measurements of p-type Mn-doped GaAs reveal signals with g-factors equal to 2.77 and 5.72. +

5. TRANSITION METALS IN III/v

GaAs

GaP

COMPOUNDS

207

InP &+/I+ eco Inr

."

FIG. 20. The energy levels of the iron impurity in GaAs, Gap, and InP. The dashed lines represent levels that are predicted but not observed yet. The energies of the valence band maxima are taken as 0 for Gap, 0.17 eV for InP, and 0.33 eV for GaAs.

TABLE I11 PARAMETERS OF THE 3dS EPR SPECTRA IN I I I p COMPOUNDS

Impurity Cr' '(Gap) MnZ'(GaAs) Mn2'(Gap) Mn2 '(InP) Fe3+(GaAs) Fe3'(Gap) Fe3+(InP)

g-Factor

AB (mT)

1.999 2.0023 _+ 0.001 2.002 0.002 1.997+0.003 2.042 2.026 2.0235 +0.001

13 2.9

*

16.8 5.3 3.8 11.8

References Kaufmann and Koshel(l978) Masterov et al. (1985) Van Engelen and Sie (1979) Masterov et al. (1981) Kirilov and Teslenko (1979) Teuerle et al. (1974) Stauss et al. (1977)

These results were interpreted by several authors (Schneider et al., 1987; Masterov et a/., 1988; Averkiev et al., 1989) in terms of a neutral [Mn' ' ( 3 d 5 )+ hole] center. Exchange antiferromagnetic interaction between this delocalized hole and the 3d5 shell is responsible for the magnetic properties of this center. In the case of Mn-doped GaP and InP, the same center probably exists, although further experiments are required to confirm this hypothesis. This property of manganese, anomalous relative to those of the other transition metal impurities in III/V compounds, manifests itself also in the photoionization spectra of p-type Mn-doped GaAs and InP (see Figs. 2 and 21). A number of sharp lines, corresponding to transitions to excited states of the loosely bound hole, may be observed in absorption (Chapman and Hutchinson, 1967; Lambert et al., 1985a); Kleverman et al., 1990) and photoluminescence excitation experiments (Plot-Chan et al., 1985). These

A. M. HENNEL

208

1688.'

'

*

l

#

k830.'

*

'

.

'

,

l

2168.'

,

,

'

P H O T O N ENERGY t C H - 1 ) FIG. 21. A detailed spectrum in the photoionization threshold region of the Mn absorption band shown in Fig. 2 (Lambert er a/.. 198Sa).

excited states are located at about 100 meV above the ground lS,,, state in GaAs, and at about 200 meV in InP. In spite of this very strong chemical shift, the relative distances between the lines may be described very well by the effective mass theory. There are only two internal optical transitions attributed to the 3d5 configuration. The first is the luminescence spectrum in Mn-doped G a P crystals (Vink and Gorkom, 1972). The second is the luminescence spectrum in Fe-doped SI InP crystals (Deveaud et al., 1984~).Both spectra are interpreted as spin-forbidden 4T,(4G) 6 A , ( 6 S )transitions.

-

6. CONFIGURATION 3d6 Electronic configuration 3d6 may be found in III/V compounds doped with iron, in the case of the Fez+ charge state. One could also expect this configuration for cobalt impurities (Co3 charge state). However, no experimental data are available that confirm this. Furthermore, recent calculations of the absolute photoionization cross-sections by Delerue et al. (1989) suggest that either the C o 3 +center is in a low-spin state, or it should be considered as a [Co2+(3d7)+hole] center, similar to that observed for Mn. The iron Fe2+(3d6)charge state is between the Fe3+I2+acceptor level and +

5. TRANSITION METALSIN III/V COMPOUNDS

209

the Fez+/' double acceptor level in III/V compounds. Both these levels lie only in the G a P energy gap (Lang and Logan, 1975; Brehme, 1986; Juhl et al., 1987). In GaAs and InP crystals, the Fe2+"+ double acceptor level is probably degenerate with the conduction band (see Fig. 20). The free-ion ground term of the d6 electronic configuration is the 'D term, which splits into the ground ' E state and the excited 5T2state in a tetrahedral crystal field. The spin-orbit interaction splits the ground ' E state into five levels, with the lowest being the A , singlet (see Fig. 22). EPR measurements of this singlet level are impossible. Absorption and emission transitions corresponding to the ' E 'T2 +

\'E

c c

*I

FIG. 22. The energy-level scheme for the d6 electronic configurationin a tetrahedral crystal field. The ground 5E state splitting is due to the second-order spin-orbit interaction.

t7

5

1

0 0348

0350

0352

€(el/)

FIG.23. The luminescence spectrum of the 5T2=> 5 E intracenter transition in the Fe2+(3d6) centers in InP (Leyral et al., 1988).

210

A. M.HENNEL 20

InP : Fe T=1.3K

15 10

as 080

078 I

L,

,

116

1%

120

Energy lev)

FIG. 24. Two sets of sharp lines in Fe-doped InP crystals, observed by means of calorimetric absorption spectroscopy by Juhl et a/. (1987), at the thresholds of the photoionizing bands corresponding to transitions from the valence bands to the ' E and 'T2 states of the Fe2+(3d6) charge state.

optical transitions were observed in all three compounds (Baranowski et al., 1967; Leyral er al., 1982; West et al., 1980; Koshel et al., 1977; Thonke et al., 1989). All these spectra begin with a characteristic structure of four sharp ZPLs, which represents the ground ' E spin-orbit splitting (Fig. 23). It should be mentioned that this luminescence was successfully used to obtain a laser effect in Fe-doped InP crystals (Klein et a/., 1983). Additional absorption structures were found at the thresholds of the photoionizing bands corresponding to transitions from the valence bands to the ' E and 5T2states. These sets of sharp lines start at 0.77 eV (Fig. 24) and 1.13eV in Fe-doped SI InP crystals, at 0.49 eV and 0.87 eV in GaAs crystals, and at 0.83 eV in G a P crystals (Juhl et al., 1987; Hennel et al., 1991; Wolf et ul., 1991). Proposed interpretations of these structures-bound states of a hole and the 3d6 shell, or localized excitons bound to the iron impurity-still require further experimental results, as well as a theoretical analysis.

7.

CONFIGURATION 3d7

The 3d7 electronic configuration may be found in III/V compounds doped with iron, cobalt, and nickel, in the case of the Fe'+, Co2+,and Ni3+ charge states. The iron Fe'+(3d7) charge state exists only in G a P crystals, above the Fez+/'t double acceptor level (Brehme, 1986).

5. TRANSITION METALS IN III/V COMPOUNDS

211

The cobalt CoZ+(3d7) charge state lies between the Co3'1' acceptor level and the Coz+ / l + double acceptor level in III/V compounds. The former level is in the energy gaps of GaAs, Gap, and InP crystals (Baranowski et al., 1972; Loescher et al., 1966; Skolnick et al., 1983b). The latter level is in the energy gap only in the case of GaP (Kaniewski et al., 1990)and is degenerate with the GaAs (and, undoubtedly, InP) conduction band (Wasik et al., 1986) (see Fig. 25). The nickel Ni3+(3d7)charge state is below the Ni3+I2+acceptor level in III/V compounds. This level lies in the GaAs, Gap, and InP energy gaps (Brown and Blakemore, 1972; Peaker et al., 1984; Korona et al., 1990) (see Fig. 26). The free-ion ground term of the d7 electronic configuration is the 4F term, which splits into the ground 4Az state and the excited 4T2and 4T1states in a +

FIG. 25. The energy levels of the cobalt impurity in GaAs, Gap, and InP. The dashed line represents a level that is predicted but not yet observed. The energies of the valence band maxima are taken as 0 for Gap, 0.17 eV for InP, and 0.33 eV for GaAs.

GaAs

GaP

InP

m

+

nuulllc

FIG. 26. The energy levels of the nickel impurity in GaAs, Gap, and InP. The energies of the valence band maxima are taken as 0 for Gap, 0.17 eV for InP, and 0.33 eV for GaAs.

212

A. M. HENNEL

tetrahedral crystal field (see Fig. 27). In analyses of optical spectra, one should also take into account other d7 terms, such as the 4P term and several lowspin terms, located above the ground 4F term. EPR measurements of high-resistivity Co- and Ni-doped III/V compounds, and n-type Fe-doped Gap, reveal spectra attributed to the 4A, state. Their g factors and linewidths are collected in Table IV. There are no reports in the literature of any intracenter optical spectra of the Fe1+(3d7)and Ni3+(3d7)charge states in III/V compounds. In the case of the CoZ+(3d7)charge state, a number of absorption bands with sharp ZPLs are observed between 0.5 eV and 1.7 eV in GaAs (Ennen et al., 1980; Hennel and Uba, 1978); GaP (Weber et al., 1980 Radlinski and Liro, 1985) and TnP (Skolnick et al., 1983b). The three main bands are attributed to the 4 A , => 4T,(4F), 4A2 4T1(4F),and 4A, 2 4T,(4P) transitions (Fig. 28). In InP crystals, only in the case of the second 4A, * 4T1(4F) band was a ZPL observed. In other compounds, no ZPL was reported for this band. In G a P crystals, the third band is surrounded by a few weak, spin-

-

FIG. 27. The energy-level scheme for the d' electronic configuration in a tetrahedral crystal field.

TABLE IV PARAMETERS OF THE 3d7 EPR SPECTRA IN III/V COMPOUNDS Impurity Fe'-(GaP) Co"(GaAs) Coz'(Gap) Co2*(InP) Ni3'(GaAs) Ni3+(GaP) Ni '*(InP)

g-Factor

AB (mT)

2.133 2.1 89 & 0.002 2.164 2.192 2.114 2.089 2.098

2.8 8.5 7.0 15.0 12.0 6.0 9.7

References Kaufmann and Schneider (1977) Godlewski and Hennel (1978) Kaufmann and Schneider (1978) Lambert et al. (1983) Kaufmann and Schneider (1978) Kaufmann and Schneider (1978) Kaufmann and Schneider (1978)

5. TRANSITION METALSIN III/v COMFQUNDS

213

Wavelength (pm)

2.2 I

2.04 -

I

1

4.4

1

4.8

.

1.5

1 1 1 ,

1

1

I

,

I

1

1.0I

I

I

I

1

0.8 I

I

6.0 8.0 10.0 12.0 Wavenumber (lo3 cm-'1

0.6I

I

I

I

14.0

I

1

2

I

-

16.0

FIG. 28. The absorption spectrum of the 4A2 * 4T2(4F),4A, * 4T1(4F), and 4A2 34T1(4P) intracenter transitions in the Co2+(3d7)centers in GaP (Radlinski and Liro, 1985). The small absorption details shown in the inset correspond to the spin-forbidden4A, 3'T,, 4A, 3 ,TZ, and 4A, 3' A , transitions.

forbidden transitions (4A2 3 'T2, 'T', 'A1, 'TI) also observed in the photoluminescence excitation measurements of Radlinski and Liro (1985). Such a spin-forbidden transition was also observed as an anti-resonance at 0.8 eV in the absorption band in InP crystals (Skolnick et al., 1983b). The complementary 4T2(4F)=> 4A2 emission bands were found in all three compounds (Deveaud et al., 1986a; Weber et al., 1980; Skolnick et al., 1983b). Some cobalt-related complexes were also observed in absorption and luminescence. One of them was identified as the Co2'(3d7)-Te trigonal complex by Deveaud et al. (1986a). The number of Co atoms involved in complexes with Te is about one order of magnitude smaller than that with isolated cobalt centers. It was also found from photoluminescence excitation measurements that the C O ~ + / ~ +acceptor - T ~ level of this complex is located about 0.1 eV above the acceptor level of an isolated cobalt center. 3d8 8. CONFIGURATION The 3d8 electronic configuration may be found in the III/V compounds doped with cobalt and nickel, in the case of the Co'+ and Ni2+charge states. One could also expect this configuration for copper centers (Cu3+ charge state). However, all the copper-related centers investigated in III/V com-

214

A. M. HENNEL

pounds exhibit low symmetry. This fact suggests that their structures are more complex than that of an isolated substitutional impurity center (see, for example, Kullendofi et al., 1983, or Milnes, 1983). In Gap, the cobalt Co'+(3d8) charge state is above the Co2+'l+double acceptor level (Kaniewski et al., 1990). This level is in the GaAs conduction band and may be activated either under hydrostatic pressure (Wasik e l al., 1986) or by very high doping with donors (see Fig. 25). The nickel Ni2+(3d8)charge state is between the Ni3+"+ acceptor level and the Ni*+" double acceptor level in III/V compounds. Both these levels lie in the GaAs, Gap, and InP energy gaps (Brown and Blakemore, 1972; Brehme and Pickenhain, 1986; Peaker et al., 1984 Yang et al., 1984 Korona et al., 1990; Korona and Hennel, 1989) (see Fig. 26). The free-ion ground term of the d S electronic configuration is the 3F term, which splits into the ground 3T1state and the excited 3G and 3A2 states in a tetrahedral crystal field. The spin-orbit interaction splits the ground TI state into several levels, the lowest being the A , singlet (see Fig. 29). EPR measurements of this singlet level are impossible. In analyses of optical spectra, one should also take into account the 3 P term and several low-spin terms located above the ground 3F term. in the case of the Co1+(3ds)charge state in Gap, only one absorption line is observed, and attributed to the 3T,(3F)3 3T2(3F)transition by Jezewski et al. (1990). The excited 3T2(3F)is in the conduction band, which explains the absence of a luminescence spectrum. In the case of the Ni2+(3d8)charge state in Gap, three absorption bands are seen between 0.8eV and 1.5eV, these being attributed to the 3 3T2(3F), 3T(3F) 3T1(3P),and 3T1(3F) lT2transitions (Liro and 3T1(3F) Baranowski, 1982; Jezewski et al., 1987). The last identification is not definitive; another possibility is 3T,(3F)=> 3A2(3F). A similar three-band spectrum was observed in GaAs between 0.5eV and 1.3eV, and was interpreted in a similar manner by Ulrici et al. (1986b). No resuits are reported on the Ni2 '(3d') charge state in InP crystals. +

-

=j

FIG. 29. The energy-level scheme for the d 8 electronic configuration in a tetrahedral crystal field. The ground 'T, state splitting is due to the spin-orbit interaction.

5. TRANSITION METALSIN IIIjV COMPOUNDS

215

9. CONFIGURATION 3d

The 3d9 electronic configuration may be found in III/V compounds doped with nickel, in the case of the Nil+ charge state. One could also expect this configuration for copper impurity (Cu2 charge state). However, as was explained in the previous section, there are no conclusive data in the literature concerning isolated copper centers in III/V compounds. In all three compounds, the nickel Ni'+(3d9) charge state is above the Ni2+/'+ double acceptor level (Brehme and Pickenhain, 1986; Yang et al., 1984; Korona and Hennel, 1989) (see Fig. 26). The free-ion ground term of the d9 electronic configuration is the 2 D term, which splits into the ground 2T2state and the excited 2 E state in a tetrahedral crystal field. The spin-orbit interaction splits the ground T2 state into two levels-a Tsquartet and lower-lying r, doublet (see Fig. 30). EPR measurements of n-type Ni-doped GaP and GaAs crystals reveal very weak isotropic signals of this r,(2T2)level, with g-factors equal to -0.934 and - 1.05, respectively (Kaufmann et al., 1979; Clerjaud et al., 1990). There are no EPR results for the Ni'+(3d9) charge state in InP. Absorption spectra with sharp ZPLs, corresponding to the 2q* ' E intracenter transitions within the Nil +(3d9) centers, were observed in all three compounds (Drozdzewicz et al., 1984; Kaufmann et al., 1979 (Fig. 31); Korona and Hennel, 1989).The complementary 2 E = 2T2emission band was observed only in GaP crystals by Kaufmann et al. (1979) (see Fig. 32). In GaAs and InP, this luminescence was not observed because the excited ' E state is degenerate with the conduction bands. Some additional lines were observed in the region of Nil +(3d9)absorption and luminescence spectra in GaAs and Gap. The presence of these lines was correlated with the presence of S, Se, Te, Si, Ge, and Sn donors by Ennen et al. (1981) (Fig. 33). All the spectra were thus interpreted in terms of internal Ni1+(3d9) transitions within Ni-donor complexes. As was the case for the +

\

r8 r,

FIG. 30. The energy-level scheme for the d 9 electronic configuration in a tetrahedral crystal field. The ground 'Tt state splitting is due to the spin-orbit interaction.

216

A. M. HENNEL 056

a68

I

030

1

I

I

0.72 I

034

1

cV

1

G a p : N i (3d9)

T+SK 333

83 111

I I

217

I

1

I

I

I

I

'

5000

5600

5400

todio em"

FIG. 31. The absorption spectrum of the 'T2 ' E intracenter transition in the Ni1+(3d9) centers in GaP (Kaufmann et oi., 1979).

0.62

0.65

0.6 L

0.63

0.66 eV

I

GaP : Ni(3d9)

5351cm

I

T=ZK

107

213

46

I

I r25

.l

0

---

5000

5100

5200

-7-

5300 crn"

FIG.32. The luminescence spectrum of the ' E 3 'T2transition in the Ni'+(3d9)centers in GaP (Kaufmann et al., 1979). This band is complementary to the absorption presented in Fig. 31.

Cr2+ complexes, observation of these bands implies that in Ni-donor complexes in GaAs the excited states of Ni1+(3d9)are in the GaAs energy gap.

5. TRANSITION METALS I N III/v COMPOUNDS

217

EN E R GY ( cm-' LLOO

Lf

1

LBO0

5001

I I I

-

n - G a A s : Ni 5K

Bo

in

c

A0

z

c-

3

a

Ni -S -

K

Bb

>

a

t

Niiso

-

5 doped

m

->a K

c

in

z

W

n A

a 2 c n.

0

FIG.33. The absorption spectra of Ni-diffused GaAs:S, GaAs:Se, and GaAs:Te. The central A, line corresponds to the isolated Ni1+(3d9)charge state. The B, C, and D lines correspond to Nil +-S, Nil+-Se, and Ni'+-Te complexes, respectively. (Ennen et al., 1981).

IV. 4d" and 5d" Transition Metals Investigation of 4d" and 5d" TM impurities is at a rather early stage, and it is difficult to draw any general conclusions. The theoretical calculations performed by Makiuchi et al. (1986, 1989) predict that crystals some of these impurities should form acceptor levels in GaAs and GaP (W, Mo, Ir, Rh, Os, Ru, and Re), and some should form donor levels (Nb, Ta, Os, Ru, and Re). Low-spin ground states are predicted for W2+ and Mo2+, and high-spin ground states are predicted for Nb3+ and Ta3+. Serious problems for crystal growers arise as a result of the low solubilities and diffusivities of these impurities. The only exceptions seem to be silver and gold. In this situation, most of the existing experimental results come from luminescence and DLTS measurements performed on implanted samples.

218

A. M. HENNEL

Luminescence spectra were found for tantalum in GaAs and G a P (Ushakov et al., 1983; Vavilov et al., 1983; Wolf et a!., 1988);niobium in GaAs and G a P (Ushakov et al., 1981; Vavilov et al., 1983; Aszodi et al., 1983; and Gabilliet et a[., 1986);tungsten in GaAs (Ushakov and Gippius, 1980; Vavilov et al., 1983);and molybdenum, palladium, and zirconium in GaAs (Vavilov et a / . (1980)). Niobium and tantalum spectra are interpreted in terms of intracenter transitions within the Nb3+(4d2)charge state by Aszodi et al. (1983) and Gabilliet et al. (1986), and within the Ta3+(5d2)charge state by Wolf et al. (1988).These results are in line with theoretical predictions, although the spin states of the 4d2 and 5d2 configurations are not yet established. Tungsten gives rise to two luminescence bands in GaAs, one in n-type crystals, and another in p-type crystals. According to Gippius et al. (1989a), this Fermi-level position dependence suggests that they could correspond to intracenter transitions within the W2+(5d4)and W3+(5d3)charge states. Some levels attributed to Ta, W, and N b were observed in the DLTS measurements of GaAs and G a P of Chernyaev er al. (1987) and Gippius et al. (1989a). Definitive identification of these levels as TM donors and acceptors requires further experiments. On the other hand, acceptor levels of silver and gold impurities in GaAs were observed in many different experiments (Blatte et al., 1970 Hiesinger, 1976; and Yan and Milnes, 1982). However, it is not yet known whether these levels correspond to isolated or complexed impurities.

V. Semi-insulating TM-Doped III/V Materials The first, and still the most important, application of TM impurities in IIUV compounds is their ability to compensate shallow impurities and thus produce semi-insulating materials. To obtain an ideal semi-insulating TM-doped semiconductor, one should choose a TM impurity with the following properties: (a) a mid-gap acceptor or mid-gap donor level, and (b) good thermal stability. It is not easy to fulfill both these conditions. The first SI material (patented in 1967) is Cr-doped GaAs. The chromium Cr3+I2+acceptor level is able to compensate shallow donors in the concentration range of 10'6-1017~ m - ~ , and stabilize the Fermi level at the mid-gap position. Consequently, resistivity values of 108-109Rcm were achieved (Grand et al., 1982). The only serious problem is chromium thermal stability. The chromium atoms diffuse out of substrates during epitaxial crystal growth, and the first few microns of a nominally undoped layer have a resistivity that is much higher than

5. TRANSITION METALSIN IIIjV COMPOUNDS

219

expected. Furthermore, accumulation of chromium was observed at surfaces after postimplantation annealing, or at substrate-layer interfaces after epitaxial growth (see the reviews by White, 1980, and Tuck, 1984). This outdiffusion process was found even at relatively low temperatures (500700°C) (see Fig. 34) and may have serious impact on electronic device properties. In the 1980s, successful growth of undoped GaAs LEC material with EL2 reduced the role of SI Cr-doped GaAs. However, about 50% of production of Sumitomo Electric Industries (the first GaAs producer) is still horizontal Bridgman Cr-doped GaAs. Several V-doped SI GaAs with resistivities of around 107-108 Q cm were reported-LEC by Kutt et al. (1984); VPE by Terao et al. (1982); MOCVD by Akiyama et al. (1984), and HB by Hennel et al. (1986b)).This material could be a very promising, one since the diffusivity of V in GaAs was shown to be one order of magnitude lower than that of Cr (Kiitt et al., 1984). However, it was shown by Hennel et al. (1986b, 1987)that the mid-gap level responsible for the high resistivity of these materials is the deep donor EL2. In these crystals, vanadium plays only a chemical role (gettering of donors) during the crystal growth process (KO et al., 1989). The first reported SI InP was a Cr-doped material, but the chromium

layer

substrote

FIG. 34. Chromium profile in an MBE layer measured by SIMS (Linh et al. (1980). The substrate was heated to 530°C for 30 minutes before growth.

220

A. M. HENNEL

Cr’ acceptor level is located in the upper part of the energy gap in InP, and a very high resistivity range was impossible to achieve. In 1975, Mizuno and Watanabe (1975) from Nippon Electric Co. obtained SI Fe-doped InP crystals. The mid-gap position of the Fe3+”+ acceptor level makes it possible to obtain SI InP with resistivities above lo7R cm. Up to now, this material remains the main SI InP substrate. Unfortunately, outdiffusion properties similar to those of Cr in GaAs were reported for Fe in InP (Tuck, 1984, and Kamada et al., 1984). Other TM acceptors, such as Co, were also used to obtain SI InP (see, for example, Hess et al., 1988),but because the C 0 3 + i 2 + level is in the lower part of the energy gap, the resistivity obtained is only around loJ Rcm. Furthermore, the Co impurity diffusion coefficient is larger than that for Fe, and one cannot expect thermal stability better than that for Fe-doped InP for this material. In the mid-l980s, this situation stimulated serious activity in search for new, thermally stable SI TM-doped substrates, as presented in the review paper of Clerjaud (1988b). In the case of SI GaAs, no serious TM alternative to Cr was proposed. The best solution seems to be a co-doping of GaAs with Cr and In, proposed in the two patents of Clerjaud et al. (1985b) and Morioka and Shimizu (1985). Indium is an isoelectronic impurity that does not affect the electrical properties of SI GaAs, but is strongly reducing its dislocation density and, as a result, impurity diffusion processes. Such thermally stable SI material was obtained at Sumitomo Electric Industries (Clerjaud, 1988b). Fe-doped InP material can also be improved by co-doping, which is reducing the dislocation density, as proposed by Clerjaud et al. (1985b). Its growth with the isoelectronic Ga impurity was performed by CoquillC et al. (1987). Thermal stability of Fe- and Ga-doped InP was shown by Toudic et al. (1986) to be much better than that resulting with no Ga co-doping. Another possibility, developed recently for InP, is co-doping with deep TM donors and shallow acceptors. Such an idea was proposed for two deep midgap TM donors in InP (Ti and Cr) by Brandt et al. (1986) and Lambert et al. (1986).SI crystals of Cr-doped InP, co-doped with Cd or Hg, with resistivities of up to lo6 R cm,were grown by Toudic et al. (1988). However, the thermal stability of Cr was found to be similar to that of Fe in InP. SI crystals of Ti-doped InP, co-doped with Be, Cd, Hg, and Zn, with resistivities of up to 5 x lo6 R cm, were grown by several groups (see Clerjaud, 1988b, and Hennel, 1991). To check their thermal stability, Ti profiles were measured in Ti and Hg-doped InP (Toudic et al., 1987), as well as Ti and Zn profiles in Ti- and Zn-doped InP (Katsui, 1988). All these measurements, performed in the 800-975°C temperature range, showed very high thermal stability of the Ti and Zn profiles. +

+

5. TRANSITION METALSIN III/v

221

COMPOUNDS

The last possibility that should be mentioned is co-doping of InP with Fe and Ti (Dentai et al., 1987). The material obtained, with resistivity higher than lo7 R cm, remains SI with shallow donors as well as shallow acceptors. In conclusion, one can predict further investigation of new SI materials (such as III/V compounds doped with 4d" and 5d" TM impurities), as well as improvements of the SI systems already known. Appendices 10. TM ENERGY LEVELS

Tables V-VII. TABLE V ENERGY LEVELSIN GaAs Energy" (eV)

E" E, +0.1 1

Identificationb

Experimental Technique'

var OA

Pressure Coefficientd (meV/GPa)

12k2(v)

PL

E,+0.14 E, + 0.15

OA OA PL

E, + 0.2

TDH

E, +0.2 E, +0.24

DLTS DLTS

E, + 0.25 E, + 0.32 E, + 0.4

PLE TDH DLTS

E, +0.40 E, +0.5

DLTS DLTS PLE DLTS

E, +0.6

3 f:2(v)

5 2 2(v)

-87+25(c)

References

Hennel et al. (1987) Chapman and Hutchinson (1967) Schairer and Schmidt (1974) Samuelson and Nilsson (1988) Kleverman et al. (1990) Baranowski et al. (1972) Willmann et al. (1971) Willmann et al. (1973) Nilsson and Samuelson (1988) Janzkn et al. (1990) Brown and Blakemore (1972) Gippius et al. (1989a) Yan and Milnes (1982) Pistol et al. (1988) Deveaud et al. (1986a) Look et al. (1982) Kullendorff et al. (1983) Kumar and Ledebo (1981) Yan and Milnes (1982) Lang and Logan (1975) Shanabrook et al. (1983) Brandt et al. (1989) Nolte et al. (1987) Scheffler et al. (1990) (Continued)

222

M.HENNEL

A.

TABLE V (Cont.) Energy (ev)

Identification*

Experimental Technique'

E,+0.65 E,+0.74 E,-0.40

W 3 + (A)? Cr3-"'(A) Ni'-"+ (AA)

'+

DLTS OA DLTS

E , -0.27 E,-0.2

Ta3*,'*(A)'? Ti3+ (A)

DLTS DLTS

E,-0.15

V3'

(A)

DLTS

E , + 0.05

Cr'

'(AA)

HHP

E,+O.ll

CO2'"'

'I

(AN

Pressure Coefficientd (meV/GPa)

References

Gippius et al. (1989a) 30+7(v) Martinez et al. (1981) - 155+ l q c ) Brehme and Pickenhain (1986) - 136k 12(c) Nolte et al. (1989) Babinski et al. (1991) Gippius et al. (1989a) - 116k 12(c) Brandt et nl. (1989) Nolte et al. (1987) Schemer et al. (1990) - 116f 12(c) Hennel et a/. (1987) Nolte et al. (1987) - 63 f5(c) Hennel and Martinez (1982) -75+5(c) Wasik ef al. (1986)

HHP

"(E,) rel. VB, (E,) rel. CB. b(D)donor, (A) acceptor, (AA) double acceptor. 'Abbreviations: OA-optical absorption, TDH-temperaturedependent Hall effect, PLphotoluminescence, PLE-photoluminescence excitation, DLTS-deep level transient spectroscopy. HHP- Hall effect under hydrostatic pressure, var-various techniques.

TABLE VI ENERGY LEVELS IN GaP Energy" (eV)

E , +0.2 E, + 0.4 E , + 0.41 E,+0.5 E , + 0.5 E , + (3 E , + 0.7 E , + 0.8

Identificationb

Experimental Technique' var DLTS OA TDH var DLTS OA var var DLTS PLE PC

References

UIrici et al. (1989) Brunwin et al. (1981) Abagyan et al. (1975) Loescher et al. (1966) Grimmeiss et a/. (1978) Peaker et al. (1984) Abagyan et al. (1976) Kaufmann and Schneider (1980a) Grimmeiss et a!. (1978) Brehme (1986) Shanabrook et al. (1983) Yang et al. (1983) (ContinW d )

5. TRANSITION METALS IN III/V COMFWJNDS

223

TABLE VI (Cont.) Identificationb E, + 1.0 E, - 1.2 E, -0.8 E , -0.65 E,-0.58 E,-0.5 Ec-0.5 E,-0.31 E , -0.28 E,-0.26

Experimental Technique‘ DLTS var DLTS DLTS TDH DLTS var DLTS DLTS DLTS

References

Roura et al. (1987) Clerjaud et al. (1981) Yang et al. (1984) Gippius et al. (1989a) Ulrici et al. (1987) Roura et al. (1987) Clerjaud et al. (1981) Chernyaev et al. (1987) Kaniewski et al. (1990) Brehme (1986)

“(E,) rel. VB, (E,) rel. CB. *(D) donor, (A) acceptor, (AA) double acceptor. ‘Abbreviations: OA-optical absorption, TDH-temperature-dependent Hall effect, PCphotocapacitance, PLE-photoluminescence excitation, DLTS-deep level transient spectroscopy, var-various techniques.

TABLE VII IN InP ENERGY LEVELS ~~

Energy“ (ev) E, +0.20 E,+0.21 E , + 0.3 E,+0.32 E, +0.48 E,+0.61 E, + 0.55 E, + 0.79 E,-0.55 E, -0.5 E, -0.4 E, -0.27

Identification

Mn(A) v4+/3+ (D) Cu(4 Co3+12+(A) ~ i 3 + / 2(A) + cr4+/3+ (D) Cu(AA)? Fe3+l2+(A) Au(D) Ti4+/3+ (D)

(A) Ni2+/1+(AA)

cr3+/2+

Experimental Technique‘ OA DLTS DLTS var TDH DLTS DLTS var OA DLTS DLTS DLTS var DLTS DLTS

References

Lambert et al. (1985a) Takanohashi et al. (1988) Deveaud et al. (1986b) Kullendorff et al. (1983) Skolnick et al. (1983b) Korona et al. (1990) Bremond et al. (1988) Kullendorff et al. (1983) Juhl et al. (1987) Parguel et al. (1987) Lambert et al. (1987) Brandt et al. (1989) Wasik et al. (1989) Bremond et al. (1986a) Korona and Hennel(l989)

“(E,) rel. VB, (E,) rel. CB. “D) donor, (A) acceptor. ‘Abbreviations: OA-optical absorption, TDH-temperature-dependent deep level transient spectroscopy, var-various techniques.

Hall effect, DLTS-

224

A. M. HENNEL

11. ABSORPTIONAND EMISSIONT M

AND

R E SPECTRA

This section contains information about the absorption and luminescence intracenter transitions of TM and rare earth (RE) impurities. There is no information yet about any energy levels of R E impurities in III/V compounds, but their spectra have been investigated for several years. All these bands are interpreted as intracenter transitions within trivalent R E ions. However, observed spectra are slightly dependent on doping technique as well as growth and annealing conditions. These facts suggest that a number of different R E centers may be present in III/V crystals. There already are three reviews concerning the R E centers in III/V compounds (Ennen and Schneider, 1985; Masterov, 1984; and Masterov and Zakharenkov, 1990). Tables VIII-X.

TABLE VIII

ABSORPTIONAND EMISSION INTRACENTER TRANSITIONS IN GaAs Impurity Ground (Charge State State) --_ _ _ _ _ be2+(3d6) 5E 2960 AE Fez - ( 3d6) 5E 2971 AE Fez +(3d6) 'E 2988 AE Fez+ ( 3d6) 'E 3002 AE Fez'(3d6) complex (7) 3057 E Co"(3d')- Y complex (?) 3545 E Co2+(3d7)-Te complex 3861 E Co2 "(3d')-Te complex 3885 AE Co2'(3d')-X complex (?) 3983 E 4035 AE co2 '(3d7) 4A2 Ni' '(3dy)-Te complex 4369 AE 44410 A€ NI' *(3d9)-Se complex NI' '(3d9)-S complex 4421 AE TI' * (3d') *€ 4565.6 AE TI' '(3d') 2E 4589.4 A 4615 A NI' '(3d9) Tz 4621 AE Nil '(3dy)-Sn complex 4699 AE NI' '(3dy)-Si complex 4740 AE NI' '(3d9)-Ge complex Cr-complex (7) 4630 E Cr-complex (7) 4646 E Cr-complex (7) 4710 E Cr-complex (7) 4767 E

ZPL" (cm ')

References

Excited State

Baranowski e t a / . (1967) Omel'yanowski et a/. (1970) Yu (1981) Leyral et a/. (1982) Leyral et a/. (1988) Deveaud er a/. (lY86a)

Ennen et ul. (1980) Ennen er al. (1981)

Hennel et a/. (1986a) UIrici et al. (1986a) Drozdzewicz et al. (1984) Ennen et a / . (1981)

Yu (1982)

(Canf inued)

5. TRANSITION METALSIN III/v

COMPOUNDS

TABLE VIII (Cont.) ZPL" (cm - ')

Impurity (Charge State)

4823 E 5160 E 5365 E 5368 E 5370 E 5468 E 5694 E

Cr-complex (?) Ta3+(5d2)? Ti complex (?) Ti complex (?) Cr3+(3d ')? W2+(5d4)? W3+(5d3)?

5958 AE 5968** AE 6200* E 6246 E 6416.4 AE

V3+(3dZ) 3A2 V3 +(3d2) 3A2 Pr3+(4f2) 3H4 u3+(5f3) or u4+(5f2) A,? Nb3+(4d2)?

6500* E 6620* AE

Er3+(4f '') Cr2+(3d4)

6750* E 6770* AE

Cr2+(3d4)-Se complex Crzf(3d4)-V(As) complex

6810 E 6907 E 7041 E 7000* E

CrZf(3d4)-Te complex Cr2+(3d4)-In-VA, complex CrZ+(3d4)-In-VAscomplex 411312 Nd3'(4f3)

7333 A 7650* E 8100* E 8131 A 8634* A 9000* E

V3+(3d2) Pr3+(4f ), Tm3'(4flZ) V3+(3d2) Ni2+(3ds) Nd3'(4f3)

9700* E lO,OOO* E 10,773 A 11,OOO* E

Pr3+(4f ), Yb3+(4f' 3, V3 (3d2) Nd3+(4f3)

11,317 A

Co2+(3d7)

+

Ground State

A,?

4T1(F)?

411512 T2

'A2 3H5 3H6

3A2 TIP) 4111,2

'H4 2F712

3A2

4A2

"(A) abs., (E) em. bA star means that there is more than one line.

Excited State

A,?

1

'E(G)?

'A,? 41i3~z

5E

References

Wolf et al. (1988) Ushakov and Gippius (1982) Gippius et al. (1989b) Deveaud et al. (1984b) Ushakov and Gippius (1980) Vavilov et al. (1983) Gippius et al. (1989a) Clerjaud et al. (1985a) Aszodi and Kaufmann (1985) Pomrenke et al. (1989) Pomrenke et al. (1990) Aszodi et al. (1983) Gabilliet et al. (1986) Pomrenke et al. (1986) Clerjaud et al. (1980) Williams et al. (1982) Deveaud et al. (1984b) Fujiwara et al. (1986a) Lightowers et al. (1979) Barrau et al. (1982a) Deveaud et al. (1984a) Fujiwara et al. (1986b) Miiller et al. (1986) Nakagome and Takahei (1989) Clerjaud et al. (1985a) Pomrenke et al. (1989) Pomrenke et al. (1989) Clerjaud et al. (1985a) Ulrici et al. (1986b) Miiller et al. (1986) Nakagome and Takahei (1989) Pomrenke et al. (1989) Ennen et al. (1985) Clerjaud et al. (1985a) Miiller et al. (1986) Nakagome and Takahei (1989) Hennel and Uba (1978)

225

A. M. HENNEL

226

TABLE IX ABSORPTION AND

ZPL" (em-')

Impurity (Charge State)

EMISSION INTRACENTER TRANSITIONS IN G a p

Ground State

3303.6 AE 3319.6 AE 3330.7 AE 3343.5 AE 3468 E 3788 A 4506 AE 4713 AE 4981 AE 4873 AE 4877 AE 4904 AE 4952 E 5354 AE 5432 E 5455 E 5502 AE 6103 E 6307*' A 6382 AE 6398* AE 6500* E 6972 A 6996 A 7000* E 7040* A 8307* AE

5E Fe"(3d") Fe2'(3d6) 5E Fe2'(3d6) 5E Fez'(3d6) 5E Ti' '(3d2) 3A2 Co''(3d") Tl Co2 '(3d') ,A2 NI' *(3d9)-Te complex Ni"(3d9)-S complex Ti ' +(3d') 2E Ti3'(3d') 2E TI' (3d') 2E ,T13 Ta2+(5d3)" NI' ( 3d9) T2 Ni' '(3d9)-Sn complex Ni' '(3d9)-Si complex NI' '(3d9)-Ge complex Nb3+(a2)? Ni2-(3dR) Tl V3 '(3d') 3 ~ V3+(3d2) 3 ~ Er3'(4j ") ,115 2 V4'(3d') 2E V4 '(3d') 2E Nd3 '(4f3) 41i3 2 Cr' '(3d4) T2 Cr3'(3d3) 'TI

8699 A 8713 A 8763 A 9000* E 9300* E 9934 A

V3'(3d2) V 3 * (3d2) V3 +( 3d') Nd3'(4f3) Pr3'(4j 2)? Ni2'(3dR)

lO,OOO* E 10,900* E 11,OOO* E 11,370 A 12,215 A 12,257 A

Yb3'(4fI3) Pr3+ (4f z)? Nd3'(4f3) Ni2+(3ds) Co2'(3d') co ( 3 8 )

'F,

12,374 E 12.385 E

Mn2'(3d5) Mn2+(3d5)

bA2 6A2

Roura et al. (1989) Jezewski et al. (1990) Weber et al. (1980) Ennen et al. (1981)

'T2

= T2 2Tl? 2E

2 2

'A2 342 'A2

"Il1 3H,?

3T1(F)

,A2 4A

Ulrici et al. (1988)

2 T2

-

-

References

West et al. (1980) Baranowski et al. (1967) Vasil'ev et nl. (1976)

+

,I, 2 Tl

Excited State

Vavilov et al. (1983) Kaufmann et al. (1979) Ennen er al. (1981)

Aszodi er al. (1983) Jezewski et al. (1987) Clerjaud et al. (1985a) Aszodi and Kaufmann (1985) Pornrenke et al. (1986) Ulrici et al. (1989) Miiller et al. (1986) Kaufmann and Schneider (1980b) Halliday et a!. (1986) Eaves et al. (1985) Thomas er al. (1987) Ulrici et al. (1987)

Miiller et al. (1986) Gippius et al. (1986) Baranowski et al. (1968) Liro and Baranowski (1982) Ennen et al. (1985) Kasatkin et al. (1981) Miiller et al. (1986) Jezewski et al. (1987) Baranowski el al. (1967) Weber et al. (1980) Radlinski and Liro (1985) Vink and Gorkom (1972) (Continued)

5. TRANSITION METALSIN IIIjV COMPOUNDS TABLE IX (Cont.) ZPL" (cm-')

13,873 A 13,888 A 13,946 A 14,000* E 16,400* E 18,500* E

Impurity (Charge State) V3+(3d2) V3+(3d2) V3+(3d2) Pr3+(4f2)? Pr3'(4fz)? Pr3'(4f2)?

Ground State

Excited State

'A2

3T1(P)

References

Ulrici et al. (1987)

3A2 TIP)

3A2

Kasatkin et al. (1981)

"(A) abs., (E) em. bA star means that there is more than one line.

TABLE X ABSORPTIONAND EMISSION INTRACENTER TRANSITIONS IN InP ZPL" (cm-')

2801 E 2819 AE 2830 AE 2844 AE 3103 A 3117 A 3823 E 4300 E 4317 E 4409 A 4437 A 4601 A 5690 AE 5702*b AE 5988 E 6100* A 6189 A 6338 A 6500* E 7150* AE

Impurity (Charge State)

Ground State

'E Fe2+(3d6) Fez +(3d6) 5E Fe2+(3d6) 5E Fez+(3d6) 5E Fez +(3d6) 5E Fez+(3d6) 'E Co2+(3d7) 4Az Fe3+(3d5) 6A1 Fe3+(3d5) 6Al Ti3+(3d1) 2E Ti3+(3d1) 2E Nil +(3d9) T2 V3+(3d2) 'A2 V3+(3d2) 'A2 u3+(5f3)or V + ( 5 f 2 ) CrZ+(3d") Tz V4+(3d') T2 Co2*(3d7) 4A2 Er"(4f") 411512 Cr-complex?

7096 A 8009 A 10,428 A lO,OOO* E "(A) abs., (E) em. 'A star means that there is more than one line.

Excited State

References

Koshel et al. (1977) Leyral et al. (1988) Thonke et al. (1989) Pressel et al. (1991)

Skolnick et al. (1983b) Deveaud et al. (1984) Brandt et al. (1986) Brandt et al. (1989) Korona and Hennel(l989) Clerjaud et al. (1985a) Skolnick et al. (1983a) Pomrenke et al. (1990) Clerjaud et al. (1984) Clerjaud et al. (1987b) Skolnick et al. (1983b) Pomrenke et al. (1986) Barrau et al. (1982b) Clerjaud et al. (1984) Clerjaud et al. (1985a)

Ennen et al. (1985)

227

228

A. M. HENNEL

REFERENCES Abagyan, S. A.. Ivanov,G. A,, Korolewa, G . A., Kuznetsow, Y. N., and Okunev, Y. A. (1975). Sou. Phys. Semicond. 9, 243. Abagyan. S. A,, Ivanov, G. A., and Korolewa, G. A. (1976). Sou. Phgs. Sernicond. 10, 1056. Akiyama, M.. Karawada, Y., and Kaminishi, K. (1984). J . Crystal Growth 68, 39. Allen, J. W. (1986). Deep Centers in Semiconductors (S. Pantelides, ed.), p. 627. Gordon and Breach Science Publ., New York. Aszodi, G., and Kaufmann, U. (1985). Phys. Rev. B 32, 7108. Aszodi, G.,Ennen, H., Weber, J., Kaufmann, U., and Axrnann, A. (1983).4rh “Lund” Int. ConJ on Deep I h e l Impurities in Semiconducrors. Eger. Hungary. Unpublished. Averkiev, N. S., Gutkin, A. A., Krasikova, 0.G., Osipov, E. B., and Reshchikov, M. A. (1989). Crystal Properties & Preparation, Vol. 19-20, p. 125.Trans. Tech. Publications, Switzerland. Babinski, A,, Baj, M., and Hennel, A. M. (1991). Acta Phys. Pol. A 79, 323. Baranowski. J . M., Allen, 3. W., and Pearson, G. L. (1967). Phys. Reu. 160, 627. Baranowski, J. M., Allen, J. W., and Pearson, G. L. (1968). Phys. Rev. 167, 758. Baranowski, J . M.. Grynberg, M., and Magerramov, E. M. (1972). Phys. Stutus Solidi ( B ) 9.433. Barrau, J., Thanh, D. X.. Brosseau, M., Brabant, J. C., and Voillot, F. (1982a). Solid State Comm. 44, 395. Barrau, J., Thanh, D. X., Brosseau. M., Brabant, J. C., and Voillot, F. (1982b). Physica 116B, 456. Bates. C. A,, and Stevens, K. W. H. (1987). Rep. Progr. Phys. 49, 783. Bishop, S. G. (1986). Deep Centers in Semiconductors (S. Pdntelides, ed.), p. 541. Gordon and Breach Science Publ., New York. Blatte, M., Schairer, W., and Willmann, F. (1970). Solid State Cornmun. 8. 1265. Brandt, C. D. (1987). Ph.D thesis, MIT, Cambridge, MA. Brandt, C. D., Hennel, A. M.. Pawlowicz, L. M., Dabkowski, F. P., Lagowski, J., and Gatos, H. C. (1985). Appl. Phys. Lett. 47, 607. Brandt. C. D., Hennel, A. M., Pawlowicz, L. M., Wu, Y. T., Bryskiewicz, T., Lagowski, J., and Gatos, H. C . (1986). Appl. Phps. Lett. 48, 1162. Brandt, C. D., Hennel, A. M., Bryskiewicz, T., KO, K. Y., Pawlowicz, L. M., and Gatos, H. C. Appl. . Phys. 65, 3459. (1989)..I Brehme, S. (1986). J. Phys. C: Solid Stare Phys. 18, L319. Brehme. S., and Pickenhain, R. (1986). Solid State Commun. 59, 469. Bremond, G., Guiilot, G., Nouaihat, A,, and Picoli, G. (1986a). J. Appl. Phys. 59, 2038. Rremond, G.. Guillot, G., Nouailhat, A., Larnbert, B., Toudic, Y., Gauneau, M., and Deveaud, B. f 1986b). Defects in Semiconductors (H.J. von Bardeleben, ed.), Material Science Forum, Vol. 10- 12, p. 657. Bremond, G., Guillot, G., Lambert, B., and Toudic, Y. (1988).Semi-insulating III-V Materials. Mnlmo’ 1988 (G. Grossmann and L.A. Ledebo, ed.), p.319. Adam Hilger, Bristol and Philadelphia. Bremond, G., Hizem, N., Guillot, G., Gavand, M., Nouaihat, A., and Ulrici, W. (1989). J. Electron. Mater. 18, 391. Brown, W. J., and Blakemore, J. S. (1972). J. Appl. Phys. 43, 2242. Brunwin, R. F., Hamilton, B., Hodgkinson, J., Peaker, A. R.,and Dean, P. J. (1981).Solid Stare Electron. 24, 249. Butler, N.. Challis, L. J., Sahraoui-Tahar, M., Sake, B., Ulrici, W., and Cockayne, B. (1989). Defects in Semiconductors (G. Ferenczi, ed.), Material Science Forum, Vol. 38.~41,p. 905. Caldas, M., Figueiredo, S. K., and Fazzio, A. (1986). Phys. Reu. B 33, 7102. Chapman. R. A,, and Hutchinson, W. G. (1967). Phys. Reo. Lett. 18, 443.

5. TRANSITION METALSIN III/v

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Ushakov, V. V., Gippius, A. A., and Dravin, V. A. (1983). Sou. Phys. Semicond. 17,743. Van Engelen, P., and Sie, S. G. (1979). Solid State Commun. 30,515. Vasil’ev, A. V., Ippolitowa, G. K., Omel’yanovski, E. M., and Ryskin, E. M. (1976). Sou. Phys. Semicond. 10, 713. Vavilov, V. S., Ushakov, V. V., and Gippius, A. A. (1980). J . Phys. SOC. Japan 49 suppl., 267. Vavilov, V. S., Ushakov, V. V., and Gippius, A. A. (1983). Physica 117B &118B, 191. Vink, A. T., and Gorkom, G. G. P. V. (1972). J. Luminescence 5, 379. Vogl, P. (1985). Festkiirperprobleme (Advances in Solid State Physics) (P. Grosse, ed.), Vol. 25, p. 563. Vieweg, Braunschweig. Vogl, P., and Baranowski, J. M. (1985). Acta Physica Polonica A 67,133. Wasik, D.,Baj, M., and Hennel, A. M. (1986). Phys. Rev. B 34, 4099. Wasik, D., Baj, M.,and Hennel, A. M. (1988). Semi-insulating III- V Materiuls, Malmo 1988 (G. Grossmann, and L. A. Ledebo, eds.), p. 399. Adam Hilger, Bristol and Philadelphia. Wasik, D., Baj, M., and Hennel, A. M. (1989). Proc. of the 19th Int. Conf. on the Physics of Semiconductors, Warsaw 1988 (W. Zawadzki, ed.), p. 1095. Inst. of Physics, Polish Academy of Science, Warsaw. Weber, J., Ennen, H., KauGnann, U., and Schneider, J. (1980). Phys. Rev. B 21, 2394. West, C.L., Hayes, W., Ryan, J. F., and Dean, P. J. (1980). J. Phys. C: Solid State Phys. 13,5631. White, A. M. (1980). Semi-indating III- V Materials. Nottingham 1980 (G. J. Rees, ed.), p. 3. Shiva, Orpington, U.K. Williams, P. J., Eaves, L., Simmonds, P. E., Henry, M. O., Lightowers, E. C., and Uhlein, C. (1982). J. Phys. C: Solid State Phys. 15,1337. Willmann, F., Blatte, M., Queisser, H. J., and Treusch, J. (1971). Solid State Commun. 9, 2281. Willmann, F., Bimberg, D., and Blatte, M. (1973). Phys. Rev. B 7,2473. Wolf, T., Bauer, R. K., Bimberg, D., and Schlaak, W. (1988). Semi-insulating III-V Materials, Mulmii 1988 (G. Grossmann, and L. A. Ledebo, ed.), p. 391. Adam Hilger, Bristol and Philadelphia. Wolf, T., Bimberg, D., and Ulrici, W. (1991). Phys. Rev. B 43, 1OOO4. Wysmolek, A,, and Hennel, A. M. (1990). Acta Phys. Pol. A 77,67. Wysmolek, A., Liro, Z., and Hennel, A. M. (1989). Defects in Semiconductors (G. Ferenczi, ed.), Material Science Forum, Vol. 38-41, p. 827. Yan, Z. X., and Milnes, A. G. (1982). J. Electrochem. SOC. 129, 1353. Yang, X. Z., Grimmeis, H. G., and Samuelson, L. (1983). Solid State Commun. 48, 427. Yang, X. Z., Samuelson, L., and Grimmeis, H. G. (1984). J. Phys. C: Solid State Phys. 17,6521. Yu, P.W. (1981). J. Appl. Phys. 52, 5876. Yu, P. W. (1982). Semi-indating Ill-V Materials. Evian 1982 ( S . Makram-Ebeid and B. Tuck, eds.), p. 305. Shiva, Nantwich, U.K. Zigone, M., Roux-Buisson, H., and Martinez, G. (1986). Defects in Semiconductors (H. J. von Bardeleben, ed.),Material Science Forum, Vol. 10-12, p. 663. Zunger, A. (1986). Solid State Physics (H. Ehrenreich, F. Seitz, and D. Turnbull, eds.), Vol. 39, p. 275. Academic Press, New York.

SEMICONDUCTORS AND SEMIMETALS, VOL. 38

CHAPTER 6

D X and Related Defects in Semiconductors Kevin J . Malloy CENTER FOR HIGHTECHNOLOGY MATBERIALS AND DEPARTMENT OF ELECTRICAL AND COMPUreR ENGINEERING

NEWMEXICO ALBUQUERQUE, NEWMEXICO

UNIWRSITY OF

Ken Khachaturyan CENTER FOR MATERIALS SCIENCE LOS ALAMOSNATIONAL LABORATORY Los ALAMOG, NEWMEXICO

I. INTRODUCTION . . . . . . . . . . . . . . 1. BandDiagrams . . . . . . . . . . . . . 2. Configuration Coordinate Diagrams . . . . . . 11. ELECTRICAL PROPERTIES . . . . . . . . . . . 3. Hall Measurements. . . . . . . . . . . . 4. Persistent Photoconductivity. . . . . . . . . 5. Kinetic Properties and DLTS . . . . . . . . 6. Nonexponential PansientslAlloy Broadening . . . 7. DX in GaAs . . . . . . . . . . . . . . 111. OPTICAL PROPERTIES . . . . . . . . . . . . IV. MODELSOFDX. . . . . . . . . . . . . . 8. Chemical Shifts . . . . . . . . . . . . . V. MICROSCOPIC STRUCTURE OF THE DX CENTER . . . VI. MAGNETIC PROPERnES OF D X : THENEGATIVE-U ISSUE VII. TECHNOLOGY AND DX. . . . . . . . . . . . VIII. SUMMARY. . . . . . . . . . . . . . . . ACKNOWLEDGMENTS . . . . . . . . . . . . REFERENCES. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . .

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . .

235

. . 237 . . 240 . . 243 243 245 247 250 255 256 262 266 267 274 280 284 285 285

I. Introduction

Substitutional donors in compound semiconductors, such as Al,Ga, -,As, show considerable variation from ideal hydrogenic-donor behavior. Initially, models invoked the existence of a donor-defect complex to explain the unusual properties. Later, it became increasingly clear the class of properties 235

Copyright 0 1993 by Academic Press, Inc. All rights of reproductionin any form reserved. ISBN 0-12-7521384

K. J. MALLOYAND K. KHACHATURYAN

236

associated with these complexes, referred to as “ D X centers,” could be ascribed to many purely “substitutional” donors for many multiconduction-band-minima semiconductors. As we shall see, much current research assumes the D X center to be the isolated substitutional donor. More generally, however, the D X center exemplifies the growing class of defects whose properties can only be explained by including interactions with the host lattice. Often, the most difficult aspect of research into semiconductor defects is arriving at an accurate description of the properties of the defect enabling study of the defect by any laboratory. While observations of the optical, electrical, and environmental behavior of a defect form a useful starting point, uncertainty over the necessary and sufficient properties for observation and investigation of the defect can linger for a surprisingly long time. Research on the D X center fully reflects these difficulties. Only when the atomic nature and workings of the defect are understood d o the interpretations of the defect begin to converge. Such explicit atomic-level understanding has been the goal of recent D X studies, along with attempts at first-principles theories of D X centers. However, as of this time, theoretical attempts have failed to explain one or more well-accepted D X properties, and characterization of D X remains incomplete. Moreover, in our viewpoint, understanding D X centers requires an awareness of the variety of materials in which DX-like behavior occurs. As we have passed the 10-year point since the labeling of D X (Lang et al., i979a) and as a considerable body of literature has accumulated since the first review of the field in 1983 (Fig. l), we feel it appropriate to attempt another review. We note that while this chapter was under preparation, another review (Mooney, 1990 J . Appl. Phys. 67, R1) and several special issues of journals devoted to D X centers appeared (see “Special Issue on D - X Centers and Other Defects,” edited by D. J. Wolford, Journal of Electronic Materials, 60 v)

z

: g

50

40

0 Y

0 K

30

w

20

5z

10

m

1970 1980 1081 1982 1985 1984 1981 1988 1987 1088 1989

FIG. 1. Number of entries in Science Citation Index citing Lang et al. (1979a) by year.

6. D x

AND

RELATEDDEFECTS IN

SEMICONDUCTORS

237

Vol. 20 (The Minerals, Metals and Materials Society, Warrendale, Pennsylvania, 199 1) and “Physics of DX Centers in GaAs and Alloys,” edited by J. C. Bourgoin, Solid State Phenomena, Vol. 10 (Sci-Tech publications, Vaduz, 1990). Our chapter begins by detailing the electrical and optical properties of DX in Al,Ga, -,As. After discussing the phenomenological interpretation of the behavior in terms of the configuration coordinate diagram, we turn to an examination of microscopic models for the DX center. We then examine the recent application of advanced analytical techniques in order to determine the atomistic nature of the DX center. We then conclude with a brief description of the technological implications of DX and techniques for circumventing the limitations DX places on semiconductor technology. Throughout our discussion, DX-like behavior in other compound semiconductors will be mentioned. It is ironic to note that a list of semiconductor and donor impurity combinations for which no DX-like behavior has (yet) been observed might prove shorter. In addition to A1,Gal -,As, a fair body of literature details DX centers in GaAs,P, - x (Craford et al., 1968; Craven and Finn, 1979; Ferenczi, 1980; Henning and Thomas, 1982; Calleja et al., 1983, 1985; Kaniewska and Kaniewski, 1988; Khachaturyan, et al., 1991). Other semiconductors where we are aware of DX-like behavior are listed in Table I. Furthermore, semantic misunderstandings often confuse newcomers to this field. For instance, as we shall detail below, DX centers are closely associated with simple substitutional donors, and in all likelihood are the manifestations of substitutional donors under the proper alloy concentration or applied pressure. However, because DX behavior is not always apparent, it may seem that “DX-free” n-type samples exist. This is decidedly not the case in AI,Ga,-,As, as even if DX is not directly observed, it can be detected relatively easily. Therefore, observation of DX-like behavior in these systems asserts that under some specified alloy concentrations and applied pressure, one or more of the properties we will describe in the following sections has been observed for some donors in these semiconductors. 1. BANDDIAGRAMS

Many investigations of DX seek variations with the conduction band structure of the semiconductor. To that end, it is convenient to rely on the coincidental effects of band structure of alloy composition and pressure for compound semiconductors,as illustrated in Fig. 2. Here we show band gaps as functions of pressure for GaAs and as a function of A1 content, x, in Al,Ga, -,As. The similarity is emphasized by examining expressions for the r, L, and X conduction band-gaps at 300 K as a function of A1 mode content

TABLE I DX-LIKEDONORS IN Semiconductor - _

-

GaAs,P,_, (epitaxial)

DX-like Donors

COMPOUND SW(ICONDUCM)RS, OTHER THAN

DX-like under Pressure

S, Te

S

AI,Ga, _,Sb

Te

S

Te

Te, Se

Si Si S

,

CdTe Zn, Cd

-

PYAS,-,

- ,Te

References

-

GaAs,P, -, (bulk, grown by chloride vapor transport) GaSb

Ga,In InSb

Hydrogenic Donors

AI,Ga, _,As

unknown species CI In, Ga, CI

Se

unknown species Ga, In, Br

I, AI A1

Pb,Sn,-,Te

In

Ga, TI

CdF,

In

Y,Gd, Tm

Craven and Finn, 1979 Calleja et al., 1983, 1985, 1986; Ferenczi. 1980 Kaniewska and Kaniewski, 1985, 1988 Craford et al., 1968 Khachaturyan et al., 1991 Kosicki et al., 1966, 1968; Vul et al., 1970; Dmowski el al., 1979 Zhu et al., 1988; Koncewin et al., 1983 Hong et al., 1987 Nojima et al., 1986 Kitahara et al., 1986% 1986b; Watanabe et al., 1985; Yoshino et al., 1984 Yoshino, 1984 Porowski et al., 1974; Dmowski et al., 1982 Iseler et al., 1972; Legros et al., 1978 Burkey et al., 1975; Khachaturyan et al., 1989b Kaidanov and Ravich, 1985; Shimomura et al., 1989 Trautweiler et al., 1968; Lee and Moser, 1971; Piekara et al., 1977; Langer et al., 1979

6. DX

AND

RELATEDDEFECTS IN SEMICONDUCTORS

239

EkVk 0 . 5 4 ~ + 1.57

GaAs

% .-c

2.4

AIAs We Froction, .x

AlAs

: GaAs

2.2

1.6 1.4

Pressure, in kbars FIG. 2. (a) Variation of r-,L-, and X-band energy minima in Al,Ga, -,As as a function of AlAs content, x. The solid line through the experimental points represents the position of the Sirelated DX center in the band gap. The dotted line represents the position of the shallow level (from Chand, et al., 1984). (b) Variation of the r-,L,and X-band energy minima in GaAs as a function of applied hydrostatic pressure. Notice the similarities with Fig. 2a, and also the differences, particularly the lack of a pressure where all three bands are in close proximity.

x, and pressure P in kilobars: E:(x,

P)= 1.42 + 1 . 4 3 ~+ O.O107P,

EgL(x, P) = 1.71 + 0 . 6 6 ~+ O.O055P, EgX(x, P) = 1.90 + 0.125~(1+ 1 . 1 4 ~) 0.00134P.

240

K. J. MALLOY AND K. KHACHATURYAN

We note that for the r and L bands, a 1% increase in alloy content is equivalent to a slightly greater than 1 kbar increase in pressure. However, some situations are not adequately duplicated, such as the close proximity of all three band edges near the r-X crossover in Al,Ga, -,As (x = 37%) as opposed to the corresponding pressure induced crossover in GaAs at 39.5 kbar. Furthermore, while the difference in energy of the r and X bands follows this rule, the decrease in energy of the X band with pressure also distorts the equivalence. In spite of these limitations, applied pressure reduces the number of samples required for an experiment, separates the effect of alloy scattering on the measurement, and eliminates any errors introduced by sample-to-sample variations. In all semiconductors, pressure coefficients remarkably similar to those for GaAs have been observed. An important example of this analogy will become apparent when we discuss the 1985 results of Mizuta et al., showing the characteristic D X electron emission signal in GaAs under pressure.

2. CONFIGURATION COORDINATE DIAGRAMS A configuration coordinate (CC) diagram is a useful tool to describe the properties of defects that induce a change in lattice configuration when their charge state changes. In a CC diagram, the sum of the elastic and electron energy is displayed as a function of some generalized lattice distortion (or configuration coordinate) for the different charge states of the defect. The elastic energy of the lattice is usually taken in the harmonic approximation, and the electron-lattice interaction taken in a linear approximation (Huang and Rhys, 1950), so a CC diagram consists of various parabolas placed in proper position on a total energy as a function of a generalized lattice coordinate plane. The skill comes in ascertaining the relevant states of the system and assigning the appropriate curvature and locations for the parabolas representing those states. Figure 3 depicts a CC diagram displaying total energy of the semiconductor-defect system versus the generalized configuration coordinate. In Fig. 3, the lower curve E,(q) and the upper curve E,(q) represent the empty defect, its electron donated to the valence and the conduction band, respectively; they differ at every lattice coordinate by the band-gap energy, E,, and are centered at the undistorted lattice coordinate, q = O . The middle curve, Ed(& represents the relaxed occupied defect with a minimum total energy at some new lattice coordinate, 4,. Strictly speaking, the top two curves should take into account two additional factors: one, that since E J q ) represents the ground state, E,(q) and E,(q) also consist of a free hole; and two, that the kinetic energy of the hole in the case of E,(q) and of the free hole

t 4

t

i FIG.3. Configuration coordinate showing small lattice relaxation (a) and large lattice relaxation (b). E,(q), E,(q), and E,(q) are the sums of electronic and elastic energy corresponding to the valence and conduction bands and to the occupied DX center, is electronic energy alone (Eq. (2)). E , and E,,, are the thermal respectively, as a function of configuration coordinate q. Ecrectron(q) and optical depth, respectively; E,, and Eeapare electron emission and capture barriers, respectively; E, is the lattice relaxation energy; E , is the hole capture barrier. Kinetic energy contributions to E,(q) (unoccupied D X + and free electron) will blur the exact energy as a function of configuration coordinate.

242

K. J. MALLOYAND K. KHACHATURYAN

and free electron for the case of &(q) should also be included. The kinetic energy effects blur the outlines of E,(q) and &(q) and are ignored here both in the spirit of the Born-Oppenheimer approximation and for the sake of clarity (see the discussion by Baraff, 1986). Another important assumption made here and quite often by others is that the force constant, K , which controls the ”curvature” of the parabolas, remains unchanged upon occupancy of the defect (strictly speaking, one would anticipate a softening upon occupation, as the localized electron is antibonding in nature and screens the bond charge of the defect configuration). The CC diagram is therefore uniquely determined by two parameters, the lattice relaxation energy E , , and the thermal energy, or donor activation energy, E,. The lattice relaxation energy, E , , can be expressed as the elastic energy released by the occupied defect in relaxing from 4 = 0 to 4,. The thermal energy is the difference in total energy gained transitioning from E,(O) to Ed(q,). Note also that &(q) is the sum of E,(q) and the electron energy, E,(q). The electron energy is assumed to follow the linear approximation and has the form

E M = E,

- Eo

+ E , - 2E,q 4r

At the intersection of E,(4) and Ed(& the electron energy is E,, while at the intersection of &(q) and E,(q), E , = 0. Although configuration coordinate diagrams offer a powerful basis for phenomenological understanding of defect behavior, they have obvious limitations. One of the (ongoing) controversies about D X centers is over whether large lattice relaxation (LLR) or small lattice relaxation (SLR) is associated with the occupied defect. An indirect measurement of the degree of lattice relaxation lies in the distinction between the so-called “inner crossing” and “outer crossing” for electron capture from E,(q) into Ed(q).As shown in Figs. 3a and 3b, we see that as E , increases, the E,(q) and &(q) crossing moves from q < 0 to q > 0. This is equivalent to differentiating between SLR and LLR as

SLR: E , < E ,

(inner crossing),

(34

LLR: E, > E ,

(outer crossing).

(3b)

However, no physical distances can be directly extracted from these distinctions because of the approximations inherent in CC diagrams. Accordingly, the arguments over SLR versus LLR are really about small versus large lattice relaxation energies and not distances or lengths. In principle, if we assume a mode of distortion and estimate a force

6. DX AND RELATEDDEFECTS IN SEMICONDUCTORS

243

constant from either LO phonon frequencies (Maguire et al., 1987) or from a knowledge of the bulk modulus (Harrison, 1980), distance can be associated with the configuration coordinate. However, given the force constant and other approximations used in constructing the CC diagram, consistency with experimental observations is only a necessary and not a sufficient condition for validity. Our initial CC diagram describing the properties of D X centers is depicted in Fig. 3b, using a LLR (outer electron crossing) with an outer hole capture crossing as well. As we expand upon the properties of D X , we shall see several enhancements are necessary to explain the experimental data.

11. Electrical Properties

3. HALLMEASUREMENTS

A typical Hall measurement consists of a plot of the logarithm of the Hall electron concentration as a function of the inverse temperature 1/T in kelvins. The slope of such an Arrhenius plot is, strictly speaking, the standard free enthalpy change of an electron transition from a bound state to the conduction band minimum. Typically, because of the complications due to band structure and the uncertain variety of other defects present, the experimentally determined Hall concentration is reported as the free electron concentration and the slope of the Arrhenius plot as E , for DX centers. The first reports of group IV and group VI donor activation energies, E,, in Al,Ga, -,As were the studies of Al,Ga, -,As:Sn by Panish (1973) and Al,Ga, -,As:Te by SpringThorpe et al. (1975). They both noted the deepening of the donor level with increasing A1 content, and SpringThorpe mentioned both similarities to the behavior of S in GaAs,P, -, (Craford et al., 1968) and an apparent connection between the donor level and the L conduction band minima (Fig. 2) (although both of these references assumed an incorrect conduction band ordering in GaAs). This spawned a whole series of papers on the “deep donor” problem in n-type Al,Ga,-,As, and the lessons learned serve as a good example of how difficult it can be to interpret a simple experiment such as the Hall effect. a. Nonequilibrium

As shown in Fig. 4, the logarithm of electron concentration, logn, as a function of 1/T shows a characteristic double slope behavior. The steeper slope, above about 150K, is associated with the D X center as the primary donor present. The region with a shallower slope became the inspiration for

244

K. J. MALLOYAND K. KHACHATURYAN 17

c

'6

5

Y

c

15

ul 0

A

14

13

1Ooorr (K-1) FIG. 4. Logarithm of the carrier concentration as a function of inverse lattice temperature obtained from Hall measurements on a 14.3-pm layer of A1,,,,Ga,.,,As:Si. Labelled on the diagram are the temperature regions showing:(a) freeze-out of deep donor ( D X center), (b) freezeout of the hydrogenic donor in the dark, (c) persistent photoconductivity after illumination at 10 K, and (d) annealing of persistent photoconductivity.

what was first believed to be a chemically distinct shallow donor (Saxena, 1979; Schubert and Ploog, 1984; Watanabe et al., 1984; Chand et al., 1984; ElJani et a!., 1988) usually present in low concentrations. However, Mooney et al. (1987) pointed out that the existence of a kinetic barrier to capture of electrons (as shown in Fig. 3) in the free state into the occupied center prevents equilibrium from being established. Thus, as the temperature is lowered, electron capture is suppressed and the carriers are left in the conduction band. If a shallow level is present, somehow associated with the lowest conduction band, the freeze-out would now occur on this shallow level. However, as we shall discuss later, the shallow level is not a chemically distinct level, but the hydrogenic manifestation of the same substitutional donor. The shallow level can never be made the only donor level present in the bulk material. h. Compensation Ratio

In assessing the magnitude of the free enthalpy of the D X center, the occupation statistics naturally enter into the temperature dependence. However, many authors have failed to properly account for the effects of compensating acceptors, even while claiming to do so. The point arises in assigning an activation energy based on the slope of the electron concentration Arrhenius plot; for uncompensated material (the concentration of shallow acceptors N , = O), the slope is - &/(2kB). For closely compensated materials N , - N , < N , , the slope is everywhere - E,/k,. For the intermediate situation, both slopes will exist, -E,/kB for low temperatures and

6. DX

AND

RELATEDDEFECTS IN SEMICONDUCTORS

245

- E0/(2k,) for intermediate temperatures. The errors take two forms: assuming the absence of compensation in the case of nonamphoteric group VI impurities substituting for As, or assuming that the background acceptor concentration is the same in doped and undoped material. In a series of careful studies of transport properties in doped GaAs, Wolfe and Stillman (1975) showed that the Compensation ratio in doped GaAs was remarkably independent of both doping density and dopant type, for column IV or column VI impurities, at N,/Nd x 0.25. This permits only a small region of - E,/(2kB) slope. Indeed, the lowest reported compensation ratio we are aware of is the results of Colier et al. (1983), with N,/Nd x 0.07. While Wolfe and Stillman (1975) speculated as to the native defect origin of the compensating acceptors, it is clear that with more to gain energetically in the wider gap and more ionic AI,Ga, -,As, the compensation ratio will generally be higher. The issue of compensation arises again when we deal with kinetic barriers in DX centers. Since the number of positively ionized DX centers able to capture electrons will be equal to (assuming charge neutrality) the number of electrons plus the number of acceptors, the kinetic equations governing electron concentration can depend significantly on NJN,,. This issue also arose more recently in attempts to reconcile Hall measurements with the proposed negative4 character of the DX center (Khachaturyan, 1989c; Chadi and Chang, 1988). Again, uncertainties in the compensation ratio (Theis et al., 1989) or an unwillingness to accept a high compensation ratio (Dmochowski and Dobacewski, 1989) prove Hall effect measurements to be inconclusive. Finally, we must point out the difficulties in analyzing Hall measurements in a semiconductor in the presence of multiminima conduction-band and alloy scattering. Saxena (1981), Lee et al., (1980), and Lee and Choi (1988), have carefully analyzed Hall data by treating both band occupation and scattering mechanisms. The preponderance of unknown parameters make it unlikely that a reliable assessment can be made of the compensation ratio, or of the Hall factor connecting the electron concentration measured by the Hall effect with the actual electron concentration. 4. PERSISTENTPHOTOCONDUCTIVITY First reported for Te in AI,Ga,-,As by Lang and Logan (1977) and Nelson (1977), persistent photoconductivity (PPC) is the most singular feature of the DX center. As Fig. 4 shows, upon illumination at low temperature, the free electron concentration in Al,Ga, -,As increases and remains high until the temperature is raised beyond 100-150K. Most researchers now agree the low-temperature PPC of n-Al,Ga,-xAs is due to

246

K. J. MALLOYAND K. KHACHATURYAN

the microscopic capture barrier apparent in the CC diagram of Fig. 3 and directly related to the nature of the defect. Other views held since 1977 included (1) macroscopic inhomogeneities or (2) capture at multicharged defects by overcoming the Coulombic repulsion barrier. Lang (1986) argued against both of these other possibilities by pointing out that the quality and the heavy doping of the samples obviate considerations of sample inhomogeneities as a cause of PPC, and that the capture cross-section of Coulombic repulsive centers is too large and too temperature-independent. Since Lang’s last review, however, the macroscopic barrier model arose again in the form of the effects of a parasitic two-dimensional electron gas (2DEG) (Collins et al., 1983) present in many of the early structures upon which DX studies were conducted. The parasitic 2DEG suggestion answered, albeit temporarily, another difficult question about DX centers. Other than the early study of Nelson (1977)and a report by Kunzel et al. (1983),the mobility measured by the Hall effect increases upon illumination and during the PPC (Saxena and Sinha 1983; Chand et al., 1984). This observation appears contradictory with the supposed donor nature of D X and the understanding that mobility should decrease in the presence of more ionized donors. Yet although studies since Collins et al. (1983) have included undoped spacer layers to eliminate the possibility of 2DEG formation (see Chand et al., 1984, as an example), the mobility increases after illumination are still observed. The most telling report is of mobility increases in bulk n-type, GaAs,P, - x : S (Craford et al., 1968) upon illumination and ionization of D X , clearly showing that the phenomenon is (sometimes) unrelated to heteroepitaxy. Another possible explanation of the increase in mobility after illumination can be based on inferences about sample compensation. In a heavily compensated sample, the number of charged defects increases only sIight after photoionization. O n the other hand, the concentration of free electrons could increase by several orders of magnitude. The resulting substantial decrease in screening length would have a greater impact on electron mobility than the slight increase in the number of charged defects (this mechanism has also been advanced in connection with the proposed negative4 character of DX, which we will discuss later). Thus, in the heavily compensated samples the increase in mobility after illumination should be expected, whereas in lightly compensated samples mobility should decrease. Experimental data d o not yet exist to validate this model. As discussed earlier, compensation in all doped samples depends not on the site of the dopant atom, but on self-compensation typical for all wide-gap semiconductors. The true compensation ratio can only be assessed by a careful analysis of magnetotransport in a multi-conduction band minima semiconductor, already mentioned as a difficult problem. Mobility after illurnination

6. D x

AND

RELATEDDEFECTS IN SEMICONDUCTORS

247

does seem to decrease in Al,Ga, -,As:Te, as reported by Nelson (1977), and increase in Al,Ga,-,As:Si, as reported by Chand et al. (1984), and it is tempting to assert that AI,Ga, -,As:Te is less compensated than Al,Ga, -,As:Si since Te is not an amphoteric donor. However, both Kunzel et al. (1983) and Maude et al. (1987) report mobility decreases upon illumination in Al,Ga, -,As: Si and GaAs: Si (under pressure), respectively. 5. KINETICPROPERTIES AND DLTS

Another issue occurring since Lang’s review has to do with the A1 mole fraction, x (Chand et al., 1984) and pressure dependence (Goutiers et al., 1989) of PPC. As Fig. 5 shows, the magnitude of the PPC effect, as measured in a somewhat arbitrary manner by the ratio of the free electron concentration at 77K in the light to the total donor concentration, shows a distinct concentration/pressure dependence with a peak at x = 0.32 (and the corresponding pressure), and a decrease to small values outside this range. Some authors use the observation of PPC as an indicator of the existence of D X , but as we have indicated, PPC conclusively proves little about the presence or absence of DX centers in a semiconductor. We use the observation of an alloy dependence of PPC as the demarcation

(

1

65

EQUIVALENT A1 CONTENT, X* .32 0.245

0.40

/ ~10.165

Ft

lU’

I-

4

i 3

t

a lop

l$

Si-Doped Al,Gal.,As

10

PRESSURE (kbar)

FIG. 5. Persistent change in electron density An in AI,Ga,-,As as a function of applied pressure after exposure to light at 77 K normalizedto the Si atomic density Nsi. (After Goutiers et al., 1989.)

248

K. J. MALLOY AND K. KHACHATURYAN

between experiments on the equilibrium properties and experiments on the kinetic barriers inherent in the D X center. We start by examining the CC diagram more closely. In addition to the characteristic energies, E , and E , , there are the energies from the configuration minima to the crossing point, E , and E,, for the electron case. These represent the activation barriers to be surmounted before electronic transitions between the states can occur (Fig. 3). Ecaprepresents the activation barrier to capture of a free electron by the relaxed state, and E,, the barrier to emission of an electron from the relaxed state to the conduction band. The general relationship Ecap Eo = E,, holds from detailed balance. These are the thermal barriers restricting equilibrium, and they are crucial to understanding the properties of D X . In a Hall measurement, as previously mentioned, the capture barrier prevents freeze-out at the D X center at low I; changing the slope of the Arrhenius plot. In general, the capture rate depends on the Fermi level position, E,, and can be written as

+

where c, is the capture coefficient in cm3/s, and onis the capture cross-section in ~ r n - ~A,. = N,t.,,/T2 is a constant independent of temperature; N , is the relevant conduction band effective density of states, and 0th is the thermal velocity of electrons in cm/s. The capture barrier enters into the picture through the temperature-activated capture cross-section, on = ooexp( - E,,,/kBT) predicted by multiphonon emission theory (Henry and Lang, 1977). Therefore, the actual slope of the capture cross-section will be -(Ecap + E,)/kB. Similarly, the emission rate depends on the thermal depth, E,, of the D X center, and it can be rewritten as

where g is degeneracy factor). With a similar capture cross-section, an Arrhenius plot will give a slope of - ( E , + E , ) / k , . Usually the capture-cross section is the key experimental quantity of interest. In D X the capture and emission cross-sections can be measured by deep level transient spectroscopy (DLTS) (Lang, 1974) measurements. DLTS attempts to match the temperature-dependent thermal emission process to a fixed reference; after traps are filled, the temperature is increased. The temperature at which the exponental decay of the physical emission process

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249

(as monitored by changes in a depletion region capacitance)matches the time constant set by the spectrometer produces a peak in the output signal. Capture barrier measurements under hydrostatic pressure can distinguish between the SLR (Fig. 3a) and the LLR (Fig. 3b) models of the DX center. The multiphonon emission theory predicts that (in the direct band-gap region of Al,Ga,-,As, when valley is the lowest) in the SLR case, the capture barrier should increase with hydrostatic pressure, while in the LLR case the capture barrier, on the contrary, decreases with hydrostatic pressure. Indeed, the pressure derivative of the capture barrier can be expressed as (Li and Yu, 1987)

where E , and E , are the thermal depth and the lattice relaxation energy of the DX center, respectively, and y is the Gruineissen parameter (Fig. 3). Since the term in square brackets is always positive in the direct band-gap region, the sign of dE,,,/dP is the same as that of Eo - E,. According to the definition of LLR and SLR cases, Eo - E, > 0 for the SLR case and E , - E, c 0 for the LLR case. Therefore dEca,/dP > 0 for the SLR case and dE,,, fdP < 0 for the LLR case. The value of dECap/dPmeasured by Li et al. for the DX center in the direct band-gap region of Al,Ga, -,As value is negative (1987a, 1987b); therefore they conclude that the LLR case holds for the D X center. The negative sign of dE,,,/dP is also consistent with the decrease of Ecapwith A1 mole fraction, observed by Calleja et al., (1988) in the direct band-gap region (see Fig. 7b, later). Distinctions between LLR and SLR can also be made by measuring the hole capture cross-section. For the SLR case, the hole-capture barrier should be very large, much larger than the electron capture barrier (E, >> Ee), and consequently the hole capture cross-sectionshould be much smaller than the electron capture cross-section (cp<< 0,) (Fig. 3a). The opposite, up>> u,,, should be true for the LLR case (Fig. 3b). The experimental values of hole capture cross-section ap for the DX center turned out to be five to seven orders of magnitude greater than the electron capture cross-section a,,. In GaAs,P,-,:S, opz 106a, (Craven and Finn, 1979); in epitaxial GaAs,P,-,:Te, ap x 10’0, (Calleja et al., 1985). Another report on A10.,,Gao.3,As:Te (Munoz et al., 1986) gave ap> lo5a,. Finally, an investigation of the photoluminescence transients associated with the photoionization of D X gave up > 10-16cm2, or op> 106u, at about lOOK (Brunthaler et al., 1989). This extremely large-cross-section for holes clearly supports LLR for the D X center (Fig. 3b). However, there have been several areas of controversy over interpreting

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K. J. MALLOY AND K.KHACHATURYAN

the DX results. While DLTS can be shown to be an exact, spectroscopic measurement of defect state density, fundamental limitations arise because of electrostatic limitations on electric field changes in the measurement volume. These and effects arising from local atomic environment changes around the defect will be discussed next. 6. NONEXPONENTIAL TRANSIENTS/ALLOY BROADENING

DLTS can characterize the capture cross-section by measuring the trap filling time, as reflected in the capacitance transient, as a function of filling pulse duration. In spite of the exponential form of the capture cross-section and the capture rate as expressed in Eq. (7), and of the emission rate in Eq. (8), for DX centers in Al,Ga,-,As (Caswell et al., 1986) and GaAs,P,-, (Ferenczi, 1980) and DX-like In and Ga donors in Zn,,,Cd,,,Te (Khachaturyan et al., 1989b), the capacitance transient appears logarithmic rather than exponential function of time for varying fill pulse duration (Fig. 6). Accompanying this nonexponential behavior is a considerable broadening of the resulting DLTS spectra over the spectra of an ideal level. Two factors have been offered in attempts to model this behavior.

t (-1

FIG. 6. Capture transients at different temperatures (from Caswell et al., 1986): (a) Al, ,,Ga,,,,As:9.8 x l O I 7 Si/cm3, (b) A1,,,Gao.,,As: l O I 7 Si/cm3.

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The first complicating factor in a DLTS measurement on DX centers is their high concentration. Since NDx is the dominant ionizable impurity, the capacitance changes by more than 10%during a DLTS experiment. This is caused by large increases in the free electron concentration, which in turn lead to significant movement of the Fermi level as emission proceeds. The capture rate in Eq. (7) depends directly on the Fermi level (for instance, if the Fermi level moves into the conduction band, the capture barrier is reduced) and the capture coefficient becomes concentration-dependent. The logarithmic capture behavior was successfully modeled by Caswell et al. (1986), who in addition to accounting for the factors mentioned above, made two other ad-hoc assumptions to fit the data: (1) only the electrons in the L minimum are allowed to recombine, and (2) the recombination occurs only via capture of an electron into a resonant state of the DX center. As the recombination proceeds, the number of carriers in the r valley decreases, the quasi-Fermi level drops to the bottom of the r minimum, and its separation from the bottom of the L minimum increases. Since a conduction electron must first be excited to the L valley before it can be captured, the downward shift of the quasi-Fermi level results in increase in capture barrier as predicted in Eq. (7). The effect can be significant:The quasiFermi level drops by more than 50 meV when the electron concentration in (Caswell the conduction band drops from n = lo'* cm-3 to n = 10'' and Mooney, 1989). That shift results in an increase in the capture barrier by more than 50 meV by the end of the capture process in a sample doped to the n = lot8cm-3 level. The increase in capture barrier leads to slowing down of capture after most of the conduction electrons have already been captured, leading to the nonexponential, logarithmic capture behavior. The typical broadening factor needed was 45 meV, independent of N D x . The observed DLTS spectra are considerably broadened over the theoretical spectra for a single level. In some situations, separate contributions to these broadened peaks can be resolved. Alloy disorder is often cited as the origin of these effects. In a random alloy, a defect will have different local environments. This randomness was assumed to phenomenologically broaden the distribution of trap energies in CraAs,P, -, (Omling et al., 1983), In,Ga, -,P (Yoshino et al., 1984), and for DX in Al,Ga, -,As (Caswell et al., 1986; Mooney et al., 1987), and directly led to a broadening in the DLTS emission spectra and of the capture transients. The capture process was similarly treated by Kaniewska and Kaniewski (1985) and applied to GaAs,P, -,:Te (Kaniewska and Kaniewski, 1988). Legros et al. (1987) and Bourgoin et al. (1988) noticed that exponential

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transients were observed under optical, as opposed to thermal, stimulation of electron emission (Calleja et al., 1985, 1986a; Munoz et al., 1986), and they have tried to explain the broadening and nonexponential transients using only Fermi-level variations without alloy broadening. However, experimental evidence now exists that supports alloy rather than band-structure effects as the origin of multiple DLTS peaks from the DX center in AI,Ga, -,As. The role of the alloy disorder was demonstrated by Mooney et ul. (1989a), who showed that while there is only one peak from the resonant D X center level in heavily doped GaAs:Si at E,, = 0.33 eV, two additional peaks, both with E,, = 0.43eV, appear starting from AI mole fractions as low as 494. These two peaks increased at the expense of the peak at E = 0.33 eV when the Al mole fraction was increased. Finally, at x=O.19, the E,,, = 0.33 eV peak completely disappeared. Note that the DLTS peaks shifts in discrete steps in the dilute alloy as x is increased, showing that it is the alloy disorder rather than the band structure that causes the shift. Most strikingly, the weight of the E,, = 0.43 eV peak is very much greater (factor of 6 for x = 0.04) than one might expect from the assumption that Al and Si are randomly distributed. One possible explanation of the data is a preferential tendency for Si atoms to be incorporated near Al. Another explanation (Baba et al., 1986; Morgan, 1989) is simply that the lower energy of the E,, = 0.43 eV peak receives a larger electron population during the DLTS fill pulse. This explanation is consistent with the direct experimental observation by EXAFS (Sette et al., 1988) of preferential incorporation of S near Al in AI,Ga, -,As:S. An alternative explanation by Morgan (1989) is based on the assumption that Si moves towards an interstitial site upon electron capture. This assumption, however, contradicts the direct structural data, discussed later in this review. The most dramatic demonstration of preferential association of Si donor with more electronegative group 111 elements in Al,Ga, -,As comes from the boron doping experiments (Li et al. 1989a). As little as 2 x loi8B/cm3 in GaAs:2 x lo’’ Si/cm3 resulted in the complete disappearance of the DLTS signal from pressure-induced D X centers with E,, = 0.30eV and Ecap= 0.22eV, strongly suggesting that all Si had formed complexes with B. These complexes gave rise to two new DLTS signals with E,, = 0.18 eV, Ecap= 0.16 eV, and E,, = 0.14eV, Ecap= 0.09 eV. Baba et al. (1989) solved the problem of identification of individual DLTS peaks of resonant Si D X center with specific local environments of Ga and Al second nearest neighbors. To obtain well-defined environments of the Si DX center, Baba used a sample consisting of one monolayer of AlAs and 14 monolayers of GaAs, made repeatedly to a total thickness of 3,000 A. Si was doped in the center part of 10 monolayers of GaAs and occupied three well-

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Al mole fraction (a)

& 0.4 -& 0.3 g 0.2 -

50.5 %

0

Y

L

e

___--J--

a

go

&+-"-

/4.aN*--

t go.1a 0

(b)

FIG. 7. (a) Thermal emission barrier and (b)capture barrier of the Si-DX center in AlGaAs, obtained from DLTS measurements. Samples measured under pressure have been represented using an equivalent A1 mole fraction given by the energy distance between the two lowest conduction band minima (from Calleja et al., 1988).

specified sites. Si donors deep in the binary GaAs layer occupied site A, with only Ga atoms as second nearest neighbors. Si donors adjacent to and within the AlAs monolayer occupied sites B and C , respectively, with four A1 atoms as second nearest neighbors (in different arrangements). Each site produced a distinct DLTS peak with an exponential transient, well-defined emission barrier and formed a distinct energy level. The emission barrier and the energy level of each of the three resonant DX centers were E,, = 0.32 eV and EDx- E , = 0.295 eV for site A; E,, = 0.40 eV and E D , - E , = 0.245 eV for site B; E,, = 0.43 eV and E D x - E , = 0.225 eV for site C .

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K. J. MALLOYAND K. KHACHATURYAN

In spite of the complications, several observations about the kinetic properties of D X can be made. We have already mentioned the pivotal observation of D X by DLTS in GaAs under pressure (Mizuta et al., 1985), but Theis et al. have observed D X in x < 0.2 Al,Ga, -,As (1986) and in heavily doped GaAs at atmospheric pressure (1988). Theis goes on to discuss the properties of resonant D X in low-x AI,Ga, -,As, including its influence on limiting the maximum electron concentration in GaAs. Many authors (Theis et al., 1988; Calleja et al., 1988; Mooney et al., 1986) have concluded from experimental evidence that the capture process involves two steps: a promotion to the L conduction band minima, and then capture into DX over an Al-concentration-independent barrier. Similarly, the emission barrier is independent of A1 content (and therefore pressure) (Fig. 7a). A lesson we can apply to the CC diagram is that the curve representing Ecap in Fig. 3b represents the L or X conduction band, not necessarily the lowest conduction band (r for Al mole fraction <0.37). Therefore, we need to add another configuration parabola, lower in energy by the T-L band separation, to account for this, as shown in Fig. 8. This new CC diagram will have implications for the optical properties we will examine in the next section.

Fic. 8. Configuration coordinate diagram modified to take into account the possibility that capture occurs via the L valley (large lattice relaxation case). E&), E,(q), and E,(q) are the sums of electronic and elastic energy corresponding to the electron in the r and L valleys of the conduction band and on the DX center, respectively, as a function of configuration coordinate. is the energy separation between the bottoms of the r and L valleys, and E,, is the capture barrier of an electron from the L valley into the D X center. The capture barrier of an electron from the valley is then the sum ArL+ Ec,. E,,, and E,, are the optical depth of the DX center and its emission barrier, respectively.

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This assumption of thermal emission to higher-energy band minima has been invoked before to explain PPC (Iseler et al., 1972; Vul et al., 1970) and the discrepancies in separate measurements of E, and E,, in other GaAs traps (Majerfeld and Bhattacharya, 1978). While it may hold that D X is tied to the L conduction band minima, the results of Shan et al. (1989) loosen the restriction. Upon studying the DLTS spectra of Al,Ga, -,As:Te under pressure, they found the pressure derivative of the capture and emission energy barriers for DX changed sign at the direct-indirect crossover, indicating that thermal emission and capture switched from the L to the X conduction band. Since the pressure derivatives of the L and X bands are of opposite signs (Eq. (l)), the experimental interpretation is straightforward. In fact, for DX centers in GaAs,P,-,, studies seem to show a much closer connection between DX and the X minima (Craford et al., 1968; Craven and Finn, 1979; Calleja, et al., 1985). The consequences of this mixing are not drastic for our conclusions with respect to capture and emission barriers; instead, we observe that DX seems associated with either of the high densityof-states indirect minima. Recent investigations of the possible negative4 characteristics of DX centers (Theis et al., 1991) suggest a different reconciliation of the discrepancy between the relationship Ecap E , = E,, and the actual measurements for DX without invoking an L-state transition. If two electrons were captured or emitted per kinetic event, Ecap E , = E,, would be experimentally satisfied. Again, however, the negative4 model as currently formulated contradicts a key magnetic experiment.

+ +

7. D X

IN

GaAs

There are interesting implications for the existence of DX in GaAs and in AI,Ga, -,As for x 0.22. At these x values, E , < 0, or, in other words, D X becomes resonant with the r conduction band. The first reported observation of resonant D X in GaAs might be traced to the original studies of n-type GaAs under hydrostatic pressure of Paul (1961) (we are indebted to E. Weber for pointing this connection out). In that study, resistivity as a function of pressure showed a significant increase at about 25 kbar of applied pressure. This was attributed to transfer to an indirect band, but now we know that the direct-indirect crossing occurs at 38.5 kbar, not at 25 kbar. In retrospect, the cause of the increase in resistivity below the T-X crossover is incomplete ionization of the DX center, as its energy level is no longer resonant with the conduction band but occurs in the energy gap. Normally, such resonant levels are assumed to be energetically broadened because of their very short lifetimes before scattering into another state at the same energy. However,

-=

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K. J. MALLOYAND K. KHACHATURYAN

Hjalmarson and Drummond (1988) argue that for LLR, such states can have long lifetimes. In this situation, since E , < E,, and the electron energy is in a region of zero density of states, recombination is impossible. As mentioned earlier, the first modern observation of deep donors in GaAs under pressure analyzed in terms of D X was the DLTS study by Mizuta et al. (1985). Not only can D X be observed under pressure in GaAs when it becomes nonresonant (Mizuta et al., 1985; Li et al., 1988), but for doping levels high enough to partially occupy D X in low-x Al,Ga,-,As at atmospheric pressure, the characteristic DLTS emission spectra can be observed (Theis et al., 1986). Theis et al. (1988) also proposed that this resonant D X level functions as a concentration-limiting mechanism for heavily doped GaAs; since the degenerate electrons and the concentration of resonant D X levels originate from the same donors, any increase of the Fermi level will be pinned by occupancy of the resonant D X at an equivalent ~ . observation that InP, with twice concentration of about 1.1 x 10'' ~ m - The the T-L separation, can be doped to an electron concentration an order of magnitude higher than that of GaAs (Baumann et al., 1976; Hawrylo, 1980) supports the suggestion of such a mechanism. However, given the finding by Sallese et al. (1990) placing the Te-related D X center well above the Si-related D X center in GaAs, the apparent equality between the maximum electron concentration in GaAs:Si and GaAs:Te is puzzling unless the Te-DX and Si-DX levels have different pressure coefficients.

111.

Optical Properties

Optical studies of defects with lattice relaxation provide information complementary to thermal studies since, if the Frank-Condon principle holds and the transition occurs fast with respect to the lattice rearrangement, the optical transitions occur at constant configuration. At a given temperature, the vibration amplitude is defined by the number of occupied phonon modes above the ground state. However, even at 0 K, an optical transition is broadened because of the zero-point vibrations. When we examine the candidate CC diagrams in Fig. 3, we note that optical absorption (or photoionization) energy, En, is equal to E , + E,. The optical studies of D X have involved three basic types of experiments: photoionization of D X , photoluminescence associated with D X , and far IR studies of D X in the ionized state. Photoionization has proven to be the most contentious and the photoionization threshold the most widely varying parameter. Photoionization experiments usually involve monitoring the photocapacitance or the photoconductivity of a sample as a function of the

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energy of the incident light. The optical cross-section is given by the optical emission rate divided by the photon flux and is plotted as a function of wavelength (see Fig. 9 for an example). It can be fitted by several similar theories (Lucovsky, 1965; Grimmeiss and Ledebo, 1975; Jaros, 1977), which predict the photoionization threshold and the phonon mode involved in lattice relaxation. Using this formalism, Lang et al. (1979a) found an optical photoionization threshold of En = 0.85 eV for Al,Ga, -,As:Te. The threshold was independent of A1 concentration and exhibited thermal broadening. The fitted phonon frequency was 10 meV. Thus, Lang (1986)was able to offer a complete picture of the DX; the phonon involved in the lattice relaxation was shown to be a low-energy TA acoustic mode. Also, the large photoionization threshold (En > E,) was consistent with LLR and with the kinetic barriers as determined by DLTS. A pivotal experiment, reported in 1984, began to show other aspects of the DX center. Theis et al. (1984), observed using far-IR transmission that upon illumination at low temperature, a transition characteristic of a 1s-2p transition in a hydrogenic donor was observed in Al,Ga, -,As:Si. As we mentioned previously, Hall and PPC studies implied the existence of a shallow state, observable if occupied and if capture was thermally suppressed, but the implication of Theis’s results was that D X itself was the source of the hydrogenic donor since it was only detectable after D X was (partially) emptied.

0.001 0.8

1.2

1.6

2.0

Photon Energy (eV) FIG.9. Normalized photoionization cross-section as a function of photon energy at T = 84 K for three samples of different alloy composition (from Legros et al., 1987).

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K. J. MALLOYAND K. KHACHATURYAN

Confirmation and extension of Theis's observations came with the same experiment performed on lightly doped, indirect-gap Al,Ga, -,As:Si (Dmochowski et al., 1988). The far-IR absorption detected was metastable, as it lasted for over a day after the optical emission ceased. The concept that D X had a metastable configuration was familiar from other impurity studies (Benton, 1989).This complements the reverse process, observed by Mizuta et al. (1985) at about the same time, whereby an isolated hydrogenic donor was converted to the D X center in heavily doped GaAs under hydrostatic pressure experiments (Li et al., 1987a, 1987b; Maude et al., 1987). Both lowtemperature PPC and the characteristic D X DLTS signal were observed from n-GaAs under hydrostatic pressure. Other optical investigations cast doubt on this straightforward interpretation. Henning and coworkers (Henning et al., 1984, 1988; Henning and Ansems, 1988) observed broad donor-acceptor pair (DAP) photoluminescence (Fig. 10)for AI,Ga, -,As:Si for x > 0.22. Their spectra, while similar to the donor-related luminescence observed by Dingle et a!. (1977),contained an additional peak approximately 200 meV below the L minima. The lineshape can be decomposed into a sum of three Gaussians with a separation of 48 meV, the LO phonon energy. The connection between the broad donor-acceptor photoluminescence in AI,Ga, _,As:Si and the D X center could be established from several observations. First, the broad DAP band appears only in the samples with x > 0.22, and its intensity grows with increasing Si concentration. Second, the energy separation of the broad DAP band from the L minimum of the conduction band was independent of A1 mole fraction, a feature already

FIG. 10. Photoluminescence spectrum of A1,,,.@3,,6&:Sl h o = 2.00eV, P = 1.5 W / m 2 (from Henning and Ansems 1987a).

at T

=4

K. Excitation:

6. DX AND RELATEDDEFECTS IN SEMICONDUCTORS

259

mentioned as characteristic of the D X center. Also, the photoluminescence intensity could be enhanced by selective excitation to a feeding level, tied to the L minimum of the conduction band. According to Henning and Ansems (1987a), the strength of coupling of the DX center to the lattice can be estimated from the width of the donor-acceptor photoluminescence curves and the spacings between the phonon replicas. The width of the donoracceptor pair photoluminescence line, AE, can be expressed through the Huang-Rhys S factor (Huang and Rhys, 1950), defined previously in connection with E,, on Fig. 3, which characterizes the strength of the electron-phonon coupling:

AE = h o [ S ( 2 n , + 1)]1’2,

(7)

where ho is the energy of a phonon mode with which the defect couples, and the average number of thermally excited phonons n,, = [exp(hw/kT) - 13 The energy of the phonons can be obtained from the spacings between the phonon replicas. The ratio of the width of the DAP line to the spacing between the phonon replicas would yield the Huang-Rhys factor of the defect. From the aforementioned photoluminescence data, S = 0.5 was determined, and a lattice relaxation energy E, = S h o of 25 meV, considerably different than the E, = 750 meV obtained from the photoionization and kinetic measurements. There are two points to consider. There is no evidence that the phonon giving rise to the replicas in the photoluminescence spectrum is the same phonon responsible for the lattice distortion in D X . Indeed, the temperature dependence of photoionization spectra and the capture crosssection point to soft TA phonons; typically, photoluminescence can only detect coupling to optical phonons. Furthermore, there is the question of just what state is emitting light. At low temperature and under illumination, presumably very few un-ionized DX centers remain, with a resulting short radiative lifetime. Zigone et al., (1989) doubt the identification of the broad DAP photoluminescencein A1,Gal -,As with D X centers. His conclusion is based on the photoluminescence studies of GaAs:Te under hydrostatic pressure, where Te is expected to form DX centers. Like Henning, he observed a broad DAP photoluminescence band, the intensity of which scaled with the donor concentration. The energy of the band, however, did not follow the L valley of the conduction band. At pressures below 38 kbar, the luminescence band followed the r minimum, shifted down from it by 300meV. At higher pressures the band followed the X minimum, shifted down by 360 meV. At atmospheric pressure, the energy of the photoluminescence band is 1.21 eV, an often-observed band believed to arise from a complex of a donor impurity and a gallium vacancy, the vacancy acting as singly charged acceptor (Williams, 1968; Williams and Bebb, 1972; Birey and Sites, 1980;Chiang and

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Pearson, 1975). Such a donor-vacancy complex may be responsible for selfcompensation of n-GaAs (e.g., Wolfe and Stillman, 1975) and is in general typical for ionic semiconductors (see the earlier discussion). Results on GaAs : Si were similar to those on GaAs : Te. If the broad photoluminescence band is attributed to the D X center (Henning, and Ansems, 1987a, 1987b, 1988; Henning et al., 1984, 1988), the low value of E , from the DAP photoluminescence would indicate a moderate lattice relaxation, not the LLR previously proposed. The missing piece in the SLR (or moderate lattice relation) theory was the photoionization threshold; the 0.85 eV threshold observed by Lang was absolutely incompatible with SLR. Legros and coworkers (1987) essentially rechecked Lang’s data using Al,Ga, -,As:Si instead of Al,Ga, _,As:Te where the larger E , of Si D X centers permitted observation of photoionization over a wider temperature range. The results supported Lang; En = 1.2eV for Si in Al,Ga,-,As of 0.22 < x < 0.74. This prompted a rejoinder from Henning and Ansems (1987b), showing evidence in A1,,,,Ga,,,,As:Si of a threshold at 0.2 eV. Another IBM group repeated the experiment on AI,Ga, -,As:Si using more intense long-wavelength sources, and again the experimental results supported the original observations (using a different equation for the crosssection and taking into account the alloy-broadened distribution of states, they came up with a still larger value for En, 1.4-1.8 eV). Finally, the Philips group exchanged samples with IBM and reported (Henning and Ansems, 1988) two distinct ionization thresholds, one at 0.2-0.3 eV, and one at 0.7 eV. Accompanying these thresholds were markedly different transient behavior. The low-energy threshold exhibited small, fast photocapacitance transients, while the high-energy threshold exhibited large, slow transients characteristic of PPC. All of this prompted Henning et al. (1989) to call the DX “doublefaced,” with two configurations, one metastable and exhibiting SLR, and one exhibiting LLR. The issue is by no means settled. The observation of fast, nonpersistent photoconductivity has been made by Schubert and Ploog (1984) in heterojunction structures. However, they chose to analyze the transients on the basis of tunneling-assisted trap recombination at the heterojunction. On the other hand, supporting evidence exists in other materials; Fig. 11 shows a quick jump in resistivity, followed by a gradual slow increase observed at 77 K in Zn,Cd, -,Te:In or Cl (Khachaturyan et al., 1989b), the ratio of the magnitudes of the quick and slow transients being sample-dependent. More remarkably, S is responsible for several types of relaxation of electron concentration in GaSb. Photoconductivity of GaSb: S has the transient and persistent parts (Dmowski et al., 1979; Vul et al., 1970). The slow process is thermally activated. Yet a number of errors can creep into such measurements, the most critical being ensuring that the transients are from DX

6. DX

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RELATEDDEFECTS IN SEMICONDUCTORS

1

2

3

261

4

Time (min) FIG. 11. Resistance transient of the sample of Zn,,,Cd,,,Te:In at 77 K after illumination is switched off. An initial small positive jump in resistance is followed by a slow (lasting for many hours) increase in resistance with time (from Khachaturyan et al., 1989b).

centers and not from some other background impurities. The LLR proponents can rely on the measurement of Merz et al. (1979),who observed the predicted saturable absorption occurring at the LLR proponents’ photoionization threshold. As the intensity of light increased at wavelengths above the photoionization threshold, DX was emptied and the absorption coefficient decreased. In our opinion, this is a key experiment associated with any attempt to measure the photoionization threshold of DX, as it provides the assurance that DX is indeed being measured. The SLR proponents have only the correlation of threshold with photoluminescence energy as proof DX is being measured. Additionally, the low threshold energy cannot be attributed to the hydrogenic metastable state, since the observed lattice relaxation energy is too large to be consistent with a truly shallow level. A new insight in a possible cause for the LLR-SLR controversy was provided by the recent DLTS study of A,,,,Ga,,,,As: Si under strong illumination (Jia et al., 1990). They discovered a new trap, populated by illumination, which is shallower than DX, with emission and capture activation energies 0.2 eV and 0.17 eV, respectively. The maximum achievable concentration of these donors was comparable with that of DX centers in the dark. The existence of shallow donors explains the observation of transient photoconductivity with the fast decay time constant at helium and nitrogen temperatures, coexisting with the later slow decay due to DX centers (see earlier discussion). Accordingly, we are left with the possibility that other metastable states of DX exist that reconcile the optical properties of DX: the “normal” configuration possessing an equilibrium LLR configuration and a metastable hydrogenic configuration, and a second defect occupied only under illumination and possibly possessing a SLR configuration.

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K. J. MALLOY AND K. KHACHATURYAN

IV.

Models of DX

The original model of Lang et al. (1979a) invoked a complex of the donor atom and an unknown intrinsic defect, such as a vacancy, together with the theory of multiphonon emission to account for the large lattice relaxation. Although Lang (1986) later speculated on the interstitial-like properties of D X , for a number of reasons, the model of a complex consisting of an accompanying “X” for a substitutional “D” has fallen out of favor. For one, D X is remarkably ubiquitous in all p-type AI,Ga, -,As, regardless of growth method or other processing steps, and, upon closer examination, appears to occur quite frequently in most other semiconductors. Most assume that the occurence of vacancies (as well as other intrinsic defects) should depend in some fashion on the growth method and processing of the sample. For example, LPE growth from a G a melt favors the appearance of As vacancies. If, indeed, As vacancies are needed for formation of the D X centers, at first glance the DX center should be abundant in LPE-grown Al,Ga, -,As and less so in MOCVD- or MBE-grown samples. However, it turns out that occurrence of D X centers is independent of growth techniques. Also, for the same method and conditions of growth, both As-site group VI donors and Ga-site group IV donors give rise to D X centers. The concentration of D X centers is never insignificant compared to the concentration of dopant atoms. In reality, for A1 mole fractions between 35% and SO%, almost all the donors form the DX centers. The most telling point was made when what were thought to be hydrogenic donors in GaAs:Si and GaAs:Sn were shown to have the properties of D X centers (Mizuta et al., 1985; Li et al., 1987a, 1987b; Theis et al., 1988). Local vibrational mode experiments on GaAs:Si under pressure then showed that almost all Si donors are overwhelmingly substitutional on Ga sites (Maguire et a!., 1987). Similarly, donors in n-InSb (Porowski et al., 1974); In, Ga, and Br in CdTe (Iseler et al., 1972);and Te and Se in GaSb behave as hydrogenic shallow donors at atmospheric pressure, but are converted to a deep DX-like state under hydrostatic pressure (Kosicki et ul., 1968). These proved (intuitively) difficult to reconcile with D X as a complex involving an arsenic vacancy. However, not all have accepted these arguments. Van Vechten (1985) points out the high equilibrium concentration of As vacancies in any GaAs sample, and observes that the critical compensating defect may only be a weak function of growth condition. Additionally, Farmer et al. (1988) have seen sample-dependent DLTS spectra, also implying the existence of some sample-dependent accompanying defect. Intriguing hints of the elimination of the “X” components, such as Lang et al.3 (1979b) early work on D X and dislocation climb, and the recent work of Basmaji et al. (1989), continue to surface. In spite of its success in explaining the kinetic and optical properties of D X ,

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the Lang (1986) model left the very obvious connection between DX and the band structure (see Fig. 3) largely unexplained. On the other hand, a number of purely electronic models of DX (arising from the “deep donor” problem) in Al,Ga, -.As were developed that primarily addressed the band structure dependence of E,, leaving the kinetic and optical properties less precisely clarified. In general, DX models may be categorized in any number of ways. However, we choose to follow the historical route and explicitly call out two contributions to the total energy of DX. Therefore, we express the Hamiltonian for the D X center as

where Htot is the total Hamiltonian, He, is the Hamiltonian describing the electronic system, and Hel.latdescribes the interaction between the electron and lattice. If a model attempts to consider both components, inevitably one or more are the subject of considerable simplifications. If a model considers one portion in full detail, one can legitimately question how the results would change with the other components. The ultimate arbiter might be the results of an ab-initio total energy calculation treating the lattice dynamics and electron energy in a self-consistent, large-scale computer calculation. The state of the art of this approach is exemplified by the work of Chadi and Chang (1989). Thus, several purely electronic theories of DX exist, with the concomitant implication of SLR. These include the original theory of Hjalmarson and Drummond (1986) and the work of Yamaguchi (1986). One of the most durable is the multiminima effective mass theory, which follows the ramifications for the hydrogenic approximation on HeIfor multiple and degenerate conduction band minima (Resca and Resta, 1982; Bassani et al., 1974; Chand et al., 1984). Briefly stated, the intervalley coupling between the T-L, T-X, and L-X conduction band minima, and the intravalley coupling between the four degenerate L minima and between the three degenerate X minima, lowers the energy of the appropriate symmetry hydrogenic state to the point where it can have a significant binding energy (strictly speaking, the proximity of both the X, and X , minima in many III/V alloys requires that both be included). At this point, a shallow-deep electronic instability is invoked to explain the rest of the properties of DX centers (Bourgoin and Mauger, 1988). Such theories are appealing, since they readily explain the data displayed in Fig. 2. A supercell-based calculation from first principles (Yamaguchi, 1990) has recently been reported. The donor energy as a function of distortion modes of different symmetry was reported. It was found that the minimum energy configuration corresponded to a small (few percent), fully symmetric A, mode

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K. J. MALLOYAND K. KHACHATURYAN

distortion. The model explained the donor thermal energy as a function of x and pressure, and explained the large optical ionization threshold as the first step of an internal A,-to-T, photoionization process. However, the model did not account for the large kinetic barriers exhibited by DX. A theory including some aspects of both Hamiltonian components is the displaced donor model of Morgan (1986). Here a complete account of the electronic states of a substitutional donor in a multiconduction band minima system is developed, followed by a Jahn-Teller-type interaction of the degenerate T2 hydrogenic state derived from the L valleys of the conduction band, with the lattice. Morgan makes a further assumption that the JahnTeller vibronic mode is trigonal, effected by an off-center displacement of the donor atom. However, as we shall discuss, structural studies do not support this type of relaxation. The phenomenological models such as that used to derive the CC diagram or Emin-Toyazawa extrinsic self-trapping attempt to derive general qualities and they seem applicable to the general DX situation. Let us from consider the phenomenological theory of extrinsic self-trapping, independently proposed by Emin and Toyozawa. The extrinsic self-trapping theory explains how acoustical distortions of the lattice can convert an isolated hydrogenic donor into a deep donor and accounts for the phenomenon of PPC (Emin and Holstein, 1976; Toyozawa, 1978). The theory treats the electronic energy, H e , , in the tight binding approximation and considers shrinking of the electron wavefunction size from the Bohr radius (hydrogenic donor) to the bond length a, (DX-like donor). The driving force for shrinking of the wavefunction is the joint action of the potential well created by lattice distortion and the electron-ionized impurity interaction. This process is similar to the creation of a polaron (called intrinsic self-trapping), where an electron, through its interaction with the lattice, digs itself a potential well and must move together with the lattice distortion. The main difference, however, is that the polaron is created by Coulombic interaction of the electron with polarization of the lattice. Thus, polarons occur only in the most ionic compounds, such as I/VII compounds, whereas the DX-like defects are created by interaction with acoustical phonons and can occur in covalent or weakly ionic compounds. This difference is important. Whereas a Coulombic interaction, however weak, can always create a bound state, the situation is completely different when the potential well is created by short-range forces, such as an acoustical distortion of the lattice. In the latter case, the magnitude of the short-range potential well must exceed a certain threshold to trap an electron from the conduction band. If the short-range potential well is too shallow, the kinetic energy increase due to localization of the electron in the well would exceed the potential-energy decrease. As a result, it is energetically unfavorable for

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an electron to become localized in a shallow potential well. The acoustical distortion, therefore, must be large enough so its potential well can bind an electron. Until the electron is bound, the increase in elastic energy upon distortion is not offset by the electron-phonon interaction. A threshold acoustical distortion must be reached to enable capture and localization of the electron. Once the electron is bound, then further distortion would be stabilized by electron-phonon interaction. In other words, the donor electron can be considered as antibonding, and its localization on the donornearest neighbor bonds would result in lengthened bonds. These ideas can be expressed quantitatively in a simple phenomenological theory. The expression for the energy of the DX-like donor can be obtained by trial function quantum mechanical analysis. The total energy of the defect and the electron can be expressed as a function of the electron wavefunction localization radius, a,:

E = B r:)2-(V+Eop)

(:)-(U+E.,)

3 ):(.

(9)

Here B represents the kinetic energy of the electron completely localized within the bond length distance a,. B is of the order of conduction band width. V and U are the Coulombic and central cell components of the impurity potential, respectively. E,, is the polaron term, the electrostatic interaction energy of the electron with the polarization of the lattice. Finally, E,, is the interaction energy of the localized electron with acoustic deformation, Y2

where 5 is the deformation potential and K is the force constant. Analysis of Eq. (12) enables one to construct a phase diagram (Fig. 12). The impurity potential U can be of critical importance in determining whether the donor is DX-like or hydrogenic. For example, in bulk GaAs,P, -, grown by chloride vapor phase transport, Te is a hydrogenic donor for all alloy compositions (Craford et al., 1968; Khachaturyan et al., 1991a), unlike epitaxial GaAs,P, -,: Te (Henning and Thomas, 1982; Calleja et al., 1983, 1985), but S is always a DX-like bistable donor. In GaSb, S is a DX-like donor, but Te and Se are hydrogenic and become DX-like only under hydrostatic pressure (Kosicki, 1966,1968).In Gao.szIno,48P, S is a DXlike donor (Kitahara, 1986a, 1986b),but Se is a hydrogenic donor (Watanabe, 1985). In Zn,Cd, -,Te and CdTe under hydrostatic pressure, In, Ga, Br, and

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K. J. MALLOYAND K. KHACHATURYAN

g,

(W+E&B+

FIG. 12. Regons of stability of free conduction electron (F)of a completely localized electron (S) and the regions of shallow-deep bistability F(S) and S(F) derived from the extrinsic selftrapping theory. In the F(S) region, the free electron is the ground state, while the localized electron is the excited state. The contrary is true for the S(F) state. Parameters determining the diagram are defined in the text (from Toyozawa, 1978).

C1 are DX-like donors, whereas I and A1 are hydrogenic donors (Iseler et al., 1972; Khachaturyan et al., 1989b; Burkey, 1975). These differences in behavior can be understood. The greater the electronegativity difference between the donor atom and the original host lattice atom, the greater the short-range impurity potential (central cell correction). For GaSb and GaAs,P, -,, S is more electronegative than Te, and therefore the central cell correction for S donor is greater than for Te donor. Therefore, S is more likely than Te to exhibit DX-like behavior. Greater electronegativity of S compared to Se explains why S is the DX-like donor in Gao,521no,48P, while Se is a hydrogenic donor. Similarly, in CdTe under hydrostatic pressure and in Zn,Cd,-,Te, A1 is the most metallic and therefore the least electronegative element of the Cd-site group I11 donors, and I is the least electronegative element of the Te-site donors. One would therefore expect the central cell correction for A1 and I donors is smaller than for the other donors, and they are least likely to show the DX-like behavior.

8. CHEMICAL SHIFTS In n-Al,Ga,-,As, all donors form DX centers. However, differences in electronegativities of different donors leads to chemical shifts of thermal and optical energies of the DX center and the barriers for emission and capture (Lang and Logan, 1979). The variation of the kinetic barriers of DX with donor species was reported by Lang and Logan (1979) and Kumagai et al. (1984).The emission barriers for the column IV donors in Al,.,Ga,,,As were

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found to decrease from 0.43 eV for Si to 0.33 eV for Ge to 0.21 eV for Sn, while in A1o,,,Gao,,,As, the column VI emission barriers were found to be independent of donor species at 0.28eV (Kumagai et al., 1984). Thermal ionization energies were measured as a function of x for Si by Chand et al. (1984), who found a peak at 0.16 eV at x = 0.43, and Ishikawa et al. (1982), who found E , to peak at 0.14 eV for x = 0.37. Tin was reported to have a peak Eo of 0.17 eV at x = 0.37 (Kaneko et al., 1977),Lifshitz et al. (1980)reported a peak E , of 0.13 eV at x = 0.43. Yang et al. (1982) studied Se and found a peak of 0.16 eV (corrected by a factor of 2) at x = 0.47. Finally, studies of Te give a peak of 0.14eV for x = 0.37 (SpringThorpe et al., 1975) and a peak of E , =0.13eV at x=0.405 (Lee and Choi, 1988). Various other reports indicate a decrease in E , as the doping density increases: for Sn, MorkoG et al. (1980) and for Si, Chand et al. (1984). These chemical shifts do have other implications for behavior of DX in alloys of AI,Ga, -,As. The differences between Si and Te, for instance, result in lower capture barriers for Te and a higher resonant energetic position in the conduction band for Te than Si. This results in the absence of a pressureinduced transition up to 15 kbar, while GaAs:Si shows the emergence of DX at 10 kbar (Sallese et al., 1990). As extrinsic self-trapping is a phenomenological model, we are left with no real quantitative predictive power as to the occurrence of DX centers. In principle, because of the larger effective mass associated with holes, extrinsic self-trapping should occur more often for acceptors than for donors. The electronic energy approximations used by Toyazawa and Emin have only recently been extended to accurately consider band-structure effects (Morgan, 1988), and therefore, insight into the well-known correlations between DX and multiminima conduction bands is only just emerging. A simple extension might combine extrinsic self-trapping with multiminima effective mass theory. The consequences imply that even in a low-effectivemass direct-gap semiconductor, a central cell shift would enhance the interand intravalley coupling and increase the donor binding energy. This increase would also come with increased localization of the bound electron and the resulting opportunity for extrinsic self-trapping.

V. Microscopic Structure of the DX Center

Even though the configuration coordinate diagram model of the DX center predicts that the atomic arrangement around DX must be distorted, no direct experimental data about the symmetry or magnitude of the distortion are available. According to group theory, the distortion of the lattice around a

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K. J. MALLOY AND K. KHACHATURYAN

substitutional donor can be described by one of the three irreducible representations of the point group G: 0

0

0

The A , irreducible representation describes a fully symmetric, symmetry-preserving distortion. This is often referred to as the “breathing mode” distortion (Yamaguchi, 1986, 1990). The T, irreducible representation describes a distortion of trigonal symmetry where the donor atom moves off-center (Fig. 13a) (Morgan, 1986; Chadi and Chang, 1988; Kobayashi et al., 1985). The E irreducible representation describes a distortion of tetragonal symmetry. This is an angle bending distortion with no average displacement of the substitutional donor atom (Fig. 13b) (Oshiyama and Ohnishi, 1986).

We now examine two experiments that attempt to directly assess the microscopic structure of the D X center. These are extended X-ray absorption fine structure (EXAFS) and Mossbauer experiments. Relatively recent experi-

t

FIG. 13. Atomic displacementscorresponding to (a) trigonal T2distortion, and (b) tetragonal E distortion.

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ments giving information about the microscopic structure of DX are also briefly discussed. In an EXAFS experiment, the measured quantity is the donor-nearest neighbor bond length. In this experiment, x-rays are absorbed by the inner shell electrons. The electrons are then emitted and undergo interference with the nearest neighbor atoms. This interference phenomenon gives rise to the extended fluorescence fine structure, modulates the x-ray absorption, and thus allows the measurement of the donor-nearest neighbor distance. EXAFS was performed on Al,.,,Ga,,,,As:Se by Mizuta and Kitano (1988), both in the dark and after illumination. The results indicated no bond length changes to within the experimental accuracy of 0.04 A. EXAFS measurements have also been reported on GaAs:S (Sette et al., 1986), for Al,Ga,-,As:S with 0.2 < x < 0.5 (Sette et al., 1988), and for Al,Ga,-,As: Sn (Hayes et aZ., 1989), all with similar results. The EXAFS results rule out significant trigonal T2 and the fully symmetric A , distortions, as both involve bond length changes. The concern that the xrays might photoionize the DX center and thus measure only the undistorted metastable state rather than the distorted ground state was dealt with in two ways. First, Mizuta and Kitano (1988) report a negligible increase in the photoconductivity during the experiment; second, the x-ray flux is negligible compared to the optical flux during a photoionization measurement. Thus, we conclude that E, the tetragonal bond-bending distortion, in the only option remaining for a significant lattice distortion associated with the D X center. The other experiment illuminating the microscopic structure of the DX center is the Mossbauer spectroscopy on the Sn-related DX center in Al,Ga, -,As (Gibart et aZ., 1988). In a Mossbauer experiment, a nucleus of I19Sn in CaSnO, source emits a y-ray, which is then absorbed by a nucleus of II9Sn in AI,Ga, -,AS:~'~S~ (Fig. 14). However, because of the differing chemical environments of the I19Sn between the source and absorber, the energy differences between the ground and excited states of the nucleus in both materials will be slightly different. To obtain a resonance conditions, the absorber should be moved with a certain velocity with respect to the source, so that the frequency offset due to the Doppler effect would compensate for the chemical environment-induced resonance frequency differences. The velocity of the absorber with respect to the source at the resonance condition is a measure of the difference between the chemical environments of the Sn nucleus in the source and absorber materials, and is referred to as the isomer shift,

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K. J. MALLOY AND K. KHACHATURYAN

3

0

3

VELOCITY ( m n )

~ S ~solid . line passing through the FIG. 14. Mossbauer spectra from A I , G ~ , _ , A S : ~ ' The data is a least squares fit orthe three Lorentzian-shaped lines indicated (from Gibart eta/., 1988).

where C is a constant for a given isotope (dependent on nuclear parameters), A R / R is the relative change of nuclear radius between excited state and ground state, and the term in parentheses represents the difference in the total electron density evaluated at the nucleus &O)', between absorber and source isotopes (see, for example, Gonser, 1975). While the isomer shift reflects differences in chemical bonding between

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absorber and source nuclei, the width and splitting of the Mossbauer spectral lines is a measure of the electric quadrupole interaction. This interaction is proportional to the change of the electric quadrupole moment of the nucleus upon excitation and the gradient of the electric field at the nucleus. In a position of tetrahedral symmetry, the electric field gradient is 0. It is only when the defect undergoes a symmetry-breaking distortion that the electric field gradient at the nucleus appears. For the case of "'Sn in Al,Ga, -,As, a very large quadrupole splitting of 0.6 mm/s is observed, which is almost two times larger than that observed for 'I9Sn in the tetragonally distorted structure of 8-Sn (Williamson, 1986). However, the possibility of several species of 'l'Sn, in different chemical environments, as a cause for multiple Mossbauer peaks also cannot be ruled out (Williamson, 1986). For a small angle-bending E tetragonal distortion, the electric field gradient will be proportional to the magnitude of the distortion. The trigonal T2 distortion is dipolar to a first approximation and has no quadrupole component that would interact with the quadrupole moment of the nucleus (a quadrupole component for a trigonal distortion appears only as a secondorder effect,quadratic in distortion). To summarize the experimental data thus far on the microscopic structure of the D X center, EXAFS rules out fully symmetric A , and trigonal T, distortion modes of the DX center, leaving only an angle-bending tetragonal E mode as a possibility. The probable quadrupole splitting observed in the Mossbauer experiment can be accounted by either T, or E distortion modes, but the very large magnitude of the effect suggests the tetragonal E mode. Thus, the tetragonal E distortion mode is supported by these structural experiments. Other modes are, of course, also possible, but only if the magnitude of the distortion is less than the sensitivity of the techniques involved, i.e., less than 0.04A for either the T, or A l distortions. Several recent experiments also give clues as to the atomic-level structure of D X . For instance, the shift and height change of the DLTS peaks of D X centers in A1,Gal -,As:Te under uniaxial pressure were observed (Li et al., 1989b). The effect was maximal when uniaxial stress was applied in the [lo01 direction, but quite small when the stress was in [lll]. This result is indicative of the tetragonal symmetry of the DX center, although another explanation based on the multiminima bandstructure is also possible (Li et al., 1989b). Double-crystal x-ray diffraction of AI,Ga, -,As:Te samples at 77 K with and without illumination implies a distortion of the unit cell of 0.1-0.4A (Leszcznski et al., 1991). The rocking curve of samples exhibiting PPC was narrower than that of the same samples without illumination. Another experiment, studying the local vibrational mode (LVM) spec-

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troscopy of Si in GaAs under hydrostatic pressure (Wolk et al., 1991) gives apparently contradictory results to those discussed above. These experiments suggest that the lattice relaxation of the D X center may, after all, be quite small. In this experiment, two local vibration modes were found for Si in GaAs under hydrostatic pressure. For a pressure of 35 kbar, the local vibration mode of Si+ was found at 405cm-’, while the LVM of the Sirelated DX center was at 395 cm- A small splitting of only 2.5% suggests a small lattice relaxation of D X . If D X is a symmetry-breaking defect, its LVM should be expected to be split into two components. No such splitting was observed, suggesting that the D X center has a tetrahedral Td symmetry (compare with the model of Yamaguchi, 1990).However, if the distortion is of the angle-bending E type, the LVM splitting would be quadratic in distortion and possibly too small to detect. The earliest experiments reported on the symmetry of the microscopic structure of D X were the ballistic phonon scattering studies by Narayanamurti et al. (1979).In this experiment, attenuation of fast transverse phonons, creating trigonal strain, and of slow transverse phonons, creating tetragonal strain, were measured as a function of the flight time of the phonon in undoped, Te-, and Sn-doped Al,Ga, -,As samples. The measurements were made in different propagation directions before and after illumination at 1.5 K. Narayanamurti et al. (1979)concluded that the Sn-related D X center is of ( 1 11) trigonal symmetry, whereas the Te-related DX center is of (1 10) orthorhombic symmetry. However, these conclusions raise many more questions than they answer. Differences in attenuation were seen only after illumination, when DX is presumed to be in the relatively undistorted metastable state. In the dark, when D X is occupied and in the relaxed, distorted state, no difference in attenuation was reported between the doped and undoped samples. If the observed changes are indeed due to the D X center, then it is the metastable hydrogenic state that is distorted, a situation opposite to assumptions and discussions thus far. Some aspect of the phonon transport not clear to us might alter this conclusion, but Van Vechten’s (1985) elaboration of Lang et al.’s (1979a) original model for D X ,

’.

where D + is either IV; or VI;$, a column IV donor on a M (A1 or Ga) site or a column VI donor on an As site, has the requisite symmetry in the “conducting” or left-hand state and a random orientation of the M-’ in the “nonconducting” or right hand configuration. Thus, the transition from the metastable D X to the ground state involves the change from an As vacancy to a metal vacancy-metal antisite pair, capable of trapping three electrons. It is possible, however, that the observed phonon attenuation arises from

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the increase in photoconductivity and not from changes in the microscopic structure. Differences between the trigonal fast and tetragonal slow ballistic phonon attenuation could arise from asymmetry in the electromechanical coupling coefficients. Moreover, the absence of attenuation at low temperature does not prove the ground state DX center is undistorted. A distorted defect may not be able to reorient on the time scale of the THz ballistic phonons if an activation barrier is present. It is well known that angle-bending forces are of lower energy than bondstretching forces (Harrison, 1980). Other more indirect evidence in favor of the angle-bending E mode and against the T, mode lies in the lowtemperature capture behavior of the DX center. The probability of the ionized DX center acquiring sufficient distortion to be able to capture an electron is not described by the Boltzmann equation. Rather, the ionized DX center should be considered as a quantum oscillator, with quantized vibrational energy levels, which can overcome the energy barrier not only by thermal activation but also by tunneling. The probability of the quantum oscillator acquiring a sufficient distortion q to overcome the energy barrier E , is described by a quantum statistical equation (Landau and Lifshitz, 1980),

where w is the oscillator frequency, T is temperature, k, is the Boltzmann constant, and E , = M o 2 q 2 / 2 ,where M is the reduced mass of the oscillator, and all terms that are independent of E, and 4 are included in a constant. This equation tends to the Boltzmann form only in the limit as hw/k,T 3 0. In the opposite limit of holk, T >> 1, the oscillator overcomes the barrier by tunneling, and the resulting capture rate is temperature-independent. Thus, the thermally activated capture of the Boltzmann form can only extend to temperatures above hw/(2kB).For the case of Si-related DX centers in very heavily doped GaAs, or n-GaAs under hydrostatic pressure, the frequency of the off-center vibration of the Si' donor atom is known from the infrared absorption measurements of the local vibration mode: hw = 384cm-' = 47.6 meV (Maguire et al., 1987). The same off-center vibration frequency, 48 meV, can be obtained from phonon replica spacings in the DAP photoluminescence spectrum from Al,Ga, -,As: Si (Henning et al., 1987a, 1987b). So, below room temperature, the rate of electron capture by the Si' ions would deviate from the Boltzmann law, and at 150K the capture would become temperature-independent. This is in contradiction with experimental data. Lang (1980, 1986) pointed out that the thermally activated capture behavior (Boltzmann form) of DX down to below 77 K can

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FIG. 15. Logarithm of the electron capture cross-section vs. inverse lattice temperature for defects coupled with phonon modes of different energies (from Lang, 1980).

only be explained if the distortion mode leading to D X formation, in the ionized state of the D X center, is very soft (Fig. 15), hw < 10meV. In the occupied state of the D X center, the distortion-inducing phonon energy was obtained from the temperature dependence of the optical ionization crosssection and was found to be hw = 10meV (Lang, 1986; Legros et al., 1987). Such soft modes can only be attributed to the angle-bending tetragonal E mode. VI.

Magnetic Properties of DX: The Negative4 Issue

The presence of lattice relaxation modifies the electron-electron correlation (or Hubbard) energy U . In the absence of lattice relaxation, the Hubbard energy is simply the Coulombic repulsion energy of two electrons localized on the same defect. Lattice relaxation reduces the Hubbard energy since the localization of two electrons stabilizes the distorted configuration to an even greater extent than the localization of one electron. If the lattice relaxation is large enough, the Hubbard energy U is negative and the disproportionation defect reaction 20' + D f -t D-, (13)

6. DX

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AND

275

spontaneously occurs (Anderson, 1975). A simple phenomenological model helps illustrate this effect. In the presence of an electron-phonon interaction on an impurity atom, the total energy V may be expressed as V ( x )= $cx2 - t x n

+ Y(n),

(14)

where x is the bond length change, is the eiectron-phonon interaction constant, n is the total number of electrons with all spin directions on the bond (0,1, or 2 in this case), c is the spring constant of the bond and Y ( n )= Ucoulif n = 2 and Y(n) = 0 otherwise (Ucoulis the Coulombic repulsion of two electrons on the same defect). Minimizing the energy d V / d x = 0 and eliminating x we find the effective correlation energy (Anderson, 1975) as Veff = UCOUl

t2

-

-.c

The bond may have three possible values of energy depending on the number of trapped electrons: Energy

Number of Electrons

E=O

n=O

E = El

n=l

E = 2E1

+ Ueff

n=2

Thus, if the effective Hubbard correlation energy Ueff is negative, either none or two electrons should be localized at the defect. Several examples of solids exhibiting both large lattice relaxation and the disproportionation reaction Eq. (13) are known to exist. They include the electron-irradiation induced M-center in InP (Levinson, 1983), the vacancy and interstitial B in Si (Watkins, 1986), group I11 dopants in PbTe (Kaidanov, 1985). If DX were indeed a negative-U defect, many properties can be explained. However, it is crucial to remember that the sole atomic model (Chadi and Chang, 1988)for negative4 is inconsistent with a number of structural results, and the crucial magnetic susceptibility results do not yet indicate the diamagnetism of DX.While many recent indications suggest DX may be a multi-electron center, that in itself is not sufficient for proof of negative-U. Other classes of models, including those with accompanying defects (“X”) also have multi-electron kinetic properties (e.g., Van Vechten, 1985). This proposal is also attractive since it offers a possible explanation for the

K. J. MALLOYAND K. KHACHATURYAN

276

observed increase in mobility associated with persistent photoconductivity. In the negative-U model, photoionization converts D- ions into D+ without changing the total number of charged scattering centers. However, the resulting increase in the free electron concentration provides more effective screening of the charged scattering centers and results in an increase in mobility. The most direct way to determine the sign of the Hubbard electronelectron correlation energy U is through a magnetic measurement. According to the Pauli Principle, two electrons in the same orbitally non-degenerate state of the defect should have opposite spins. For that case, the defect should be diamagnetic. On the other hand, the defect with only one unpaired electron should be paramagnetic. In turn, there are two possible magnetic experiments with the potential of determining whether the DX center is a paramagnetic or diamagnetic defect. The first experiment is electron paramagnetic resonance (EPR). EPR measurements have been performed on bulk GaAs, -,P,:S (Khachaturyan et al., 1991) (Fig. 16), and on epilayers of n-Al,Ga,-,As (Khachaturyan et al., 1989a,c; Mooney et al., 1989b) and did not detect any signal from the occupied ground state of the D X center. This is despite the fact that the EPR signal from the metastable hydrogenic ionized state is readily observable in the same samples after illumination at low temperatures (Khachaturyan et af., 1989a,c; Mooney et al., 1989b; Kennedy and Glaser, 1991). Even though no EPR signal from the DX could be seen, one cannot conclude that the DX center is a diamagnetic impurity. Other reasons for the

I

I

3240

I

I

3320

I

I

3400

I

I

3400

I

I

b

H (GI

FIG. 16. Electron Paramagnetic resonance spectrum from the S-like hydrogenic donor in GaAs,.,P,., :S in the dark (dashed line) and after illumination (solid line).

6. DX AND RELATEDDEFECTS IN SEMICONDUCTORS

277

absence of the EPR signal are possible, such as signal broadening (more than a few thousand gauss would render the signal amplitude below the detection limit). The only way to unambiguously determine whether D X centers are diamagnetic or paramagnetic is to make magnetic susceptibility measurements (Fig. 17). The number of paramagnetic impurities in the dark can be obtained from the temperature dependence of magnetic susceptibility of nAl,Ga,-,As, and then compared with the number of D X centers in the sample, as measured by capacitance-voltage techniques. To determine the concentration of paramagnetic impurities, the temperature dependence of magnetic susceptibility is fitted to the Curie law,

Here N is the number of paramagnetic impurities, k , is the Boltzmann constant, p, is the Bohr magneton, T is temperature, and xL is the temperature independent diamagnetic susceptibility of the host lattice. The 5

13

4 1

0.2

0.3

0.5

0.4

0.6

'

4.5 0.7

1/T

FIG. 17. Diamagnetic susceptibility measurements vs. inverse temperature before (squares) and after (circles) illumination in a field of 3.7G. Illumination was made with 500pW at E = 1.6 eV. The data offset is arbitrary, but the same for the plots before and after illumination (from Khachaturyan et al., 1989a). (a) A1,,,,Gao,,,As:3 x l O I 7 Si/cm3. Hall data from this sample are presented in Fig. 4. (b) A1,~,,Gao,,7As:3.6 x 101'Te/cm3.

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K. J. MALLOYAND K. KHACHATURYAN

concentration of paramagnetic impurities should then be compared to the number of the D X centers derived, for instance, from capacitance-voltage measurements. Thus, magnetic susceptibility can determine whether the D X center is a diamagnetic or paramagnetic defect. Magnetic susceptibility measurements have been performed on D X centers in GaAs, -,As,:S (Khachaturyan et al., 1991) and on MBE and MOCVDgrown n-A1,Ga,-xAs (Khachaturyan et al., 1989a). In both systems, it was found that the D X center is a paramagnetic defect. This conclusion was made more convincing by the illumination dependence of the susceptibility (Khachaturyan et al., 1989a). Since the D X center is the only known defect in Al,Ga, -,As which is persistently ionized by illumination, the Curie paramagnetism arising from the ground state of a paramagnetic D X should disappear upon illumination, as the susceptibility of a degenerate Fermi electron gas is temperature independent (the sum of the Landau-Peierls-Pauli diamagnetism and the factor-of-three larger Pauli paramagnetism). Figure 17 shows the persistent disappearance of the Curie susceptibility that was observed after illumination in n-AI,Ga, -,As (Khachaturyan et al., 1989a). It is much more difficult to distinguish between the positive-U model and the negative-U model when both electrons have parallel spins for a total spin of one. The energy of the negative-U, s = 1 state has been shown in recent theoretical calculation (Dabrowski er al., 1990)to be within 0.1 eV of the state with s = 0. An attempt was made to distinguish between negative-U, s = 1 and the positive-U, s = 9 by using the fact that the Curie paramagnetism in the first case should be greater than the second by one-third. Magnetic susceptibility measurement were performed on indirect gap AI,Ga, -,As: Si where even the metastable hydrogenic state is sufficiently deep that electrons remain unionized. N o change in the magnetic susceptibility was seen, indicating the spin of the D X center is the same as that of the hydrogenic donor, s = i.However, more precise, state-of-the-art magnetic susceptibility measurements are needed to convincingly distinguish between the negativeU , s = 1 and the positive-U, s = $ models. Another report on magnetic susceptibility has appeared with different results. In this work (Katsumoto et al., 1990) a 200pm LPE grown film of Al,Ga,. .As with lo'* cm-3 Te was measured at 20 mK to 1 K temperatures and at 5 0 G field. On the one hand, a persistent decrease in Curie paramagnetism was found after illumination, suggesting that the D X center is a paramagnetic donor. On the other hand, the observed Curie paramagnetism corresponded to the concentration of paramagnetic impurity 20 times lower than the total concentration of D X centers obtained from photoHal1 measurements, indicating that only a fraction of D X centers are paramagnetic. However, it is well known that LPE growth of AI,Ga, -,As:Te results in precipitates of Ga,Te, and AI,Te, (Wagner, 1978),

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even at relatively low Te concentrations, so these results could be clouded by sample heterogeneity. This experiment has been recently independently repeated on a similar LPE Al,Ga, -,As:Te sample (Dreszer et al., 1992). After illumination, the concentration of paramagnetic impurities either weakly decreased if the sample had been cooled slowly, or increased if the sample had been cooled quickly. Illumination also gave a strong increase in the Landau-Peierls-Pauli temperature independent free electron gas diamagnetism which eventually saturated. After illumination, the Curie paramagnetic impurity concentration was found to have a value close to the Hall effect free electron concentration. These results can be explained again by assuming that there are two forms of the Te D X center. One form is the negative4 diamagnetic center with spin s = 0 which can be persistently photoionized at low temperatures. The other form is a paramagnetic, positive-U donor which cannot be photoionized at low temperatures. The relative concentrations of the two forms of DX may depend on growth conditions and alloy composition. The conclusion that negative-U and positive-U D X centers coexist also follows from the observation by Jantsh et al. (1990) that mobility in Al,Ga, _,As:Si is not a single-valued function of carrier concentration, but exhibits hysteresis upon turning on and off IR illumination. However, the case for the dominance of the positive4 center also follows from Hall effect studies. One-electron positive4 donors exhibit different carrier statistics than negative4 donors. For negative-U donors, the free carrier concentration obeys the following relationship (Khachaturyan et al., 1989~;Li et al., 1989b)

where the symbols have their usual meaning. From Eq. (18),it follows that in the limiting case of n << N , and n << N A , the free electron concentration no longer depends on the doping concentration. This obvious contradiction with experimental results (Chand et al., 1984) was pointed out by Li et al. (1989b). Furthermore, a recent series of electrical and optical studies have been reported attempting to distinguish between the negative- and the positive-U models of the D X center (Gibart et al., 1990, Jantsch et al., 1990, Fujisawa et al., 1990, Mosser et al., 1991, Dobaczewski and Kaczor, 1991, Theis et al., 1991, Wolk et al., 1991). In most electrical studies, however, compensation is not taken into account when the interpretation of the results is attempted (e.g. Fujisawa et al., 1990). The case of positive-U and strong compensation may be difficult to distinguish from the case of negative4 (see above and the discussion by Theis et al., 1991).A study of photoionization kinetics indicate

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the photoionization process occurs in two steps suggesting an intermediate state (Dobaczewski et al., 1990). The existence of the intermediate state was interpreted within the framework of the negative4 model. Gibart et al. (1991) extended their Mossbauer studies to GaAs doped with ‘19Sn under pressure and concluded that D X localizes two or three electrons. The careful study of Mosser et ai. (1991) fit the capture kinetics of D X to a model requiring that the D X ground state is negative. In other semiconductors, the situation can be more clear-cut. For instance, in Pb,Sn, -,Te (a narrow-gap semiconductor with the rocksalt structure) which exhibits persistent photoconductivity below 20 K (Kaidanov and Ravich, 1985; Shimomura et al., 1989), In is indeed a 2-electron7 negative-U, D - donor. The x-ray photoelectron spectroscopy studies (Drabkin et al., 1982) showed two peaks corresponding to two charge states of the In atoms, I n + 3 and In+. Thus all In+’ ions on Pb sites must have disproportionated according to the reaction In+’ I n + 3 + I n + .Since both In+ and I n + 3ions are diamagnetic, all In impurities in Pb,Sn, -,Te, according to this model, should be diamagnetic. This is indeed the case, as not only EPR measurements (Andreev et d., 1975), but also magnetic susceptibility measurements (Drabkin et a/., 1979 Lykov and Chernik, 1980) showed that there are no paramagnetic impurities in Pb,Sn, -,Te:In, even though as much as several atomic percent of the In donor could be introduced in Pb,Sn, -,Te.

VII.

Technology and DX

The existence of DX,particularly in Al,Ga, _,As, has had implications for electronic device designs. For instance, the DX strongly influences the operation of the MODFET (modulation doped field effect transistor). A MODFET, whose structure and band diagram are shown in Fig. 18, separates a conducting channel of electrons in GaAs from the donor source of electrons in Al,Ga, -,As through the use of a heterojunction conduction band barrier. This separation significantly enhances the mobility of the electrons confined to the two-dimensional electron gas (2DEG) by the elimination of ionized impurity scattering. However, the D X character of the donors in AI,Ga, -,As, including the existence of barriers to capture and emission, significantly changes the device performance at low temperature and under illumination. Three general phenomena are observed after illumination at low temperature and associated with DX centers. First, as reported by Drummond et al. (1983) and Fischer et al. (1984), the 2DEG channel conductance changes upon illumination at low temperature.

6. DX

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RELATEDDEFECTS IN SEMICONDUCTORS

Depletion. Dopect Al,Ga,.fis . Undowd ALGa. A s /

k

6

o

o

A

A

281

ciuctrori I..I-+I..~ I,',.a".'"',

kiooA

FIG. 18. (a) Schematic cross-section of a MODFET indicating a possible mechanism by which I-V collapse occurs (from Fisher et al., 1984). (b) Conduction band diagram for a MODFET, T = 300 K, with no bias (from Caswell et al., 1986).

This is easily understood in terms of the PPC effect, where the photoionized electrons from the DX centers in AI,Ga, -,As increase the electron concentration in the 2DEG. This increase in ionized DX centers also increases the remote ionized impurity scattering and decreases the mobility of channel electrons. Second, the threshold voltage, defined as the least positive gate voltage necessary to sustain the 2DEG channel, shifts as a result of the persistent change in ionized impurity content in the AI,Ga, _,As after illumination at low temperature. The threshold voltage, t&, is given by

where d)b is the Schottky barrier height at the gate metal-Al,Ga,-,As interface; AE,, is the conduction band offset at the Al,Ga,-,As-GaAs heterojunction; q is the electronic charge; and w is the thickness of the Al,Ga,-,As layer. As Nix changes upon photoionization and at low temperatures where recapture is suppressed, F h will decrease.

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While illumination will induce these persistent phenomena, similar phenomena will occur in the dark. For instance, cooling the MODFET in the dark will result in a freeze-out of carriers at D X , a decrease in N&, and the resulting increase in qh.If the structure is cooled under a reverse bias much will not less than Kh, then no electrons will be available to be trapped and be changed. However, if the MODFET is then forward-biased, hot electron injection from the ZDEG over the heterojunction band offset during electron transport from the source to the drain will result in the trapping of electrons at D X centers, and the threshold voltage will increase as before. In fact, Caswell et al. (1986) and Mooney et al. (1985, 1987), made something of a virtue out of this vice, by using MODFET structures to study the electron capture and emission kinetics of the DX centers in the AI,Ga, _,As layer. Another phenomenon observed in MODFETs is the so-called “collapse” of the I - V (current-voltage) characteristics at low temperature (Fischer et al., 1984). As shown in Fig. 18b, under operating conditions, the electric field is higher at the drain end of the device than at the source end. Hot electrons can be injected into the A1,Gal-,As at the drain, neutralizing the ionized D X centers, and reducing the 2DEG concentration at the drain of the structure. This effectively adds a high series resistance to the channel, reduces the transconductance of the MODFET and gives the observed ‘‘collapse.’’ The times associated with the emptying and filling of DX centers might also be expected to be observable during room-temperature operation of MODFETs. These effects are most noticeable in comparison of the static or low-frequency behavior of MODFETs with their transient or high-frequency properties. Indeed, as discussed by Nathan et al. (1985), a transient, negative gate pulse should turn the source-drain current off. However, the relatively slow emptying of the D X centers in the Al,Gal -,As layer continually shifts q h . Therefore, the MODFET turns back on with a time constant on the order of microseconds as electrons from D X reenter the ZDEG channel and yh becomes more negative. D X centers contribute to the thermal noise properties of electronic devices. In studies on the generation-recombination noise voltage as a function of frequency, Loreck et al. (1984) showed traps in the AI,Ga, _,As layer as the dominant source of noise in MODFETS. Kirtley et al. (1988) later identified the D X center as a significant source of this noise. There have been several approaches to eliminating the effects of D X centers on electronic devices. One approach is to reduce the A1 concentration of the barrier Al,Ga, -,As layer (indium can be added to the GaAs layer to increase the conduction band offset). This solves the problem of freeze-out at low temperatures, and since the effective capture barrier increases as x is

v,,

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283

decreased, some immunity to hot electron emission over the heterojunction and capture at DX is gained. However, DX still exists as a localized resonant state in Al,Ga, -,As for x < 0.2 (Theis et al., 1988), is still a source of noise (Kirtley, 1988), and still can capture electrons and alter device properties (Theis et al., 1986). Furthermore, when Al,Ga,-,As with x < 0.2 is doped heavily enough, the Fermi level reaches the DX resonant level and the DX level becomes occupied, with all the attendant problems. We should point out that the critical doping level decreases with increase in x and tends to 0 when x approaches 0.23 for Si-derived DX centers. Another approach has been to completely change materials systems and build MODFETs using a lattice-matched Alo~48~no,52As: Si on Ga,.,&o.,,AS on InP structure. While no DX centers were detected by DLTS and no PPC observed for the lattice-matched system (Hong et al., 1987), DX characteristics were observed for non-lattice-matched Al,In, -,As with A1 contents near the direct-indirect crossover at x = 0.55. Further studies are needed to indicate the exact A1 dependence of DX-like properties in Al,In, -,As. The final approach that has met with some success for device structure uses superlattice phenomena to modify the properties of DX. A superlattice consists of alternating layers of semiconductors, each layer thin enough so some overlap of electronic wavefunctions occurs (e.g., Esaki, 1986). The resulting structure will exhibit a band structure along the direction of growth characteristic of the superimposed ordering and usually quite different from the band structure of the starting materials. Several attempts at modeling the electronic properties of deep defects in superlattices have been made (Bourgoin and Lanoo, 1988; Dow et al., 1988; Beltram and Capasso, 1988), and based on these, the electronic properties of DX might be expected to be quite different in a superlattice. However, the localized interactions with the lattice some authors believe dominate the properties of DX might not be significantly altered by these purely electronic approaches. A simple approach to using superlattices to reduce the influence of DX would be to confine the donors to the GaAs layer, where DX centers have relatively little influence on the electronic properties, and use undoped Al,Ga, -,As layers to increase the bandgap of the resulting structure. This was proposed by Baba et al. (1983) and used by Pearah et al. (1985) in MODFETs. Using various Si doping schemes in the Al,Ga, -,As/GaAs materials system, Baba et d.(1986, 1989), Bourgoin et al. (1989), and (using the concept of planar doping) Etienne and Thierry-Mieg (1988) all show modification of DX properties in superlattices compared with equivalent alloys.

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VIII. Summary We have attempted to examine the DX center and DX-like phenomena in the widest possible context, covering not only donors in Al,Ga, -,AS, but also donors in a variety of other semiconductors. Since certain essential properties recur consistently-persistent photoconductivity, capture and emission barriers, thermally activated capture, large photoionization thresholds, and double-sloped Hall measurements-we have tried to seek a commonality in understanding. One aspect of that understanding involves the interaction of the electronic state of the defect with the lattice. While purely electronic approaches to D X like properties explain thermal activation energies, we think lattice relaxation or rearrangement best explains the equilibrium and kinetic electronic properties and the optical properties of DX. Extrinsic self-trapping provides a phenomenological framework for understanding the origins of such interactions with the lattice, but a predictive theory is still lacking. The majority of the optical data are best explained if the magnitude of this lattice relaxation energy is large compared to the donor activation energy. However, the magnitude and type of this lattice relaxation are in considerable doubt, Structural studies thus far place an upper limit of 0.04 8, on the magnitude of off-center distortions and support an angle bending distortion of tetragonal symmetry. This is consistent with the type of lattice interaction observed for other defects, such as the vacancy in silicon (Watkins, 1975) or C r2 +in GaAs (Krebs and Straws, 1979). The negative4 and multi-electron issues have moved to the forefront of current research. Clearly, a model consistent both with the multi-electron characteristics and with structural studies needs to be developed. Will such a model retain the identification of DX as the isolated substitutional donor, or will it be necessary to re-invoke “X” to fully explain the observed properties? As the techniques applied to the study of DX become more sophisticated, results echo our opening comments. Is DX multifaceted? Are there both positive- and negative4 forms of DX present in most samples? Progress will depend on the ability to precisely define the defect being studied, a goal DX continues to frustrate. Future DX studies should clarify the lack of a clear EPR signal for the paramagnetic occupied state, give better understanding of the role of indirect minima in the capture and emission process and of the mobility increases upon illumination, and reconcile reports that epitaxial GaAs,P, -,:Te (Henning and Thomas, 1982; Calleja et al., 1983) exhibits metastability, while bulk GaAs,P,-,:Te does not (Craford et al., 1968; Khachaturyan et al., 1991). For other semiconductors, as much may be gained from the study of

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donors not exhibiting DX-like behavior as from the study of those that do, If we speculate (further), we might ask two other questions: Why does DX behavior (PPC, capture and emission barriers, etc.) not occur for holes, and what other systems are candidates for DX-like behavior? The larger effective masses of holes would appear to make them candidates for large interaction energies with the lattice. If the electronic energy contributions driven by the conduction band degeneracies are crucial, then the Si,Ge, -, system exhibits the proximity of the L and X conduction band minima that occurs frequently in systems exhibiting DX behavior. Some evidence already exists for a deepening of the core exciton energy near the L-X crossover at x = 0.15 (Bunker et al., 1984;Newman and DOW,1984),but other explanations based on alloy scattering have been advanced (Krishnamurthy et al., 1985). Germanium under hydrostatic pressure would give a similar crossing of the L and X conduction band minima without alloy scattering. Studies of Ge and Si,Ge, -, could give information on the degree of ionic bonding necessary for DX-like behavior. Many of us view study of DX centers as a fundamental and technologically relevant challenge. While ultimate understanding of the properties and origins of DX is yet to come, we have tried to convey a sense of the challenge and the implications for defects in all semiconductors.

Acknowledgments The authors thank Prof. Eicke R. Weber for many stimulating discussions. One of the authors (KK) was financially supported by the AT&T foundation. KJM would like to acknowledge the support of the Air Force Office of Scientific Research and to remember the late Gerald L. Pearson for encouraging his initial interest in the subject.

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SEMICONDUCTORS AND SEMIMETALS. VOL . 38

CHAPTER 7

Dislocations in III/V Compounds V. Swaminathan AT&T BELLLABORATORIES SOLIDSTATETECHNOLOGY CENTER PENNSYLVANIA BREINIGSVILLE.

Andrew S . Jordan AT&T BELLLABORATORIES MURRAY HILL.NEWJERSEY

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . 294 I. DISLOCATION TYPES AND STRUCTURES . . . . . . . . . . . . . . . . 295 1. Perfect Dislocations . . . . . . . . . . . . . . . . . . . . . 295 2. Partial Dislocations and Stacking Faults . . . . . . . . . . . . . . 298 111. MECHANICAL PROPERTIES . . . . . . . . . . . . . . . . . . . . . 299 299 3. Glide System . . . . . . . . . . . . . . . . . . . . . . . . 4. Stress-Strain Curves . . . . . . . . . . . . . . . . . . . . . 300 5 . Deformation Microstructure . . . . . . . . . . . . . . . . . . 303 6. Critical Resolved Shear Stress (CRSS) . . . . . . . . . . . . . . . 304 I . Impurity Hardening . . . . . . . . . . . . . . . . . . . . . 306 8. Microhardness and Plasticity at Room Temperature . . . . . . . . . . 309 IV. DISLOCATION GENERATION AND REDUCTION DURING GROWTH OF BULKCRYSTALS . 310 9. Mechanisms Leading to Dislocation Generation . . . . . . . . . . . . 310 10. Deoiation from Stoichiometry . . . . . . . . . . . . . . . . . . 310 11. Thermal Stress . . . . . . . . . . . . . . . . . . . . . . . 312 12. Methods to Reduce Dislocation Density . . . . . . . . . . . . . . 315 V. DISLOCATIONS AND DEVICE PERFORMANCE . . . . . . . . . . . . . . . 321 13. Photonic Devices . . . . . . . . . . . . . . . . . . . . . . 321 14. GaAs FETs . . . . . . . . . . . . . . . . . . . . . . . . 332 NOTE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . 336

293

Copyright 0 1993 by Academic Press. Inc. All rights of reproduction in any form reserved. ISBN 0-12-752138-0

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I. Introduction The material quality of semiconductors, whether in bulk or in thin-film form, is often the overriding factor in determining device performance. Improved device characteristics can often be traced to better materials. The quality of the material is generally determined by crystalline imperfections, such as point defects, dislocations, stacking faults, grain boundaries, interfaces, etc., that are invariably present. Foreign impurities are generally intentionally added to the material during growth to obtain desired electrical properties. Even when the material is grown “undoped,” unintentional impurities such as C, Si, and S are present because of contamination from graphite crucibles (C, S) and quartz containers (Si) used for crystal growth. In VPE and MOCVD growth, the gaseous precursors are often impurity sources. In this chapter we discuss dislocations in bulk III/V compounds. For discussions on point defects (e.g., impurities and vacancies) in bulk crystals and thin films, as well as dislocations in thin films, the reader is referred to other chapters. Dislocations can be present in the as-grown bulk material because of a variety of causes such as thermal stress, excess point defects precipitating to form prismatic dislocation loops, etc. Dislocations are also introduced during the various device processing steps that include, for example, diffusion and ion implantation. When bulk crystals are used as substrates for epitaxial growth, dislocations in the substrate can propagate into the epitaxial films. Since the presence of dislocations is, in general, harmful to the devices, the asgrown crystals should contain as few dislocations as possible. In discussing dislocations in IIIjV compounds, we restrict ourselves to GaAs and InP, the two most technologically important compounds, in view of their application in a variety of photonic and electronic devices. GaAs substrates play a major role in microwave devices, in high-speed digital integrated circuits, and in lasers emitting in the wavelength range 0.680.9 pm. For InP the use is almost exclusively as substrates for growing latticematched epitaxial films of alloy semiconductors such as GaInAs and GaInAsP. These ternary and quarternary compounds are the materials of choice for making sources and detectors for the present-day fiber optic communication systems. Promising developments in these device areas have served as the impetus for improving the quality of GaAs and InP substrates. The major objective of this paper is to review dislocations in GaAs and InP, with the emphasis on the theoretical and experimental aspects of reducing the dislocation density in these crystals. Hence, we exclude such topics as electrical properties of dislocations in compound semiconductors. The organization of this chapter is as follows. In Section I1 the types and the structure of dislocations in III/V compounds are briefly discussed. Since

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COMF'OUNDS

295

dislocations are carriers of plasticity, such mechanical concepts as glide systems, critical resolved shear stress, and impurity hardening, important issues in the considerations of dislocation generation during crystal growth, are introduced in Section 111. The mechanisms of dislocation generation during bulk crystal growth and the ways to reduce the dislocation density are presented in Section IV. Finally, the effects of dislocations on device performance are discussed in Section V with illustrative examples from photonic and electronic devices.

11. Dislocation Types and Structures

1. PERFECT DISLOCATIONS III/V semiconductors crystallize in the zincblende structure, which can be described as two interpenetrating fcc lattices. The close packed { 11l } planes of the fcc lattice become pairs of { 111) planes in the zincblende structure, as shown in Fig. la, or in a two-dimensional projection on the { 1lo} plane as in

FIG. 1. (a) The zincblende unit cell; (b) stacking of (111) planes; (c) projection of (b) on the (110) plane (from Alexander and Haasen, 1968).

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V. SWAMINATHAN AND A. S. JORDAN

Fig. 1b. Because of the presence of two type of atoms, in GaAs and InP, there is a polarity in stacking of the { 111) planes. If ABCABC is the stacking order of { 1 1 1) planes in the first sublattice and aPyaPy in the second, then aB,/?C,yA are closely spaced pairs of planes connected by three times as many bonds as are between the three times wider spaced Aa, BP, Cy pairs of planes. Hornstra (1958) first examined the possible configuration of dislocations in crystals with diamond cubic structure, and later Holt (1962) extended the analysis to zincblende. The important types of dislocations are the 60" and the screw types in the (111) plane. The creation of a 60" dislocation is illustrated in Fig. 2. For this dislocation the angle between the dislocation line and the Burgers vector is 60". The characteristic properties of perfect dislocations having Burgers vector 4 2 [l lo], where a is the lattice constant, are shown in Table I. Because of the lack of a center of symmetry in the zincblende structure, Haasen first pointed out that there are two types of edge dislocations

SLIP

PLANE

FIG. 2. (a) The GaAs structure with a { 1 11) direction vertical. The dislocation line direction and the Burgers vector of a 60'dislocation are shown in a slip plane. (b) The result of moving a 6 0 dislocation in the crystal from right to left is to produce the relative moments of the atoms indicated by the arrows. (c) The 60" dislocation of the shuffle set. (Reprinted with permission from J . Phys. Chem. Solids 23, 1353, D. B. Holt, Copyright 0 1962, Pergamon Press PLC.)

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291

TABLE I TYPFS OF

No.

DISLOCATIONS HAVING BURGERS VECTOR U/2 [110] (HORNSTRA, 1958) Direction of Dislocation Axis

Angle between Axis and Burgers Vector 0" (screw) 60" 90" 30" 90" 73"13' 54"W 90" 45"

IN THE

ZINCBLENDE LATTICE

Glide Plane

Number of Broken Bonds per cm" 0 1.41 2.83 or 0 0.82 1.63 2.45 or 0.82 1.63 or 0 2.0 or 0 2.0 or 0

"For dislocations with { 111) glide plane, the number of broken bonds is proportional to the sine of the angle between the dislocation axis and the Burgers vector (Read, 1954).

depending on whether the extra half-plane ends with a row of group I11 or group V atoms (Haasen, 1957). However, the extra half-plane can terminate either between the Aa planes or between the aB planes (Fig.3), which determines whether the dislocation ends on a row of group I11 atoms or ends with a row of group V atoms, respectively. These two types of dislocations are

FIG. 3. The glide and shuffle set dislocation for the a-configuration in GaAs. The glide dislocation is formed by removing the extra half plane (1561) and the shunle dislocation is formed by removing the extra half plane (1234) (from Kuesters et ul., 1986).

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referred to as the shuflle set (extra half-plane between Aa planes) and glide set (extra half-plane between aB planes) (Hirth and Lothe, 1982). In a compound AB, the glide set is denoted as A(g) and B(g) and the shuffle set as a (or A(s)) and j3 (or B(s)).'

DISLOCATIONS AND STACKING FAULTS 2. PARTIAL A stacking fault occurs in the zincblende structure in the same way as it does in the fcc lattice. Since there are two (111) planes in the zincblende lattice, the formation of the stacking fault involves removal (intrinsic fault) or insertion (extrinsic fault) of a pair of planes to preserve the tetrahedral coordination. If the AaBj3Cy stacking sequence of { 11l} planes is written simply as ABCABC, then the extrinsic fault gives rise to ABCJBIABC stacking, and the intrinsic fault to A / C ABC stacking. A low-energy fault is formed only between the closely spaced aB planes (glideset) (Hirth and Lothe, 1982). A stacking fault is a region bounded by two partial dislocations formed by the dissociation of a perfect dislocation. By the use of weak beam contrast analysis in the transmission electron microscope, it has now been established that the perfect a/2 [l lo] dislocations in III/V compounds are dissociated into Shockley partials (Gomez and Hirsch, 1978; Gottschalk et al., 1978; Carter et al., 1981; Mader and Blakeslee, 1974) according to

Since the long-range strain energy associated with a dislocation is proportional to lbI2,where b is the Burgers vector, it can be seen from Eq. (1) that dissociation is energetically favored. The repulsive elastic interaction between the two partials pushes them apart to form a stacking fault between them. A 60" dislocation of the glide set dissociates into a 90" (edge) and a 30" partial. As opposed to the 60" dislocation, the screw dislocation dissociates into two 30" partials and the edge dislocation into two 60" partials. In GaAs (Gomez and Hirsch, 1978), both A(g) and B(g) dislocations,'

' For explanation of the notation, see the foreword to Conference of Dislocations in TetrahedrallyCoordinated Semiconductors in Hunfeld, 1978, in J . de Physique 40,Colloque C6 ( 1979). * The A(g) and B(g) notations, instead of z and b, are used to denote the dislocations introduced by bending, since it is now widely accepted that the mobile dislocations are of the glide set configurations.However, it should be mentioned that experimentallythe core structure of the dislocation that is the carrier of plastic deformation is not unambiguously known.

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299

TABLE I1 STACKING FAULTENERGIES IN GaAs AND InP Semiconductor GaAs

InP

Doping (~m-~)

--

undoped Te 10" Sn Sn 10''

-

Stacking Fault Energy (mJ m-') 48 f6" 23' 1W 6'

18"

"Gomez and Hirsch (1978). bH.Gottschalk, G. Patzer, and H. Alexander, Phys. Stat. Solidi a 45,207 (1978). 'V. M. Astakhov, L. F. Vasileva, Yu. G. Siodorov, and S. I. Stenin, Sou. Phys. Solid State 22, 279 (1980).

introduced by bending the samples at 65OoC,were found to be dissociated and to have the same separation, suggesting that the different core structures of the two dislocations do not have any effect on the separation. Even in alloy semiconductors dissociation was observed. From the separation of the partials, the intrinsic stacking fault energy (SFE) can be determined. Table I1 gives the stacking fault energies for GaAs and InP. The SFE depends on doping. It decreases with increasing doping, an effect that is responsible for the formation of stacking faults in dislocation-free heavily doped GaAs (Kamejima et al., 1979). It should also be noted that the formation of twins is inherently connected with that of stacking fault, the tendency for twinning being large when the SFE is low (Hirth and Lothe, 1982). The lower SFE of InP would therefore suggest that growing twin-free InP crystals is more difficult compared to GaAs.

111. Mechanical Properties

3. GLIDE SYSTEM

Semiconductors are brittle at room temperature. This is due to their high Peierls force, the minimum force that has to be overcome before glide occurs. The Peierls force is high because dislocation glide involves severing of the strong directional bonds between the atoms. However, semiconductors become increasingly ductile at temperatures above 20.5TM, where TM is the melting point in kelvins. In this temperature range the plasticity of semicon-

300

V. SWAMINATHAN AND A. S. JORDAN

ductors is similar to that of fcc metals (Siethoff and Schroter, 1984;Schroter and Siethoff, 1984). The lowest temperature at which plastic deformation under uniaxial loading conditions was observed is 250°C (0.2TM)in the case of in the case of GaAs (Swaminathan and Copley, 1975)and is 480°C (0.56TM) InP (Brown et al., 1980). In InP plastic deformation occurred by a combination of slip and twinning in the temperature range 0.56TMto 0.75TM (Brown et al., 1980),and only by slip at higher temperatures. No twinning was observed in the case of GaAs, however (Swaminathan and Copley, 1975; Laister and Jenkins, 1973),for high-temperature deformation. Like other fcc structures, the primary slip system in GaAs (Swaminathan and Copley, 1975;Laister and Jenkins, 1973) and InP (Brown et al., 1980, 1983;Brasen and Bonner, 1983;Muller et al., 1985)is (1 1 l } (1 10). Although the primary slip plane in the cubic semiconductors is { 1 1 l}, an important question arises as to whether shear occurs between aB or Bfl planes (Fig. lb). For a long time it was thought that glide occurs between Bfl planes, since this involves breaking of the smallest number of bonds (Shockley, 1953). However, high-resolution transmission electron microscopy studies on the nature of dislocations in semiconductors reveal that dislocations in semiconductors are dissociated into partials and that they remain so during their motion (Gomez and Hirsch, 1978;Gottschalk et al., 1978;Carter et al., 1981). These observations regarding dissociation raise doubt whether dislocations glide in the BP planes (shuffle set), since dissociation in these planes produces a high-energy stacking fault. At present it appears that the most plausible model for glide in semiconductors is that it occurs between the closely spaced crB planes (glide set) (Hirsch, 1981).

4.

STRESS-STRAIN CURVES

The mechanical behavior of any crystalline solid is represented by a stressstrain curve. The most common method for obtaining stress-strain curves of solid materials, including semiconductors, is the compression (or tension) test. This is done in a constant displacement-rate machine in which the specimen is kept between two rigid crossheads while one of them moves at a fixed speed. The deflection of a stiff string attached to the crosshead measures the axial force on the specimen at any instant. The force is recorded as a function of the crosshead displacement, which can then be converted into shear stress-shear strain curves from the specimen dimensions. The total strain rate, i, under these conditions is the sum of the elastic strain rate in the specimen, the plastic strain rate in the specimen, and the strain rate due to elastic displacements in the machine, which can be written as

7. DISLOCATIONS IN III/V COMPOUNDS bTo, = Z/G

301

+ bNv,

where G is the effective shear modulus of the system specimen-machine. The macroscopic deformation curves can be qualitatively described by Eq. (2) and the basic mechanical transport equation for a given glide system, which is given by b = bNv,

(3)

where 8 is the shear strain rate and v is the average velocity of the dislocation. It is also appropriate to use in Eq. (3) the value of the mobile rather than the total dislocation density for N . In a crystal with a few grown-in dislocations, at the beginning of deformation a constant strain rate according to Eq. (2) can be maintained only if the elastic deformation rate b/G produces high stresses. Since dislocation velocity v depends on stress, in the medium to high stress range, as

with a stress exponent (m)between 1 and 2, the velocity of dislocation rises with increasing stress. The dislocation density increases as a result of a regenerative process, and the increase tends to facilitate further flow. Once again according to Eq. (2), to maintain the strain rate the velocity decreases. This in turn leads to a reduction in stress (Eq. (4)). The term +/G becomes zero and negative. Since strain rate is constant, the slope of the stress-strain curve becomes zero and negative and the upper yield point is produced. With further increase in the dislocation density, further flow is inhibited by the interaction of dislocations and work hardening sets in. The applied stress must rise again to keep the dislocation velocity at the level determined by the transport equation. The slope of the stress-strain curve becomes positive once again, giving rise to a pronounced minimum in stress-strain curve. The stress at this point is the lower yield point. The pronounced yield point in the stress-strain curves of semiconductors is thus the result of the multiplication of the initial few dislocations and is not the result of the dislocations breaking away from impurities (Cottrell effect). The values of the upper and lower yield stress and strains depend on temperature, strain rate, machine compliance, orientation and initial dislocation density of the crystal. Combining Eqs. (3) and (4)together with the temperature dependence of the dislocation velocity, which follows an Arrhenius type of relation, exp- E/klT; and further noting that the dislocation density increases as the square of the stress, the following equation can be obtained to represent the temperature and strain rate dependence of the

v. SWAMINATHAN AND A. s. JORDAN

302

upper and lower yield stresses in semiconductors (Alexander and Haasen, 1968): 5, = Cy.il'"exp(E,/kT), (5) where the constants C , and n and the activation energy E, are different for the upper and lower yield stresses. The constant n is related to the exponent rn in Eq. (5) as n = 2 rn, and E , is related to E, the activation energy of dislocation motion, a more fundamental quantity, as E, = E/n. The upper and lower yield points thus produced are clearly seen in the ~ ) single stress-strain curves from S-doped n-type (n 1.4 x 1OI8 ~ m - InP crystals compressed at constant strain rate in the temperature range 475675°C shown in Fig. 4 (Brasen and Bonner, 1983). The InP crystals were oriented such that the compression axis was parallel to [ 3 z ] and the side . [ 3 u ] stress axis facilitates the faces were parallel to [ 1111 and [E5]The operation of only one of the possible { 111) (1 10) slip systems in the initial stages of deformation. Also, the specimens had an aspect ratio of 2: 1 to ensure a purely uniaxial state of stress in a significant volume of the material (Swaminathan and Copley, 1975).

+

-

28n-TYPE InP

25r

% GLIDE STRAIN

Fic. 4. Resolved shear stress-glide strain curves of S-doped InP (n 1.4 x 10" cm-3) at temperatures indicated. The compression axis was [123], and the loading was at a constant strain rate 6.7 x 10- s - '. The stress-strain curves exhibit pronounced yield behavior. The three stages of deformation I, 11, and 111 denote easy glide, work hardening, and recovery, respectively (from Brasen and Bonner, 1983). 5

7. DISLOCATIONS IN III/V COMFQUNDS

303

The stress-strain curve measured under a constant strain rate exhibits typically three stages of deformation: Stage I is characterized by a yield drop and followed by an easy glide region; stage I1 represents a hardening stage where the slope of the stress-strain curve is constant; stage I11 characterizes a recovery stage. The three stages are marked in the strain-strain curves in Fig. 4.At a high degree of deformation at low strain rates and high temperatures (> 0.8Td,a second hardening stage (stage IV) and a second recovery (stage V) have been seen in Si, Ge, and InSb. They can be expected in InP and GaAs as well. At high temperatures the first recovery stage is associated with a diffusion-controlled recovery process involving point defects, while the second stage is associated with dislocations moving from one glide plane to another (cross-slip). In the intermediate temperature range OST', to OAT',, where the deformation is limited up to stage I11 only, because of the reduced concentration of point defects the recovery will be akin to the cross-slip recovery of stage V at high temperatures.

5. DEFORMATION MICROSTRUCTURE

The three-stage stress-strain curve exhibited by semiconductors is very similar to that exhibited by many materials. This similarity underscores the point that the various dislocation interactions that are responsible for the three stages of deformation are more or less independent of structure. A further point to be noted is that the dislocation microstructures in semiconductors deformed to strains in the three stages are very similar to those of fcc metals. The distribution and nature of dislocations in deformed GaAs and InP have been studied using transmission electron microscopy after various stages of deformation. The dislocations in the deformed sample have Burgers vectors of the type u/2 (1 lo), and most of them are of the 60" type. For small amounts of strain, during stage I, the deformation microstructure is characterized by the presence of long straight dislocations aligned along the (1 10) direction (Laister and Jenkins, 1973; Swaminathan, 1975), which is presumably the direction of low Peierls energy. Pure edge dislocations with (1 12) axis have also been seen. With an increasing degree of deformation (stage I1 and beyond), a highly disordered dislocation structure, which is similar to that in deformed fcc metals, is developed. Dislocation walls that lie along (1 10) directions form, and the interior of the cell structure becomes relatively dislocation-free. In some cases Lomer dislocations with { 100) slip plane have also been observed in samples tested up to or beyond stage I1 (Brasen and Bonner, 1983; Swaminathan, 1975). In stage 111, subboundary formation becomes quite pronounced (Swaminathan, 1975).

V. SWAMINATHAN AND A. S. JORDAN

304

6. CRITICAL RESOLVEDSHEARSTRESS (CRSS) A mechanical parameter of great interest that is obtained from the stressstrain measurement is the critical resolved shear stress (CRSS, zcrss). Since the volume change of the crystal in plastic deformation is not large, the stress component that causes glide is the shear stress. For a given stress axis the resolved shear stress acting on the glide plane and in the glide direction is the one that is important. This is given by t = ( P / A o )cos

4 cos A,

(6)

where P is the applied load, A, is the cross-sectional area of the specimen, 4 is the angle between the normal to the glide plane and the axis of the applied stress, and E, is the angle between the glide direction and the applied stress axis. T is the critical resolved shear stress, which has to be exceeded for the beginning of plastic flow in a certain glide system. The cos 4 cos Iz term in Eq. (6) is called the Schmid factor (Schmid and Boas, 1935). When there are

50

-

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20 -

-a -I

10

0 0

-

0

0

5-

0 0

0

0

0

u)

$ u

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im 0.5

0

-

0.20.1

6.5

I

I

I

I

I

I

0

40

42

14

16

18

20

305

7. DISLOCATIONS IN III/V COMFQUNDS

10 -

20

-p

//

O//

o o o /

5-

v)

/

8

A

p/o

0

v)

0 W :

/ /

0.

2-

0

;/a

5’

’-O

/

0.5-

/ /

0.2 0.1

-

/

I

I

I

I

I

I

FIG. 6. Temperature dependence of lower yield stress (equated to CRSS) for S-doped and ) et al., 1985); open undoped InP single crystals. Open circles-S-doped (10’’ ~ r n - ~(Miiller squares--&doped (1.3 x 10l8m-’)(Miiller et al., 1985);closed circles-undoped (Miiller et al., 1985);closed squares-S-doped (1.35 x 10l8~ r n - (Brasen ~) and Bonner, 1983); open trianglesundoped (Brasen and Bonner, 1983).

several crystallographically equivalent glide systems the one with the maximum resolved shear stress acting on it will operate first. Figure 5 shows the logarithm of CRSS as a function of reciprocal temperature for GaAs (Swaminathan and Copley, 1975; Guruswamy et al., 1987, 1989). A similar plot for InP is shown in Fig. 6 (Brasen and Bonner, 1983; Miiller et al., 1985). As expected, with increasing temperature the Peierls barrier is easily overcome and CRSS decreases. For Si-doped GaAs crystals, Swaminathan and Copley (1975) obtained the CRSS values by multiplying the yield stress (taken as the stress corresponding to 0.2% strain in the stress-strain curves measured in a constant stress rate experiment) by the appropriate Schmid factors. When the stress-strain curves are measured under constant strain rate, the question arises as to whether qYor zUyshould be taken for calculating the CRSS values. Since the pronounced yield behavior at the beginning of deformation is caused by the multiplication of the initial few dislocations, the value of zUydepends on the initial dislocation density of the crystal (Alexander and Haasen, 1968). The upper yield point is

306

V. SWAMINATHAN AND A. S. JORDAN

attained at a smaller stress in a crystal with a higher dislocation density than in a crystal with a lower dislocation density. Muller et al. (1985) have shown that the onset of dislocation formation occurs at a stress level 10 to 20% lower than the lower yield point, T , ~ It . thus appears that qYis the proper value to determine CRSS. The CRSS values shown in Fig. 6 for InP are normalized to a strain rate of 10-4s-'. For data taken at different strain rates, the normalization to one strain rate is done using the relation between zly and 8 given by Eq. ( 5 ) taking the value of rn as unity (Alexander and Haasen, 1968; Gottschalk et al., 1978).

HARDENING 7. IMPURITY The addition of dopants has a profound effect on the dislocation velocity and thus on T~~~ in semiconductors. In this respect the compound semiconductors differ from elemental semiconductors such as Si and Ge. In Si and Ge, addition of donors softens the lattice, while that of acceptors hardens the lattice (Pate1 and Chaudhuri, 1966). On the other hand, the effect of dopants on the mechanical strength of compounds is quite the opposite. Several investigations have shown that in GaAs the addition of donors such as Si or Te to give a carrier concentration 2 10'8cm-3 increases the yield stress, while the addition of acceptors such as Zn to give a hole concentration 10l8cm-3 decreases it (Swaminathan and Copley, 1975; Laister and Jenkins, 1973; Sazhin el al., 1966). The hardening due to donors is generally more pronounced than the softening effect due to acceptors, as shown in Fig. 7 (Swaminathan and Copley, 1975). In fact, at high acceptor concentrations ( > 10l8cm-3), a certain hardening of the material was observed, though still less than that produced by donors (Osvenskii et al., 1969; Ninomiya, 1979). In the case of InP, addition of S (donor) to give electron concentrations of 10'8-1019cm-3 increases the yield stress compared to the undoped crystals (Fig. 6).Brown et al. (1983) found that for Ge, which acts as a donor in InP, at doping levels corresponding to carrier concentrations of l o i 7 cm-3 the crystals are weaker compared to undoped (n 4 x 1015~ m - crystals. ~ ) However, at high Ge doping levels (n loi9cm-3), tUywas temperatureindependent over the range 823-923 K, unlike undoped and low-doped crystals where rUy decreased with increasing temperature. At temperatures above 6oo"C, highly doped crystals had high zuy. The improved mechanical strength in turn produced low dislocation density in Ge-doped crystals (Brown et al., 1981) (Section IV.11). Zinc, which acts as an acceptor in InP, produces a hardening effect even at low doping levels (< 1OI8 cm-3), unlike in GaAs (Muller et al., 1985). Further, Zn-doped crystals show a stronger on temperature than the S-doped crystals (Muller et al., dependence of

-

-

7. DISLOCATIONS IN III/V COMPOUNDS

20

-I n 0

-

I

I

I

Si-DOPED (f.6xiO'*/cm3) 0 Cr-DOPED o UNDOPED (- 1 0 4 6 1 ~ ~ 3 ) 4 Zn-DOPED ( 5 x IO1*/cm3)

-

307 I

-

v,

v)

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p 10v)

0

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w>

-

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0 200

300

400

500:

I 600

TEMPERATURE OC FIG. 7. Temperature dependence of yield stress obtained from repeated yielding experiments on single crystals of undoped and doped GaAs (Swaminathan and Copley, 1975).

1985). For both Zn- and S-doped crystals, qYis found to vary roughly as C1I3, where C is the dopant concentration (Volkl et al., 1987). In the case of GaAs the doping effect on yield stress is also reflected in dislocation velocity measurements (Ninomiya, 1979; Choi et al., 1977). The velocity was measured by double etch technique in specimens that were stressed by three-point bending in the temperature range 150-500°C (Choi et al., 1977). Based on geometrical considerations on expanding dislocation loops, the dislocation type was determined and the velocities of As(g), Ga(g) or screw dislocations were determined at resolved stresses 0.2 to 10kg/mm2. Screw and Ga(g) dislocations were found to have roughly equal velocities in n-type material, and the velocity of Ga(g) dislocations was found to depend strongly on donor concentration, decreasing with increasing donor concentration. In p-type samples, both As(g) and Ga(g) dislocations had nearly equal velocities, and the velocities were constant up to a carrier concentration of 3 x lo'* cm-3 and decreased with further increase in concentration. The doping effect on yield stress can also be understood from the velocity data with the assumption that the slowest dislocations determine the yield stress. First, in p-type GaAs, dislocations move faster than the slowest Ga(g) dislocations in n-type undoped and doped GaAs. Therefore, the yield stress of p-type material would be smaller than that of undoped or n-type material, as observed (Fig. 7). Second, at high doping levels (> 3 x 10" cm-3) in p-type GaAs, the velocity decreases rather suddenly, which could explain the slight hardening observed in heavily Zn-doped GaAs (Osvenskii et al., 1969).

308

V. SWAMINAMAN AND A. S . JORDAN

Detailed dislocation velocity measurements in InP as a function of doping have not yet been done to confirm whether in both Zn- and S-doped crystals, dislocations move more slowly compared to undoped crystals, so as to be consistent with the yield stress data. A preliminary study by Nagai (1981) indicated that P(g) dislocations in undoped InP have a similar velocity to As(g) dislocations in undoped GaAs. But, surprisingly, in S-doped crystals they had a higher velocity compared to the undoped ones. More experiments are needed to confirm this result. Further, the velocity of In(g) dislocations needs to be determined. If In(g) dislocations behave like Ga(g) dislocations in GaAs, they would be the slowest and the yield stress would be affected by them and not by P(g) dislocations. The doping effects on dislocation velocity and plasticity are mostly ascribed to electronic effects rather than to metallurgical ones. The latter, which give rise to solution hardening in metals, include mainly elastic interactions between impurities and dislocations. This interaction arises from the misfit strain due to the size differences between the impurity atom and the host atom, and to a second order from the changes in the elastic constants due to the presence of the impurities. Obviously such an interaction cannot explain the dependence of hardening only on the electrical activity of the dopant rather than on the size of the dopant atom. In some special cases, metallurgical effects such as precipitation hardening (Zn at high concentrations in InP (Mahajan et al., 1979) or in GaAs (Osvenskii et al., 1969)),and hardening by asymmetrical defect complexes (impurity-vacancy pair, Si in GaAs (Swaminathan and Copley, 1976 Chen and Spitzer, 1981)) have been proposed. Generally, the doping effects on plasticity are ascribed to predominantly electronic influences (Hirsch, 198 1). Dislocations are expected to have energy levels in the band gap of semiconductors because of the presence of unsaturated (dangling) bonds along their axis. Thus, kinks on dislocations can be neutral or charged, depending upon the relative position of the Fermi level and the kink energy levels. The change in the Fermi level brought about by doping can, in turn, affect the concentration and/or migration energy of charged kinks. This, in turn, affects dislocation velocity, since the motion of dislocations occurs by the motion of double kinks (Celli et al., 1963). Besides donors and acceptors, isovalent impurities also have a profound effect on mechanical strength of III/V compounds for reasons other than the electronic effect just discussed. A notable example is In in GaAs (Guruswamy et al., 1987). The addition of In up to 0.25-1 atom% to GaAs makes possible the growth of nearly dislocation-free crystals, essentially because of the increased resistance to thermal stress-induced glide near the growth temperature (Section IV.ll). Measurements of stress-strain curves of In-doped GaAs crystals in the temperature range 700-1,100"C (0.64-0.91 T,) show that there

7. DISLOCATIONS IN III/V COMPOUNDS

309

is a factor of 2 to 4 increase in CRSS (see Fig.5) compared to crystals containing no In (Guruswamy et al., 1987; Djemel and Castaing, 1986; Tabache et al., 1986; Hobgood et al., 1986).The hardening due to In perhaps occurs because of metallurgical effects rather than electronic factors, since In, being an isovalent dopant, does not change the electrical activity of GaAs. This increase in CRSS is roughly in agreement with the hardening predicted based on a solid solution hardening model where an In atom with four nearest As neighbors (a solute molecule) is the hardening agent (Ehrenreich and Hirth, 1985). Also consistent with the hardening effect, Yonenaga et al. (1986) observed that the velocity of the As(g) dislocations is greatly reduced under low stresses in the temperature range 350-750°C in In-doped (2 x 10'' cm-3) GaAs and is lower than that of the usually slow-moving Ga(g) dislocations.

8. MICROHARDNESS AND PLASTICITY AT ROOMTEMPERATURE Although GaAs and InP are brittle at room temperature, plastic deformation may be induced by using indenters. This is because a large hydrostatic stress component around the indenter with a superimposed shear stress inhibits the onset of fracture, and plastic deformation may therefore occur at temperatures where uniaxial loading alone would lead to fracture. The low-temperature deformation characteristics of semiconductors are studied by microhardness measurements. Further, the microhardness measurements are easily suited to determining the plasticity of epitaxial films. For example, the mechanical hardening and softening produced by donors and acceptors, respectively, have also been verified in epitaxial GaAs and AlGaAs films via microhardness measurements (Swaminathan et al., 1983). Semiconductors exhibit a hardness anisotropy that is dependent upon both the orientation of the indenter and the plane of indentation (Brasen, 1976; Watts and Willoughby, 1984). Brasen found in InP that the hardness was highest on the (100) plane followed by (110) and ( l l l ) , and that in the (100) and (110) the hardness varied with the direction of indentation. The variation in hardness with direction and plane of indentation has been explained in terms of the slip systems that are activated (Brasen, 1978). In addition to the anisotropy mentioned earlier, there is also an effect of polarity in hardness o n l 1 1 ) faces of III/V compounds. In general, the hardness of (1 11) and (1 11) faces is different. For n-type GaAs, the surface terminating in Ga atoms is harder than that terminating in As atoms, while for p-type material the As face is harder than the Ga face. This polarity of hardness has been explained in terms of the differences in the velocities of the As(g) and Ga(g) dislocations for n- and p-type material (Hirsch et al., 1985).

310

V. SWAMINATHAN AND A. S. JORDAN

The hydrostatic stress around the indenter that prevents brittle failure at room temperature can also be used in compression experiments (Rabier et al., 1985; Lefebvre et al., 1985). Rabier et a!. performed uniaxial compression experiments at room temperature on n- and p-type GaAs under a confining hydrostatic pressure. Unlike the high-temperature deformation characteristics, the n-type crystals were found to be softer than intrinsic or p-type crystals. This suggests that the influence of doping can be different at low temperature and high stress from that at high temperature and low stress. Further, microtwinning has been observed in deformed crystals, indicating it as a deformation mode (Lefebvre et al., 1985; Androussi et al., 1986).

IV. Dislocation Generation and Reduction during Growth of Bulk Crystals LEADING TO DISLOCATION GENERATION 9. MECHANISMS There are three main mechanisms leading to the generation of dislocations during growth (Mutaftschiev, 1980): (1) condensation of the excess point defects present near the growth temperature to form prismatic dislocation loops; (2) nonuniform heat flow during solidification and the ensuing thermal stresses, causing plastic deformation; and (3) defective seed crystal or accidental introduction of macroscopic foreign particles during growth, causing generation and multiplication of dislocations. Of these three mechanisms, the first two are the most important to be considered.

10. DEVIATION FROM STOICHIOMETRY

Brice and King (1966) and Brice (1970) in the late 1960s noted that the partial pressure of As during growth of GaAs is a parameter to control the dislocation density in horizontal Bridgman crystals and pulled crystals. More systematic study later demonstrated the critical role of melt stoichiometry in the generation of dislocations (Holmes et al., 1982; Ta et al., 1982; Parsey et al., 1981, 1982; Lagowski er al., 1984). In small GaAs crystals (< 1.5cm) grown under reduced thermal stress by the horizontal Bridgman method, in which the stoichiometry was controlled by controlling the arsenic source temperature, TA,, it was found (Parsey et al., 1981, 1982) that the dislocation density was a minimum at a TAs 617"C,as shown in Fig. 8. Deviations from the minimum arsenic temperature gave high dislocation densities similar to

-

7. DISLOCATIONS IN III/V COMPOUNDS

31 1

1

p - TYPE

613 615 617 619 621 623 ARSENIC SOURCE TEMPERATURE, TA, ("C)

FIG. 8. Dislocation density versus arsenic source temperature for lightly doped n- and p-type GaAs (from Lagowski et al., 1984).

those obtained in crystals grown under large thermal stresses. The dislocations generated due to deviations from stoichiometry are essentially the dislocation loops formed by the condensation of point defects. The formation of dislocations by point defect condensation also showed a unique dependence on conductivity type in GaAs. For n-type doping at levels of 10'' ~ m - less ~ ,than that required for impurity hardening, the dislocation density decreased. In contrast, with p-type doping the dislocation density increased. These results are interpreted as a Fermi level effect on point defect condensation (Lagowski et al., 1984). Specifically,the effect is supposed to be a change in gallium vacancy concentration. The formation of prismatic vacancy loops requires the presence of vacancies from both sublattices. However, the presence of Vc, alone would be sufficient, since VA, can be created upon migration of V,, (Lagowski et al., 1984).Since V,, behaves as an acceptor with an energy level close to the middle of the energy gap, the shift of the Fermi energy towards the valence band with p-type doping increases the concentration of neutral V,,, which promotes migration and condensation. Melt stoichiometry also plays a minor role in reducing dislocation density in liquid encapsulated Czochralski (LEC) grown crystals. The standard encapsulant is liquid B,O,, which prevents escape of the volatile component

312

v. SWAMINATHAN AND A. s. JORDAN

As or P in the case of GaAs or InP, respectively. Kirkpatrick et al. (1985) have reported that in LEC GaAs growth, controlling the As atom fraction in the melt between 0.505 and 0.535 may be advantageous for minimizing dislocation density. Tomizawa et al. (1987) have obtained 5-cm diameter GaAs crystals with dislocation densities as low as 2,000 cm p z by Czochralski growth (without the encapsulant) under controlled As pressure. The observed dislocation density is lower by an order of magnitude than that in conventional LEC-grown crystals. These authors attributed the reduction in dislocation density to improved melt composition by As vapor pressure control and reduced thermal stress due to low temperature gradient just above the melt. The As pressure effect seen in small crystals (up to 2 cm in diameter) grown by the horizontal Bridgman technique has not been reproduced in crystals of large sizes of commercial interest. It is believed that for the commercial-size material there is incomplete solid-vapor equilibrium (Jordan and Parsey, 1986) leading to an apparent insensitivity to As pressure. Nevertheless, it is believed that for dislocation density below 3,000 ern-', stoichiometry control and point defect condensation are important considerations in the growth of commercial-size crystals (Jordan et al., 1986).

-

11. THERMAL STREW

The primary cause for the large density of dislocations in most III/V semiconductor crystals grown from the melt by the Czochralski technique is the plastic deformation caused by thermal stresses (Milvidskii and Bochkarev, 1978). Jordan et al. (1984,1986) have reviewed some of the early work on thermal stress-generated dislocations. Qualitatively, the thermal stress effect can be described as follows (Bennett and Sawyer, 1956). The main cause of the thermal stress is the heat dissipation from the growing crystal. The heat enters the crystal at the solid-liquid interface and leaves through the external surfaces by radiation and convection. This leaves each cross-section of the crystal with a cooler periphery than core, and consequently, because of thermal contraction and expansion, the periphery is left under tension and the core under compression.- If the corresponding resolved shear stress components of the (111) (110) system are exceeded, then the resulting plastic deformation would exhibit the same symmetry as the observed dislocation pat tern. a. Quasi-steady State Heat TransferlThermal Stress Model

Jordan et al. (1980) developed a quasi-steady state heat transferlthermal stress model of the Czochralski process that provided the first fundamental

7. DISLOCATIONS I N III/V COMPOUNDS

313

description of dislocation generation in III/V compounds. The analysis consists of solving for the temperature distribution of the growing crystal (taken to be a cylinder) assuming that (1) the solid-liquid interface is planar at a temperature equal to the melting point, T,, (2) the ambient temperature around the boule is a constant value T, < T,, and (3) the heat loss by natural convection and radiation from the lateral and top surfaces is proportional to the temperature difference between the surfaces and the ambient fluid. Classical thermoelastic principles are used to obtain the radial, tangential, and axial thermal stresses caused by the nonuniform temperature profile. The resolved shear stress for the { 11l} (170) system is then determined. Only five of the 12 slip systems are linearly independent and need to be considered. The stress in excess of the critical resolved shear stress for the five slip systems gives rise to plastic flow, and thus the overall dislocation density is proportional to the total glide strain, which in turn is proportional to the total excess shear stress, oex.In regions o,, = 0, the dislocation density will be zero. Figure 9 shows the calculated oexor dislocation pattern in half a {loo} GaAs grown at an average ambient temperature 200K below the melting point (T, - T.= 200 K) (Jordan et al., 1986). The adjacent macrophotograph shows the dislocation structure, revealed by etching in fused KOH of a {loo} wafer cut from a Te-doped boule. The idea that excessive thermal stresses are the cause of dislocation generation is supported by the good agreement between the calculated and observed patterns in Fig. 9.

*<110 > c

FIG.9. Comparison of predicted dislocation density contour map (left side) with KOH etched pattern of pits for (100) GaAs (right side). A computerized scan generated the etch pit distribution (from Jordan, Von Neida and Caruso, 1986).

314

V. SWAMINATHAN AND A. S. JORDAN

In large-diameter LEC crystals, the radial dislocation distribution is not homogeneous, but dependent on crystallographic orientation. The (100) dislocation distribution exhibits fourfold symmetry, with a minimum in the (1 10) direction at 60% of the radius value. The center and edge of the wafer are heavily dislocated, with maximum dislocation density at the (100) edge. The pattern across the diameter of the wafers thus exhibits the Wshaped profile that has been reported by several authors in correlating physical properties and dislocation density. Figure 10 shows the etch pit density as a function of radial distance along the ( 100) direction for a 50 mm diameter and a 75 mm diameter LEC GaAs (100)wafers (Thomas et al., 1984). The W-shaped distribution is observed for both wafers. Distribution along the (1 10) direction also exhibits the W-shaped distribution, but the dislocation density is lower than that along the (100) direction. A similar W-shaped dislocation distribution has also been observed for InP (Morioka et al., 1987). The observed dislocation distribution for (100) wafers is in accord with the thermal stress model (Jordan et al., 1980).The model predicts that the excess shear stress is maximum near the edge and center of the crystal, the edge stress being higher than the center stress. The stress is minimum at about onehalf of the radius. Further, in moving from the (1 10) to the (100) direction on a { 100) wafer, the stress increases. Both the observed W-shaped pattern of the dislocation distribution and the relatively higher dislocation density along the (100) direction compared to the ( 110) direction are in excellent

-

i

EDGE

0.6

0.2 0 0.2

0.6

NORMALIZED RADIUS

4

EDGE

FIG. 10. Radial dislocation density distribution along (100) direction in 50 and 75mm diameter LEC (100) GaAs slices (from Thomas er al., 1984).

7. DISLOCATIONS IN III/V COMPOUNDS

315

agreement with the calculated thermal stress distribution, indicating that dislocation generation in large-diameter (> 20 mm) LEC crystals is primarily due to thermal stress-induced plastic deformation. The predicted dislocation patterns for { 11 l} wafers display a sixfold symmetry and are also in satisfactory agreement with the etch pit distribution obtained on both LEC-grown GaAs (Jordan et al., 1984) and InP (Jordan et al., 1985) crystals. The agreement improves when axial gradients and displacements are also considered in the thermoelastic model, in addition to radial extension (Kobayashi and Iwaki, 1985). The clearly defined radial distribution of dislocation in the seed end of the crystal becomes more diffuse as the tail end is approached. The dislocation distribution is dense, and no definite symmetry is observed. This is believed to be due to increasing dislocation multiplication along the length of the crystal by dislocation climb and other mechanisms, and to dislocation-dislocation interactions. The tail end distribution cannot be explained on the basis of the thermal stress model described earlier, which does not consider these dynamic aspects of dislocation multiplication.

12. METHODS TO REDUCE DISLOCATION DENSITY Jordan and co-workers (1986) have investigated the effect of various parameters in the quasi-steady state heat transfer/thermal stress model on dislocation generation. They find that decreasing the pull rate would have only a minor effect on reducing the dislocation density. On the other hand, the magnitude of the heat transfer coefficient has a profound influence on dislocation density. The higher the heat transfer coefficient, the higher the dislocation density, especially near the periphery. The incorporation of a radiation shield and/or an after-heater in the growth system would help lower the heat transfer coefficient. Alternatively, replacing the B,O, liquid encapsulant with a gaseous ambient such as As, can also achieve the same goal. For the standard LEC growth conditions for small diameters, the dislocation density rises superlinearly with crystal diameter for d < 2 cm. With increasing size, the density saturates at the periphery and declines in the interior (Jordan and Parsey, 1986). a. Reducing Temperature Gradients

By far the most important parameter that influences dislocation generation in large-diameter LEC crystals is the axial and radial temperature gradients existing at the melt-B,O, interface and across the B 2 0 3layer itself. Reducing these gradients reduces the thermal stresses, and hence the dislocation

V. SWAMINATHAN AND A. S. JORDAN

316

density. For example, thermal stress calculations show that a 10-fold decrease in ambient temperature gradient (Tf - T, is reduced by a factor of 10) results in a 13-fold reduction in dislocation density at the periphery, as illustrated in Fig. 1I (Jordan and Parsey, 1986). However, modifications required in the conventional LEC growth furnace to reduce temperature gradients are by no means simple. The advantage of low thermal gradients in reducing dislocation density in LEC crystals has been demonstrated in the case of both GaAs (Von Neida and Jordan, 1986; Von Neida et al., unpublished; Elliot et al., 1984; Fukuda, 1983) and InP (Morioka er al., 1987; Katagiri el al., 1986; Shinoyama et al., 1980, 1986; Muller el ul., 1983). Reducing the temperature gradient can be accomplished by increasing the thickness of the B,O, encapsulant and/or introducing radiation shields and after-heaters (to increase T,) in the growth chamber (Jordan et al., 1980). By using a heat shield, Elliot et al. (1984) were able to reduce the gradient to 6"C/cm, compared to a typical value of 1002WC/cm, and achieved average dislocation densities less than 1,000cm-* in

-

PERIPHERY r / r o : I

(00

-

RELATIVE CRSS

FIG. 11. Dependence of CT,, for a 75-mm diameter boule on relative CRSS (relative to the \ d u e for GaAs shown in Fig. 5) at - T, = 200 and 20 K. The radial locations along a (100) direction displayed are center, relative radius (rir,) = 0.6, 0.8, 0.9, and 1. This plot may be interpreted as showing dislocation density versus degree of impurity hardening (from Jordan, Van Neida and Caruso, 1986).

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6-cm diameter, In doped (2.8 x 10'' cmP3)GaAs crystal. In an rf-heated LEC puller to grow 5-cm diameter undoped GaAs, Von Neida et al. (Von Neida and Jordan, 1986; Von Neida et al., unpublished) reduced the gradient to 20"C/cm by increasing the thickness of the B203. This resulted in a dislocation density of 5,000cm-2 at the center and 8,000cm-2 near the periphery of seed end wafers. Similar benefits of reducing thermal gradient on dislocation density have been realized in InP LEC growth as well. In growing (1 11) InP crystals, Muller et al. (1983) increased the B 2 0 3 thickness from 7 to 30mm, which decreased the gradient from 80 to 20"C/cm. For a 3-cm diameter crystal, the average dislocation density was reduced from lo5 to lo4 cm-2. Shinoyama et al. (1980, 1986) also adopted the method of increasing B 2 0 3 thickness to reduce temperature gradients and achieved a nearly proportional reduction in dislocation density. Katagiri et al. (1986) employed a heat shield above the heater and the crucible and succeeded in reducing the temperature gradient near the melt-crystal interface from lWC/cm to 40"C/cm. As a result, the dislocation density was reduced from 8 x lo4 cmP2to 3 x lo4 cmP2.A similar approach was also adopted by Morioka et al. (1987) in their growth of 5-cm diameter Sn-doped InP crystals. Under the reduced temperature gradient, not only is the dislocation density reduced, but also its radial distribution becomes more uniform (Morioka et al., 1987; Katagiri et al., 1986). Low-gradient LEC growth is, however, not without problems. One of them is the diameter instability associated with the lack of confining radial gradient present in standard LEC growth. Further, the lower temperature gradient increases the surface temperature of the crystal as it emerges from the encapsulant. This leads to decomposition of the surface, giving rise to excess Ga or In droplets. These droplets can cause polycrystalline growth if they migrate through the crystal or reach the solid-liquid interface (Thomas et al., 1984; Morioka et al., 1987). In the growth of InP, twinning becomes a problem under a low-temperature gradient. To achieve diameter control and suppress thermal decomposition under low-gradient LEC growth, several schemes have been tried. To reduce surface damage, the pulled crystal is kept in B 2 0 3 at all times. This technique is called the fully encapsulated Czochralski (FEC) method (Nakani et al., 1984). The application of a vertical magnetic field has been found to improve diameter control by suppression of laminar thermal convection in the melt (Osaka and Hoshikawa, 1984). Using a vertical magnetic field in the FEC growth, Kohda et al. (1985) grew 5-cm diameter, completely dislocation-free semi-insulating GaAs under a temperature gradient of 30-5O0C/cm. By using an x-ray imaging scheme to monitor crystal diameter, Ozawa et al. (1986) were able to achieve diameter control under a low-temperature gradient GaAs LEC growth, which also had an As ambient to minimize surface

318

V. SWAMINATUAN AND A. S. JORDAN

decomposition. In the absence of these modifications, low-gradient LEC growth is a difficult technique for routine applications. The Kyropoulous method, which uses B,O, encapsulation, also permits low gradients and low dislocation density (Duseaux, 1983; Jacob, 1982a, 1982b). For achieving low-dislocation density crystals under low thermal gradients, vertical (VGF) (Gault et al., 1986; see also Clemens et al., 1986) or horizontal gradient freeze (HGF) techniques appear more promising. The horizontal Bridgman technique, which is a low-gradient process, produces crystals of low dislocation density, but has certain disadvantages compared to the LEC technique. First, the crystals are D-shaped instead of round, which make them less attractive for IC applications. Second, the inevitable contamination with Si from the quartz boat hinders the making of semiinsulating crystals. In this regard, the HGF technique, employing pyrolytic boron nitride (PBN) boats, produced low-dislocation density (1,0004,000 cm 2, and semi-insulating two-inch D-shaped GaAs crystals and appears useful for further scale-up (Young et al., unpublished). A more promising technique is vertical gradient freeze, where the solidifying liquid conforms to the shape of the PBN crucible (Gault et a]., 1986; Clemens et al., 1986). Five-centimeter diameter Gap, InP, and GaAs boules have been prepared by the VGF technique with dislocation densities comparable to those of HGF material (Gault et al., 1986; Clemens et al., 1986). Adding a minute amount of In (2 x 1OI9 cm-3) has resulted in an average dislocation density of less than 1,OOo~rn-~ (Abarnathy et a/., 1987). Recently, the VGF technique has been extended to the growth of 7.5-cm diameter GaAs with a dislocation content less than 2,500 cm-’ (Clemens and Conway, 1988). b. Impurity Hardening

The best solution to achieve stable growth of large-diameter and lowdislocation crystals by the LEC method appears to be a combination of moderate temperature gradient and impurity hardening of the lattice that would raise the CRSS for dislocation generation. As illustrated in Fig. 11, in a low-temperature gradient growth (Tf - T, = 20 K), a factor of 3 increase in CRSS would produce crystals completely free of thermal-stress-induced dislocations. Moreover, a mere 2504 enhancement in xcRSS would produce wafers clear of defects over 90% of the radius (Jordan et al., 1984). We have discussed in Section 111.6 the increase in CRSS in the medium temperature range due to the addition of donors in GaAs and of Zn and Ge besides S in InP. Since addition of these impurities results in reduced dislocation density, it should be supposed that the hardening prevails even near the growth temperature. It has been found that addition of S (Seki et a/., 1978;Katagin et al., 1986),Zn (Mahajan et al., 1979; Seki et al., 1978),Te (Seki et al., 1978),and

-

7. DISLOCATIONS IN III/V COMPOUNDS

319

Ge (Brown et al., 1981) in InP and Si (Matsui et al., 1979), Te (Seki et al,, 1978), S (Seki et al., 1978), and Se (Jacob et al., 1982) in GaAs at levels exceeding lo’* reduces the dislocation density. This is illustrated in Fig. 12 for GaAs containing S, Te, or Zn and InP containing S or Zn (Kamejima et al., 1979). Doping with high concentrations of electrically active impurities would not, however, be practical for growing semi-insulating crystals. Lowdislocation-density conductive wafers are suitable for use as substrates required for such applications as heterostructure lasers, LEDs, and photodetectors. Even in these optical devices, if light is allowed to pass through the substrates, optical absorption as a result of high doping can be a problem. In addition, impurities from the substrates can diffuse into epitaxial layers grown on them. For these reasons, it is highly desirable to grow lowdislocation-density substrates by decreasing the doping level and by using electrically inactive impurities. In this regard, isovalent impurities such as In, Ga, and Sb have been remarkably effective in reducing dislocation density (Jacob, 1982),once again because of lattice hardening effects. Particularly, the addition of 1019-1020cm-3 In has produced 7.5-cm diameter GaAs wafers with substantial areas (up to 70%of the diameter) having less than 400cm-’ dislocations. This is illustrated in Fig. 13, which shows the dislocation etch pits on a (100)GaAs wafer that contains 2 x 10” cm- In. At least 70% of the diameter is nominally dislocation-free. In the case of InP growth, isovalent impurities such as Sb, Ga, and As have been used (Shinoyama et al., 1980,1986;Jacob, 1982; Tohno et al., 1984; Ye et al., 1986).Of these, Ga is preferred, since it has a distribution coefficient k > 1 (k w 2.5-4.0), which permits lower concentration of impurities in the melt and minimizes constitutional supercooling problems. Essentially dislocation-free crystals of 25-30mm diameter have been obtained with 1019cm-3Ga doping.

-

-

-

Te Zn

10”

rote

ds

ro20

CARRIER CONCENTRATION ( ~ r n - ~ )

FIG. 12. Etch pit density versus carrier concentration in (a) GaAs crystals and (b) InP crystals (from Kamejima et al., 1979).

320

V. SWAMINATHAN AND A. S. JORDAN

FIG. 13. Macrophotograph of a 75-mmdiameter KOH-etched (100)GaAs wafer grown by the LEC technique. The crystal contains 2 x 10’’ cm-’In. Marker represents lOmm (from Jordan, Von Neida and Caruso, 1986).

Since the distribution coefficient of Ga is greater than 1, its concentration is lower at the tail end of the crystal, which has higher dislocation density. To achieve uniform dislocation reduction along the entire crystal, a doubledoping method, with one impurity having k > 1 and another having k < 1, has been adopted. In the case of InP, Ga and Sb (k < 1) (Shinoyama et al., 1986) or G a and As (k < 1) (Monoka et al., 1987) have been used as codopants. Doping the crystals to reduce dislocation density, even with isovalent impurities, has its problems. First of all, impurity hardening, whether achieved by electrically active dopants or isovalent impurities, is effective in reducing dislocations, particularly in small-diameter crystals. When the thermal gradients are high, dislocations near the edges of the crystals are relatively insensitive to the degree of hardening (Jordan and Parsey, 1986). Impurity hardening, combined with smaller thermal gradients, renders these regions dislocation-free. At a high concentration of impurities, the lattice parameter of the crystal changes, which causes lattice mismatch when 2-3 pm epitaxial layers are grown.

7. DISLOCATIONS IN III/v

COMPOUNDS

321

When GaAs substrates contained 2 6 x lo’’ cm-3 In atoms, the lattice constant increases toward that of InAs. This results in lattice mismatch when GaAs layers are grown on such substrates. The degree of mismatch measured by double crystal x-ray rocking curves shows that the difference in the diffraction angle between the GaAs:In substrate and a 2-3 pm thick GaAs epitaxial layer increases from 12 to 44 arc s as the In doping of the substrate varies from zero to 6.2 x lo1’ cm-3 (Inoue et al., 1986). For 2-3 pm thick layers, an In concentration of 3.7 x lo1’ cm-3 introduced no misfit dislocations. For In >6.2 x lo1’ ~ m - many ~ , misfit dislocations were generated independent of epitaxial layer thickness. The change in the lattice parameter of the substrate by isovalent doping is also encountered in InP co-doped with Ga and As (Morioka et al., 1987).Because of lattice mismatch problems, it is desirable to achieve dislocation reduction at lower concentrations of isovalent impurities.

V. Dislocations and Device Performance The presence of native defects and dislocations has a profound influence in determining the performance of semiconductor devices. However, the correlation between device characteristics and defects has remained, for the most part, elusive. The reason for this is that it is often difficult to isolate pure dislocation effects when the possibility of dislocation-point defect interaction exists. In the case of native defects, it has been even more difficult to correlate device parameters with any specific defect. The implication of such defects is often based on circumstantial evidences. Only in certain instances-for example, in the degradation of GaAs-AlGaAs lasers-are the effects of defects clear-cut. In the development of GaAs-AlGaAs lasers there was a steady increase in lifetimes to lo5 hours, from a few seconds, when the first continuous operation at room temperature was demonstrated, once the degradation in lasers due to dark-line defects became understood. Device degradation is a complex phenomenon involving both dislocations and point defects. In this section we limit our discussion to degradation of electronic and photonic devices caused primarily by dislocations. 13. PHOTONIC DEVICES a. Degradation in Lasers and Light-Emitting Diodes

Dislocations have been closely linked with the degradation of lightemitting devices. This follows from the fact that dislocations cause nonradiative recombination and decrease luminescence efficiency. Ettenberg

322

V. SWAMINATHAN AND A. S. JORDAN

(1 974) showed that dislocations reduce the minority carrier diffusion length, and when the spacing between them is comparable to the diffusion length, luminescence efficiency decreases. By doing spatially resolved photoluminescence in GaAs and InP at a spatial resolution of 3 pm, Bohm and Fischer (1979) found that the half-width of the photoluminescence reduction around dislocations is larger than the diffusion length. They suggested that the quenching of luminescence near dislocations is due to enhanced bulk nonradiative recombination. That dislocations act as nonradiative centers is clearly shown in the cathodoluminescence micrograph in Fig. 14 from an Al,Gal -,Asl -yP, epitaxial film on a GaAs substrate (Petroff et al., 1980). Figures 14a and 14b are, respectively, electron-beam-induced current (EBIC) and cathodoluminescence micrographs showing the recombination characteristics of the misfit dislocations parallel to the [llO] and [llO] directions. Figure 14c is the bright-field electron micrograph from the framed area in Figs. 14a and 14b. Dark contrast in the EBIC indicates reduced carrier collection efficiency, and dark contrast in the cathodoluminescence micrograph indicates reduced luminescence due to nonradiative recombination in the vicinity of the misfit dislocations. The dislocations labelled D,, D,, and D, that show dark contrast are dissociated 60" dislocations. The dislocation labelled D, is an edge sessile dislocation and does not cause nonradiative recombination, as evidenced from the absence of contrast in Figs. 14a and 14b. The absence of recombination at D, is taken to imply that perhaps the core of the dislocation is reconstructed, leaving no dangling bonds (Petroff et al., 1980). Sometimes it is difficult to separate pure dislocation effects from effects produced by dislocation-point defect interactions. It is well known that impurities segregate at dislocations because of the associated stress fields. For example, a fast-diffusing impurity such as Cu in GaAs segregates near dislocations and quenches band edge luminescence. In such cases the quenching of luminescence may be mistaken to be due to nonradiative recombination near dislocations. Heinke (1975; see also Heinke and Queisser, 1974) noted a large effect of luminescence quenching in GaAs when fresh dislocations were introduced by bending, compared to as-grown dislocations. Bohm and Fischer (1979) suggested that this difference was in fact due to segregation of Cu at the deformation-induced dislocations. The relation between dislocation and luminescence efficiency is rather well illustrated in Fig. 15, which shows the external quantum efficiency of graded band-gap Si-doped AI,Ga, -,As LEDs as a function of dislocation density (Roedel et al., 1979). The dislocations in the epitaxial layer have propagated from the substrates, implying that low-dislocation-density substrates would produce a fewer dislocations in the epitaxial layer, and hence more efficient LEDs.

7. DISLOCATIONS IN III/V COMPOUNDS

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FIG. 14. Misfit dislocation network in AI,Ga, -,As,P, -p epitaxial film grown on (100) GaAs substrate by LPE. (a) EBIC micrograph. (b) Monochromatic (A = 790 nm) cathodoluminescence (CL) micrograph of the same area as in (a). (c) Bright field electron transmission micrograph of the same area as in (a). The operating reflections are (220) and (220), and the incident delectron beam is parallel to (001). _Dislocations labelled D,, D,, and D, are misfit dislocations parallel to the [I101 and [llO] direction, and they are of the 60" type. The dislocation labeled D, shows no contrast for the (220) reflection in (c) and is a sessile edge dislocation with Burgers vector parallel to the [llO] in the plane of the interface. Note the absence of contrast for D, in (b) (from Petroff, Logan, and Savage, 1980).

The degradation of lasers can be divided into three categories: (1) A rapid degradation that occurs after a relatively short duration of operation; (2) a slow degradation occurring during long-term operation; and (3) a catastrophic degradation process that occurs at high optical power densities because of mirror facet damage. In the case of LEDs, degradation proceeds via processes (1) and (2).

V. SWAMINAMAN AND A. S. JORDAN

324

lo3

lo4

105

106

pd(crn-* 1

FIG. 15. Efficiency versus dislocation density for 45 individual AI,Ga, -,As:Si LEDs. The dashed line is a calculated curve. (Figure 5 from a paper entitled “The Effect of Dislocations in Gal -,AI,As:Si Light-Emitting Diodes” authored by R. J. Roedel, A. R. Von Neida, and R. Caruso, 3. Electrochem. Soc. 126, p. 639, 1979.)

b. Dark-Line Defect ( D L D ) The rapid degradation of lasers and LEDs has been linked to linear defects known as dark-line defects (DLDs) (DeLoach et al., 1973). The DLDs develop mostly along the ( 100) direction but sometimes along the ( 1 10) direction as well. The nature and origin of the DLDs have been identified by transmission electron microscopy as three-dimensional dislocation networks consisting of long dislocation dipoles and small dislocation loops (Petroff and Hartman, 1973). The DLDs originate from precursor defects in the active layer that are classified as dark spot defects (DSDs) since they appear as dark regions in luminescent images from the active layer (Yonezu et a/.,1974; Ito et al., 1974, 1975; Ishida and Kamejima, 1979). From the very beginning of the discovery of DLDs, it was realized that the growth of DLDs and subsequent degradation of the device was aided by recombination enhanced motion of defects. When electron-hole recombination occurs, the energy may be released as photons (luminescence), used to excite another carrier to higher energy levels (Auger process), or transferred to the lattice as heat (phonon production). In the last situation the excess energy may be deposited locally as vibrational energy at the recombination center, which then increases the rate of defect reactions such as diffusion, dissociation, and annihilation (Kimerling, 1978). Kimerling et al. (1976) showed by in situ TEM studies that electron beam-enhanced dislocation climb motion occurred in Al,Ga, -xAsl -,,P,, that contained point defects introduced by a prior 1 MeV electron bombardment. The enhancement

7. DISLOCATIONS IN III/V COMPOUNDS

325

occurred not only under electrical injection conditions, as in lasers or LEDs, but also under optical injection conditions (Johnston and Miller, 1973; Petroff et al., 1974, 1977).

-

(ZOO) DLD and Dislocation Climb. The growth rate of (100) oriented DLDs is typically cm/s and is dependent on the injection current of the laser (Petroff and Hartman, 1974). The (100) oriented DLDs, which consist predominantly of dislocation dipoles and dislocation loops, have been suggested to arise by a dislocation climb process (Petroff and Hartman, 1973; Hutchinson and Dobson, 1975). The dipoles are interstitial in character, lying in (110) planes (Hutchinson et al., 1975; Petroff et al., 1976). Although the (100) dipoles are predominant, in some instances dipoles along the ( 1 10) direction have also been observed [19771 the small dislocation loops inside the main dipole have been identified to be of the vacancy type (Hutchinson et al., 1975; Petroff et al., 1976). Based on the similarity between the dislocation configuration in degraded lasers and LEDs and that found in fcc metals due to climb of dissociated dislocations, Petroff (1979) suggested that the dislocations forming the dipole may indeed be dissociated into partials. This is consistent with the general observation that dislocations in zincblende semiconductors are dissociated (Section 11.2). However, in the climb models that have been proposed to explain the (100) DLD structure, dissociation has not been considered. The vacancy loops inside the main dipole of the (100) DLD structure are supposed to be the by-product of the climbing dipole. Generally, the absorption or emission of point defects at jogs in the dislocation core would produce dislocation climb motion. Since in a zincblende semiconductor two fcc lattices are involved, the climb process requires addition or removal of two kinds of atoms of the structure. The interstitial character of the dipoles would imply dislocation climb by either the absorption of interstitials or the emission of vacancies of both atoms. Since a supersaturation of point defects associated with each sublattice is not likely, Petroff and Kimerling (1976) proposed a new point defect model for dislocation climb in zincblende semiconductors that requires an abundance of point defects in one sublattice only. Consider an As dislocation and Ga, as the excess point defect. Dislocation climb proceeds as follows: Ga, migrates to the climbing dislocation and attaches itself at the core, creating an arsenic vacancy at the core, in that process. An As atom fills this vacancy and V', in the bulk is created. This vacancy moves around to relieve the tensile stress at the dislocation, and the dislocation has completed the climb process. The excess VA, left behind the climbing dislocation, along with VGa created by the reaction V, GaGa+ GaAs VGa,cluster and collapse to form the vacancy-like prismatic dislocation loops, which are observed inside the

c,,

+

+

326

V. SWAMNATHAN AND A. S. JORDAN

(100) DLD dipoles. In the case of lasers or LEDs grown by LPE, group 111 interstitials are likely to be the excess point defects, since growth occurs from a group 111 metal solution. In the case of structures grown by VPE, group V atoms are presumed to be in excess, yielding V,, as the defect left behind the climbing dislocation. In the preceding model, the diffusion of the Gai toward the dislocation core would determine the rate of dislocation climb. Under carrier injection conditions, the migration of Ga, would be assisted by recombinationenhanced motion. A further outcome of the model is the formation of antisite defects in the As sublattice. A point defect concentration of atom fraction is suggested by the observed dislocation structure. Such a high concentration of defects is supposed to be generated at the hetero interfaces of the epitaxial layers. In view of the uncertainty of the existence of a high concentration of native interstitials required for the climb process in solution, O’Hara et al. (1977) proposed an intrinsic defect generation process. According to this process, the energy released by the electron-hole recombination process at the dislocation allows a host atom on a substitutional site near the dislocation to move onto the next dislocation, creating a vacancy. This intrinsic model requires emission of both group 111 and group V vacancies. To substantiate that the defects needed for the dislocation climb come from the energy released by the electron-hole recombination and are not present a t thermal equilibrium, Hutchinson et al. (1978) investigated dislocation dipole structure in Te-doped n-type GaAs under optical pumping. The sample showed small interstitial dislocation loops after an annealing treatment at 880°C. The concentration of interstitials in these loops is estimated to be of the order of 10’’ cm-3. The presence of the interstitial ioops suggested that no excess interstitials are present in solution. However, under optical pumping the sample developed the dislocation dipole structure characteristic of degraded lasers, indicating that dislocation climb had occurred in spite of the low interstitial concentration. This experiment, according to Hutchinson et al. (1978), confirmed the vacancy emission model for the climb process. Only some of the vacancies emitted by this process are observed as vacancy-type prismatic loops inside the dipoles, and the majority of them are believed to form submicroscopic clusters not observable in the transmission electron microscope. The intrinsic point defect model would predict that there should be no saturation of the climb process. On the other hand, in the extrinsic process, once the available point defects are consumed by the climbing dislocation, the formation of dislocation loops and the growth of the dislocation dipole network would stop. Petroff and Kimerling (1976) observed saturation of the

7. DISLOCATIONS IN III/V COMPOUNDS

327

dipole growth under electron-beam injection conditions. Also, the dislocation networks that were fully developed failed to show any further growth under carrier injection. Further, in broad-area optically pumped laser devices, new defect structures appeared only on the freshly formed DLD network, showing that the point defects enabling the climb process are localized. Thus, some experimental results are not explained by either the extrinsic or the intrinsic model-the saturation effects by the intrinsic model or the growth of DLDs in samples containing no interstitials by the extrinsic model. While each model has some deficiencies, in the intrinsic model it is difficult to envisage the creation of point defects entirely by the recombination energy, which can at most only be equal to the band gap, oiz. 1.4eV for GaAs, when the defect formation energies are likely to be greater than this value. In another experiment it was shown that the point defect needed for the climb process may be provided by an existing defect. By a scanning DLTS technique, Lang et a/. (1979) found that near the dislocation climb network, the concentration of the D X center, a common defect in the n-type Al,Ga, -,As (x 2 0.30) cladding layer of the laser structure at the lo” cm-3 level, decreased by -40%. This suggested that there is a relationship between the D X center and the dislocation network. Although the change in the concentration of the D X center could have occurred either as a result of supplying the point defects directly for dislocation climb or as a result of an indirect interaction with point defects generated by the climb process, Lang et al. (1979) conjectured that the former mechanism is the most reasonable one. They proposed that the decay of the D X center under electron-hole recombination proceeds by the emission of Ga, needed for the dislocation climb in the extrinsic model. Consistent with the picture of two types of dislocations and their different velocities in GaAs (Section 11.2), Hutchinson and Dobson (1980) observed anisotropic (100) DLD growth; i.e., the climb of one type of dislocation is greater than that of the other. Similarly, Imai et al. (1979) observed a fast and a slow growth component in elongation of (100) DLDs under optical pumping, reflecting probably the asymmetry in climb of a and dislocations. We noted earlier that the precursor defects for DLDs originate from threading dislocations in the active layer, which in turn propagate from the substrate. Therefore, the use of low dislocation density substrates for epitaxial growth should yield highly reliable devices. Figure 16 compares the lifetime at 70°C of two classes of Al,Ga, -,As injection lasers having Ga(As, Sb) active layers. The devices that have poor 70°C median lifetimes were made from LPE wafers that were grown on substrates having a dislocation density of -4 x lo4 cmP2,as compared to the good devices for which the substrates had dislocation densities < 3 x lo3cm-’(Anthony et al., 1982).

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V. SWAMINATHAN AND A. S. JORDAN

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FIG. 16. Normal probability plot of the time to failure (solid symbols) or the accumulated testing time (open symbols) for Ca(As,Sb) lasers operated at 3mW at 70°C.The Ga(As,Sb) devices have GaSb concentrations of between 0.4 and 2 mol%, while the GaAs controls have GaSb concentrations of zero or less than 0.1 mol%. These were grown on GaAs substrates having dislocation densities i3 x I03cm-*. The Ga(As,Sb) devices grown on defective substrates had substrates with dislocation densities of - 4 x 104cm-2(from Anthony ef al., 1982).

(110) DLD and Recombination-Enhanced Glide. The dark line defects that lie along (1 10) directions in degraded lasers, the (1 10) DLDs, have been identified by transmission electron microscopic study as relatively straight dislocations lying on the glide plane (Ishida et al., 1977). The growth rate of (110) DLDs is also faster than that of (100) DLDs (It0 et al., 1975; Monemar and Woolhouse, 1977), 10-3-10-2 cm/s compared to cm/s. It has also been observed that the ( 1 10) DLDs can be sources of (100) DLDs (Kamejima et al., 1977). Since process-induced stresses can induce the (1 10) DLDs, they should be kept as low as possible to avoid the rapid degradation of the devices.

-

These DLDs have been shown to be caused by recombination-enhanced dislocation glide (Hutchinson and Dobson, 1975), consistent with their high growth rates and with the fact that the glide direction in the zincblende structure is the ( 1 10) direction. Recombination-enhanced dislocation glide motion has been observed in GaAs-A1GaAs laser diodes under current injection (Ishida et al., 1977; Kamejima et al., 1977), optical pumping (Monemar and Woolhouse, 1977; Kishino et al., 1976; Nakashima et al.,

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329

1977), and electron beam injection (Kamejima et al., 1977; Chin et al., 1980; Maeda and Takeuchi, 1981), with (Kamejima et al., 1977; Nakashima et al., 1977; Kishino et al., 1976) or without (Chin et al., 1980 Maeda and Takeuchi, 1981) an externally applied stress. Maeda et al. (1983) measured the velocity of c1 and p dislocations under electron beam injection in a scanning electron microscope containing a bending apparatus as a function of temperature and stress. Their results for GaAs and InP are shown, respectively, in Figs. 17a and 17b. The velocities of n - GaAs r-26MN/m2 UNDER IRRADIATION

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1

2.2

FIG. 17. (a) Temperature dependence of dislocation velocities of a and fi dislocations in GaAs under 30 keV electron beam irradiation and in darkness (from Maeda et al., 1983). (b) Temperature dependence of jdislocation velocity in InP under 30 keV electron beam irradiation and in darkness (from Maeda and Takeuchi, 1983).

v. SWAMINATHAN AND A. s. JORDAN

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both u and fl dislocations follow an Arrhenius relation in dark as well as under carrier injection conditions. In GaAs, the activation energies are reduced by -0.7 eV for u dislocations and 1.1 eV for fl dislocations in the latter case. These results clearly illustrate recombination-enhanced dislocation glide motion. The enhancement was observed only below a certain critical temperature, T,. From measurements of irradiation intensity, I, and stress, z, dependences, Maeda et al. (1983) expressed the dislocation velocity under carrier injection as V =

Ko exp[ - E,(s)/kT]+ K*(I/Z0)0.84exp{ - [Ed(?)- AE]/kT},

(7)

where AE, the reduction in the activation energy due to the recombination enhancement, is independent of 7 and I. Maeda et al. proposed that the observed A€ values (see Fig. 17) are the energies released during the recombination events at the dislocations. Maeda and Takeuchi (1985) found that AE is different for the same dislocation, depending on the conductivity type of the sample, which suggested a possible difference in the minority carrier capture cross-section of the dislocation levels according to the dislocation charge state in thermal equilibrium. Recombination-enhanced glide of dislocations has also been observed in InP (Maeda and Takeuchi, 1981). Figure 17b shows the temperature dependence of velocity of dislocation under dark and under irradiation of 30 kV electron beam conditions (Maeda and Takeuchi, 1983). The value of AE is 0.9 eV, which is comparable to the value for the dislocation in GaAs.

-

Rapid Degradation of LEDs. Just like the lasers, AlGaAs LEDs also show a rapid and gradual mode of degradation (Yamakoshi et af., 1977). Transmission electron microscopic investigations of rapidly degraded LEDs indicated that the defect structure produced is very much similar to that in degraded lasers. Both (100) and (110) DLDs were present, though the former were predominant (Ueda et a/., 1977, 1979). The (100) DLDs consisted of extrinsic dislocation dipoles, helical dislocations, and dislocation loops. The DLDs were found to develop rather readily in material with a high density of defects, and their propagation required minority injection (Chin et a/., 1980). Therefore, the use of low-dislocation-density GaAs substrates and general cleanliness during epitaxy to minimize defect density in the epitaxial layers have served to reduce the incidence of DLDs and thus to improve reliability (Zipfel, 1985). Gradual Degradation in Lasers and LEDs. Even after elimination of the rapid degradation mode by employing high-quality substrates combined with careful growth and processing procedures, there is still a gradual mode of

7. DISLOCATIONS IN I I I p COMP~UNDS

331

degradation exemplified by a gradual increase in drive current for lasers or a gradual decrease in output power for LEDs (Ueda, 1988). Table I11 summarizes the characteristics of the gradual degradation in AlGaAs and GaInAsP devices (Matsui, 1983; Chu et ul., 1988). The devices that have degraded by accelerated aging at elevated temperatures show dark areas containing extrinsic (interstitial) Frank-type dislocation loops with Burgers vectors u/3 (111). These loops are supposed to have been formed by the condensation of point defects whose migration is assisted by the recombination-enhanced motion. In long-wavelength (1.3-1.55 pm) InGaAsP lasers and LEDs, the effect of substrate dislocations on device performance is less pronounced. Perhaps this can be attributed to the lower recombination energy available for recombination-enhanced motion in InGaAsP compared to AlGaAs devices. Chu et al. (1988) have studied in detail the defect mechanisms in degradation of 1.3 pm GaInAsP/InP wavelength channeled substrate buried heterostructure lasers. They studied the defect structure in devices that showed gradual and rapid degradation under accelerated aging. In devices that showed gradual degradation, the defect mechanism was associated with the nucleation of extrinsic dislocation loops along the V-groove { 111) sidewall TABLE 111 FEATURES OF GRADUAL DEGRADATTON IN AIGaAs/GaAs AND GaInAsP/InP DEVICES‘ Material AlGaAs/GaAs

GaInAsP/InP

Appearance Uniform darkening or DSD formation increase in deep level defects Uniform darkening or DSD formation Dark line defects

Defect Structure Dislocation loop, stacking fault

Precipitates Multiple dislocations Extrinsic dislocation loops

“Ueda (1988); Matsui (1983); Chu et al. (1988).

Mechanism Formation of point defect clusters or loops by climb

Formation of point defects at epilayer-substrate interface and their subsequent growth in the active layer due to recombination assisted diffusion

V. SWAMINATHAN AND A. S. JORDAN

332

interfaces between the Cd-diffused p-InP and LPE-grown n-InP buffer inside the groove. These loops subsequently grow out of the interfaces into the buffer layer, assisted by recombination-enhanced defect motion. Some of the loops that entered the active region eventually became dark-line defects. The extrinsic nature of the loops implied that the { 1 1 l} sidewall interfaces, as well as the GaInAsP active region, contained a high density of interstitials. 14. GaAs FETs

In the early phase of GaAs FET research and development, it was commonly held that majority carrier devices were unaffected by dislocations because of the absence of recombination. However, careful studies initiated by investigators at NTT Laboratories in Japan have cast doubt on the conventional view based on discrete microwave experience (Miyazawa and Nanishi, 1983) Beginning in 1982, quantitative relationships for the effect of dislocation density of standard (100)LEC GaAs on drain-source current, I d s , and threshold voltage, have been obtained for reasonably large levels (more than 1,OOO gates) of integration (Nanishi et al., 1982). Computercontrolled scanning measurements over wafers containing FET arrays and I,, contour maps that fabricated by direct ion implantation provided exhibit good correlation with the fourfold (100)dislocation distribution. In a given crystallographic direction (say ( 1 10)) across a wafer, the W-shaped I,, and M-shaped track the W-like dislocation profile (Miyazawa and Nanishi, 1983; Nanishi et al., 1983). The influence of individual dislocations on K,, has been carefully examined by Miyazawa and coworkers employing FET microscopy. An enhancementmode FET array with gate length/width of 1 pm/6pm and with 200-pm spacing was prepared by mesa etching, photolithography and 28Si implantation on a two-inch diameter LEC substrate with the usual high of each FET, the authors etched dislocation density. Having measured the the wafer in molten KOH to reveal the etchpits associated with dislocations. Then, over the entire wafer for each gate, its distance to the nearest etchpit was determined (Miyazawa et al., 1984). The data plotted in the form versus gate-to-etchpit distance showed a qh swing from - 1 to 3 V as the distance increased to -20-30pm. This “proximity effect” can extend to a FET to dislocation separation in excess of 50 pm. The global standard deviation in was nearly 100 mV. There has been worldwide concern with regard to these results, since prospects for LSI of GaAs FETs using high-dislocation-density substrates would be discouraging. Winston and colleagues have fabricated depletionmode FETs on In-alloyed substrates that exhibit significant low-dislocation-

vh,

v,,

vh

v,,

v,,

v,,

-

7. DISLOCATIONS IN III/V COMPOUNDS

333

density regions (Winston et al., 1984a, 1984b). They have not observed distance dependence in K,, and concluded that &h is independent of dislocation density in material containing less than 30,000per cmz defects. But comparing the spread in y,, values, a drop from 1 V to 400mV was observed for undoped LEC (dislocation density: 104-105 cm-’) and Inalloyed substrates, respectively (Winston et al., 1984b). Moreover, in the standard material the mean Y,, for local areas became more negative with increasing dislocation density. The controversy provided an opportunity for Miyazawa and Hyuga to reexamine the proximity effect in conventional LEC wafers (Miyazawa and Hyuga, 1986). Along the (110) direction, FETs were examined from the high-defect-density edge, the intermediate minimum area with lineage features, and the relatively high dislocation-density center having a cellular structure. The envelope of the complete &,, versus gate-to-etchpit data is shown in Fig. 18. It is seen that in the high-defect-density region-occupied by FETs from the edge, and the vicinity of central cellular walls-the large scatter in K,, is insensitive to distance. The proximity in the transition zone between 30 and 50pm is in effect the consequence of a dislocation lineage intersecting an FET array at a low angle. At 50pm and beyond, K h is independent of distance and tightly distributed with a standard deviation of

-

FIG. 18. Range of threshold voltage versus FET gate-to-etchpit distance measurements. The high and low dislocation-density areas are separated by a hatched region where the proximity effect starts to break down. The upper envelope represents horizontal Bridgman data (from Jordan, Von Neida and Caruso, 1986).

334

V. SWAMINATHAN AND A. S. JORDAN

-

40 mV, and the regions can be considered locally dislocation-free. Besides these considerations, it is likely that enhancement mode device arrays are more sensitive to dislocations than depletion mode FETs (Miyazawa and Hyuga, 1986). In Fig. 18 we also display the outline of the v,-distance plot when wafers from HB boules are used in FETs (Ishi et al., 1984).Clearly, in relatively lowdislocation-density material (3,000-6,000 per cm2) grown in a low gradient, the proximity effect is absent and the standard deviation in q h is comparable to that in the dislocation-free zone. Similarly, after high-temperature wafer annealing, the influence of FET-to-etchpit distance on is negligible and the standard deviation in v h is reduced to 48mV (Nanishi et al., 1985). Yamazaki et al. have confirmed that In-alloyed material with very low dislocation density shows a uniform with a standard deviation of 2030mV (Yamazaki et al., 1984). SEM examination of GaAs substrates corroborates the above findings. Within a 50 pm zone, the cathodoluminescence (CL) signal exhibits a high image brightness around individual dislocations, indicating diminished impurity concentration in the region. The impurities migrate to the dislocation core because of the strain energy of the misfit. Within the depleted region, Si implant activation efficiency is high, resulting in an increase in (Chin et al., 1982). It is noteworthy that SI crystals grown by horizontal gradient freeze show no bright CL areas around dislocations (Chin et al., 1985). With annealing, the CL image becomes broader and less distinct on account of impurity redistribution. Heat treatment at 1,200"C for 6 h reduces the microscopic CL efficiency variations from 100% to 5% (Chin et al., 1985). The luminescence intensity from the region surrounding dislocation cell walls is no longer significantly different from that in the region within the dislocation cells. This result suggests that point defect concentration fluctuations due to dislocation gettering are reduced. The uniform CL that arises upon annealing is consistent with the v h improvement. Heat treatment also produces a nearly constant concentration of the dominant deep donor EL2 across the wafer (Rumsby et al., 1984). In normal LEC material the W-shaped EL2 profile follows the dislocation distribution (Martin et al., 1981). Likewise, the EL2 wafer map, obtained from IR absorption data at 1 pm, and the fourfold (100) etchpit pattern are correlated (Holmes et al., 1984 Dobrilla and Blakemore, 1985). However, Dobrilla and Blakemore (1986) have found no direct cause for the EL2 correlation with dislocations. Clearly, the SEM image, v h , and EL2 results reflect changes in local impurity levels. Dislocations via the denuded zones affect the impurity atmosphere. Therefore, the device-dislocation interaction is most likely indirect.

v,,

v,,

vh

-

7. DISLOCATIONS IN III/V COMPOUNDS

335

More recently, there have been additional studies concerned with the origins of variations in &,. Deconinck et al. (1988)have determined that Vh is more uniform if the Schottky grates are parallel to (170) than (110). Suppressingunstable convective flow, and thus striations in LEC growth, has also reduced microscopic t&, variations (Fujisaki and Takano, 1988).It has been conclusively demonstrated that &, decreases with increasing EL2 concentration and that F,, follows the microscopic EL2 fluctuations. While the dislocation distribution may not be the direct cause for the variations in EL2 and V,, common roots are suspected in view of the similar print defect environment (e.g., V,,, As,,) associated with dislocations and EL2 (Alt et al., 1988). Undoubtedly, more work is required to further elucidate these important questions. In the meantime efforts to improve the perfection of GaAs and InP crystals are definitely warranted.

Note

A few reports that have appeared in the literature since this review was written merit consideration. Borvin et al. (P. Borvin, J. Rabier and H. Garem, Phil. Mag. A 61, 619 (1990)) have investigated the plastic deformation of GaAs in the temperature range 150-650°C as a function of doping and found the results to be consistent with dislocation velocity measurements. Observation of deformation microstructures by transmission electron microscopy showed that screw dislocations control the deformation at low ( < 200°C) temperatures. Siethoff et al. (H. Siethoff, R. Behrensmeier, K. Ahlborn and J. Volkl, Phil. Mag. A 61, 233 (1990)) measured stress-strain curves of GaAs between 415 and 730°C and determined the activation energy and stress exponent in Eq. (5) to be 1.24eV and 3.5, respectively. They also found evidence to suggest that dislocations move by the emission or absorption of point defects. I. Yonenaga and K. Sumino (Appl. Phys. Lett. 58,48 (1991))measured the dislocation velocities in undoped n-type (4 x 1015~ m - ~ S-doped ), n-type (8 x 1 O I 8 ~ m - ~ and ) , Zn doped p-type (6 x loi8~ r n - ~InP ) crystals. The velocities of In(g), P(g), and screw dislocations decreased by nearly two orders of magnitude with Zn doping, consistent with the yield stress data. On the other hand, with S-doping the effect was considerably less. The velocity of the P(g) dislocation increased, but that of In(g) and screw dislocations decreased with S-doping. These results suggest that in n-type InP the yield stress is not affected by P(g) dislocations. The quasi-steady state heat transfer/thermal stress model has been extended to VGF-grown GaAs and InP crystals (A. S. Jordan, E. M.

336

V. SWAMINATHAN AND A. S. JORDAN

Monberg, to be published in The Journal of Applied Physics). Semi-insulating GaAs boules up to 7.5 cm in diameter with dislocation densities in the range of 1,000-3,000cm-2 have been produced. InP boules with diameters up to 6.3 cm seeded in the (1 11) direction contain dislocations in the range 1001,OOO cm - 2 . A novel 23-zone, high-pressure vertical furnace for the electrodynamic gradient freeze growth of InP has also been developed with the objective of easily modifying thermal profiles during growth. Crystals with 5cm diameter and seeded in the (1 11) direction with dislocation densities < 1,OOO cm-2 have been obtained. Watanabe et al. (K. Watanabe, F. Hyuga, and N. Inoue, J . Electrochem. SOC.138,2815 (1991))reported that the required uniformity of of direct Siimplanted FETs can be obtained as a result of both Si,, and Si,, homogenizations at 1,100"C. The annealing mechanism is explained in terms of the amphoteric behavior of Si in GaAs and local off-stoichiometry, which is determined by EL2 measurement. Saito et al. (Y. Saito, K. Fukuda, C. Nozaki, S. Yasuami, J. Nishio, S. Yashiro, S. Washizuka, M. Watanabe, M. Hirose, Y. Kitaura and N. Uchitomi, Japanese J . Appl. Phys. 30,2432 (1991)) investigated variation in Si-implanted WN self-alignment gate MESFETs made from crystals grown with different melt compositions and in furnaces with different ratios of bottom versus side heating. They found that Kh variations are reduced in crystals grown with As-rich melts and in furnaces with the smallest ratio of heat radiation from the furnace bottom to that from the furnace side. These results suggest that melt composition, together with the consecutive thermal cooling cycle after crystallization, affects . Oda et al. (0. Oda, H. Yamamoto, M. Seiwa, G. Kano, T. Inoue, M. Mori, H. Shimakura and M. Oyake, Semicond. Sci. Technol. 7 , A215 (1992)) proposed a multiple wafer annealing technology in which wafers are annealed first at 1,lOO"C and then at 950°C. By this process highly uniform substrates with low As precipitate densities, uniform photoluminescence, uniform cathodoluminescence, uniform microscopic resistivity distribution, and uniform surface morphology were obtained. Further, low variation for ionimplanted MESFETs was obtained for both multiple ingot anneal and multiple wafer anneal conditions (standard deviation in 8-14 mV) compared to high-temperature (1,l00OC) ingot anneal (standard deviation in i$, 20mV). The decrease in i$ variation , is supposed to be caused by the reduction, by the high-temperature annealing of the large amount of As precipitates present in conventional LEC GaAs.

v,,

v,,

v,,

vh

<,, -

-

REFER EN cEs Abarnathy, C. R., Kinsella, A. P., Jordan, A. S., Caruso, R., Pearton, S. J., Temkin, H., and Wade, H.(1987). J . Cryst. Growth 85, 106.

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SEMICONDUCTORS AND SEMIMETALS. VOL. 38

CHAPTER 8

Deep Level Defects in Epitaxial III/V Materials Krzysztof W. Nauka HEWLEI-T-PAC- COMPANY PALOALTO.CALIFORNIA

I. INTRODUCTION. . . . . . . . . . . . . . . 11. oBswvAT10N OF DEEP STATESIN EPITAXIAL LAYERS . 1. Definitions . . . . . . . . . . . . . . . 2 . Characterization . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . IIr. EPITAXIALBINARIES . . . . . . . . . . . . . . . . . . 3. Gallium Arsenide . . . . . . . . . . . . . . . . . 4 . Indium Phosphide . . . . . . . . . . . . . . . . . 5. Gallium Phosphide . . . . . . . . . . . . . . . . . 6. Other Binary Compounds . . . . . . . . . . . . . IV. EPITAX~AL TERNARIES AND QUATERNARIES . . . . . . . . . 7. Aluminum Gallium Arsenide . . . . . . . . . . . .

8 . Gallium Arsenide Phosphide . . . . . . . . . . 9. Gallium Indium Arsenide . . . . . . . . . . . 10. Gallium Indium Phosphide . . . . . . . . . . . 11 . Aluminum Indium Arsenide . . . . . . . . . . . 12. Aluminum Indium Phosphide . . . . . . . . . . 13. Gallium Indium Arsenide Phosphide . . . . . . . . 14. Aluminum Gallium Indium Arsenide . . . . . . . . 15. Aluminum Gallium Indium Phosphide . . . . . . . v. QUANTUMWELLS, SUPERLATI'ICES, AND INTERFACES . . . 16. Lattice-Matched Quantum Wells and Superlattices . . . 17. Strained Layers . . . . . . . . . . . . . . . . 18. Interfaces . . . . . . . . . . . . . . . . . . VI . DEP LEVELS IN STRUCTURALLY DISORDERED III/V LAYERS. 19. Relaxed Lattice-Mismatched Epitaxial Layers . . . . 20. Layers Grown at Low Temperatures. . . . . . . . 21 . Layers Grown on Misoriented Substrates . . . . . .

VII .

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CONCLUSION

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357 361 . 364 . 365 . 366 . 370 . 370 . 372 . 373 . 313 . 374 . 375 . 375 . 376 . 376 379 380 . 381 . 382 . 386 . .387 389 389

Copyright 0 1993 by Academic Press. Inc. A11 rights of reproduction in any form reserved. ISBN 0-12-752138-0

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1. Introduction Epitaxial III/V materials play an increasingly important role in a variety of electronic, optoelectronic, and optical applications. The development of new epitaxial growth processes and improvements to already existing techniques have enabled the growth of layers of a quality (expressed by the quantity of structural and electronic defects) previously unobtainable for bulk III/V crystals. Therefore, the III/V material-based devices are now frequently fabricated using homoepitaxial layers grown on the corresponding bulk substrates. But the even greater importance of III/V epitaxial processes stems from the fact that they facilitate the growth of heteroepitaxial structures with properties unavailable for devices fabricated using bulk crystal materials. A few examples of the unique properties offered by the heteroepitaxial III/V layers are tuning of the band structure parameters by changing the composition of ternary and quaternary III/V alloys; heterojunctions with band offsets tailored according to the device requirements; quantum effects in the low-dimensional heterostructural devices such as quantum wells and superlattices; modification of the electronic structure by built-in stress in the strained epilayers; and unusual defect populations in the layers grown at low temperatures, thus facilitating new device applications. The electronic properties of the III/V epilayers are in many instances, as in the case of bulk crystals, modified by the deep states present in their band gaps. Some of them are beneficial and have been succesfullyemployed either to improve existing devices or to obtain structures with new characteristics. Examples include a nitrogen-introduced deep level in gallium phosphide (Gap) that allows the fabrication of Gap-based green LEDs, and deep levels in low-temperature gallium arsenide (GaAs) buffers that supress sidegating and backgating in the GaAs field effect transistors (GaAs FETs). However, many deep states can have a deletorious effect on device performance, so understanding and controlling them is essential for the successful development of the majority of devices fabricated using III/V materials. Although there are many excellent reviews of deep states in III/V semiconductors (Mirceau and Bois, 1979; Kaufmann and Schneider, 1982; Neumark and Kosai, 1983; Milnes, 1983; Bhattacharya and Dhar, 1988), only a few discuss deep states in the epitaxial layers. Because of rapid progress in the field of epitaxial growth, most of the results have appeared only recently and are not yet available in the form of a condensed review. The purpose of this chapter is to fill that gap by compiling the available information into a concise review of deep states in III/V epitaxial semiconductors. A detailed discussion of specific defect characteristics is neglected here. Instead, the basic information allowing identification of the deep level defects for a given epitaxial system is offered. Because of the limitations

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imposed by the lack of available information and the size of this book, the present review discusses a limited number of n- and p-type, nominally undoped or lightly doped (i.e., within the range of dopant concentrations that do not cause the formation of additional defects) binary, ternary, and quaternary compounds consisting of aluminum (Al), gallium (Ga), and indium (In) (group 111) and arsenic (As) and phosphorous (P) (group V) elements. Discussion of the deep states introduced by metals and intentional deep level impurities is mostly omitted, although ample references are offered to works describing such states. An emphasis is placed on the deep levels inherently present in the layers that are grown under variety of conditions and that constitute a “footprint” of the layers. It must be realized that the picture of deep level defects that is presented here is far from complete. We are just beginning to comprehend the complexity of the factors that shape electronic properties of defects in III/V epitaxial semiconductors. Little is known about the relationship between growth conditions and deep states and there are contradictory reports describing the chemical identity of deep level defects. Only now are we starting to understand the effects of strain and band discontinuites on the properties of deep states.

11. Observation of Deep States in Epitaxial Layers

1. DEFINITIONS The complexity of the defect states encountered in III/V semiconductors requires defining which of them are to be treated as “deep levels.” We shall follow the definition used by Hjalmarson (Hjalmarson et al., 1980), which is focused on the spatial localization of an electronic defect rather than its “depth” below (or above) the respective band or its occupancy probability. Hjalmarson states that a defect introduces a deep level if the central cell potential alone, without any significant participation of the Coulombic potential, binds an electronic state within the band gap. This definition has important consequences with reference to the properties of an epilayer. It implies that the deep state can be constructed from a large number of wavefunctions originating from various points within the Brillouin zone, and likely from many bands. Thus, when the band arrangement is changed by an external perturbation, such as pressure or alloying, the deep level does not necessarily follow any particular band, but its behavior is rather the sum of the responses from all the constituent bands. It will be shown that the described effect of an external perturbation on the deep state behavior can be tested for a variety of III/V alloy systems. The preceding definition has also

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become the basis for a series of theoretical studies of deep states in epitaxial III/V structures (Hjalmarson et al., 1980; Vogl, 1984; Ren et al., 1988, 1989; Jenkins et al., 1989). In this chapter we will consider four epitaxial processes used to grow the majority of IIi/V semiconducting layers: liquid phase epitaxy (LPE), vapor phase epitaxy (VPE), organometallic phase epitaxy (OMVPE), and molecular beam epitaxy (MBE) with its derivative employing gas sources (GSMBE). We will not distinguish between different modes of this process, such as chemical beam epitaxy (CBE), organometallic beam epitaxy (MOMBE), and true GSMBE. An epitaxial process consists of the following steps: the transport of the atomic or molecular species to the surface, their adsorption, diffusion on the surface, and surface reactions. Each of these steps can affect the formation of deep level defects. Since detailed descriptions of these steps can be found in the literature (Rode, 1975; Joyce, 1985; Nakajima, 1985; Stringfellow, 1985; Beuchet, 1985; Razeghi, 1985), we limit the discussion here to a few comments designed to illuminate the differences between the deep states in layers grown by different epitaxial processes. These epitaxial processes are often conducted at different temperatures. Broad temperature ranges are available for MBE, VPE, and OMVPE, while LPE is normally conducted in a narrow temperature range. Growth temperature is one of the major factors determining the kinetics of surface reactions. It can also control the surface nucleation processes, the incorporation of impurities, and the interaction of defects at the surface and the bulk of a grown epilayer. Surface preparation, which is different for each technique, is also critical. It can determine surface topography and the available nucleation sites. Epitaxial techniques that facilitate in-situ surface etching (LPE, VPE) offer better conditions for surface preparation than the technique in which most of the surface preparation must be done outside the reactor (MBE). LPE is normally conducted under thermal equilibrium. It employs saturated Iiquid metal sources that introduce large amounts of group 111 elements. Other processes are conducted under far from equilibrium conditions. They employ excessive amounts of group V elements in order to compensate for their volatility. This can lead to nonequilibrium concentrations of these elements in the grown layers. MBE is a physical deposition process. The amount of the adsorbed species depends on both its arrival rate and its sticking coefficient, which is often dependent on surface coverage. i n VPE and OMVPE, reagents undergo complex chemical reactions that can cause the formation of parasitic components that produce stoichiometric changes and unwanted homogeneous nucleation. In addition, because of the existence of a stagnant layer, the rate of arrival for various components often depends on their diffusion coefficients. Although LPE is ultimately controlled by phase equilibrium, additional processes, such as

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MATERIALS

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supersaturation of solute during growth, parasitic nucleation, and convection due to temperature gradients, can determine the composition of an epilayer. Finally, deep level defects can also depend on the number of contaminant atoms that are introduced during growth. This number, in turn, is determined by the design of the growth apparatus and the purity of chemical sources that are employed in the epitaxial processes.

2. CHARACTERIZATION

When a deep level defect is located at least a few atomic distances from either an interface or a surface, its electronic properties can be treated as if the defect were located within the bulk crystal material. This allows us to employ both the extensive literature available for deep states in bulk III/V materials and experimental techniques developed for their characterization. References to works that describe deep level defects in the bulk materials are available later in this chapter. The characterization of deep states in epitaxial layers is subject to the limitations imposed by the normally small thicknesses of epilayers. Many of the characterization techniques that rely on a large number of defects in the probed volume are inapplicable. Unfortunately, most of the characterization methods that probe both the atomic arrangement and the chemical identity of a defect, such as electron spin resonance (ESR), optically detected magnetic resonance (ODMR), and electron nuclear double resonance (ENDOR), fall into this category. Therefore, in many cases the chemical identification of a deep level defect must rely on either comparing it with bulk materials or deducing its identity from the stoichiometric conditions of the epitaxial process. Optical measurements of deep states in the epitaxial layers are more successful. Although both absorption and localized vibration modes spectroscopies of deep levels are usually unreliable because of the volume limitation, luminescence measurements (photoluminescence (PL), cathodoluminescence (CL), and electroluminescence (EL)) can yield much useful information about deep states. Deep level luminescence is determined by the recombination properties of a defect. When the probability of radiative transitions is higher than the probability of a nonradiative recombination, the transition energy can be dissipated in the form of photons. Deep level luminescence peaks can be very broad because of phonon coupling and the variety of spatial arrangements available to the point defect in compound semiconductor. They can also appear in the form of the narrow lines that are frequently observed for the intracenter transitions of some impurities. Detailed discussion of the physics of defect luminescence can be found in previous volumes of this treatise (Bebb and Williams, 1972; Neumark and

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Kosai, 1983). Although only a small number of deep states act as radiative recombination centers, some of the sub-band luminescence peaks are unique “footprints” of deep level defects in the epitaxial III/V compounds. Some of these peaks are listed in subsequent sections of this chapter. Resistivity and Hall measurements have rather limited applications for monitoring deep levels in the epitaxial layers. Normally, these techniques are not limited by the thickness of an epilayer. However, since the signal originating from a small number of deep states frequently overlaps the signal due to large number of free carriers, their resolution is rather low. They can play an important role in characterizing deep states in the semi-insulating and heavily compensated III/V epitaxial films. Junction techniques that measure the capacitance or the current response of an electricaljunction with deep states within its depletion layer to electrical or optical perturbations are particularly well suited for studying deep states in thin layers. Because of their sensitivities and abilities to probe narrow depletion layer regions, they are rarely limited by the small volume of an epilayer. Junction techniques have been extensively described before (Sah et al., 1970 Miller et al., 1977; Lang, 1979; Bourgoin and Lannoo, 1983), so we will define only the basic terms used in this review. The principle of junction measurements stems from the fact that the depleted region of an electrical junction is virtually free of mobile carrier. Thus, the rate equations are linear and the junction response to an external perturbation decays exponentially with time. The application of the principle of detailed balance leads to the well known equations that relate the thermal emission rates en, e p to the defect ionization enthalpies AH,,, AHp(e,p-electrons and holes, respectively): en = C,T2anerp(’)exp( e p = C2Tzcpexp(?)erp(

-$), -), AH,

-

where C1 and Cz are constants, T is the temperature, k is the Boltzmann constant, an and ap are capture cross-sections, and ASn and A S p are defect entropies. When the electrical excitation is replaced by the optical pulse, the change in the trap population can be expressed in terms of the optical generation rates, e,O, ep:

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where o,”,0: are optical cross-sections, z describes the quantum efficiency, ) the photon flux at wavelength 1. Values of the capture crossand ~ ( 1is sections are determined by the capture mechanism for a given deep level defect. In the case of multiphonon capture (the most frequently encountered capture process in III/V semiconductors), its temperature dependence can be described by the exponential relationship

where tsrnis a constant, and E, is the capture activation energy. A large number of characterization methods have been proposed that are based on the idea of perturbing an equilibrium deep level population within the depletion region of a junction. The more frequently employed techniques include thermally stimulated current (TSC); thermally stimulated capacitance (TSCAP) (corresponding, optically stimulated techniques have also been developed); and admittance spectroscopies. However, deep level transient spectroscopy (DLTS) has become particularly popular. DLTS is a truly spectroscopic technique that enables the study of individual deep states present in the depletion region of a diode. The slope of the ln(e/TZ)vs. 1/T plot (Eq. (1)) yields the defect enthalpy, commonly called the thermal activation energy ET of a defect. Measurements of the DLTS signal as a function of pulse duration give information about the capture cross-section value and its temperature dependence. DLTS allows the determination of deep state concentrations and their spatial macroscopic distributions. Also, a microscopic version of DLTS, scanning DLTS (SDLTS), where the electron beam pulses perturb the equilibrium deep state populations images the distribution of deep states with a spatial resolution that is determined primarily by the majority carrier diffusion length. Since DLTS measurements can supply almost a complete set of information about the properties of a measured deep state, DLTS spectra are accepted as “signatures” of deep level defects, and they are recognized as a means of identifying deep states when spectra originating from different samples are compared. An approach in which deep levels are identified and “tagged using junction techniques has been adapted in the following parts of this chapter. Deep levels in epitaxial III/V layers are described in terms of their parameters that are obtained mostly from DLTS measurements, namely thermal and optical activation energies ET and Eo, capture cross-sections onand op,and the dominant trapping mechanism that defines whether the deep state behaves as an electron or a hole trap. In addition to the activation energy, an

K. W. NAUKA

approximate temperature at which the DLTS peak can be observed is listed. It is selected to correspond to the DLTS experiment with a rate window between 1 and 10ms. For many deep states, values of the capture crosssection at temperatures corresponding to the DLTS peak positions are also given, or the temperature dependence of the capture cross-sections (Eq. (3)) is expressed in terms of the capture activation energies E , and prefactors cm. DLTS peak temperatures and capture cross-sections quoted here must be treated only as approximate values that help both to identify deep states and to estimate their impact on the behavior of a device. The parameters that are found in the literature differ greatly; the numbers given here correspond to the most frequently quoted values. Classification into either electron or hole traps can be misleading, since the trapping and recombination processes depend on temperature and dopant concentrations; a deep level that acts as a trap in one case can behave as a recombination center in another. A trap is defined as a level for which the probability of capture and release for one type of carriers is higher than for the other type of carriers. Recombination centers trap both electrons and holes and cause their recombination. Thus, the trap must have a large capture cross-section for one type of carrier and a small capture cross-section for the other. The recombination center has a relatively large capture cross-section for both types of carriers. In addition to the listed parameters, complete Arrhenius plots of e/T2 vs. 1/T are shown for many common deep levels in the epitaxial III/V layers. The Arrhenius plots presented here were constructed using data from the quoted references or were measured by the author. An interpretation of data from junction measurements must include interactions between the defect center and the surrounding lattice. Change of a defect charge can cause lattice relaxation, either by a temporary lattice deformation (breathing mode) or by a permanent change of the symmetry of a defect. A change in the defect symmetry can lead to unwanted effects that complicate the junction measurements, such as persistent photoconductivity or a large difference between the thermal and optical activation energies observed for D X states in the epitaxial III/V alloys. In addition, an electric field applied to the junction can modify the electronic structure of a defect. Either it can lower the potential barrier surrounding the defect (FrenkelPoole effect), or it can cause tunneling between the defect level and one of the bands (direct or phonon-assisted tunneling). Understanding these effects is particularly important in the case of low-dimensional epitaxial structures, such as quantum wells and superlattices, for which a large part of the measured volume can remain permanently in an electric field introduced by the heterojunction.

8. DEEPLEVELDEFECTS IN EPITAXIAL III/V MATERIALS

351

111. Epitaxial Binaries

3. GALLIUM ARSENIDE

The availability of commercially grown, doped and semi-insulating GaAs substrates, combined with the electronic properties of GaAs, makes the epitaxial GaAs very attractive for a large number of optoelectronic and highspeed device applications. GaAs can be easily obtained by any of the epitaxial processes discussed in previous sections. Deep states in GaAs (mostly in bulk crystals) have been the subject of many previous studies (Martin et al., 1977; Mitonneau et al., 1977; Neumark and Kosai, 1983). Bourgoin (Bourgoin et al., 1988) discussed deep states introduced by native point defects in bulk GaAs crystals. Extensive reviews of the deep levels introduced by metallic impurities were given by Kaufmann and Schneider (1982), Milnes (1983), Bishop (1986), and Allen (1986). Figure 1 and Table I compile information about the deep states commonly observed in epitaxial GaAs. a. MBE GaAs

MBE GaAs layers grown under normal, As-rich conditions and temperatures in the range 480-600°C have three major deep electron traps with thermal activation energies of 0.19,0.33, and 0.52eV (Lang and Logan, 1975;

2

3

4

5

6

7

8

9

1

0

1

1

103/T(K-’)

FIG. 1. Arrhenius plot of temperature-corrected thermal emission rates e/T2 for the deep states common in epitaxial GaAs (for references, see Table I).

352

K. W. NAUKA TABLE I DEEPSTATESIN EPITAXIAL GaAs

MBE

ME1 ME3 ME4

ME2

OMVPE

VPE

LPE

0.19(E) 0.33(E) 0.52(E) 0.03 (E) O.lO(E) 0.22(E) 0.27(E) 0.58 (E) 0.62 (E) 0.81 (E) 0.85(E)

0.04

10-120 (140K) 2(165K) lo00 (235K)

M1 Main electron M') traps M4 in MBE GaAs

1-4 1-4 1-4

0.02 (40K)

MOO MO M2' M2 M5 M6 M7 M8

1-4 1-4 1-4 1-4 1-4 1-4 1-4 1-4

0.12

90 (150K)

5-8

0.19 (E)

OEl 0E2 OE3

0.82(E)

VEl VE2 VE3 YE4 VES

0.18(E) 0.32 (E) 0.42 (E) 0.48 (E) 0.82(E)

LH1 LH2

0.40(H) 0.70 (H)

1, O r AS,,. 10-40 (240K) 100-800 (380 K) EL 2, main trap in OMVPE GaAs.

0.44(E)

3 (115K) 200 (210K) 500(220~) 0.09 0.06

Soob 20-8P

40-60 (190K) 10-20 (340K)

intrinsic defectimpurity complex. Ni. EL2, main trap in VPE GaAs. VE5 = OE3. A, B, G a , related.

5-8

9-12 9-12 9-12 9-12 9-12 1,13, 14

YE)-electron trap, (H)-hole trap. value. 'From: (1) Lang and Logan, (1975); (2) Blood and Harris (1984); (3) Dejule et a/. (1985); (4) Xin et al. (1982);(5)Bhattacharya ez ul.(1980);(6)Zhuetal.(1981);(7)Samuelson etal. (1981);(8) Watanabeet al. (1983); (9) Mirceau and Mittoneau (1975); (10) Partin et a!.(1979); (1 1) Diegner et af. (1986);(12) Auret et al. (1988); (13) Hasegawa and Majerfeld (1975); (14) Wang et a/. (1984).

Blood and Harris, 1984; DeJule et al., 1985). Additional electron traps with lower concentrations have also been observed. These electron traps are only weakly dependent on the type and concentration of a dopant. However, their concentrations depend strongly on the temperature and stoichiometry of the MBE process. When the growth temperature is lowered below 480°C, new deep electron states begin to appear (Stall et al., 1980). They are related to simple point defects, such as vacancies and interstitials, which are known from studies of bulk GaAs crystals (Bourgoin et al., 1988). Annealing at

8.

DEEP

LEVELDEFECTS IN EPITAXIAL 111/v MATERIALS

353

temperatures above 600°C using either a cap or an As-controlled ambient (Day et al., 1981; Xin et al., 1982), decreases the trap concentrations. A similar effect is observed when the MBE GaAs is exposed to a hydrogen atmosphere (Dautremont-Smith et al., 1986; Pao et al., 1986). The layers grown under Garich conditions exhibit a different spectrum of deep states. The spectrum consists of two electron states with thermal activation energies of 0.29 and 0.85 eV, and contains only traces of defects seen in the As-rich layers (Lang and Logan, 1975; Xu et a]., 1987). The replacement of the As4 by dimeric As, lowers the trap concentration (Neave et al., 1980; Kunzel et al., 1982). Electron traps in the MBE GaAs exhibit a strong dependence on the presence of unwanted impurities. Introduction of high-purity sources and cleaner MBE apparatus (Lang and Logan, 1975; Chand et al., 1987) can reduce trap concentrations below the 10" level. Experimental data indicate that electron deep states in the MBE GaAs grown under normal As-rich conditions are mostly due to native point defect-impurity complexes. Their exact microscopic structures are unknown, but most of the observations favor reactions between the Ga, As vacancies and As interstitials as one reactant and the impurities such as oxygen, carbon, silicon, germanium, and metallic contaminants, as another reactant. This could explain the reduction in the deep level concentrations when high-purity sources are introduced. Similarly, both the growth temperature and the stoichometry of the MBE process control the native point defects that undergo reactions with impurities. At low growth temperatures, the point defects cannot overcome the energy barrier to form complexes, so the spectrum of the deep states changes drastically. High temperatures can lead both to dissolution of the complexes and to reduction of the overall concentration of deep levels. Change in the deep level concentrations when hydrogen atoms are introduced could result from the interactions between the hydrogen and the native point defects or impurities that suppress formation of the deep level defects. It was also shown that In isoelectronic doping reduces the trap concentration (Bhattacharya et al., 1986; Ioannou et al., 1988). This phenomenon could be explained as being caused by the reduction of the vacancy formation rate due to the fast surface diffusion of the In atoms. The hole traps in the MBE GaAs that is grown under normal conditions (growth temperature above 480°C and As-rich atmosphere) are mostly caused by metallic impurities that are introduced either from the contaminated sources or from the substrate. Layers grown using high-purity sources and a state-of-the-art MBE apparatus are free from these defects. When the GaAs films are grown at temperatures below 450"C, hole traps related to simple native point defects can be observed (Bhattacharya and Dhar, 1988). A luminescence spectrum of undoped or lightly doped GaAs at temperatures below 10K consists mostly of excitonic recombination and transitions

354

K.W. NAUKA

between the bands, shallow donors, and shallow acceptors (Williams and Bebb, 1972; Briones and Collins, 1982; Skromme et al., 1985). Since the trap concentrations are relatively low, infrared transitions related directly to deep states (Batavin and Popova, 1974; Chiang and Pearson, 1975; Haegel et al., 1987) can only be seen in the layers grown at temperatures below 450°C (Gonda et al., 1975). Three features in the luminescence spectrum of layers grown at temperatures above 450°C can be indirectly correlated with the occurence of deep states: (1) a series of sharp peaks (9-u transitions) in the range 1.512-1.504eV, (2) defect-related luminescence (d, - d4 bands) that is observed between 1.482 and 1.466eV, and (3) transitions that are between the bands and shallow donors and acceptors introduced by unintentional impurities such as carbon, silicon, germanium, zinc, vanadium and manganese, and that occur at lower energies (Williams and Bebb, 1972; Low et al., 1982; Skromme et al., 1985; Chand et al., 1988). The g-u transitions are due to an excitonic recombination that is introduced by residual defect complexes (Kunzel and Ploog, 1980 Beye and Neu, 1985; Skromme et al., 1985). The highest energy line (g line) has been associated with the neutral acceptors (Contour et al., 1983), while the occurrence of the lower energy lines depends on the type of As species (dimeric or tetrameric) and the growth temperature (Kunzel and Ploog, 1980; Dobson et al., 1982). The d , - d4 luminescence bands are probably due to transitions between the shallow hydrogenic donor and shallow acceptor (Skromme et al., 1985). Their presence has been correlated with residual impurities, particularly carbon (Briones and Collins, 1982; Kunzel et al., 1982). Since residual impurities are one of the components responsible for electron deep states, a correlation between impurities-related luminescence and deep states can be established (Kunzel et al., 1982). Early reports indicated that GSMBE GaAs contained electron traps similar to the levels observed in conventional MBE GaAs (Kanamoto et al., 1987a). Seven electron traps were observed in lightly doped n-type GSMBE GaAs; five of them corresponded to traps previously observed in the MBEgrown films (Fujisaki et al., 1985). Additional traps that were seen when a high As/Ga ratio was used were probably due to the precipitation of the excessive As. More recent results demonstrate that the application of clean gas sources and the optimization of growth temperature (Cunningham et al., 1989; Sonoda et al., 1989) can suppress deep electron traps below the 5 x 1OI2emw3level. The low-temperature PL spectra of GSMBE GaAs (Chiu et a/., 1987; Cunningham et al., 1989) demonstrate the excellent quality of materials that are grown at low temperatures that reduce the amount of carbon incorporated into the layers and that preserve the sharp dopant profiles.

8. DEEPLEVELDEFECTS IN EPITAXIAL I I I P MATERIALS

355

b. OMVPEGaAs

An electron trap with a thermal activation energy of approximately 0.8 eV (EL2 trap) is the major feature observed in the OMVPE GaAs deep state spectrum (Bhattacharya et al., 1980; Samuelson et al., 1981; Li et al., 1985; Cherifa et al., 1987; Wang et al., 1988; Feng et al., 1991). Two additional electron traps with thermal activation energies within the ranges 0.180.20 eV and 0.48-0.60eV and with concentrations lower than that of EL 2, can also be observed. Their concentrations do not depend on the dopant type, but exhibit a strong dependence on the growth temperature and the As/Ga ratio. Watanabe demonstrated (Watanabe et al., 1983) that the concentration of EL 2 is proportional to (As/G~)'/~ at temperatures below 680°C and to (As/Ga)''2 at higher growth temperatures. The temperature dependence of the EL 2 concentration is related to the chemical state of the As reactants on the substrate, which in turn is determined by the substrate temperature (Okabe et al., 1990). The EL 2 concentration also depends on the localization of As atoms in the lattice. When the As concentration exceeds solid solubility and the As precipitates start to form, the EL 2 Concentration drops even when the As/Ga ratio is further increased (Fujisaki et al., 1985). Modification of the OMVPE process (flow rate modulated epitaxyMakimoto et al., 1988) with a more balanced As/Ga ratio reduces the EL 2 concentration below the 1013~ r n level. - ~ Concentrations of the remaining electron traps scale linearly with As abundance, which demonstrates that they are caused by As-related native point defects. It was proposed (Zhu et al., 1981) that the 0.45eV trap was due to interstitial As atoms, or antisite As occupying Ga sites. As in the case of MBE GaAs, hole traps in the OMVPE GaAs are due to metallic impurities. They either originate from the contaminated sources and the growth apparatus (Bhattacharya et al., 1980; Wang et al., 1988), or diffuse from the substrate at elevated growth temperatures (Zhu et al., 1981; Auret et al., 1988). The most frequently observed hole traps are introduced by iron, copper, and nickel. The application of high-purity OMVPE sources, the growth of a buffer between the substrate and epitaxial layer, and the introduction of high-quality semiinsulating GaAs substrates (Auret et al., 1988) allow the growth of OMVPE GaAs with hole trap concentrations below the 5 x 10"- lOI2cm-3 level. Features similar to those of MBE GaAs are seen in the luminescence spectrum of OMVPE GaAs (Samuelson et al., 1981; Low et al., 1982). Lowtemperature PL measurements have been used to monitor presence of unintentional impurities, such as carbon, silicon, germanium, tin, zinc, manganese, cadmium and copper (Hess et al., 1982; Low et al., 1982).Their concentrations depend on the source purities, the design of OMVPE

K.W.NAUKA

356

apparatus, the As/Ga ratio, and the growth temperature (Low et al., 1982; Roth et al., 1983; Menna et al., 1986; Shastry et al., 1987).Deep state radiative transitions were observed in the range between 1.3eV and 1.0eV (Samuelson et al., 1981); they are thought to be due to gallium vacancy-impurity complexes. c.

VPEGaAs

VPE GaAs layers that are grown by hydride and chloride processes exhibit similar deep state spectra (Mirceau and Mittoneau, 1975; Partin et al., 1979; Huang et al., 1988). EL2 is the major electron trap with concentrations frequently higher than l O ’ ’ ~ m - ~This . deep state is responsible for the partial compensation often seen in these materials. Additional electron traps with activation energies of 0.18 eV, 0.32-0.33 eV, 0.40-0.42 eV, and 0.48 eV, and with concentrations that are orders of magnitude lower than that of EL 2, can also be observed. Experiments in which the growth conditions were varied (Diegner et al., 1986; Auret et al., 1988)demonstrated that the 0.18eV trap was related to native point defects. The remaining traps, except for the 0.48 eV level, were associated with complex defects involving native point defects and impurities. The 0.48 eV trap is introduced by nickel atoms occupying Ga sites. Hole traps in the VPE GaAs are introduced by metallic impurities. Fe-related deep states with an activation energy of 0.5eV and copper-related traps with activation energies of 0.42 eV and 0.15 eV have been reported (Martin et al., 1977; Auret et al., 1988; Huang et al., 1988). Similarly to the OMVPE-grown layers, metallic contaminants are introduced by contaminated VPE sources, or they diffuse from the substrate at elevated growth temperatures. Low-temperature PL measurements have been used to investigate residual acceptor and donor impurities, such as carbon, zinc, silicon, germanium, and magnesium (Low et al., 1982; Abrokwah et al., 1983; Colter et al., 1983; Diegner et al., 1986). Noticeable differences were seen for the layers grown by hydride and chloride processes (Low et al., 1982).These differences were probably caused by the differencesin the purity of the source materials. PL measurements also demonstrated the radiative transitions directly related to deep states (Abrokwah et al., 1983; Diegner et al., 1986). The 1.36eV transition was associated with coppershallow donor complexes, and the luminescence band between 1.21 and 1.26eV was due to the defect complexes that involved gallium vacancies.

d. LPE GaAs Deep states in the LPE GaAs are drastically different from the defects that are observed in the materials grown by other epitaxial processes. LPE growth conditions favor the formation of point defects that require excess Ga atoms;

8. DEEPLEVELDEFECTS IN EPITAXIAL IIIN MATERIALS

357

the defects that consist of excess As atoms are suppressed. GaAs epilayers grown under normal LPE conditions are free of electron traps and have only two hole traps, with thermal activation energies of 0.40 eV and 0.70eV (Hasegawa and Majerfeld, 1975; Lang and Logan, 1975; Mitonneau et d., 1977). These traps can be suppressed when the dopants that occupy Ga sites are introduced; the introduction of the As-site dopants increases trap concentrations (Krispin, 1989). Wang proposed that these traps could be due to the Ga on As site (Ga,,) double acceptor (Wang et al., 1984). However, the experiments of Nouailhat (Nouailhat et al., 1986) demonstrated that two separate defects involving GaAsare a more likely source of these defects. 4. INDIUM PHOSPHIDE InP is the second most important III/V binary. Because of its direct band gap, smaller than that in the GaAs, it is primarily used for a variety of light sources and optoelectronic detectors, Its very high carrier mobilities make InP an attractive material for fabricating high-speed devices. As in the case of GaAs, both bulk and epitaxial technologies are now mature, economically viable, and allow the fabrication of structures with properties desirable for commercial applications. Review of the electronic defects in bulk InP can be found in Volume 31 of this treatise and in the work of McAfee (McAfee et al., 1981a)and of Yamazoe (Yamazoe et al., 1981). The major deep level defects in the epitaxial InP are shown in Fig. 2 and Table 11.

2

3

4

5

6

7

8

9

10

I?

1 0 ~ (K-1) 1 ~

FIG. 2. Arrhenius plots of temperaturecorrected thermal emission rates e/Tz for the deep states common in epitaxial InP (for references, see Table 11).

358

K. W. NAUKA TABLE I1 DEEPSTATESIN EPITAXIAL InP

Growth Process

Trap

MBE

ME1

M E2 OMVPE OEl OE2 OE3 VPE

VEl VE2 VE3 VE4 VES VE6 VE7 VHl

LPE

&(Type)” (ev)

E, (ev)

0.42 (E) 0.24 (E) 0.32 (E) 0.52 (E) 0.57 (E) 1.1 (PL) 0.47 (E) 0.37 (E) 0.53 (E) 0.58 (E) 0.15-0.18 (E) 0.30 (E) 0.40 (E) 0.42 (E) 0.53 (E) 0.58 (E) 0.68 -0.70 (E) 0.80 (E) 0.27 (H)

0.38

0.09

(I

x

(a2) Comment

26,000 (230 K)

Vp complex.

130 (260 K) 70,000 (245 K)

native point defects. Fe complex.

180 (190 K) 4,2w 4.3 (340 K)

Fe precipitates. I, and y , related. Fel”.

0.06-1 (95 K) 0.0008 (140 K) -(160K) 3.4* >20 (210 K) 10-30 (250 K) 2- 150 (270 K) 60 (330 K) 130 (110 K)

T, V, complex. Co or Ti related. R, Fe,,.

0.53 (H) 0.44 (H)

0.023 (330 K) 0.76 (180 K)

0.54 (E)

0.3 (330 K)

TE)--electron trap, ( H b h o l e trap, (PL)-photoluminescence

Q. oxygen related. V,-impurit y complex.

Tiln.

Ref.‘

6-9 6-9 6-9 6-9 6-9 lo, 11

12

peak.

*am value. ‘From: (1) Asahi et al. (1981); (2) Iliadis et al. (1987); (3) Ogura et al. (1983a);(4) Nicholas et al. (1987); (5) Takanohashi et al. (1988); (6) White et al. (1978); (7) Wada et al. (1980); (8) Tapster (1983); (9) Inuishi and Wessels (1983);(10) Choudhury and Robson (1979);(11) Sun et al. (1983); (12) Knight et 01. (1988).

a.

MBE InP

A deep level with a thermal activation energy of 0.42eV is the major electron trap observed in nominally undoped, n-type MBE InP grown under normal, phosphorus-rich conditions at temperatures around 500°C (Asahi et al., 1981; Iliadis et al., 1989). This defect can be attributed to a point defect complex involving P vacancies; increase of the P vapor pressure lowers its concentration. Additional electron traps with concentrations smaller than the 0.42 eV level and activation energies of 0.24,0.32,0.52, and 0.57 eV have also been reported (Asahi et al., 1981; Iliadis et al., 1987). The last two traps

8. DEEPLEVELDEFECTS IN EPITAXIAL III/V MATERIALS

359

were seen only in the materials grown at low temperatures (<500OC). Under normal conditions, DLTS measurements do not reveal any hole traps in high-quality undoped MBE InP layers, although it is known that the transition metal impurities outdiffusing from semi-insulating substrates during growth can introduce deep acceptors that cause partial compensation (Asahi et a]., 1981). The low-temperature luminescence spectrum of epitaxial InP consists of features similar to those seen in GaAs films (Joyce and Williams, 1970; Skromme et al., 1983). Exciton-related emission can be observed near the band-gap energy. A large number of radiative transitions between bands, some shallow donors, and acceptors are seen below the exciton peaks. Radiative transitions due to deep levels can be seen at lower energies. PL measurements of a nominally undoped MBE InP that was grown on semi-insulating substrates (Asahi et al., 1981; Iliadis et al., 1987) demonstrated a deep-level-related emission at about 1.1eV and 1.18eV. The 1.1 eV peak consisted of a large number of superimposed, phonon-assisted transitions from the P vacancy-metallic impurity complexes (Yu, 1980). It was correlated with the presence of a 0.42eV electron trap. The 1.18eV radiation is due to the substitional manganese. Epitaxial InP has also been grown by GSMBE (Panish et al., 1985).Temperature-dependentHall and PL measurements demonstrated that the application of gas sources improved the overall material quality and allowed the selective growth of device-quality structures (Andrews et al., 1989). It also lowered the concentration of deep states that were responsible for the partial compensation and suppressed the carbon incorporation into the layers grown at temperatures around 480°C (Morishita et al., 1989). b. OMVPE InP Concentrations of deep states in OMVPE InP are mostly controlled by the growth temperature and the purity of the OMVPE sources. Nominally undoped, n-type InP grown at temperatures around 600°C and a high P/In ratio contains two electron traps with activation energies of 0.37 eV and 0.53 eV (Ogura et al., 1983a).Since the decrease in the P/In ratio lowers their concentrations, they can be associated with P interstitials and In vacancies. Deep states observed in the OMVPE InP are also controlled by growth pressure. Defects found in the layers grown at atmospheric pressure differ from the deep states observed in low-pressure material deposited under similar stoichiometric conditions (Nicholas et al., 1987). Impurities can be another source of deep states. They are frequently introduced by contaminated OMVPE sources. It was observed (Nicholas et al., 1984) that the materials grown from presynthesized adducts contained many more traps than the layers grown from in-situ formed adducts. Iron is the most frequently

360

K. W. NAUKA

encountered impurity. It can either diffuse from the semi-insulating Fe-doped substrates during growth or it can originate from the metallorganic sources and growth apparatus. Highly compensated OMVPE InP can be grown by intentional doping with Fe. Fe atoms occupy In sites that introduce a deep electron state with thermal activation energy in the range 0.58-0.61 eV (Tapster et al., 1981; Ogura et al., 1983a; Nakai et al., 1987; Nicholas et al., 1987).When the iron exceeds the solid solubility, iron precipitates are formed and give rise to an additional electron trap with an activation energy of 0.47 eV (Takanohashi et al., 1988). Luminescence measurements can be used to identify the impurities responsible for shallow donors and acceptors in the OMVPE InP. Optimization of the growth process produces layers with only traces of shallow donors and negligible compensation. This indicates a lack of deep acceptor states (DiForte-Poisson et al., 1985). The growth conditions and the purity of metallorganic sources determine the type of impurities present in the OMVPE InP (Hsu et al., 1986; Stringfellow, 1986). For example, zinc is a dominant background shallow acceptor in atmosphericpressure OMVPE InP, while C dominates in the low-pressure OMVPE InP (Zhu et al., 1985; Stringfellow, 1986; Nicholas et al., 1987). Deep-level luminescence at 1.leV was reported for the InP grown using precursors prepared outside the reactor. It disappeared when in-situ synthetized precursors were used (Nicholas et al., 1984). As with MBE InP, this luminescence band can be associated with complexes that involve phosphorus vacancies and metallic impurities. c.

VPE InP

A large number of electron traps have been reported for the InP grown by VPE processes (White et al., 1978; Wada et al., 1980; Lim et al., 1982; Inuishi and Wessels, 1983; Tapster, 1983). The most frequently encountered deep states have thermal activation energies of 0.68-0.70eV, 0.58 eV, and 0.42 eV. Origin of the 0.68-0.70eV trap is unknown. The 0.58eV state is due to substitional iron occupying In sites, and the 0.42eV trap is introduced by a complex involving phosphorus vacancy. The additional electron states that can be observed in VPE InP have lower concentrations and are most likely associated with impurities and their complexes. In addition to electron traps, hole deep states with thermal activation energies of 0.53, 0.44, and 0.27eV have been observed (Choudhury and Robson, 1979; Sun et al., 1983). The 0.27 eV trap is probably related to a phosphorus vacancy-impurity complex; the origin of other traps is unknown. Deep states in VPE InP can cause partial compensation (Pickering et al., 1983;Sun et al., 1983).Since most deep states are related to impurities, the introduction of high-purity reactants can reduce the number of traps and lower the compensation ratio. Takanohashi

8. DEEPLEVELDEFECTS IN EPITAXIAL III/V MATERIALS

361

and co-workers (1988) deposited high-purity layers that were free of hole traps and that contained only trace amounts of the 0.42 eV electron trap. The low-temperature PL measurements of an undoped VPE InP demonstrated the presence of unintentional impurities acting as shallow donors and acceptors (White et al., 1978; Skromme et al., 1983).Their chemical identities and their concentrations were dependent on the purity of the VPE sources and the growth parameters (i.e., hydride or chloride VPE process, growth temperature-Pickering et al., 1983; Skromme et al., 1984). Deep-levelrelated radiation has been seen in VPE InP as a broad luminescence peak between 1.17 and 1.28eV observed at temperatures below 70K (Skromme et al., 1983; Sun et al., 1983). This radiative recombination could be due to manganese or to native point defects.

d. LPE InP Nominally undoped, n-type LPE InP appears to be free of any deep levels measured by DLTS (Wada et al., 1980; Knight et al., 1988). However, temperature-dependent Hall measurements often show the presence of deep states causing partial compensation (Groves and Plonko, 1981; Pearsall and Hirtz, 1981). Semi-insulating LPE InP can be grown by simulataneous doping with titanium and zinc (Knight et al., 1988). Titanium introduces a deep donor with an activation energy of 0.54 eV corresponding to the intracenter Ti3+/T.i4+ transitions (Lambert et al., 1986; Knight et al., 1988), which is similar to the 0.58eV transitions between the Fez+ and Fe3+ states observed in Fe-doped OMVPE InP layers (Nicholas et al., 1984). Lowtemperature luminescence revealed the presence of unintentional impurities acting as shallow donors and acceptors (Baumann et al., 1976; Skromme et al., 1984; Skolnick et al., 1984). Deep-level-related transitions were observed at l.leV and at around 0.5eV at temperatures below 80K (Groves and Plonko, 1981). The 0.5eV transitions were probably due to native point defect complexes. An intense 1.1eV luminescence was caused by P vacancyimpurity (Fe) complexes. This luminescence can also be seen, although with much lower intensity, in the layers grown by other epitaxial techniques. The prominence of this radiative transitions in the LPE InP is due to the fact that LPE processes favor formation of defects with phosphorus deficiency. 5. GALLIUM PHOSPHIDE

GaP is an example of a semiconductor in which radiative transitions caused by deep states (most notably the deep level introduced by nitrogen) are efficient enough to facilitate many of the optoelectronic applications of

362

K.W.NAUKA

this indirect and wide band-gap material. However, GaP can also contain unwanted impurities, which introduce deep states that act as very efficient nonradiative recombination centers that, in turn suppress luminescence. A review of the deep states in GaP was given by Kaufmann and Schneider (1982), and Newnark and Kosai (1983). Dean (1986) discussed the deep levels introduced by oxygen, and Peaker and Hamilton (1986) reviewed the major nonradiative recombination centers in bulk Gap. Information about the extensive system of deep states introduced by transition metals can be found in the reviews of Kaufmann and Schneider (1982) and Brunwin et al. (1981). Characteristics of more common traps observed in the epitaxial GaP are shown in Fig. 3 and Table 111. a.

OMVPE GaP

There are only a few reports describing the deep states in OMVPE GaP (Yang et al., 1988; Leys et aL, 1989). They demonstrate the effect of stoichiometry on deep states observed by DLTS, photocapacitance, and luminescence. According to Yang (Yang et al., 1988) the majority of deep states in the OMVPE GaP are due to the antisite P defects (P occupying Ga site-P,,) and to unintentional impurities. The presence of a large number of P,, states can be related to the abundance of P in standard OMVPE processes. P , can be present as a neutral or a single ionized donor. Single ionized P, introduces an electron deep state with a thermal activation

2

3

4

5

6

7

0

9

10

11

1 0 ~ (K-') 1 ~

FIG. 3. Arrhenius plots of temperaturearrected thermal emission rates e / T z for the deep states common in epitaxial GaP (for references, see Table 111).

8. DEEPLEVELDEFECTS IN EPITAXIAL III/V MATERIALS

363

TABLE 111 DEEPSTATESIN EPITAXIALGaP Growth Process OMVPE VPE

LPE

Trap

ET(TYFY (eV)

Ec

U

(ev)

x 10-'5(cm2)

Comment

Ref.'

0.08b

neutral PGa. ionized PG,.

1 1

OEl OE2

0.23 (E) 1.05 (E)

0.053 0.039

O.2lb

VE1 VE2

0.16(E) 0.27(E)

0 0.15

0.01b 0.5b

V,-shallow donor. complexes.

2-5 2-5

VH1

0.92(H) 1.0 (E)

0.17

1600*

Ni. Cr.

2-5 2-5

LH1

0.75(H)

&-impurity complex.

5

u(E)-electron trap, (H)-hole

0.3 (330 K)

trap.

bumvalue.

'From:(1) Yang et al. (1988);(2) Brunwin et al. (1981);(3) Calleja et al. (1983);(4) Breitenstein et al. (1979); (5) Peaker and Hamilton (1986).

energy of 1.05 eV (measured by DLTS) and a corresponding luminescence peak with an energy of 0.97 eV at 77 K. Neutral P,, is responsible for both the 0.23 eV electron trap and the 1.91 eV luminescence at 77 K. Nickel, copper, and oxygen are major unintentional impurities. They either originate from the OMVPE sources and growth apparatus, or diffuse from the GaP substrate. Nickel atoms that occupy Ga sites introduce a deep state at 0.82 eV below the conduction band, as measured by the photocapacitance (Yang et al., 1988). Nickel atoms can also occupy interstitial positions. Interstitial nickel atoms act as very effective nonradiative recombination centers in GaP (Peaker and Hamilton, 1986). Copper atoms that occupy Ga sites introduce radiative transitions at around 1.7eV at 77K. They are also responsible for the deep state located approximately 0.7eV above the valence band, as determined from the photocapacitance measurements (Yang et al., 1988). Oxygen atoms that occupy P sites introduce the deep states responsible for luminescence with an energy of 1.15eV at 77 K (Yang et al., 1988). They are the only reported deep states that can be suppressed by increasing phosphorus partial pressure.

b. VPE GaP Early reports (Wessels, 1977; Tell and Kuijpers, 1978; Breitenstein et al., 1979) indicated the presence of a large number of deep electron and hole

364

K.W.NAUKA

traps. Most of them were due to metals or to metal-related complexes. Both improvements in the GaP VPE process and the introduction of high-purity reactants significantly reduced this large number of traps. More recent reports (Brunwin et al., 1981; Calleja et al., 1983, 1985)show that low-doped VPE GaP contains two electron traps with thermal activation energies equal to 0.16 eV and 0.27 eV. Occasionally, a chromium-related deep level at 1.O eV below the conduction band and a nickel trap at 0.92eV above the valence band can also be seen. Calleja (Calleja et al., 1985) investigated the dependence of the 0.16eV and 0.27eV traps on the tellurium and nitrogen doping, and concluded that they were due to phosphorus vacancy-shallow donor complexes. This result agrees well with the observation of Brunwin (Brunwin et al., 1981)that the concentration of 0.27 eV traps can be increased by annealing, which causes both the formation of a large number of phosphorus vacancies and the interactions of these vacancies with impurities. c.

LPE GaP

Lightly doped LPE GaP is free of deep states, unless it is intentionally doped with impurities, such as nitrogen and oxygen (Brunwin et al., 1981). Deep states related to metallic impurities have been found in the nitrogendoped LPE GaP (Iqbal et al., 1987);their appearance was probably due to a metal contaminated nitrogen source. In addition, a hole trap with a thermal activation energy equal to 0.75 eV is often observed (Peaker and Hamilton, 1986). This deep state, probably caused by a phosphorus vacancy-impurity complex, has also been seen in VPE GaP layers. It has large capture crosssections for both electrons and holes and forms one of two major nonradiative recombination channels (the other one is the nickel level at 0.92eV above the valence band) that degrade the GaP based light emitters (Peaker and Hamilton, 1986).

6. OTHERBINARYCOMPOUNDS

Little is known about deep states in other III/V binary epitaxial layers. In many cases, the only information available comes from studies of ternaries extremely rich in one of the group I11 or V elements; thus, they can be treated as quasi-binary compounds. Aluminum arsenide (AIAs) is an example of one such binary. Early reports on the n-type, low-doped MBE AI,Ga, -,As (with x close to 1) showed the presence of a large number of electron traps with thermal activation energies ranging from 0.2 to 1.0 eV (Yamanaka et al., 1984, 1987). The measurement of these traps as a function of growth conditions clearly demonstrated two different behaviors. The deep state at 0.42 eV did

8. DEEPLEVELDEFECTS IN EPITAXIAL IIIN MATERIALS

365

not depend on the growth conditions. Photoconductivity and Hall measurements identified this state as a DX center that was coupled to the L band minimum at about 30meV above the X minimum. All other electron states were associated with the X band minimum (the lowest conduction band minimum in the AlAs), and their concentrations were strongly dependent on the AI/As flux ratio and growth temperature. This behavior strongly resembled the correlation between electron traps and growth conditions that was observed in the early MBE GaAs films. As in the case of GaAs, the improvements in growth processes decreased their concentrations. More recent reports (Kasu et al., 1989; Feng et al., 1990)showed that the DX center was the only deep electron state found in high-quality MBE AIAs. Even less is known about epitaxial InAs. The photoluminescence measurements of the MBE InAs that is grown on both GaAs and Si substrates showed the presence of sub-band-gap luminescence that could have been related to defects (Grober et al., 1989). However, the Hall measurements demonstrated that transport properties of MBE InAs could be explained without involving any potential traps (Kalem, 1989). The band diagram of InAs shows a large separation between the r and the X or the L bands. Therefore, it is unlikely that a state with DX-like properties could be present in InAs. In addition, rather small band-gap value suggests that epitaxial InAs could be relatively free of deep state defects. IV. Epitaxial Ternaries and Quaternaries

Alloy semiconductors offer an opportunity to study deep states under variable composition conditions. Observations of the response of a deep state to changes in the electronic band structure give an excellent insight into the nature of deep-level defects. Many of the traps in ternary and quaternary III/V alloys can be derived from the deep state spectrum in corresponding binaries. In addition, some new deep state defects can appear. This is because of the increase in the number of possible point defects and their complexes when the crystallographic structure consists of three or four, instead of two, elements. In addition, as demonstrated by Das (Das et al., 1988), a semiconductor alloy may be considered as a substitionally disordered system. Local deviations from the mean composition introduce fluctuations in the defect potential broadening the deep state response, that is measured by PL, DLTS, or other techniques. In the case of DLTS, in addition to peak broadening, it also causes the measured transients to be no longer exponential. However, DLTS analysis still remains valid except for the case of very large compositional nonuniformities(Omling et al., 1983a; Das et al., 1988; Kaniewska and Kaniewski, 1988). Finally, the DX centers, rarely seen in binary

366

K. W. NAUKA

compounds, are frequently observed in the ternaries and quaternaries. This unique defect, which due to its very high concentration can control semiconductor properties, has been described in other chapters of this book. We will limit our discussion to mentioning its presence when appropriate.

7. ALUMINUMGALLIUM ARSENIDE AI,Ga, -,As alloys are particularly important for a large number of optoelectronic and high-speed device applications. They are closely latticematched to the GaAs substrate in the entire composition range and offer flexibility in both band gap and band offset engineering. Interest in the AI,Ga, -,As deep states has been driven primarily by observations of their deleterious effects, such as changes in the laser threshold current or variations of the MODFET threshold voltage, which are associated with the deep states in Al,Ga, -,As active layers. The DX center is probably the most striking feature observed in the AI,Ga, -,As films. It is resonant with the conduction band at low Al contents, although even then its trapping effect can be observed. The DX level enters the band gap at approximately x = 0.23 and becomes the dominant trap in Al,Ga, -,As when x is larger than 0.35. Figure 4 and Table IV review major deep states in the epitaxial Al,Ga, _,As.

I 1 2

1

I

I

I

I

1

I

I

I

3

4

5

6

7

8

9

10

11

1 0 ~ (1~ -~1 )

FIG, 4. Arrhenius plots of temperature-corrected thermal emission rates e/T2 for the deep states common in epitaxial AI,Ga, -,As (0.2 < x < 0.28) (for references, see Table IV).

8. DEEPLEVELDEFECTS IN EPITAXIAL III/V MATERIALS

367

TABLE IV DEEP STATESIN EPITAXIAL AlGaAs Growth Process MBE

OMPVE

Trap

Er (TYPY (ev)

U

x 10-'s(cm2)

ME1 ME2 ME3 ME4 ME5

0.18 (E) 0.27 (E) 0.42 (E) 0.55 (E) 0.65 (E)

0.007 (130 K) 0.2 (155K) 0.2-50 (190-240 K) 2 (305 K) 40 (320 K)

ME6

0.80 (E)

5-20 (360-380 K)

OEl OE2

0.25 (E) 0.62 (E)

O.OOO1 (145 K) 0.06-0.2 (320 K)

OE3

0.82 (E)

3-20 (380 K)

Comment

DX center. impurity-native point defects complexes. EL2.

Al-impurity complex. EL2.

Ref? 1-7 1-7 1-7 1-7 1-7 1-7 8-11 8-11 8-11

"(E)-electron trap, (H)-hole trap. bFrom: (1) Hikosaka et al. (1981); (2) Naritsuka et al. (1984); (3) Mooney et al. (1985); (4) Yamanaka et al. (1987); (5) Evans et al. (1987); (6) Lin et al. (1988); (7) Puechner et al. (1988); (8) Wagner et al. (1980);(9) Wallis et al. (1980); (10) Wu et al. (1982); (11) Bhattacharya et al. (1984).

a.

MBEAlGaAs

Electron traps in MBE A1,Gal -,As can be grouped into three categories, according to their properties and arrangement in the DLTS spectrum. Two electron traps with thermal activation energies of 0.17-0.18 eV and 0.260.27 eV can be seen at low temperatures (Hikosaka et al., 1981; Naritsuka et al., 1984; Evans et al., 1987). Their concentrations are typically below 10'3cm-3, and improvements to the growth process can suppress them even further (Lin et al., 1988; Puechner et al., 1988). The DX center is usually observed in the middle part of the spectrum. It has a thermal activation energy in the range between 0.2 and OSeV (depending on the type and concentration of the shallow dopants); multiple peaks are often observed (Mooney et al., 1985; Yamanaka et al., 1987). One or more deep states can also be found in the high-temperature part of the spectrum (Hikosaka et al., 1981; Naritsuka et al., 1984; Evans et at., 1987). Their concentrations are much higher than those of the low-temperature traps. The highest-energy electron state (thermal activation energy 0.79-0.82 eV) is frequently identified as EL2 (Lin et al., 1988). Another high-temperature trap, with a thermal activation energy equal to 0.66 eV (at x = 0.25) appears to be a very effective nonradiative recombination center with electron and hole capture crosssections that exceed 10-I3cm2. The presence of this trap has been directly correlated with both a decrease in the near bandgap luminescence for the

368

K. W. NAUKA

AI,Ga, -,As films, and a degradation of the AI,Ga, -,As optoelectronic devices (McAfee et al., 1981b; Lin et al., 1988). Although most electron traps (except for DX) have activation energies almost invariant with respect to alloy composition, the results of Yamanaka (Yamanaka et al., 1987) indicate that at least one of the high temperature traps has an activation energy that varies with composition. Puechner identified the 0.66eV trap (Puechner et al., 1988) as clearly different from other traps in MBE AI,Ga, -,As. It becomes deeper when x is increased, but remains invariant with respect to the valence band maximum (Fig. 5), which shows that it could be primarily composed of the valence band states. Measurements of the electron traps in layers that are grown under conditions in which both the substrate temperature and the III/V beam flux ratio were varied demonstrated that deep states in the AI,Ga, -,As films, except for the DX center, are quite similar to those found in MBE GaAs (Yamanaka et al., 1987). The concentrations of these traps can be decreased by increasing growth temperature to 750°C. They also exhibit a rather complex dependence on the V/III flux ratio; the lowest trap concentrations are seen when the ratio is between 2 and 5. The replacement of As, by As, has only a weak effect on the trap concentrations; concentration decrease by a factor of

-

2.0t

x

L

5-

1

1.2

0.4

0.1

0.2

0.3

0.4

CONTENT (x) FIG. 5. Energy levels of selected deep levels in epitaxial AI,Ga, -,As as a function of the Al mole fraction. (from: (1) Lang et al., 1977 (A, B-LPE AIGaAs); (2) Matsumoto et al., 1982 ( E L 2-OMVPE AIGaAs); (3) Puechner et ol., 1988 (ME 5-MBE AIGaAs). Plots (1) and (3) reproduced with permission of the American Institute of Physics).

8. DEBPLEVELDEFECTS IN EPITAXIAL III/V MATERIALS

369

1.5-2 has been reported (Chen et al., 1985). Similarities between traps found in binary GaAs and those found in ternary Al,Ga,-,As layers indicate their common origin. They are most likely associated with complexes formed by arsenic-aluminum-and gallium-related native point defects and impurities (Yamanaka et al., 1987; Puechner et al., 1988).

b. OMVPE AlGaAs As in the case of binary GaAs, OMVPE Al,Ga, -,As contains fewer traps than the MBE layers. DX deep donor dominates when x is larger than 0.3. It can appear in the form of single or double DLTS peaks with thermal activation energy in the range of 0.24-0.45 eV and with peak separations, in the case of double peak, of 0.02-0.06 eV. Similarly to OMVPE GaAs, at low x values an EL 2 trap is the major electron deep state. Its activation energy varies with composition, as shown in Fig. 5. Other electron traps observed in OMVPE Al,Ga, -,As have activation energies of 0.62-0.66 eV and 0.240.25 eV; their concentrations are one to two orders of magnitude lower than that of EL 2 (Wagner et al., 1980; Wu et al., 1982, Bhattacharya et al., 1984). These two traps appear to be unique for OMVPE Al,Ga, -,As, and at least one of them could be due to aluminum-oxygen complexes (Wallis et al., 1980). Hole traps in Al,Ga, -,As are mostly caused by metallic impurities. Since their activation energies are almost invariant with respect to alloy composition, they can easily be identified by comparing them with the corresponding states in GaAs (Wu et al., 1982). Deep states introduced by metals can also be seen in the luminescence spectrum of OMVPE Al,Ga,-,As. Radiative transitions with energies of 100, 130, 160, and 400meV (77 K) were reported; at least two of them were associated with zinc and manganese impurities (Zhu et al., 1983; Bhattacharya et al., 1984).

c. LPEAlGaAs LPE Al,Ga,-,As (x < 0.3) appears to be free of electron traps and, like LPE GaAs has two hole traps (called A and B-compare with traps LH1 and LH2 in Fig. 1; Lang et al., 1977; Kondo et al., 1981). Both traps have activation energies that vary with composition as shown in Fig. 5. They do not follow any of the bands exactly. However, they appear to be more closely coupled to the conduction than to the valence band. The DX state appears when x is larger than 0.3, and at high x values it controls the electronic properties of the LPE Al,Ga, -,As films.

370

K.W.NAUKA

8. GALLIUM ARSENIDEPHOSPHIDE GaAs, -xP, is used in optoelectronics as a source material for visible light LEDs. The variety of native point defects present in this ternary compound, when combined with impurities and extended defects, introduces deep states that can control device stability and light output (Tell and Van Opdorp, 1978).Three electron traps with activation energies of 0.16,0.27, and 0.38eV (Table V) have been observed in the lightly tellurium-doped VPE and LPE GaAs,-,P, layers with x > 0.3 (Craven and Finn, 1979; Henning and Thomas, 1982; Calleja et al., 1983; Kaniewska and Kaniewski, 1988). They exhibited, although on a smaller scale than All -,Ga,As, the properties of DX centers, such as large phonon relaxation, partial carrier freeze-out at low temperatures, and persistent photoconductivity. Two weak luminescence bands with energies of 1.27 and 1.46eV observed at 77K (Metz and Fritz, 1977)are likely to be related to the 0.15 and 0.27 eV deep states. The 0.38 eV trap acts as an efficient nonradiative . 7mbination center. A direct correlation between the concentration of t h s trap and a decrease in band-gap luminescencehas been reported (Tell and Van Opdorp, 1978; Kaniewska and Kaniewski, 1988). Activation energies of the traps remain constant when composition is changed (Calleja et al., 1983), which demonstrates that they are closely coupled to the X band minimum. Presence of a DX-like electron trap in GaAs, -,P, can be explained by similarities in the band structures of GaAs, -xPxand All -,Ga,As. At low x values (x < 0.3), the EL 2 trap can be seen in GaAs, -,P, films (Omling et al., 1983b).Similarly to All -,Ga,As, its activation energy changes with composition.

9. GALLIUM I m m ARSENIDE Ga,In, -,As is a direct gap semiconductor within the entire composition range. It is lattice-matched to InP substrates for x = 0.47. Similar spectra of deep states have been observed for Ga,In, -,As films grown by LPE, VPE, OMVPE, and MBE (Charreaux et al., 1985;Goetz et al., 1985; Whitney et al., 1987). An electron trap with thermal activation energy between 0.32 and 0.39eV is frequently seen in layers with x 0.4 (Table V). It can be accompanied by 0.7 eV (4 K) luminescence. This deep state is believed to be related to intrinsic defects, such as As vacancies and As vacancy-impurity complexes (Laualiche et al., 1987; Chen et al., 1988; Bacher, 1988). Its concentration depends on growth conditions; the lowest concentrations have been observed in the As-rich OMVPE layers that are grown at high temperatures; the highest concentrations can be found in the lowtemperature LPE films. Sometimes, an additional deep-state-related weak

=-

371

8. DEEPLEVELDEFECTS IN EPITAXIAL III/V MATERIALS TABLE V Deep STATES IN TERNARY III/V EPITAXIAL COMPOUNDS

GaAsP

GaInAs

0.16 (E) 0.27 (E) 0.38 (E)

0.12 0.16 0.22

0.5

1.0

0.1-lb O.OO1-O.Olb 300*

0.30-0.32 (E) 0.7 (PL) 0.44 (E) 0.15 (H)

0.69 (PL) GaInP

AlInAs

0.39 (E) 0.61 (E) 0.84 (H) 0.37 (E) 0.32 (E)

88600 (360 K) 0.29 0.27

0.7

0.25 (E) 0.56 (E) 0.60 (E) 0.71 (E) 0.27 (H) 0.45 (H) 0.65 (H) 0.95 (H) 0.35 (E) 0.54 (E) 0.55 (E)

AlInP

50 (190K) 2000 (270K)

0.29 (E) 0.66 (E)

0.1

0.61 0.95

DX centers, Te doped. recombination center.

1 1 2 3, 4

v*-impurity complexes. Fe acceptor. Fe complex. lattice mismatch.

5

L$-related. lattice mismatch. DX center, S-doped. DX center, %-doped.

6 6 7 8 8

observed in Si-doped MBE-grown material. Possible originnative point defects + impurity complexes. complexes. DX centers. lattice mismatch.

9 9 9 9 9 9 9 9 9 9 10 9

DX center. ki?v*, complexes.

11 11

3 3

"(E)-electron trap, (H)-hole trap, (PL)-photoluminescence peak. b ~ value. , 'From: (1) Calleja et al. (1985); (2) Kaniewska and Kaniewski (1988);(3) Chen et al. (1988); (4) Laualiche et al. (1987);(5) Yagi et al. (1983);(6) Zhu et al. (1989);(7) Chen et al. (1990);(8)Kitahara et al. (1988); (9) Hong ec ul. (1987); (10) Nakashima et al. (1987); (11) Watanabe and Ohba (1986).

luminescence can be seen at 0.6 eV (4 K) (Chen et al., 1988). When layers are grown on iron doped semiinsulating InP, ion atoms can diffuse into the epilayer and form additional deep states. The same states are, of course, seen in the films intentionally doped with ion (Charreaux et at., 1985; Chen et al.,

372

K.W. NAUKA

1988). Iron impurities introduce a single electron trap that is due to the ionized iron acceptor (transition between Fe3+ and Fe2+). There is no agreement as to its activation energy; activation energies of 0.37 eV (Surugawa et al., 1987),0.44eV (Chen et al., 1988),and 0.34eV (Guillot et al., 1990) have been proposed. In addition, an iron-complex-related hole trap with an activation energy of O.15eV and a corresponding luminescence at 0.66 eV (4K)can be seen. Films that are lattice-mismatched to the InP substrate exhibit additional deep states that introduce radiative transitions with an energy of 0.69eV (77 K) (Yagi et al., 1983). This luminescence band shows a strong correlation with a degree of lattice mismatch and is caused by defects formed when the epilayer relaxes. Ga,In, -,As with x > 0.7 has been grown on GaAs substrates (Mirceau et al., 1977; Prints et al., 1987). EL2 is the dominant deep state in these films. As with other GaAs-rich ternaries, its activation energy varies with x.

10. GALLIUM INDIUM PHOSPHIDE Ga,In, -,P is a direct gap ternary semiconductor for x < 0.73. Layers with has been grown using LPE, VPE, OMVPE, and MBE (Yoshino et al., 1984; Kitahara et al., 1986; Paloura et al., 1991); similar deep state spectra have been observed in all these materials. An undoped Gao.,,In,,,,P is free of deep states except for some of the LPE layers, in which the deficiency of phosphorus can cause the appearance of an electron trap with a thermal activation energy of 0.39 eV (Table V). Sulfur doping introduces a DX-like electron state with a thermal activation energy in the range of 0.37-0.4OeV. This state exhibits the all characteristics of the D X center in AI,Ga, -,As, such as carrier freeze-out, persistent photoconductivity, dependence on donor concentration, and large lattice relaxation (Yoshino et al., 1984; Watanabe and Ohba, 1986; Kitahara et al., 1988).Its concentration, because of the difference in relative positions of the L and r bands, is smaller than in Al,Ga, -,As. The D X center in sulfur-doped Ga,In, -,P is resonant with the conduction band at low x values and crosses into the band gap at x = 0.45. Replacement of sulfur by selenium shifts the crossover point to x between 0.53 and 0.66 (Kitahara et al., 1988). An even larger shift is expected for the DX state associated with silicon donors. Therefore, lattice-matched Gao,5,1no~,,Players that are doped with selenium or silicon often appear to be free of deep states. Lattice-mismatched Ga,In, -,P that is grown on GaAs substrates exhibits an additional electron trap with a thermal activation energy equal to 0.55-0.61 eV (Zhu et al., 1989; Paloura et al., 1991).A latticemismatch-related hole trap at 0.84eV above the valence band has also been x = 0.51 are lattice-matched to the GaAs substrate. Ga,In,-,P

8. DEEPLEVELDEFECTS IN EPITAXIAL III/V MATERIALS

373

observed in Ga,In, -,P that is grown on an InP substrate (Chen et al., 1990). Both traps have concentrations that strongly depend on a degree of mismatch and a distance from the epitaxial layer-substrate interface.

ARSENIDE 11. ALUMINUMINDIUM

Al,In, -,As has a direct gap for x < 0.68, and it is lattice-matched to the InP substrate when x = 0.48. High-quality LPE AlJn, -,As is free of deep states measured by DLTS (Ogura et al., 1983b). Nakashima observed (Nakashima et af., 1987) only one DX-like electron trap with a thermal activation energy equal to 0.54eV and an optical activation energy of 0.95 eV in MBE Alo.481no.52As(Table V). Hong demonstrated (Hong et al., 1987) a large number of electron and hole traps in the MBE lattice-matched layers (i.e., electron traps with thermal activation energies equal to 0.25,0.56, 0.60, and 0.77 eV, and hole traps with thermal activation energies of 0.27,0.45,0.65, and 0.95eV). None of these centers behaved like the DX state. However, when the layers were lattice-mismatched(x > 0.48), they exhibited additional electron traps with thermal activation energies of 0.35eV and 0.55eV. The 0.35 eV state behaved like a DX center. The 0.55 eV trap was introduced by lattice-mismatch defects; it was eliminated by growing a buffer that confined the defects. A large number of electron traps in lattice-matched MBE Alo.481no,52As was also reported by Whitney (Whitney et al., 1987).However, only some of these traps matched the results of Hong. An obvious disagreement between the reported data demonstrates the need for further studies of deep states, especially DX traps, in AI,In, -,As films.

12. ALUMINUM INDIUMPHOSPHIDE Al,In, -,P is lattice-matched to the GaAs substrate for x = 0.51. It is a direct gap material when x < 0.44. Two electron traps (Table V) were observed in the OMVPE lightly selenium-doped layers lattice matched to GaAs (Watanabe and Ohba, 1986). The first trap, with the thermal activation energy equal to 0.29eV, exhibited a DX-like large lattice relaxation and a correspondence between the trap concentration and the selenium dopant concentration. The second trap had a thermal activation energy equal to 0.66 eV, and its concentration remained constant when the dopant concentration was changed. This defect was probably due to the complexes involving A1 and In vacancies.

314

K.W. NAUKA

13. GALLIUM INDIUM ARSENIDEmOSPHIDE

-,

Ga,In, -,As,P, can be grown lattice-matched to the GaAs and InP substrates. Epilayers matched to InP are of considerable interest for optoelectronic applications because they offer a direct gap smaller than the InP band-gap. There have been numerous reports on deep states and their dependence on both composition and growth conditions (Sasai et al., 1979; Shirafuji et al., 1981; Bhattacharya et a/., 1981; Pelloie et al., 1986; Zhu et al., 1989). Deep states in Ga,In, -,As,P, T y can be grouped into three categories: lattice-mismatch-related defects, native point defects and their complexes, and states due to impurities (Table VI). Lattice mismatch introduces two electron traps with activation energies of 0.59-0.62 eV and 0.69 eV, and one hole trap with an activation energy of 0.25 eV. Corresponding radiative transitions were observed in the photoluminescence spectrum (Charreaux et al., 1985). The same electron traps can also be seen in the corresponding lattice-mismatched ternaries (0.61 eV trap in Ga,In, -xP and 0.69eV trap in Ga,In, -.As). As and P vacancies and their complexes give rise to a group of electron traps with thermal activation energies within the ranges 0.280.32 eV and 0.38-0.40eV. These defects are particularly visible in the LPE TABLE VI DEEPSTATESIN QUATERNARY III/V EPITAXIAL COMPOUNDS Material AlGalnP

AlGaInAs

ETVYpeY (ev) 0.66 (E) 0.2 (E) 0.29 (E) 0.48 (E)

0.64 (E)

E, (eV)

0.08 0.11 0.10 0.10

Eo (ev)

D

x

10-'6(cmz)

Comment

double DX peak, Se-doped. DX, Si doped.

0.7 1.1 1.25

9100 (270 K)

Ref? 1 1

2 3

x=0.17

0.16 (H)

lnGaAsP

0.28-0.31 (E) 0.38-0.40 (E) 0.59-0.62 (E) 0.69 (E) 0.25 (H) 0.40 (H) 0.69 (H)

1-100 (150-200K) V, and 10-100 (220-240 K) 'V complexes. lattice mismatch 0.5 (160 K) related. 0.04 (250K) metallic 600 (>300 K) impurities.

"()-electron trap, (H)-hole trap. bFrom:(1) Watanabe and Ohba (1986);(2) Nojima et nl. (1986);(3) Biswas et al. (1990);(4) Sasai et 01. (1979);(5) Zhu et a/. (1989);(6) Shirafuji et nf. (1981); (7) Pelloie et al. (1986).

8.

DEEP

LEVELDEFECTS IN EPITAXIAL III/v MATERIALS

375

materials since this growth technique frequently causes a loss of As and P. The corresponding states are present in ternaries: the 0.30-0.32 eV trap in Ga,In,-,As, and the 0.39eV trap in Ga,In,-,P. Metallic impurities are responsible for the hole traps with activation energies equal to 0.40 eV and 0.69 eV. Since they mostly occupy substitional sites, their electronic properties are not strongly affected by the compositional fluctuations in the surrounding lattice. Therefore, DLTS 'peaks introduced by these defects do not exhibit significant broadening, as opposed to the defect-complex-related 0.25eV hole trap observed in the same layer (Pelloie et al., 1986).

INDIUM ARSENIDE 14. ALUMINUMGALLIUM (Al,Ga,-,),In,-,As is lattice-matched to InP for y = 0.47. DLTS and cathodoluminescence measurements of (Al,Ga, -x)0.471n0.53A~ (Papadopoulo et al., 1987; Biswas et ai., 1990) showed the presence of both an electron and a hole trap with thermal activation energies changing linearly with composition; they appeared to follow a mid-gap line when the composition was changed. Their activation energies varied from 0.3 eV (electron trap) and 0.14 eV (hole trap) for an A1 content of 5% to 0.79 eV and 0.31 eV, respectively, when the A1 content was 30%. Corresponding electron and hole traps can be seen in the respective ternaries: a 0.3 eV electron trap in Gao.471no,53As,and 0.7-0.8 eV electron trap and 0.27eV hole trap in Alo.4,1no.53As.Some of the deep electron states are probably associated with the defect complexes that involve A1 atoms; lowering of the A1 content decreases the trap concentrations (Schramm et al., 1991).

15. ALUMINUM GALLIUM INDIUM PHOSPHIDE (Al,Ga, -,),In, -yPcan be grown lattice-matched to both GaAs and Al,Ga, -,As for all x values when y = 0.51. MBE-grown AlInP-rich layers exhibit an electron trap with a thermal activation energy equal to 0.66eV (Watanabe et al., 1986); the same trap can be seen in the MBE Al,In, -xP ternary. In addition, an electron trap with DX properties can be observed for all x values. One DX trap with a thermal activation energy of 0.48 eV (Table VI) was found in silicon-doped A10.24Ga0.271n0.49P films (Nojima et al., 1986). Selenium-doped layers exhibited a double DX peak with thermal activation energies of 0.2 eV and 0.29 eV (Watanabe et al., 1986). Measurements of the D X concentration as a function of x value show that it reaches

376

K.W. NAUKA

its maximum at around x = 0.7, corresponding to a T-X crossover in the conduction band.

V. Quantum Wells, Superlattices, and Interfaces Heterojunctions and low dimensional structures, like single and multiple quantum wells, offer new challenges in the study of deep states in 111-V epitaxial layers. It can be assumed that growth processes that introduce deep state defects in the “bulk” epitaxial films can also generate similar defects in low dimensional structures. It can also be expected that the band structure changes that are introduced by low dimensionality or by strain will affect the electronic properties of these defects.

QUANTUM WELLS 16. LATTICE-MATCHED

AND SUPERLATTICES

Consider the case of a single lattice-matched quantum well that consists of a thin layer surrounded by heterojunction boundaries (the analysis of deep states in superlattices is a natural extension of the case of a single quantum well with a discrete quantized energy levels that are replaced by minibands). Since the deep level wavefunctions are localized and extend no further than the nearest neighbor atoms (Hjalmarson et al., 1980), one can distinguish two possible locations of the deep-state point defects in a quantum well. The defects located further than a few atomic distances from the interfaces are surrounded by a bulk-like atomic arrangement, and therefore they introduce deep states similar to those observed in the “bulk” layers. Bourgoin and Lannoo (Bourgoin and Lannoo, 1987) present some rather simple calculations that are based on the concept of perturbation to the deep state energy introduced by a heterojunction potential that clearly demonstrate the bulklike nature of deep state defects located farther than two atomic layers from the interface. Similar results were obtained from the tight-binding calculations of deep substitutional impurities in GaAs/AlGaAs superlattices (Ren et a/., 1988; Dow and Ren, 1987). The invariance of a deep state in the quantum well with respect to the bulk band positions was tested experimentally in a series of luminescence measurements of the GaAs quantum wells that were doped with manganese (Plot et al., 1986; Deveaud et al., 1987). Figure 6 shows the manganese related radiative transitions in a 50 GaAs quantum well. The energy of the luminescence peak corresponds to the respective bulk value that is corrected for the change in band structure when the bulk conduction band is replaced by a miniband. The lack of peak broadening

a

8. DEEP LEVELDEFECTS IN EPITAXIAL III/V MATERIALS

377

ENTER

501%GaAs QUANTUM WELL

1.40

1.45

1.50

1.55

1.60

1.65

ENERGY (eV)

FIG.6. Donor-Mn transitions in a 50A quantum well showing the high-energy structure (D -Mn interface)originating from the Mn atoms located less than one monolayer away from the interface.Insert shows the ratio of the integrated intensity of the D-Mn interface structure to the main D-Mn peak as a function of the well thickness &(a = 2.83 A). The straight line shows the contribution expected from the Mn ions in one monolayer on each side of the well (from Deveaud et ul., 1987; reproduced with permission of the American Institute of Physics).

indicates that the manganese binding energy is constant throughout the well. A small hump observed on the low-energy side of the manganese peak originates within the vicinity of the heterojunction interfaces in which a shift in the activation energy that is caused by the heterojunction potential takes place. This observation can be further tested by varying the width of the well. In narrow wells the ratio of “adjacent to interface” to “bulk” volumes decreases, so that the ratio of luminescence peaks originating from respective regions increases (see insert in Fig. 6). As mentioned earlier, the invariance of

K.W. NAUKA deep states with respect to bulk band positions does not mean that the measured values of trap activation energies are the same as those for bulk crystal. Although the trap level remains invariant, the bulk valence and the conduction band are replaced either by the discrete energy levels or by the minibands. Changes to the quantum well width or to the superlattice period can drastically alter the observed deep state spectrum, as was experimentally demonstrated for deep states in the GaAs-AlGaAs (Martin et al., 1986) and the GaAs-A1As (Kobayashi et al., 1988) superlattices. This effect, called by Ren (Ren et al., 1988) the “change of the window of observability of a deep level,” can also give rise to some new band-gap states. Ren calculated the case of silicon dopant atoms that occupied Ga sites (SiGa)in the GaAsJAlGaAs superlattices. An 18 x 18 superlattice had a band-gap similar to that of GaAs, and the SiGastate remained within the conduction band. When the superlattice period was kept constant but the thicknesses of the GaAs wells were decreased (the case of a 2 x 34 superlattice was calculated), the superlattice band-gap increased and the Si,, level was uncovered, becoming a deep state defect. The bulk-like behavior of deep states in low-dimensional structures offers some interesting opportunities for studying the band structure in quantum wells. Since the deep level activation energy is invariant with respect to the bulk material, any changes in the electronic properties of a deep state can be related to changes in band alignment and to the local electronic structure of either a single quantum well (discrete quantized energy levels) or multiple (minibands) quantum wells. The idea of a band offset measurement that uses either transition metal atoms that are placed on both sides of an interface (Langer and Heinrich, 1985), or any well-defined deep state within the quantum well (Deveaud et al., 19871, is illustrated in Fig. 7. Assuming that the trap locations in the well and in the barrier are known, as well as their respective activation energies in the bulk materials, one can calculate the band offset and the lowest miniband position. This analysis must include the potential changes in the value of the capture cross-section activation energy, which could be dependent on the trap location in a well. Similar corrections must be made when the activation energy is determined from the optical measurements (Bourgoin and Lannoo, 1987; Takikawa et al., 1989). The successful calculation of band offsets from DLTS measurements of deep states in superlattices was reported for the A1As-GaAs (Feng et al., 1990) and AIGaAs-GaAs (Martin et QL, 1986)superlattices. The analysis of DLTS data must take into account the camer redistribution in the superlattice, the deformation of both rectangular wells and barriers by an electric field, the carrier transport via deep-state-introduced bands in the barriers (Capasso et al., 1986), and the spurious effects introduced by the defects that reside at the interfaces. One must also remember that the quantum well itself acts as a

8. DEEPLEVELDEFECTS IN EPITAXIAL III/V MATERIALS BULK

379

SUPERLATTICE

FIG. 7. Change of the parameters of hypothetical electron traps TAand Ti, when placed in the superlattice. A-conduction band offset, S-miniband position (adapted from Bourgoin and Lannoo, 1987, reproduced with permission of the Plenum Press).

“giant trap” (Hamilton et al., 1985; Lang et al., 1986; Debbar et al., 1989). Therefore, the signals coming from deep states must be separated from the carrier trapping and emission from quantized energy states within the well. 17. STRAINED LAYERS

III/V epitaxial films are frequently grown on lattice-mismatched substrates. One can consider the case of a commensurate thin and direct gap epilayer. Because of the differences in thickness, all strain is present in the epilayer, which is subjected to a biaxial strain in the plane parallel to the interface, and which responds to the strain by relaxing in the direction perpendicular to the plane. One can also assume the substrate orientation that eliminates the potential piezoelectric effects (Mailhiot and Smith, 1987), and neglect the relaxation along the edges. The total strain in this system can be resolved into its purely axial and hydrostatic components. The response of the band structure to the strain can be expressed in terms of the hydrostatic and uniaxial deformation potentials (Marzin, 1985; OReilly, 1989; Arent et al., 1989). Hydrostatic pressure is responsible for the shift of both conduction and valence bands and the respective band-gap changes. The uniaxial strain breaks the cubic symmetry and splits the degenerate bands, introducing a new anisotropic band structure. Depending on the sign of the axial strain, the highest valence band at the r point may contain heavy holes in the epilayer plane and light holes in the direction perpendicular to the plane (biaxial tension), or vice versa (biaxial compression). The strain-introduced band structure changes can be imposed on the energy quantization along the

K.W.NAUKA growth direction, giving the full picture of a strained-layer quantum well or superlattice. Strain-induced changes in the band structure must reflect on the properties of the deep states present in the strained layer. Since deep states can be composed of wavefunctions that originate from many bands within the Brillouin zone, any change of the band arrangement affects the deep state properties. This is demonstrated in a few available reports on the deep states in the strained III/V layers. Jenkins (Jenkins et al., 1989) calculated the effect of uniaxial stress on deep substitional impurities in III/V compounds and showed that they are shifted and sometimes split (depending on the defect symmetry and the strain orientation) with respect to their positions in the unstrained layers. Wolford (1986) demonstrated experimentallyboth that the behavior of nitrogen in GaAs under hydrostatic pressure is significantly different from any of the conduction bands, and that it can be described as a superposition of wavefunctions from throughout the reduced zone and likely from many host bands. Similar results were obtained for the deep silicon state in GaAs (Chandrasekhar et al., 1988). Barnes (Barnes et al., 1984) measured the DLTS spectra of the gamma-radiation-introduced deep states in GaAs,P, -,/Gap superlattices as a function of strain (the magnitude of the strain and its distribution were varied by changing both the composition and the layer thicknesses).Traps with similar activation energies were observed in the GaP layers for all measured superlattices. However, their hydrostatic pressure coefficients, dE/dp (E is thermal activation energy, p is hydrostatic pressure) were dependent on the magnitude of tensile strain in GaP films. The experimental and theoretical results demonstrate that deep levels in strained layers have different properties from those in the corresponding unstrained films. Further studies are needed to elucidate the exact correspondence between strain and deep states in the epitaxial III/V materials. 18. INTERFACES

When a deep-state point defect is located within a few atomic distances from the heterojunction interface, changes to the central cell potential introduced by the defect are additionally modified by a large number of factors, both intrinsic (the penetration and the overlap of wavefunctions across the interface, the electric field associated with the heterojunction, the change of the band structure caused by the local lattice mismatch that introduces dangling bonds) and extrinsic (local variations of the chemical composition, pile-up of point defects and impurities at the interfaces). The calculations of Bourgoin and Lannoo (1987) showed a significant shift of the deep-state level near the interface. The tight binding calculations (Ren et al., 1988) for an idealized case, in which only deep substitional impurities are

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381

present near the interface, predict both the splitting of defect levels and the large shift in their positions within the band-gap. These changes are caused both by the overlap of wavefunctions across the quantum well boundary and by the carrier quantum confinement. In addition, the shift of band edges can uncover resonant states and turn some shallow levels into deep states. Impurities and-structural defects at the interfaces not only can change the properties of deep states in the regions near the interface, but also can be a source of new deep states. The presence of unwanted impurities and defects at interfaces strongly depends on the growth process. It was demonstrated that the GaAs/AlGaAs structures that were grown by processes that facilitated insitu cleaning by back melting and back etching (LPE, VPE-Nelson and Sobers, 1978) had a lower concentration of interfacial defects than the structures grown MBE (McAfee et aZ., 1982; Sermage et aL, 1987), in which insitu cleaning was limited to thermal desorption of surface oxides. Similarly, both growth interruptions that introduced impurities and epitaxial growth that was conducted at either too low or too high temperature enhanced the formation of interfacial defects (Vook and Gibbons, 1990). Deep states at the interfaces can also be related to dangling bonds that are formed by lattice mismatch. It often happens that, because of their different thermal expansion coefficients, heteroepitaxial components are lattice-matched at room temperature and mismatched at elevated temperatures, or vice versa. Takeda demonstrated (Takeda et al., 1985) the presence of interfacial deep states in In,~,,Ga,~,,As/InP structures that were lattice-matched at room temperature and were mismatched at the growth temperature of 625°C. These defects were absent from the In,~,,Ga,~,,As/InP structures that were latticematched at growth temperature and mismatched at room temperature. The complexity of the heterointerfacial environment often results in the occurence of a continuum of deep states rather than just discrete levels (Welch et al., 1985; Feng et al., 1990, Krahl et al., 1990). However, for many heteroepitaxial III/V systems, improvements in growth techniques produced interfaces which were virtually free of deep state defects.

VI. Deep Levels in Structurally Disordered III/V Layers Many of the III/V epilayers are grown under conditions that introduce a large structural disorder caused both by one-dimensionalpoint defects, such as vacancies, interstitials, antisite defects, and point defect complexes, and by multidimensional defects, such as dislocations, precipitates, and antiphase domains. Examples of such structures include relaxed lattice-mismatched heteroepitaxial systems, layers grown at low temperatures, and films grown

382

K. W.NAUKA

on disoriented substrates. Structural defects can perturb the local periodic potential and modify the deep state spectrum. Therefore, the practical application of these epilayers frequently requires understanding of the relationship between structural imperfections and deep state defects. 19. RELAXED LAITICE-MISMATCHED EPITAXIAL LAYERS

GaAs grown on Si (GaAs/Si) is an example of a relaxed epitaxial film that can be grown on a largely mismatched substrate (“Heteroepitaxy on Si“ Symposia, 1986, 1987, 1988). Device-quality GaAs/Si epilayers are frequently grown by the two-step MBE or OMVPE process, in which first a thin buffer is grown at low temperatures and then a thick device layer is deposited at higher temperatures. The purpose of the low-temperature buffer is to enforce the two-dimensional growth of the initial GaAs layer and to keep defects away from the device area. Defect confinement can be enhanced by introducing an additional superlattice buffer. Because of the large lattice mismatch, the GaAs layer relaxes during the initial stage of epitaxial growth, and large numbers of misfit dislocations and their associated point defects are formed. In addition, the diffusion of impurities from the silicon substrate and the difference in thermal expansion coefficients between the GaAs and silicon can contribute to defect formation. A mismatch between thermal expansion coefficients has the opposite sign from that of the lattice-constant mismatch. Therefore, as-grown GaAs/Si is usually found to be under tensile strain caused by the difference in thermal expansion, and not under compressive strain caused by different lattice parameters. The growth of polar GaAs on nonpolar silicon substrates can contribute to the formation of antiphase domain defects with electrically active boundaries (i.e., antiphase domain boundaries, APBs). The formation of APBs can be suppressed by growing GaAs on tilted silicon substrates (Kaplan, 1980), and by applying a pregrowth heat treatment that causes the formation of uniformly spaced surface steps consisting of even numbers of the atomic layers (Sakamoto and Hashiguchi, 1986). MBE and OMVPE GaAs/Si layers contain deep states similar to the deep levels observed in the respective homoepitaxial GaAs films (Soga et al., 1986; Nauka et al., 1987). However, their concentrations are strongly dependent on growth parameters. Growth conditions that cause the formation of a large number of structural defects can also lead to large trap concentrations. GaAs/Si layers with particularly poor structural quality can contain traps with concentrations exceeding lox5I X - ~They . can also contain additional traps introduced by simple point defects, normally observed in electronirradiated GaAs and in the GaAs grown at low temperatures (Nauka et al., 1987). Optimization of epitaxial conditions allows the growth of layers with a

8. DEEPLEVELDEFECTS IN EPITAXIAL I I I p MATERIALS

383

lower number of structural defects and with deep levels virtually identical to those seen in the high-quality homoepitaxial GaAs films (Chand et al., 1987; Nauka et al., 1987; Reid et al., 1988). Figure 8 demonstrates the correlation between the structural perfection of GaAs/Si and deep states. In this experiment the structural perfection of GaAs/Si layers has been quantified using Rutherford backscattering (RBS)and x-ray diffraction measurements (Rosner, 1987). The degree of disturbance of an ideal crystallographic structure is expressed in terms of the half-width (FWHM) of an x-ray diffraction peak and the RBS minimum aligned yield (zmin). Despite the facts that RBS probes mostly the region near the surface and that the x-ray diffraction averages over the entire film thickness, a remarkable agreement between their results can be seen for the layers with thicknesses that exceed one micron. The results shown in Fig. 8 demonstrate that the structural defects in the relaxed GaAs layers can enhance the formation of deep states. However, these results do not demonstrate a direct one-to-one correspondence between the defects and deep levels. They only represent a general trend, in which certain structural defects introduce deep states and the overall increase in the number of structural imperfections raises the deep level concentrations. Structural imperfections in GaAs/Si can strongly modulate the spatial

"

A A

-g

F?

1015

-

"

'

c

1014

A A' A A. A.

-

8

3

4

'A A

A

6

I

OMVPE GaAs /Si

.-0 2 c C

"

MBE GaAs ISi

A

A '

5

6

RBS minimum yield (%) FIG. 8. Correlation between a structural disorder measured by RBS and x-ray diffraction and deep level concentration determined from the DLTS measurements (from Rosner, 1987, Nauka, 1990).

384

K. W. NAUKA

distribution of electronic defects (Reid et al., 1988; Nauka et al., 1990). This effect is also known for bulk GaAs, where dislocations can getter point defects and form defect-free zones (Marek et al., 1986). A defect-free region can be observed as an area of increased band-gap luminescence and higher resistivity. Cathodoluminescence (CL) and electron beam induced current (EBIC)

-I

810

820

830

Wavelength (nm) E

E L2 ME4 c

1

150

1

1

250

1

1

350

Temperature (K)

0

2

4

6

8

Distance ( urn )

FIG. 9. Correlation between the optical and electrical nonuniformities and deep states in GaAs/Si. Speckled CL (A) and EBIC (B)images demonstrate variations of the electrical and optical properties TEM plan-view (C) with near band-gap luminescence spectra (D) measured in the regions shown in (C)(Pl-distant from dislocation, P2-near dislocations). DLTS scans (F) for selected deep traps (E) were conducted along the line crossing the low-luminescence region (F)(Nauka, unpublished).

8. DEEPLEVELDEFECTS IN EPITAXIAL III/v MATERIALS

385

measurements for GaAs/Si demonstrate the speckled images shown in Fig. 9. Simultaneous scanning transmission electron microscopy (STEM) and CL measurements show that the speckled appearances of CL and EBIC images correspond to the spatial distribution of threading dislocations and are caused by nonuniformly distributed deep states (Nauka et al., 1988). Some of the states act as nonradiative recombination centers, while others either behave like traps or introduce radiative transitions with energies below the GaAs band-gap. Figure 9 shows that some of the deep states exhibit high concentration in the vicinity of dislocations and low concentrations away from dislocations, while other deep states show the exact reverse of this pattern. Therefore, a simple model of point defects gettered by dislocations cannot explain the nonuniform spatial distribution of deep states in GaAs/Si. Rather, it must be explained in terms of the complex interactions between various point defects, dislocations, and built-in strain, with all of them participating in the formation of deep states in the GaAs/Si epilayers. APBs are another group of structural defects causing microscopic variations in the electrical and optical characteristics of GaAs/Si (Nauka et al., 1990). However, their relationship with deep states is quite different from that of

FIG. 10. CL images of GaAs/Si without (A) and with (B) APBs (pt corresponds to dislocation,and p2 to APB). DLTS scans were conducted along the lines crossing dislocation (a) or APBs (b)shown here on the CL image (C).DLTS results(D) indicate a lack of correspondence between deep states and APBs (Nauka, unpublished).

386

K.W. NAUKA

dislocations. CL and EBIC measurements, combined with transmission electron microscopy in the convergent beam electron diffraction mode (CBED-TEM), showed that APBs introduced features distinctly different from both the luminescence and lifetime variations caused by dislocations (Fig. 10). DLTS scans across an APB demonstrated that these features were not caused by nonuniformly distributed discrete deep levels, but rather by a continuum of states in the band-gap. Therefore, APBs, in contrast to dislocations, do not appear to interact with deep states in GaAs/Si. Deep states can also be observed in the low-temperature luminescence spectrum of GaAs/Si (Wilson et al., 1987; Bugajski et al., 1988). They introduce low-energy luminescence peaks (measured at 5 K) with energies equal to approximately 1.18eV and 0.95-l.OeV. Both of these peaks have been observed previously in bulk and homoepitaxial GaAs and have been identified respectively as being caused by the Si on Ga site-Ga vacancy (SiGa--VG8) and Si on Ga s i t e 4 on As site (SiG8-SiAs)complexes (Batavin and Popova, 1974; Chiang and Pearson, 1975). Their location in the luminescencespectrum can vary from sample to sample because of differences in the built-in stresses (Fouquet et al., 1989).

20. LAYERS GROWN AT Low TEMPERATURES When epitaxial layers are grown at low temperatures, the deposited atoms are frequently not able to reach lattice sites, and they can form a variety of simple point defects, such as vacancies, interstitials, and antisite defects. In addition, defect formation can be enhanced by the highly nonstoichiometric conditions that prevail at low temperatures, at which normally volatile reactants tend to remain in the grown layers. At the same time, low growth temperatures do not favor the formation of extended structural defects, such as dislocations. Point defects formed during low-temperature growth introduce deep states that determine the unique properties of low-temperature III/V epilayers. MBE GaAs layers grown at temperatures between 200°C and 300°C (LT GaAs) have been applied to reduce the deleterious sidegating effects in GaAs FET structures. Sidegating currents are suppressed by a large number of traps present in the low-temperature buffers (Smith et al., 1988).At the same time, traps can introduce transients that degrade the high-frequency performance of a device (Lin et al., 1990).As-grown LT GaAs is frequently ptype and becomes semi-insulating after annealing at temperatures around 600°C. Electron paramagnetic resonance (EPR) and temperature-dependent Hall measurements (Kaminska et al., 1989) identified two defects responsible for this behavior: Ga vacancies (VGa),which act as deep acceptors with activation energies of about 0.3 eV, and As antisite (AsGa) defects, which

8. DEEPLEVELDEFECTS IN EPITAXIAL III/V MATERIALS

387

introduce deep donors. AsGa concentrations can be as high as 5 x 10'8cm-3. Thermal instability of LT GaAs makes most of the junction measurements impossible. However, application of both photoinduced current transient spectroscopy and TSC measurements revealed a large number of additional electron and hole traps (Xie et al., 1991). The electron trap with the highest concentration and an activation energy of 0.57 eV was identified as due to As precipitates. Other traps were caused by V,,, AsG,, and their complexes that could also involve impurities. Except for the high concentration of electron states introduced by As precipitates, the observed deep state spectrum was similar to defects found in poor-structural-quality GaAs/Si. This observation is in agreement with the DLTS and PL results that were obtained for structures consisting of GaAs device layers grown at normal temperatures (550-600°C) on LT GaAs buffers (Fouquet et al., 1989; Nauka, 1990). The DLTS measurements showed GaAs/Si-like spectra with deep state concentrations between 10'4cm-3 and 10'5cm-3 in the vicinity of the GaAs-LT GaAs boundary and less than 10'3cm-3 away from the boundary. Two deep-level-related peaks were observed in the low temperature (4 K) PL spectrum of these layers at approximately 1.171 eV and 0.962 eV. They were identified, as in the case of GaAs/Si, as being related to VGa-SiG, and VAs-SiAs complexes. Very low trap concentrations and no deep-state-related radiative transitions were seen in the corresponding layers that were grown without low-temperature buffers. 21.

LAYF~RS GROWN ON MISORIENTED SUBSTRATES

Substrate misorientation can drastically change the atomic arrangement on the surface. It modifies the morphology of the atomic surface terraces, altering their length, orientation, and type of exposed atomic ridges so that the population of surface dangling bonds is changed. In addition, changes in the surface atomic arrangement can alter the incorporation of impurities. This is because the local atomic environment can control the surface reactions between the native atoms and the impurities, the impurity sticking coefficients, and the impurity surface mobilities. Therefore, substrate orientation can have a significant impact on the formation of deep state defects in the epitaxial layers. Effects of substrate orientation on deep states have been studied for MBE-grown GaAs and AlGaAs (Tsui et al., 1985;Radulescu et al., 1987; Larkins et al., 1988). Figure 11 demonstrates the relationship between the degree of misorientation of a (001) GaAs substrate and three dominant electron traps in the Alo.3Gao.,As epitaxial layer that was grown on this substrate (Radulescu et al., 1987). Electrical tests showed that, in this case, dopant incorporation is practically unaffected by the substrate misorienta-

K. W. NAUKA

388

\

\

-I

3"

(111)B

I

I

0"

3"

(111)A

SUBSTRATE TILT OFF (001)

FIG. 11. Electron trap concentrationsof ME 3, M E 4, and ME 6 in AlGaAs as a function of the angle of misorientation of the (001) GaAs substrate toward (111)A (from Radulescu et al., 1987; reproduced with permission of the American Institute of Physics).

tion. Therefore, the concentration of the DX center (ME3), which is associated with dopant impurities, remains constant when the substrate orientation is changed. The other two traps are introduced by vacancy complexes. Their dependence on the substrate tilt can be explained in terms of the relationship between the substrate orientation and the number of dangling bonds of the same type available during growth. For example, in the case of (100) substrates, every Ga atom deposited on a surface has two bonds available for As atoms. When the substrate is tilted towards a (111)B (As surface), elements of the (1 1 l)B surface start to appear. Each G a atom on the ( 1 1 l)B surface has three available dangling bonds, thus increasing the probability that the As vacancy is formed. Change of the tilt from a (11l)B to a (1 1 l)A (Ga surface) reverses this trend, so that the number of As-vacancyrelated states in the layers that are tilted towards (1 I l)A is lower than in the case of the (100) films. Kanamoto (Kanamoto et al., 1987b)conducted similar experiments for GSMBE GaAs grown on (loo), (511)B, (311)B, and (211)B surfaces and obtained similar changes in the As-vacancy-related trap concentrations.

8. DEEP LEVELDEFECTS IN EPITAXIAL III/v MATERIALS

389

VII. Conclusion An interest in deep-level defects in epitaxial III/V semiconductors is primarily driven by the need to understand the properties of these defects in order to improve the quality of devices fabricated in the epilayers. However, the importance of studying the deep states in III/V epilayers reaches even further. It enhances our understanding of the basic electronic nature of point defects in crystalline structures. The investigations of deep state properties both for binaries that have been grown under the conditions unobtainable for bulk crystals, and for ternaries and quaternaries with variable composition, can help to explain the microscopic nature of deep level defects and to test their theoretical models. Deep level defects in low-dimensional structures exhibit properties unknown for the equivalent defects in "bulk" epitaxial films. Their understanding becomes critical since these structures play an increasingly important role in designing new optoelectronic and high-speed devices. Relaxed heteroepitaxial epilayers offer the opportunity to study the interactions between extended structural defects, such as dislocations, and the point defects that introduce deep states. It is expected that future research will deepen our knowledge of deep states in the epitaxial III/V layers. In particular, these efforts must be focused on a better understanding of the microscopic nature of deep states and the correlation of deep-level defects with epitaxial growth conditions.

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Omlig, P.,Samuelson, L., T i m , H., and Grimmeiss, H. G. (1983b).Nuouo Cim. 2D,1742. O'Reilly, E. P. (1989).Semicond. Sci. Technol. 4, 121. Paloura, E.C., Ginoudi, A., Kiriakidis, G., and Christou, A. (1991).Appl. Phys. Lett. 59, 3127. Panish, M.B., Temkin, H., and Surnski, S. (1985).J. Vac. Sci. Technol. B3,657. Pao, Y.-C., Liu, D., Lee, W. S., and Hams, J. S., Jr. (1986).Appl. Phys. Lett. 48, 1291. Papadopoulo, A. C., Bresse, J. F., and Praseuth, J. P. (1987).J. Appl. Phys. 62,4174. Parsons, J. D., Hunter, A. T., and Reynolds, D. C. (1985).Inst. Phys. Con$ Ser., No. 79,p. 211, Adam Hilger Publ., Bristol. Partin, D. L., Chen, J. W., Milnes, A. G., and Vassamillet, L. F. (1979).J . Appl. Phys. 50, 6845. Peaker, A. R., and Hamilton, B. (1986).Deep Centers in Semiconductors ( S . T. Pantelides, ed.). Gordon & Breach Science Publishers, New York. Pearsall, T. P., and Hirtz, J. P.(1981).J. Cryst. Growth 54, 127. Pelloie, J. L., Guillot, G., Nouailhat, A., and Antolini, A. G. (1986).J. Appl. Phys. 59, 1536. Rckering, C., Tapster, P.R., Dean, P. J., Taulor, L. L., Giles, P. L., and Davies, P. (1983).J. Cryst. Growth 64, 142. Plot, B., Deveaud, B., Lambert, B., Chomette, A.,and Regreny, A. (1986).J. Phys. (39,4279. Prints, V. Ya., Kulagin, S. A., and Maior, V. I. (1987).Sou. Phys. Semicond. 21, 1292. Puechner, R. A,, Johnson, D. A., and Maracas, G. N. (1988).Appl. Phys. Lett. 53,1952. Radulescu, D. C., khan, W.J., Wicks, G. W., Calawa, A. R., and Eastman, L. F. (1987).Inst. Phys. Con$ Ser., No.91,p. 299. IOP Publish. Rmghi, M. (1985).Semiconductors and Sem'metals (W. T. Tsang, ed.), Vol. 22A,p. 299.Academic Press, New York. Reid, G. A., Nauka, K., Rosner, S. J., Koch, S. M., and Hams, J. S., Jr. (1988).MRS Con$ Proc., Vol. 116,p. 227.Mater. Res. SOC. Ren, S. Y., and Dow,J. D. (1989).J. Appl. Phys. 65, 1987. Ren, S. Y., Dow, J. D., and Shen, J. (1988).Phys. Rev. B38, 10677. Rode, D.L.(1975).Phys. Stat. Sol. A32,425. Rosner, S. J. (1987).Ph.D. Thesis, Stanford Unioersity. Roth, A. P.,Goodchild, R. G., Charbonneau, S., and Williams, D. F. (1983).J . Appl. Phys. 54, 3427. Sah, C. T., Forbes, L., Rosier, L. L., and Tasch, A. F., Jr. (1970).Sol. St. Electron. 13,759. Sakamoto, T., and Hashiguchi, G. (1986).Jpn. J. Appl. Phys. 25, L57. Samuelson, L., Omling, P., Tim, H., and Grimmeiss, H. G. (1981).J. Cryst. Growth 55, 164. Sasai, Y., Yamazoe, Y., Okuyama, M., Nishino, T., and Hamakawa, Y. (1979).Jpn. J . Appl. Phys. 18,1415. Schramm, C., Bach, H. G., Kunzel, H., and Praseuth, J. P. (1991).J. Electrochem. SOC.138,2808. Sermage, B., Pereira, M. F., Alexandre, F., Beerens, J., Azoulay, R.,and Kobayashi, N. (1987). Inst. Phys. Con$ Ser., No. 91,p. 605. IOP Publish. Shastry, S. K., Zemon, S., and Norris, P.(1987).Inst. Phys. Con$ Ser., No. 83,p. 81.IOP Publish. Shirafuji, J., Tamura, A., Inoue, M., and Inushi, Y. (1981).J . Appl. Phys. 52,4704. Skolnick, M. S., Dean, P. J., and Groves, S.H. (1984).Appl. Phys. Lett. 45,962. Skromme, B. J., Low, T. S., and Stillman, G. E. (1982).Inst. Phys. Con$ Ser., No.65,p. 485.IOP Publish. Skromme, B. J., Low, T. S., Roth, T. J., Stillman, G. E., Kennedy, J. K., and Abrokwah, J. K. (1983).J. Electron. Mater. 12,433. Skromme, B. J., Stillman, G. E.,Oberstar, J. D., and Chan, S. S. (1984).Appl. Phys. Lett. 44,319. Skromme, B. J., Bow, S. S., Lee, B., Low, T. S., Lepkowski, T. R., Dejule, R. Y., Stillman, G. E., and Hwang, J. C. M. (1985).J. Appl. Phys. 9,4685. Smith, F. W., Calawa, A. R., Chen, C.-L., Manfra, M. J., and Mahoney, L. J. (1988).IEEE Electron Dev. Lett. 9,77.

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SEMICONDUCTORS AND SEMIMETALS, VOL. 38

CHAPTER 9

Structural Defects in Epitaxial III/V Layers Zuzanna Lilien tal- Weber CkNTER FOR IbVANNcED MATENALS

LAWRENCEBBRK~LEY LABORATORY BERKELEY, CALIFORNIA

Hyunchul Sohn DEPARTMENT OF MATERIALS SClWCE AND MINERAL ENGINEERING UMWRSITY OF CALIFORNIA BERKELEY,CALIFORNU

Jack Washburn CENTER FUR

ADVANCEDMATERIALS

LAWRENCE BERKELEY LABORATORY BERKELEY, CALIFORNIA

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 11. HOMOEPITAXY. . . . . . . . . . . . . . . . . . . . . . . . 1. Ooal Defects . . . . . . . . . . . . . . . . . . . . . . . 2. GaAs Grown by MBE at Low Temperature . . . . . . . . . . . . 111. HETWOEPITAXY . . . . . . . . . . . . . . . . . . . . . . . 3. Origin of Defects. . . . . . . . . . . . . . . . . . . . . . 4. Defects in Epitaxial Layers . . . . . . . . . . . . . . . . . . IV. METHODS TO DECWETHE DEFECT DENSITY IN THE EPITAXIAL LAYERS . . . 5. Oval Defects . . . . . . . . . . . . . . . . . . . . . . . 6. Methods to Improve the Quality of GaAs on Si . . . . . . . . . . . 7. Defect Reduction for Other III/V Heteroepitaxial Layers. . . . . . . . V. CONCLUSIONS. . . . . . . . . . . . . . . . . . . . . . . . ACKNOWLEDCMENT . . . . . . . . . . . . . . . . . . .. . . REFERENCES

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The main interest in epitaxial semiconductor layers has been concentrated on the electronic quality of the material such as carrier mobility or photoluminescence (PL)-output. Therefore, the extended structural defects 397 Copyright 0 1993 by Academic Press. Inc. All rights of reproduction in any form reserved. ISBN 0-12-7521380

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are often overlooked, even though they can be detrimental, especially in integrated circuit applications. Near-lattice-matched heteroepitaxy is the fundamental growth process for all optoelectronic semiconductor devices and for the most advanced digital devices on III/V semiconductors. However, lattice-mismatched heteroepitaxy provides increased flexibility for band-gap engineering. Strained-layer quantum wells have been used to control the band gap of the active region of semiconductor lasers, (Fisher et al., 1987; Kolbas et al., 1988), permitting lasing at previously unattainable wavelengths. For this reason, the possibility of growing high-quality lattice-mismatched heteroepitaxial layers has attracted an ever-increasing interest. Over the past few years, there has been considerable research activity in the growth and fabrication of AlInAs high electron-mobility transistors (HEMTs) (Mishra et al., 1988; Aina et al., 1988a), motivated by large conduction band discontinuities at the heterointerfaces of AlInAs and GaInAs (People et al., 1983)or InP (Aha et al., 1988b). The large conduction-band discontinuity ensures the confinement of a high concentration of two-dimensional electrons at the heterojunctions GaInAs on InP or GaAs, which also have high electron mobilities and high saturation velocities. Most of these layers have been grown by molecular beam epitaxy (MBE); however, a wide variety of AlInAs HEMT structures can also be grown by metalorganic vapor phase epitaxy (MOVPE). These developments open up the attractive possibility of integrating electronic devices and optical devices, which can be more effectively grown by MOVPE. Further research is needed on defects due to lattice and thermal mismatch, interface roughness, and interdiffusion between constituents of semiconductor multilayers that can seriously degrade device performance. In general, III/V substrates are fragile and brittle and mainly available in small wafer sizes. These disadvantages could be avoided by successful epitaxial growth of GaAs and other III/V compounds on Si. For microwave power devices, there is also the possibility of superior heat dissipation because of the higher thermal conductivity of Si compared with GaAs. III/V epitaxy on Si would enable monolithic integration of optoelectronic III/V devices with silicon integrated circuits. This would lead to a whole range of new device structures, taking into account the advantages of III/V optical device capability and silicon microelectronics. However, this system presents numerous difficulties. The large misfit between GaAs and Si ( 4%) and the growth of a polar crystal on a nonpolar substrate results in a high density of lattice defects, including inversion boundaries, dislocations, and stacking faults. High densities of dislocations and planar faults are not satisfactory for device applications. So far, growth of low-dislocation-density (below 105/cm2)GaAs epitaxial layers on Si has not been reproducibly demon-

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strated. A wider application of this system therefore requires a greater understanding of the mechanisms of defect formation. This understanding should lead to a decrease of the defect density, and a decrease in the residual strain, eventually making GaAs/Si fully usable for optoelectronic and digital devices. GaAs grown on Si can be treated as a model system that has not only a large lattice mismatch, but also a large difference in thermal expansion coefficient, both of which lead to defect formation. Therefore, much in this chapter will concentrate on the GaAs/Si system. However, lattice-matched systems (AlGaAs/GaAs, A1As/GaAs), and other systems with increasing mismatch (InGaAslGaAs or InP, InAlAs/GaAs or InP), will be considered. In this chapter it will be shown not only that defects are a common problem for heteroepitaxial layers, but that some characteristic defects are also present in homoepitaxial GaAs layers grown by MBE at high and low temperatures. Defects formed in heterostructures grown by MOCVD and MOVPE will also be discussed briefly. Some methods that have been used to suppress defect propagation in epitaxial layers will be described.

11. Homoepitaxy

1. OVALDEFECTS MBE is a very effective technique for the growth of ultrathin layers, and for the control of interface abruptness and doping profiles. It has been demonstrated that GaAs epilayers can be grown by MBE with residual impurities in the low 10i3/cm3 range (Chand et al., 1989). However, surface defects, socalled oval defects, are formed that degrade electrical and optical properties of the material. They may also cause serious problems in GaAs integrated circuits by limiting yields. The oval defects have been observed in galliumcontaining compound semiconductor layers grown by MBE, but not in those layers grown by MOCVD or chemical beam epitaxy (CBE), in which a gaseous source of Ga was used (Tsang, 1985). The nature of these defects has been carefully investigated to clarify their formation mechanism and to reduce their density. The name “oval defects” comes from their appearance in optical microscopy (Fig. 1). These defects usually are in the range of 1 to 15 pm in size, in layers up to 5pm thick (Bafleur et al. 1982), and their density is in the range from lo2 to 105/cm2.Their long axes are elongated in the (1 10) direction. Generally, these defects can be divided into two groups: one with a defined

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FIG. 1. SEM micrograph of an oval defect formed in MBE-grown GaAs (courtesy of Dr. Calawa, MIT Lincoln Lab.).

core and one without the core. Fujiwara et al. (1987) have classified them in up to seven different types. In this classification, the surface oval defects that have macroscopic core are classified as the a type (al-a6), while those without cores are classified as the B type. Electron microscopy studies showed that the central parts of a defects have a polycrystalline region surrounded by microtwins (Bafleur et al., 1982). The facets that appear on the surface of the faulted region are probably due to the growth rate variation between various low-index crystallographic planes. An analysis of these defects (Bafleur et al., 1982) by electron microprobe showed no deviation from stoichiometry or impurity accumulation. It has been suggested that these defects start from nucleation sites (Bafleur et al., 1982), which are considered to be located at the substrate/layer interface. At these points the growth was assumed to be perturbed and polycrystalline regions developed. However, this conclusion has not been supported by other investigators. There are also reports that the oval defects are related to substrate dislocations (Hwang et al., 1983). However, later studies show that defects that are formed near dislocations are a special kind of oval defect having a surfboard shape, and they are not sensitive to growth conditions. They can easily be eliminated (Shinohara et al., 1985). There has been much effort to correlate the density of oval defects with growth parameters. It was shown that the density of oval defects does not

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depend on the As,/Ga ratio, but increases with an increase in growth rate and Ga cell temperature (Shinohara and Ito, 1989). These researchers suggested that oval defect density decreases with an increase in substrate temperature. However, Metze (Metze et al., 1983)showed just the opposite, that oval defect density was closely correlated with the growth rate but not with substrate temperature. In general, the density of oval defects increases with an increase in epilayer thickness. It was reported that there are strong correlations between the density of oval defects and surface contamination by carbon (Bafleur et al., 1982) and sulfur (Chai et al., 1985). Most investigators believe that these defects are Ga-related and are caused by Ga-spitting (Wood et al., 1981; Schlom et al., 1989; Chand, 1990) or gallium oxides: Ga20(Shinohara and Ito, 1989; Akimoto et al., 1985; Weng, 1986)or Ga,03 (Wood et al., 1981;Weng, 1986). It was observed that heating the gallium source to well above its growth temperature in an attempt to outgas oxide just before the growth usually increases the density of Garelated oval defects (Schlom et ul., 1989). This outgassing can cause a large number of Ga droplets near the opening of a Ga crucible, resulting in an increase of Ga-spitting. A thermodynamic analysis of the formation mechanism of oval defects due to growth conditions and Ga oxide was first reported by Ito et al. (1984). It was shown that Ga20formed in the Ga cell or on the substrate causes oval defect formation (Shinohara and Ito, 1989).The reactions forming Ga,O vary with Ga cell temperatures. In the temperature range below 930°C, these reactions are mostly between Ga and Ga2O,; above this temperature, most reactions are between carbon and Ga20,. The relation of oval defects to carbon presence has been suggested earlier (Bafleur et al., 1982). These authors postulated that carbon contamination can occur either during the substrate preparation or during epitaxial growth. Smaller oval defects (/?type) do not have extended polycrystalline regions at their centers but contain dislocations and stacking faults. It is generally accepted that /?-type defects are due to particulates (Weng et al., 1985; Nishikawa et ul., 1986; Matteson and Shih, 1986) landing on the substrate during substrate preparation, loading, transferring, or growth. Since these external factors, clean-room conditions, and wafer-transfer mechanisms can be improved, these defects can be avoided. However, a-type defects still appear to be a real problem for MBE layers of GaAs for integrated circuits. 2. GaAs GROWN BY MBE AT Low TEMPERATURE GaAs integrated circuits are typically fabricated on semi-insulating substrates. Frequently, heavy ion implantation between devices is used to create

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additional defects in order to isolate the devices from each other. However, parasitic coupling through the substrate can still result in cross-talk between neighboring devices called sidegating. Recently, a solution to this problem was found by growing GaAs buffer layers at temperatures as low as 200°C (LT-GaAs). These layers were grown by molecular beam epitaxy (MBE) using typical Ga and As fluxes for arsenic-dominant growth condition at a rate of 1 pm/h (Smith et al., 1988, 1989). Such layers exhibit high resistivity, which is sustained even after annealing at 600°C. All backgating effects can be removed, and effective device isolation can be achieved. These layers can be applied as passivation layers as well. In addition, fast photodetectors can be built based on these layers, since the minority lifetime in this material is extremely short (in the range of a few hundred femtoseconds). Earlier studies by electron paramagnetic resonance (Kaminska et al., 1989a, 1989b) reveal 1020/cm3AsGa antisite defects in as-grown layers, a defect level that decreases at least two orders of magnitude after annealing. These layers are grown from As supersaturation and show up to 1.5% excess As, which leads to -0.1% of expansion of the lattice parameter. This expansion of the lattice parameter disappears after annealing. It was noticed earlier that the crystalline perfection of the layers is very sensitive to growth parameters (Liliental-Weber, 1990), such as growth temperature and As/Ga ratio used for the growth, often called the As/Ga beam equivalent pressure (BEP). Generally, samples grown at 200°C or higher on in-bonded molybdenum blocks with a BEP of 10 and a growth rate of 1pm/h show high crystalline perfection up to a 3 pm layer thickness (Fig. 2). With increasing sample thickness, specific defects called “pyramidal

FIG. 2. Plan-view TEM micrograph of as-grown high-perfectionmonocrystalline LT-GaAs layer showing featureless surface.

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defects,” start to appear (Fig. 3). These pyramidal defects were described (Liliental-Weber, 1990; Liliental-Weber et al., 1991a)as defects having a wellestablished polycrystalline core from which other defects, such as secondary microtwins, stacking faults, or dislocations,were formed. The thickness of the perfect material that can be grown before pyramidal defects start to appear decreased drastically with decreasing growth temperature. An increase of As concentration is observed in these layers. The dependence of the lattice parameter change on excess As is shown in Fig. 4. The structural defects of pyramidal shape with a polycrystalline core surrounded by microtwins, stacking faults, and dislocations in the LT-GaAs layers grown at 200°C bear some resemblance to the so-called oval defects described in the previous section. Their description in the TEM study of Bafleur et ai. (1982) is especially similar to the defects observed here. However, the density of oval defects in the best MBE layers, about 10’ defects/cm’, is many orders of magnitude smaller than the 3 x 108/cmzfound in LT-GaAs. Impurities such as C, H, or 0, in involved in the formation of Gaz03,or Ga,O were suggested as the source of oval defects (Shinohara and Ito, 1989; Akimoto et al., 1985; Weng, 1986, Ito et al., 1984). However, in LT-

FIG. 3. Cross-sectional TEM image of pyramidal defects formed near the surface in the LTGaAs layer grown at 190°C.

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GaAs such impurities could hardly explain the observed high densities of such defects that appear only after growth of a certain layer thickness, The crystal quality of LT-GaAs layers grown at 180-210°C is very sensitive to small changes in the growth temperature. For example, a 5°C change within this range makes a noticeable difference in crystal quality: An increased density of pyramidal defects accompanies a decrease in the growth temperature (Fig. 5). It is possible that these defects and oval defects are formed by the same mechanism. The extremely high density may just be a consequence. of the lower growth temperature. If the LT layer is grown with a beam equivalent pressure (BEP) greater than 10 (Liliental-Weber et al., 1991b; Clavene et al., 1991),a higher growth temperature is required to obtain the same thickness of monocrystalline layer. For a 1-pm layer thickness, the dependence on growth temperature for a BEP of 20 is shown in Fig. 6. Figure 7 shows the decrease in monocrystalline layer thickness with increasing BEP. Generally, the layer grown with the higher BEP can be divided into three sublayers: a monocrystalline sublayer, a layer with dislocations and stacking faults that may be the origin of pyramidai defects, and a polycrystalline layer. At a particular monocrystalline layer thickness, related to both the growth temperature and the BEP ratio, dislocations and stacking faults begin to form. With an increase in layer thickness, microtwins are formed. In these areas void formation was also observed. If a cap layer is grown on top of such a layer, microtwins propagate through the cap layer, and the surface of the cap layer is usually undulated (Fig. 8). There may be more than a single reason for the breakdown of crystallinity

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FIG. 5. Plan-view micrograph showing distribution of pyramidal defects on the surface of a 2-pm thick layer grown at 190°C.

of these layers. One factor may be strain build-up in the layer due to excess As causing expansion of the lattice parameter. Only a specific layer thickness, the "critical layer thickness" (hJ, may be possible at a given growth condition before misfit dislocation formation occurs at the surface. The dislocation loops may be pinned by segregation of excess As to the dislocation cores and eventually become nucleation sites for polycrystalline growth. Evidence for this mechanism includes dislocations and stacking faults found near the top

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growth temperature (C) FIG. 7. Thickness of the defect-free layer as a function of growth temperature for a constant BEP of 20.

of the crystalline layer (at the origin of pyramidal cores). The LT-GaAs epilayer thickness at which the onset of pyramidal defects occurs lies between the theoretical critical layer thicknesses (h,) for pseudomorphic growth predicted by People and Bean (1986) and by Matthews and Blakeslee (1974). Thus, it is possible that the elastic strain incorporated in the LT-GaAs layers as a result of the excess As is responsible for the defects formed in the layer. The presence of this strain in as-grown layers has been confirmed by largeangle and classical convergent-beam studies (Liliental-Weber et al., 1991c; Liliental-Weber, 1992).

FIG. 8. Surface undulation of the LT-GaAs layer grown at high BEP.

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It was shown that obtaining high-quality LT-GaAs layers grown at temperatures down to 200°C is possible, and a high concentration of point defects in such layers ensures high resistivity combined with low carrier mobility. These layers might as well be applied as strained layers, as was shown for GaAs grown on Si. Annealing of the layers at 600°C (the temperature used normally for MBE growth of GaAs) leads to formation of As precipitates, which removes a large part of the excess As from the GaAs unit cells, leading to the decrease in the lattice parameter (Liliental-Weber, 1990; Melloch et al., 1990; Liliental-Weber et al., 1991d, 1991e; Claverie and Liliental-Weber, 1992).

111. Heteroepitaxy

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Failure to achieve high-quality material for devices is attributed to several problems that occur in heteroepitaxy, including differences in lattice constants and thermal expansion coefficients between the substrate and epilayers, and problems related to growth parameters and surface preparation before layer growth. Any line and area defects present in the substrate usually extend into the epilayer during growth. The resulting density of these defects in the layer is at least equal to that of the substrate. Therefore, the epilayer cannot be structurally more perfect than the substrate. A second class of defects is related to the cleanness of the substrate surface. If oxides and hydrocarbides are not completely removed from surfaces, some defects (similar to those described for homoepitaxy) will be formed. Even for a perfectly clean substrate, surface topography such as surface steps can induce defects. Thirdly, stacking mistakes during crystal growth can cause stacking fault formation. Build-up of impurities at the growth surface can cause inclusions, or even polycrystalline growth can take place. Cooling from the growth temperature to room temperature can lead to clustering of point defects and formation of dislocation loops. When the difference in thermal expansion coefficient between the substrate and the epilayer is large, more complex arrays of dislocations can be formed, because of plastic deformation during cooling. Plastic deformation also takes place during growth above critical thickness. In this case, misfit dislocations can be formed that also extend through the layer at the ends of the half-loops. In the following sections, the causes of defect formation will be discussed in more detail.

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a. Lattice Mismatch (Critical Layer Thickness) In heteroepitaxial growth, the overlayer has a unique orientation relationship with the substrate. In general, epitaxial growth occurs whenever an overlayer and a substrate can have an interface with a highly coincident atomic arrangement. Such an interface has a lower interfacial free energy than other possible orientation relationships. In semiconductor heteroepitaxy, the overlayer and the substrate usually have the same orientation and structure. However, lattice constants of the layers are usually different from those-of the substrates. This lattice mismatch is initially accommodated entirely by elastic strain, but becomes partially relaxed by introduction of misfit dislocations into the interface above a critical thickness. In a perfectly coherent lattice-mismatched epitaxial system, the epilayer is strained to assume the lattice constants of the substrate, so that the epilayer strain equals ~ ) , by the misfit strain ( E ~ ~ defined

in terms of the equilibrium lattice constant of the thin film a, and the substrate lattice constant a,. For cubic crystals, this strain leads to a tetragonal distortion of the unit cell in the epilayer, resulting in a difference of the lattice spacing parallel to the interface plane all from the spacing perpendicular to it a, (=a, for these thin layers), depending on the Poisson ratio v:

The strain energy stored in the epilayer increases linearly with the thickness of the epilayer. Above a critical epilayer thickness, it becomes energetically favorable for the epilayer to assume its equilibrium lattice constant and to accommodate the misfit strain by introduction of misfit dislocations at the heterointerface. Above this “critical thickness” the commensurate (or coherent) layer will only be metastable with respect to a relaxation by forming misfit dislocations. However, nucleation and motion of dislocations into the interface to form a regular grid of misfit dislocations is a difficult process. In general, the misfit is accomodated partially by an elastic strain even though the critical thickness is far exceeded. The ideal equilibrium distance between misfit dislocations is given by

Here, b is the Burgers vector of misfit dislocations and is the misfit strain. If the misfit dislocation density does not correspond to the lattice mismatch

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or if dislocations are nonuniformly distributed, residual strain will still be present in the epilayer. Much experimental and theoretical work has been done to understand the mechanisms by which misfit dislocations are generated, and how these mechanisms relate to the density of dislocations that thread through the epilayer (People and Bean, 1985, 1986; Matthews and Blakeslee, 1974, 1975, 1976; Frank and van der Merve, 1949; Matthews, 1975a, 1975b; van der Merve, 1972; van der Merve and Ball, 1975; Dodson and Tsao, 1987; Hull and Fischer-Colbrie, 1987; Hull et al., 1988; Bean et al., 1984; Maree et al., 1987). The most obvious mechanism is that dislocations present in the substrate can glide to or within the epilayer so as to be extended along the interface. However, taking into account the extremely low defect density in many substrates, particularly Si, and the very high density of dislocations observed in semiconductor layers grown on these substrates, this mechanism often makes a negligible contribution. Different dislocation introduction mechanisms have been found to operate for low and high misfit systems. Frank and Van der Merve (1949) calculated the theoretical critical layer thickness based on the energy of interfacial dislocations. Matthews (1975a, 1975b) considered the line tension of the misfit dislocation to obtain the critical layer thickness at which dislocations would extend along the interface. Matthews and Blakeslee (1974, 1975, 1976) calculated a critical thickness based on a specific mechanism in which misfit dislocations are formed by bending pre-existing threading dislocations in the epilayer. They calculated the critical thickness from the energy balance of the epilayer without and with misfit dislocations. Their predictions of critical thickness agree well with experimental results for metals, but there are discrepancies between predictions and experimentsfor diamond or sphalerite structure semiconductors. Experiments show that in semiconductors, a thicker layer can usually be grown before misfit dislocations appear than is predicted by theory. Hull et al. (1988) found that, for GaAs on Si, the GaAs islands can grow as thick as 6nm, compared to 1.5nm predicted by the Matthews theory (Matthews, 1975a, 1975b; Matthews and Blakeslee, 1975, 1976). In an attempt to explain the discrepancy,People and Bean (1985,1986) developed an empirical model for the critical layer thickness that considered the nucleation of dislocations. Bean et al. (1984) pointed out that the activation barrier for dislocation nucleation must play a crucial role in determining a critical layer thickness. They calculated the critical layer thickness for a dislocation to be nucleated to be the point where the strain energy of the layer exceeds the areal energy density of elastic strain associated with a single screw dislocation averaged over an effective dislocation width, which was a free parameter in their fit. Their model did not take into account release of the lattice strain and dissociation into partial dislocations. Dodson

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and Tsao (1987) emphasized that the kinetics of the misfit dislocation formation must be dominated by the two activation energies for dislocation motion and dislocation nucleation. They successfully modeled the critical layer thickness, but used a phenomenological fit to describe an arbitrary dislocation multiplication process. Hull and Fischer-Colbrie(1987)measured dislocation densities and velocities and their temperature dependance and used these data in order to determine energy for dislocation nucleation, but did not introduce a specific mechanism of dislocation formation. Later, it was speculated that the discrepancies between metals and semiconductors should be attributed to the kinematical barriers to the generation and motion of misfit dislocations in semiconductors. Maree et al. (1987) suggested that there are at least two obstacles in semiconductors blocking the generation of misfit dislocations. The first obstacle is the large Peierls-Nabarro friction stress, which strongly reduces the mobility of dislocations, and through that, the length of misfit segment that can be formed along the interface. In metals, this friction stress is negligible. The second obstacle is the greater perfection of semiconductors compared to metals; therefore, new dislocations need to be generated during growth instead of just arising from the glide of pre-existing dislocations. Because of these factors, the residual elastic strain remains larger for semiconductors than for metals. If finally we take into account frictional forces and nucleation barriers, the same theoretical approach is applicable to both metals and semiconductors (Fox and Jesser, 1990a). The frictional stress can also explain asymmetry of dislocation distribution in zincblende semiconductors in the two (110) directions. Since in the zincblende structure two types of dislocations are formed (a and p) having different frictional stress for each type, a different metastable critical layer thickness can be determined for each type of dislocation. It was shown that frictional stress is also very sensitive to the dopant present in the semiconductor. Therefore, two values of critical layer thickness for two types of dislocations are expected as a result of the doping. Indeed, this phenomenon was demonstrated for GaAsP layers grown on GaAs, for which the difference in critical thickness of the two types of dislocation decreased when GaAsP was heavily doped p-type (Fox and Jesser, 1990b). Maree et al., (1987) showed that the misfit dislocations in semiconductor interfaces are usually 60" dislocations whose dissociation into two partials can also lead to a difference in strain relaxation for tensile and compressive stressed films. They concluded that half-loops are nucleated at the surface and that they glide on (111) planes inclined to the interface. Matthews (1975a) worked on the dislocation half-loop nucleation and propagation in strained epilayers and suggested that a half-loop in a perfect semiconductor

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will have a critical radius whose activation energy for formation will increase at low misfit. He showed that a minimum misfit can exist below which it is not thermodynamically favorable to nucleate dislocations at any thickness in a perfect epilayer. For misfits lower than 2%, the nucleation barrier cannot be overcome and dislocation will be not formed at any thickness. This would suggest that, at low misfit, any layer thickness can be grown (Matthews et al., 1976). Hull and Fischer-Colbrie (1987) showed empirically, however, that the defect nucleation barrier is as low as 0.7eV, in contradiction to Hirth's prediction of 6.2eV at 550°C. Kvam et al., (1987) observed that in GeSi with about 0.8% misfit levels, long (10-100 pm in length) 60" dislocations were formed in the interface for layer thicknesses above 200nm, in contrast to short (0.1-1 pm) edge misfit dislocations observed for the same material with higher misfit. These 60" dislocations were often grouped into bunches. Similar groupings of dislocations were observed by Hagen and Strunk (1978). They proposed a special multiplication mechanism, pointing out that two orthogonal misfit dislocations with the same Burgers vector of the (1 10) type intersect and react, one of the resulting right-angle nodes being repelled from the original point of intersection to the surface by image forces and back stresses, until the right-angle corner has been bent up to the surface. Upon reaching the surface, the dislocation splits into two segments, each glissile. The net result is three dislocations from the original two (Fig. 9). This process was reported in Ge/GaAs heterostructures (Hagen and Strunk, 1978) and by Rajan and Denhoff in GeSi/Si strained epilayers (1987). However, similar

4 1

FIG. 9. Schematicdrawing of the dislocation multiplicationmechanism, after W. Hagen and H. Strunk, Appl. Phys. 17, 85 (1978).

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observations by Eaglesham et al., (1989) produced a completely different interpretation, suggesting that the mechanism proposed by Hagen and Strunk is not necessary, but could be considered under specific geometric conditions. Eaglesham et al., (l989), using TEM for identification of dislocations in their early stage of nucleation, identified a heterogeneous mechanism that exists in epilayers (GeSi/Si) at misfit levels below 1%. They identified a new type of dislocation source, a diamond defect (Fig. lo), which can arise either from pre-existing defects in the substrate, or from growth-induced defects in the epilayer. This diamond defect is a faulted loop with a bounding dislocation of 1/6( 114). This bounding dislocation can dissociate into a variety of 1/6(211) and 1/2( 110) pairs. The 1/2( 110) dislocation is a glissile lattice dislocation upon which the misfit stress could operate. Gliding of this dislocation produces a glissile loop, and the bounding dislocation returns to the original configuration. When this glissile loop reaches the surface, it behaves in the same way as the half-loop described earlier, leaving a new 60" dislocation at the heterointerface. This process operates similarly to a FrankRead source and can be repeated several times. This mechanism seems to be responsible for the microstructure in low-misfit epilayers.

FIG. 10. The diamond defect in a GeSi layer as a source of dislocation multiplication, after D. J. Eaglesham et al., Phil. Mag. A 59, 1059 (1989).

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A similar mechanism of strain relaxation from a source center in four sliptrace directions, resulting in a radial stress-relieved region, was proposed by Tuppen et al., (1990). A modified cross-slip mechanism which leads to misfit dislocations in the direction orthogonal to the initial slip direction was proposed by Washburn and Kvam (1990). It was shown that this mechanism has eight crystallographic variants in (001) epitaxy. These models, described by Eaglesham et al., (1989), Tuppen et al., (1990), and Washburn and Kvam (1990), explain the configurations of dislocations observed in the epilayers for low misfits.

b. Nucleation Modes The preceding models for misfit-dislocation formation and critical-layer thickness were assumed based on layer-by-layer growth. This is not always the case. In general, epitaxial layers show three different growth modes in the early stage of nucleation: (a) the Frank-van der Merwe mode (layer-by-layer growth); (b) the Volmer- Weber mode (cluster or three-dimensional growth); and (c) the Stranski-Krastanow mode, where one or more layers can be grown layer-by-layer followed by clustered growth. Classically, these modes were rationalized in terms of force balance between surface tensions (Bauer, 1958). Let us define a quantity G = ysv - yso - yov, where ysv, yso, yov denotes the specific surface free energy of the substrate-vacuum, the substrateoverlayer, and the overlayer-vacuum interfaces, respectively. When G < 0, the Volmer-Weber mode is favored. When G > 0, the other modes are favored. It was shown that an interaction between the epilayer and the substrate and misfit strain also have an influence on the growth mode (van Delft et al., 1985; Grabow and Gilmer, 1986).Grabow and Gilmer (1986) have investigated the conditions that favor three-dimensional clustering of the epilayer by molecular dynamics computer simulations in terms of the following factors: E,, = the bond energy between two atoms in the epitaxial layer, E,, = the epilayer-substrate bond energy, Emisf = the misfit strain.

-

0. ThreeLayer-by-layer growth is favored when E,, < E,, and dimensional growth is favored when Eee > E,, and &,,,isf is not equal to 0. The Stranski-Krastanow growth mode is favored when E,, > E,, and Emisf is small. The preceding theoretical considerations were based on the assumption that the system is under conditions in which the nucleus can retain its equilibrium shape. However, real crystal growth generally occurs far from

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thermodynamic equilibrium. Therefore, epitaxial growth is very sensitive to adatom diffusion and local chemistry. In epitaxial growth, the surface diffusion depends on the substrate temperature and on the deposition rate. Low temperature may enhance layer-by-layer growth by reducing the surface diffusion length. This effect has been observed in the growth of Ge,Si, - x on Si substrates. Bean et a/., (1984) reported that the tendency for threedimensional growth is reduced by reducing the substrate temperature. The effect of growth temperature on the density of GaAs nuclei grown on Si was studied by Biegelsen et al., (1987). They showed that the nucleus density is a function of temperature. The density of islands increases when the substrate temperature decreases. The kinetic effect of short diffusion length favors the high density of small nuclei that, according to Biegelsen et al., produce the smoother surface of thick epilayers. These authors show that the size and separation between islands increases with an increase in substrate temperature, and in this case the thick epilayer surface becomes rough. In general, two-dimensional growth is not easy to obtain, because many factors can disturb this growth mode; therefore, there are not many semiconductor systems where true two-dimensional growth has been confirmed experimentally. One example of such a system is AlGaAs grown on GaAs, in which lattice mismatch is small. However, even in this system monoatomic interface abruptness has never been observed (Ourmazd, 1989; Long et al., 1991). The performance of an AlGaAs/GaAs heterostructure devices depends on the structural, electronic, optical, and morphological properties of AlGaAs. These properties of AlGaAs affect the subsequent AlGaAs/GaAs interface quality and the properties of overgrown GaAs. Because of the small surface migration of A1 and enhanced surface segregation of impurities in AIGaAs, the inverted interface (GaAs on AlGaAs) was observed to be rougher (Fig. 11) than the starting interface (AlGaAs grown on GaAs) (Petroff et al., 1984). Interface roughness increases the scattering of carriers and increases the threshold current of lasers. It was observed that the wavy nature of AlGaAs/GaAs interfaces is due to impurities in the A1 source (Chand and Chu, 1990).Impurities with smaller solubility in AlGaAs than in GaAs segregate on the surface of AlGaAs during growth and are trapped in the overgrown GaAs layer. Some of these impurities may affect the surface reconstruction and prevent the lateral propagation of the atomic layer by pinning steps on the surface, resulting in a rough interface (Petroff et al., 1984). The effect of impurities, especially oxygen contamination, on AlInAs properties is even more subtle than in the case of AlGaAs. Elimination of all sources of oxygen and moisture contamination is therefore important for growing high-quality AlInAs (Aina et al., 1991). In general, three-dimensional nucleation can be caused by many factors. One of them is strain energy due to lattice mismatch. This was demonstrated

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FIG.11. High-resolutionTEM micrograph of AlGaAs/GaAs quantum wells. Note different interface abruptness on inverted interface.

experimentally by George et al., (1990). For In-rich compounds, a larger In content leads to three-dimensional growth. This growth mode was observed for InGaAs grown on GaAs at 640°C. The island size varied between 5 and 30 nm. Similar growth was observed for AlInAs grown on GaAs by MBE. In the growth of quantum wells of AlInAs/GaInAs by MOCVD, it was observed that GaInAs grown on top of AlInAs has a more abrupt interface (width of 12 monolayers) than AlInAs grown on top of GaInAs (having a width of 3-4 monolayers). The roughness increased with an increase in layer thickness (Bimberg et al., 1989). When MBE was used at 575"C, two-dimensional growth was observed (Stolz et al., 1987). In these materials, As and In

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desorption from the surface is often observed creating column 111 vacancies and hence significant group 111 diffusion (Deppe and Holonyak, 1988). In addition to island formation, compositional variations occur in the ternaries (InAlAs) grown on InP (or GaAs) caused by surface migration effects, resulting in lateral inhomogenous strain and dislocation formation. A good example of three-dimensional growth is GaAs grown on Si (- 4% mismatch). Hull et al., (1988) observed that for GaAs on a Si substrate, the initial nucleation occurs in the three-dimensional mode and that the GaAs nucleates with a high contact angle island on the Si substrate. They reported that the GaAs islands in general appear to be associated with steps on the Si surface. These islands are strained coherently to the substrate lattice even after exceeding the critical thickness. Theoretical calculations by Northrup (Northrup et al., 1987) predict that, for GaAs grown on Si under As-rich conditions, the equilibrium structure should consist of GaAs islands surrounded by a (100) Si surface that is 2 x 1 As-terminated, and under Ga-rich conditions, GaAs islands surrounded by a surface terminated by Ga- As dimers. The model supported by total-energy calculation, by Kaxiras et al., (1989), provides a description of GaAs growth on Si surface steps. The authors emphasize the role of double-layer steps on the Si surface in initiating layered epitaxial growth. They concluded that growth of zincblende GaAs stoichiometric structure on flat regions of Si (100) is suppressed and a mixed layer can be grown. Step topology prevents mixing in the immediate neighborhood of the steps and promotes three-dimensional growth. The exposed plane at the step is no longer the (100)plane of GaAs, but rather the (211) plane, which is a nonpolar plane. Further growth continues as three-dimensional growth in the direction oblique to the surface, in agreement with experimental observations. When these layers coalesce, thick layers of GaAs are obtained. Another example of three-dimensional growth for a system with large mismatch (8% misfit) is the growth of GaSb on a GaAs substrate. For thicknesses up to 30nm, the GaSb layer is not continuous. The islands are elongated, with facets on (111) planes. This elongated shape was related to an anisotropy of the growth rates of the island facets (Raisin et al., 1991). Island height was related to growth conditions. Increasing the deposited GaSb layer thickness resulted in an increase in the lateral island size, which led to coalescence of the neighboring islands. Three-dimensional growth was also observed for InSb grown on GaAs {Zang et al., 1990). c. Diflerence in Thermal Expansion Coeficient

A difference in thermal expansion coefficients is also a potential cause of defects in the epilayer. In GaAs-on-Si heteroepitaxy, there exists a 4.1%

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lattice mismatch. This misfit strain can be relieved by forming misfit dislocations, and the GaAs epilayer can recover its equilibrium lattice constant. However, when the sample is cooled to room temperature after growth, a high residual stress is again developed in the GaAs because of the difference in thermal expansion coefficient between GaAs and Si: ol(GaAs) = 5.93 x 10-6/”C, a(Si) = 2.6 x 10-6/”C (Touloukian et al., 1977). This 2.5 times difference in thermal expansion coefficient results in a new misfit strain when the wafer is cooled to room temperature of about 2 x lo9 dynes/cm.2The associated high residual stress modifies the band structures of GaAs, resulting in reduction of the band gap and a break in the degeneracy of valence bands. Photoluminescence studies (Bugajski et al., 1988)have shown that a tensile strain is present in GaAs grown on Si, rather than the compressive strain expected from the lattice mismatch between GaAs (5.653 A) and Si (5.431 A). In our own study (Liliental-Weber et al., 1988a),we found that the number of misfit dislocations is higher at room temperature than expected from the equilibrium lattice constants of GaAs on Si. The tensile strain observed experimentally is lower than the expected value of 2.4 x implying that this strain may also have been partially relieved by plastic deformation. Cooling from 600°C to only 400°C is sufficient to generate a biaxial tensile stress far above the experimentally determined critical resolved shear stress of 15MPa at 400°C (Bourret et al., 1987),which will result in the glide of additional dislocations of various types from the interface into the epilayer. Recently it was experimentally observed by HCI vapor-phase etching of GaAs/Si and GaP/Si at growth temperature that the threading dislocation density in GaAs on Si and GaP on Si increased after cooling to room temperature (Tachikawa and Mori, 1990). For GaAs on Si at growth temperature, the density of etch pits was only 104/cm2,which is usually observed for commercially obtained GaAs wafers. When the sample was cooled to room temperature, the etch pit density using KOH increased to 8 x 106/cm2.A similar change in etch-pit density from growth temperature to room temperature was observed for GaP grown on Si. There is a much smaller lattice mismatch between GaP and Si than between GaAs and Si. Therefore, these results show that the high density of dislocations observed in both these materials is mainly due to the large difference in thermal expansion coefficient and not to the difference in lattice constants. Strain distribution in GaAs grown by MOCVD on a Si substrate has been determined by electrolyte electroreflectance (EER) spectra (Kallergi et a!., 1989). The GaAs layer was etched in certain sequences in order to reach interfacial areas. A shift of the EER peak was observed. That can be interpreted to mean that tensile biaxial stress exists in most of the GaAs epilayer because of the difference in thermal expansion coefficient, while a

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compressive biaxiai stress still exists in the layer close to the interface. Another induction that thermal expansion coefficient influences defect formation at heterointerfaces comes from the observation of the nature of misfit dislocations at GaAs/Si interfaces. As was described earlier, misfit dislocations in GaAs on Si are short lines and do not form a regular rectangular grid at the interface, as was observed for GeSi on Si. This rather complicated arrangement of misfit dislocations in GaAs grown on Si may be related to the lattice misfit, the island growth mode, combined with the thermal expansion coefficient difference. Support for this conclusion comes from a study of GaSb (a = 6.094 A) on GaAs (5.653 A) by Raisin et al., (1991). In this case the lattice mismatch between these two compounds is about 8%, but the difference in thermal expansion coefficient is very small (a = 5.93 x 10-6/C for the GaAs, and a = 5.7 x 10-6/C for GaSb). For a GaSb layer with a thickness exceeding critical thickness, misfit dislocations accommodate the lattice mismatch, so that the grown layer is unstrained. This was confirmed by Raman spectroscopy, where no frequency shift of the GaSb was observed in comparison to the reference signal. This is ditTerent from GaAs on Si. Despite the large lattice mismatch between GaAs and GaSb, long Lomer-type misfit dislocations forming a rectangular pattern along the [1 lo] and [liO] directions were contained at the interface. Their average spacing was 5.4 & 0.5 nm, in good agreement with a calculated value of 5.365nm. These two families of Lomer dislocations cross each other practicalfy without interaction so that not many threading dislocation segments were formed. The threading dislocations were related only to some imperfections of the misfit dislocation network. The density of interfacial dislocations in GaSb was on the order of 8 x 106/cm2.This perfect relaxation of GaSb was related by the authors (Raisin et al., 1991) to two factors: perfect surface preparation before layer deposition, and growth temperature, which was high enough to enable a direct plastic relaxation of the grown layer. This study shows that an epitaxial layer relaxation and Lomer type of misfit dislocation can be formed even for a very large lattice-mismatched system that does not differ much in thermal expansion coefficient.

d . Process-Dependent Factors; Substrate Contamination The preparation of substrate surface before the growth of epitaxial layers plays a very important role in the structural quality of epilayers. Therefore, different procedures for removal of residual impurities have been developed. This problem is especially important in Si technology, because it is not easy to remove oxides and hydrocarbides from the Si surface. Our own observation (Liliental-Weber, 1989)and those of others (Blakesleeet al., 1987) lead to a conclusion that some impurities, such as oxides or carbides, still

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exist on the Si surface despite the careful cleaning procedures applied to Si substrates. Most of the commonly used substrate preparation treatments employ a high-temperature silicon oxide reduction step described by Ishizaka and Shiraki (1986). Four major steps are involved in this procedure: degreasing, acid oxidation, alkaline oxidation, and boiling in HC1:H20:H,02 (3: 1 : 1) for 5-7 min followed by DI water rinse. After this procedure, the Si wafers are dried with filtered nitrogen and are mounted on a molybdenum block with In. In the MBE growth chamber, the sample temperature is raised to 800°C for 10min to disorb the SiO,. After this procedure the Si surface is considered oxide-free. However, such a high-temperature process is frequently undesirable or impossible in a given growth system. Even after this cleaning procedure, islands of impurities can still be observed (LilientalWeber, 1989; Blakeslee et al., 1987; Liliental-Weber et al., 1990). Crosssectional transmission electron microscopy (TEM) typically shows a white band at the interface between the GaAs and Si, which has frequently been attributed to artifacts of the TEM sample preparation (Fig. 12). Our own investigation of metal/GaAs heterostructures deposited in situ in ultrahigh vacuum on cleaved GaAs surfaces did not reveal such a white band (Fig. 13).

FIG. 12. High resolution TEM micrograph showing white band related to the impurities present at the interface of GaAs layer grown on Si.

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FIG. t 3 . High-resolution TEM micrograph of AI/GaAs interface for the metal deposited in UHV-cleaved GaAs substrate. Note clean interface without white band.

situ on

Only air-exposed surfaces showed the white band at the interface (LilientalWeber et al., 1986, 1990; Liliental-Weber, 1987). In GaAs/Si heteroepitaxy, the formation of this white contrast band does not occur after application of a Ga reduction process (Liliental-Weber et aL, 1982), as suggested by Wright and Kroemer (1980). This last procedure differs from those previously described in that during annealing of the Si wafer at 8WC, a beam of Ga was simultaneously impinged on the sample surface. The surface was then considered oxide-free. Lack of a white contrast layer in TEM micrographs confirms that in most cases, this white contrast is indicative of contamination at the heterointerface. Defects such as stacking faults (Fig. 14) or inversion boundaries (Fig. 15) can originate at irregularities caused by contamination at the substrate.

e. Polar-on-Nonpolar Growth In addition to all the problems previously described in the growth of all heteroepitaxial layers, the growth of GaAs on Si substrates has one more problem, polarity. The lattice structure of Si is composed of two interpenetrating fcc sublattices, both sublattices being occupied by Si atoms. The GaAs lattice is also composed of two interpenetrating fcc sublattices, but each sublattice is occupied by Ga or As atoms. The growth of polar semiconductors on nonpolar semiconductors usually leads to the formation of inversion domain boundaries when the allocation of each sublattice to a particular constituent atom is disturbed. Inversion boundaries are charged structural defects across which the same kind of atoms are bonded. The Ga-

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FIG. 14. Stacking faults originating from the impurity island present at the GaAs/Si interface..

FIG. 15. (a) Inversion boundaries in GaAs grown on Si.

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FIG. IS. (b) High resolution image of the inversion boundary shown in (a). Note a shift of (200) planes across the boundary;(c)The same boundary after Fourier image filtering.Note the a surface step at the origin of the inversion boundary.

a

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Ga bond has a bonding electron difficiency and acts as an acceptor. The AsAs bond has an excess bonding electrons and acts as a donor. An epilayer with inversion boundaries behaves as a highly compensated semiconductor. The { l00} surface of Si is generally reconstructed (Shirashi et al., 1989) in (2 x 1) and (1 x 2), with a monoatomic step between these areas. Growth of GaAs starts with preferred interfacial bonding, mostly Si-As. Therefore, such a two-domain substrate generally results in a two-domain epilayer, with inversion boundaries between the domains. STM studies confirmed that onaxis (100) Si surfaces consist of (100) terraces with monatomic steps (Tromp et al., 1985). The presence of inversion boundaries in GaAs grown on Si can be detected by etching of the GaAs surface (Upal and Kroemer, 1985; Morizane, 1977; Noge et al., 1988) and by TEM analysis using either the convergentbeam method (Liliental-Weber et al., 1988b; Liliental-Weber and Parachenian-Allen, 1986) or the (200) dark-field method (Ueda et al., 1988).

4. DEFECTS IN EPITAXIAL LAYERS a. Cross-hatches

The first criterion used to judge the quality of an epilayer is its surface morphology. Milky or foggy surfaces usually mean poor epilayer quality and represent rough surfaces. Surface roughening is attributed to unoptimized growth conditions, such as too high a growth temperature and inhomogenous nucleation. Surface roughening is particularly detrimental to strained layer superlattices or quantum well structures and also causes problems for device fabrication. Although normal optical microscopy shows the mirrorlike surface, Normanski interference microscopy can reveal cross-hatched patterns on the surface (Fig. 16). Cross-hatches are composed of ridges along two orthogonal (1 10) directions on (001) wafers and along (1 10) at 60" to each other on (111) wafers (Olsen, 1975). Structures with large lattice mismatch (f > 2%) usually do not show cross-hatches, but rather exhibit an irregular, wavy surface (Olsen, 1975). Kishino et al., (1972) reported that cross-hatches were clearly visible on a wafer of GaAsP/GaAs epitaxial system. The cross-hatches seems to be related to the mechanism of strain relaxation in strained epilayers. Cross-hatching can be removed by electrochemical polishing, which implies that cross-hatches are an indication of the surface roughness; however, their origin is not clear (Olsen, 1975). In a study of cross-hatch in InGaAs/GaAs, it was shown that sharp cross-hatch patterns developed only after misfit dislocations were formed at the interface, suggesting that there are surface steps left by moving dislocations (Chang et

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FIG. 16. Cross-hatches visible on the surface of the GaAs layer grown by MBE (after E. A. Fitzgerald et al., (1992).

al., 1990). Fitzgerald et al., (1988) showed that nonradiative recombination lines in CL in InGaAs/GaAs images come from groups of misfit dislocations formed at the interface. Comparison of the SEM and CL images shows that most of the surface ridges correlate with the dark line defects, which are groups of misfit dislocations at the interfaces. However, it is difficult to accept that surface ridges are formed solely by the slip steps if one compares the height of ridges with displacement due to one or two dislocations. These steps still may act as favorable nucleation sites during subsequent growth. Also, the strain field of misfit dislocations at the interface may make the surface just above preferable nucleation sites for growth, resulting in cross-hatched surfaces (Fitzgerald et al., 1988). Cross-hatches can be used to determine the presence of misfit dislocations at the interface by optical microscopy. b. Dislocations MisJit Dislocations. In diamond or zincblende structures, perfect dislocations have Burgers vectors b of the type a/2( 1 lo), which are the shortest translation vectors. Dislocation lines u lie preferentially along (1 10) directions in agreement with the Peierls potentials. From these Burgers vectors and line directions, one can expect three preferred orientations of perfect dislocations in the diamond structure: pure edge, pure screw, and 60" dislocations. Screw dislocations cannot accommodate misfit between

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crystals. Hence, only two types of dislocations are expected to be found at the interface: edge dislocations, with both b (e.g., a/2[011]) and u (e.g., [01 11) in the (100)interface, or 60" dislocations with only u in the interface (e.g., [01 l]), but b in the one of the four (110) directions inclined to the interface (e.g., a/2[ loll). The first type of misfit dislocation is more efficient at accomodating misfit strain. They are sessile because (100) planes are not favorable glide planes in the diamond cubic lattice. The second type of dislocation (60" dislocations)is less effective at accommodating misfit strain because only the edge component of b in the interface can relieve misfit strain, the length of which is 50% less than the Burgers vector of the dislocation.The 60" type of misfit dislocation is mobile because both the Burgers vector and dislocation line lie on a { 11 l } glide plane. Although 90" dislocations are more effective for relieving misfit strain than 60" dislocations, 60" dislocations are more often observed at the interface because they can glide into the layer from a nucleation site. Edge misfit dislocations are formed by an interaction between two 60" misfit dislocations. Both types of misfit dislocations can also dissociate into partial dislocations as a/2(101) -+ a/6(2?1) a/6( 112), forming a ribbon of stacking faults between them.

-

+

As discussed in the previous section, three-dimensional (island) growth is observed for large mismatch. In this case, the high shear stress that develops near the edge of an island as it increases in size can promote formation of defects. In the GaAs on Si system, a TEM study showed that 60" degree misfit dislocations, as well as stacking faults, were often observed near the edges of islands (Tsai and Matyi, 1989). When the islands join to form a continuous layer, these defects remain in the layer, and additional dislocations may be formed by the coalescence. Threading Dislocations. Misfit strain relaxation requires dislocations only at the interface. But a very high density of threading dislocations is often observed in lattice-mismatched epilayers. As mentioned previously in this chapter, dislocation loops are nucleated at the surface when the thickness of epitaxial layer exceeds a critical thickness. These dislocation half-loops can propagate on the (111) planes inclined to the interface, leaving a 60" misfit dislocation segment in the interface and two arms at the end extending up through the layer. These threading arms remain in the layer as threading dislocations. Each loop leaves two threading arms inside an epitaxial layer. Hence, the density of threading dislocations will correlate with the density of misfit dislocation loops nucleated at the surface. Long segments of misfit dislocations in the interface correspond to a small number of threading arms, and short segments of misfit dislocations mean high threading dislocation density. When epilayers grow three-dimensionally, island coalescence can also be a cause of threading dislocations, when extra atomic planes associated

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FIG. 17. TEM micrograph showing threading dislocations present in GaAs grown on Si substrate.

with misfit dislocations in adjacent islands do not line up with each other. In this case, densities of threading dislocations will be inversely proportional to the size of the islands at coalescence. Interaction between threading arms may lead to decreased number of threading dislocations. In the case of GaAs/Si epitaxy, the density of threading dislocations near the interface is above loiocm-2, decreasing to lo8 cm-2 at the top of the layer, even when no special effort to reduce their density has been applied (Fig. 17).

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c. Inversion Boundaries Polar on nonpolar growth is connected with the appearance of inversion boundaries (IBs) as previously described. Our observations show that very often such boundaries macroscopically lie on various planes (Fig. 18),such as { l l l ) , although microscopically they consist of terraces on (110) (Fig. 19) (Liliental-Weber et al., 1988b). Orientation of inversion boundaries on { 1 lo} is in agreement with Petroffs prediction that (110) and (112) APBs with

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FIG. 18. TEM micrograph showing formation of an inversion boundaries on different crystallographicplanes, after C. B. Carter, et al., 1987.

alternating As- As and Ga-Ga bonds have the lowest free energy (Petroff, 1987). It has been reported that misorientation of the substrate from the nominal (100) orientation by rotation of 2-4" about the [Oll] direction leads to the disappearance of inversion boundaries (Gale et al., 1981; Masselink et al., 1984; Aspen and Ihm, 1987). Our own observations show that even for such misoriented substrates, inversion domains can be found if the growth conditions are not optimized, preferentially in the areas close to the interface (Nauka et al., 1990). Many of these domains terminate inside the epilayer so that only a small number of inversion boundaries extend to the surface. Drastic changes of the IB density are observed upon changing the growth parameters. After post-growth annealing, IB-free layers were found even on nominal (100) substrates (Noge et al., 1988). The growth of IB-free GaAs is an important achievement in GaAs on Si heteroepitaxy, reached within past years. A self-annihilation mechanism was proposed by Shirashi et al., (1989) to explain the fact that after the growth of about 200 nm of the GaAs by MBE, a change from double-domain to single domain structure occurred. This annihilation was attributed to the fact that two IBs, one on (1 12) and the second on (1 12), meet during growth, resulting in annihilation. The Shirashi model was confirmed experimentally by Ueda et al., (1989). The model is consistent with the preference for (112) orientation of IBs proposed by Petroff (1987). Faceting of APDs was observed earlier by other researchers (Carter et al., 1987), and it was proposed that self-annihilation is taking place on (111) planes (Cho et al., 1985).

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FIG. 19. Inversion boundaries macroscopically formed on ( 1 11) planes but microscopically staircase of the boundaries are formed on ( 1 10) planes.

d. Stacking Faults and Twins Stacking faults and twins are major defects observed in GaAs heteroepitaxial layers grown on Si. However, it is not clear if stacking faults are always formed during growth or sometimes also during cooling. Ernst and Pirouz (1989) suggested that deposition errors in the early stages of film growth are responsible for generation of these defects. They suggested that differences in surface energy leads to faceting on low-energy planes. Deposition errors can then occur on { I l l ) facets. They assumed that the energy associated with a misdeposited atomic layer is only 50% of the stacking fault energy, and therefore the misdeposition energy is smaller than the average thermal energy of an atom. To test the idea that faceting is connected with stacking fault formation, GaAs grown on a { 110) GaAs substrate (which has been reported to form a faceted surface-see Allen et al., 1988) was investigated by plan-view and cross-section TEM. Plan-view TEM shows faceting on { 11 1) planes (Fig. 20). However, cross-section TEM performed on these samples does not reveal any stacking faults (Liliental-Weber et al., 1990) (Fig. 21). Therefore, this experiment failed to confirm Piroux’s prediction that faceted growth leads to growth errors that nucleate stacking faults. A reason for stacking fault formation that has been supported experimentally is presence of imperfections at the Si surface (Booker and Stickler, 1962). Another possible explanation for stacking faults is that these defects might

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FIG. 20. Faceted surface of the GaAs layer grown on (011) GaAs surface.

FIG.21. Lack of stacking faults at the interface with the substrate for the layer shown in Fig. 20.

be formed during cooling. Misfit dislocations could dissociate on a (111) plane inclined to the interface, leaving one partial at the interface and forming an extended stacking fault. The formation of extended stacking faults by this glide process was first found in plastically deformed semiconductors cooled

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under high stress (Wessel and Alexander, 1977; Kusters et al., 1986). A misfit lslocation partial traveling from the interface to the top of the layer during cooling and from the top of the layer back to the interface during annealing is a possible explanation for disappearance of stacking faults during annealing. Another explanation for formation of stacking faults can be their nucleation during the initial stage of growth for strain relief (Pirouz et al., 1988). It was observed by TEM that a high density of stacking faults is formed and extends parallel to the { 1111 side faces of islands in the early stages of growth. It suggests that several processes can take place that nucleate faults: accommodation of surface irregularities due to contamination, plane misplacement, or island coalescence during growth. More evidence that island coalescence is a main reason for this defect formation is supported by the work of Cho et al., (1991). They deposited amorphous GaAs on a tilted Si surface at low temperature (solid phase eipitaxy-SPE) before the growth of the GaAs layer. In this case twin distribution on two perpendicular (1 10) axes was nearly the same, in contrast to the work reported by Lee and Tsai (1987; Tsai and Lee, 1987), who found a large difference in density of the stacking faults on the two perpendicular axes. Hsieh et al., (1988) demonstrated that in two-step MOVPE growth the twin density increased with an increase in the substrate tilt angle. The number of stacking faults increased 80 times on step-rich surfaces compared to flat surfaces. In these techniques the growth is threedimensional, and island shape was dependent on the degree and the direction of Si misorientation (Rosner et al., 1988; Otsuka et al., 1986). Since in SPE growth the substrate temperature is much lower, the density of nuclei is expected to be high. Nucleation of the GaAs islands probably occurs not only at the Si surface step edges but also on the terraces. This could explain why in SPE growth of GaAs the distribution of islands becomes more independent of substrate tilt. The coalescence of three-dimensional islands appear to be the main cause of stacking fault/microtwin formation (Cho et al., 1991).

IV. Metsods to Decrease the Defect Density in the Epitaxial Layers 5. OVALDEFECTS

Oval defects have been attributed to several causes such as surface contamination, Ga-spitting, Ga oxides, and particulates. In order to reduce the density of oval defects, it is necessary that substrates be prepared carefully in an ultraclean environment to avoid C or S contaminations and adhesion of particulates. It is recommended that the growth chamber be baked out thoroughly. Also, sources cells and shutters should be outgassed with caution

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in order to remove oxides that can react with Ga. In order to avoid Gaspitting, it may be necessary to design effusion cells in such a way that the large temperature difference between the bottom and the opening of the Ga effusion cell is reduced so as to avoid the condensation of Ga droplets near the opening of the crucible. It was shown that oval defects can be avoided using chemical beam epitaxy in which Ga atoms are formed by thermal pyrolysis of the metal alkalis at the heated substrate surface, while As atoms are believed to come from the As, dimers being thermally cracked (Tsang, 1985). Replacement of solid Ga sources with gas Ga sources appears to have a fundamental advantage in the elimination of oval defects. There is experimental evidence that oval defect density is reduced by suppressing Ga oxidation, namely, the reduction of Ga,03. In this case the remaining oval defects were shown to be caused by Ga,O. The oxide Ga,O was formed by the reaction between Ga and residual water at the Ga cell with additional reaction with carbon when growth temperature increased above 930°C. It was shown (Shinohara and Ito, 1989) that in order to eliminate these remaining oval defects, not only oxidation but also water content in the growth chamber needs to be drastically reduced. TO IMPROVE 6. METHODS

THE

QUALITY OF GaAs ON Si

a. Initial Growth; Bufer Layers

Much lower dislocation density in the epilayer can sometimes be obtained when a two-step growth is applied. Usually a buffer layer is grown, followed by the growth of the epilayer. For GaAs on Si grown at 650"C, a noticeable decrease in dislocation density is observed when an initial 10-30nm buffer layer of the GaAs is grown at 400°C. Dislocation density also decreases with an increase in layer thickness because of the interaction and annihilation of dislocations. Pearton et al., (1988) showed directly by x-ray rocking curve analysis the increase in crystalline quality of the GaAs epilayer with increase in its thickness. However, even with two-step growth, the defect density in these layers was still in the range of 109/cm2.Difference in thermal expansion coefficient and large lattice mismatch are the primary reasons for such high defect density for GaAs grown on Si. Low-Temperature Growth. The density of misfit dislocations is related to the existing stress relaxation at the growth temperature. This density is too high after cooling down to room temperature (Liliental-Weber, 1989). TEM observation of this phenomenon confirms the photoluminescence observation of tensile stress in GaAs layers on Si at room temperature, instead of the

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compressive stress that would be expected based on the difference in lattice parameters. In order to have fewer dislocations at the interface and consequently a stress-free layers at room temperature, one can lower the growth temperature. However, results of growth at a temperature as low as 300°C show that instead of just a decrease in the dislocation density, there was an increase in the fraction of partial dislocations (Fig. 22) and consequently stacking faults (Liliental-Weber and Mariella, 1989). This suggests that at 3WC, atom mobility is reduced sufficiently to increase the probability of growth errors, as suggested by Pirouz et al., (1988). Therefore, 400°C appears to be the lowest practical temperature for growth of an initial GaAs layer on a Si substrate. Two-Dimensional Initial Growth. For low defect density, layer-by-layer growth is preferable instead to island growth. Application of migrationenhanced epitaxy (MEE) (Horikoshi et al., 1986) to the growth of GaAs on Si has resulted in substantial improvements in the crystalline quality of the

FIG. 22. High density of stacking faults formed at the Si/GaAs interface for a GaAs layer grown at 300°C; the insert shows the diffraction pattern obtained at this interface.

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heteroepitaxial films compared with conventional growth methods. An important feature in MEE is the precise and independent control of the group I11 and V beam fluxes during growth. In MEE growth, the group I11 and group V beam fluxes are alternately modulated by the opening and closing of the shutter of each effusion cell. In the case of GaAs growth, the absence of As molecules on the host substrate increases the surface mobility of impinging Ga atoms/molecules, thereby increasing the surface diffusion length of the Ga atoms/molecules. This along with the modulation enables a more twodimensional growth mode. It also allows the growing layer to achieve proper stoichiometry at lower substrate temperature than possible for conventional MBE. A modification of this method is modulation enhanced epitaxy (Lee et al., 1989), where only the As, beam flux is modulated (open and closed) and the Ga beam stays open during the entire growth period. A study of these samples by TEM in plan view showed moirC fringes distributed uniformly over large areas of the sample (Fig. 23). A photoluminescence study on these same samples showed very narrow lines. In these samples, the island nucleation density was increased. However, this growth technique leads to formation of a high density of V-shaped stacking fault pairs. Another promising method for promoting two-dimensional growth is to start with a lattice-mismatched system, such as AIGaP, which provides very good wetting (George et al., 1989; Noto et al., 1989). The addition of small

FIG. 23. Plan-view TEM micrograph showing moirb fringes in MEE grown GaAs on Si substrate.

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FIG.24. (a) Island growth of GaP on Si. (b) Two-dimensionalgrowth occurs after adding A1 to Gap. Note island growth of GaAs on AlGaP.

amounts of A1 causes perfect two-dimensional growth (Fig. 24). This might be due to the high affinity of Al for oxide formation, allowing A1 compounds to grow on both clean and contaminated surfaces (George et al., 1989). b. Thermal Treatments

Conoentionaf Post-growth Annealing. If the heteroepitaxial layer grows strain-free, with the right density of misfit dislocations, any change of temperature will subsequently induce strain, the sign and magnitude of which depend on the difference between the growth temperature and the annealing temperature. Thus, it is possible to move dislocations by changing temperature after growth. It has been reported that annealing of GaAs on Si at

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850°C under arsenic overpressure results in dislocation rearrangement at the interface, leading to the formation of Lomer-type dislocations and decreasing the number of stacking faults (Tsai and Lee, 1987; Choi et al., 1987). Our own observations (Liliental-Weber et al., 1990) have not confirmed these results fully. Furnace annealing at 800°C for 10 min changed the defect rearrangement only slightly (Fig. 25). The dislocation density remained in the same range as for “as-grown samples,” but dislocations were more tangled. A slight decrease in stacking fault density was observed. Rapid Thermal Annealing. Noticeable improvements in the quality of GaAs/Si epilayers grown by MBE were observed after rapid thermal annealing (RTA) at 800°C for 10 s by the capless close-proximity method in a commercial heat-pulse furnace (Liliental-Weber et al., 1990). The density of stacking faults after this treatment was reduced (Fig. 26). This result suggests that stacking faults that are removed during heating may be formed again during cooling for conventional furnace annealing by reverse migration of the partial dislocation. During rapid cooling there may be insufficient dislocation mobility for reformation. RTA is beneficial for the removal of stacking faults, but inhibits stress relief during cooling, as evidenced by cracking of the GaAs epilayers. Cracking after RTA was more severe than in as-grown samples. The heterointerfaces were also more undulated after RTA, compared to asdeposited samples. Independent electrical measurements of devices after RTA

FIG. 25. Defect arrangement in a GaAs layer grown on Si substrate after furnace annealing.

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FIG. 26. TEM cross-section of GaAs on Si after rapid thermal annealing. Note lack of stacking faults after such annealing.

(Chand et al., 1987) did show noticeable improvement for forward and reverse bias characteristics. Leakage currents were reduced by more than two orders of magnitude after this treatment. Thermal Cycling during Growth. It has been reported that in-situ annealing at 800°C for 5 min during growth is more efficient for defect reduction than ex-situ annealing (Al-Jassim et al., 1988). This causes dislocation to move, thus increasing the chance for threading dislocations to interact with each other or to move to the periphery of the wafer. After this treatment the density of dislocations was reduced (Al-Jassim et al., 1988) to 2 x 1O-’/cm2. Yamaguchi et al., (1988, 1989) carried out an even more successful thermal treatment during MOCVD growth. It involved thermal cycling during growth in which annihilation and coalescence of dislocations were caused by dislocation movement under an alternating thermal stress. The growth of the GaAs was interrupted several times, and the substrate temperature was

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lowered to room temperature, followed by a temperature increase up to 900°C and subsequent annealing for up to 15 min at this temperature in an arsine atmosphere. After this treatment, the substrate temperature was again and a new layer of GaAs was grown in the same fashion. lowered to 70O0C, This process was repeated several times. The reported dislocation density for GaAs grown on Si with such thermal cycling was estimated from the etch pit density to be as low as 2-2 x 106/cm2.Such thermal cycling during growth appears to be a very promising approach for decreasing the defect density in heteroepitaxial systems. c. Strained-Layer Superlattices

Another way to promote dislocation migration during growth is to use strained-layer superlattices (SLSs), which cause dislocations to bend into the strained interfaces, thus promoting dislocation interactions. It was reported (Liliental-Weber et al., 1982, 1988a) that by application of SLSs of InGaAslGaAs with 10-mm thick periods for the growth of GaAs on Si (21l), the blocking of dislocation propagation occurred almost entirely at the uppermost interface between the strained layers and the final GaAs layer (Fig. 27). Therefore, reduction of dislocation density was only weakly dependent on the number of periods of the SLSs. InGaAs/GaAs SLSs proved

FIG. 27. TEM cross-section micrograph of the GaAs/Si interface with 50 periods of In,,,,Ga,,,,As/GaAs SLSL grown directly at the interface with Si. Note the large number of stacking faults formed at the interface, propagating through the SLSL and stopping at the last interface with the epilayer of GaAs. Bending of dislocations was most effective at this last interface.

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Ftc. 28. Formation of new dislocations at the interface of SLSL. (Courtesy of Dr. T. George).

to be more efficient in dislocation bending than InGaAs/InGaP SLSs (Liliental-Weberet al., 1982). Because the upper interface of SLSs was shown to be most efficient in dislocation annihilation, packages consisting of five periods of SLSs (InGaAs/GaAs) were used alternating with thicker layers of GaAs. Each set of SLSs then caused additional dislocation annihilation. However, in some areas additional dislocations were also formed at the lower interface between the buffer layer and the SLS (Fig. 28). On the average, the dislocation density in these samples was in the 2 x 107/cm2range, which is very low, taking into account that all misfit dislocations in the GaAs grown on Si(211) are 60" dislocations with Burgers vectors inclined to the interface. This kind of SLS was also applied to growth of GaAs on Si(IOO), and results were similar to the ones obtained on Si(211) surfaces (George et al., 1989). Strain is an important parameter to determine the composition of SLSs and their thickness (Yamaguchi et d.,1989). Two critical thicknesses need to be considered to optimize application of SLSs: a critical thickness hCl, which must be exceeded to introduce enough strain for dislocation bending, and a critical thickness hc2, above which the generation of new dislocations becomes significant.

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d. Growth on Patterned Substrates

The growth of epilayers on patterned substrates is another promising approach to the achievement of high-quality epilayers. In general, it is difficult to grow a lattice-mismatched epilayer with a network of misfit

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dislocations confined entirely to the interface and with no threading dislocations in the epilayer. This would require the threading “arms” of the misfit dislocation half-loop to glide across a whole wafer without being blocked by other dislocations. However, it is easier to achieve this goal if the growth area is reduced by patterning the substrate into mesas. Luryi and Suhir (1986) have proposed a possible approach to obtain dislocation-free lattice-mismatched epitaxial layers on small seed pads of lateral dimension L. That approach was based on reduction of the strain energy in the epitaxial layer by limiting the strained zone to a narrow layer adjacent to the interface. It was proposed that the entire misfit strain is accommodated by elastic strain if L is smaller than a critical length Lmin, which depends on the misfit and dislocation type. They suggested that Lminis about 20nm for GaAs on Si, which is too small a dimension to attain conventional photolithography. Fitzgerald et al., (1989) have shown that for lnO~,,Ga,~,,As grown on GaAs, a drastic reduction in threading dislocation densities can be achieved as the growth area is reduced for circular or square mesas. The interface misfit dislocations were also reduced for epilayers grown on small mesa areas. The experimental critical layer thickness was estimated to be approximately 10 times thicker in these samples compared to large-area samples. Small-area samples had a lower misfit dislocation density than expected from theory. Cathodoluminescence intensity increased approximately 25% as mesa size decreased from 400 to 25 pm, which is a direct proof of reduction in interfacedislocation density. A difference in the dislocation density in the two orthogonal (110) directions was also observed. This was related to the existence of a and j type dislocations in GaAs. Three different sources of misfit dislocations were considered: fixed sources (related to defects in substrates), dislocation multiplication, and surface halfloop nucleation. It was shown that a dislocations nucleate more readily than j dislocations. Two-thirds of the fixed sources acted as nucleation sites of a [llO] misfit dislocations, whereas one-third acted as the nucleation sites of j [llO] misfit dislocations. When mesa size was decreased close to zero, the dislocation density didn’t go to zero. This result was related to the dislocation origination at the substrate surface and was additional proof that only fixed sources were responsible for dislocation nucleation. High elastic strain (Fitzgerald et al., 1989) is necessary for the nucleation of half-loops at the surface. For a layer thickness much greater than the critical layer thickness, this heterogeneous surface nucleation does take place at mesa edges. Dislocation nucleation at round mesas was observed more often than at rectangular mesas. For mesa sizes up to 200 pm, the misfit dislocation density had a linear dependence on mesa size. For larger mesa size, dislocation density increased drastically, possibly because an interaction mechanism

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FIG. 29. Cross-section micrograph near the patterned boundary. Note stacking faults present at the boundary with material grown over SiN and very low density of defects within the stripe of GaAs gown on lOOnm stripe of Si.

such as cross-slip or the modified Hagen-Strunk mechanism (Hagen and Strunk, 1978) became possible. It has been shown (Yamaguchi et al., 1990) that in as-grown GaAs films on Si substrates the major component of the large residual stress of about 1.5 x lo9 dyn/cm2 is caused by differential thermal contraction. Substantial reduction in the biaxial stress was obtained by post-growth patterning of GaAs grown by MBE on Si substrates. It was shown that reduction in stress is dependent on the pattern size and shape. For stripe patterns less than 15pm wide, the stress becomes uniaxial with stress relief normal to the stripe direction. Rectangular patterns exhibited stress relief in orthogonal directions and had the lowest stress in the narrow direction of the rectangle (van der Ziel et al., 1989; Lee et al., 1988). High-quality GaAs films with low etch-pit density were obtained from lowpressure MOCVD and MBE on patterned Si films with various mesa sizes (Yamaguchi et al., 1990, Sohn et al., 1991). Cathodoluminescence peak shift was used for residual stress measurement in the MOCVD-grown samples (Yamaguchi et al., 1990). Results (Lee et al., 1988)on the growth of GaAs on Si through openings in an oxide or nitride show that GaAs deposited on the Si3N, mask was polycrystaliine, but lower dislocation density was observed in the open areas where the nitride had been removed, similar to the observation for mesa growth (Sohn et al., 1991). The stacking fault density was also much lower in

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the monocrystalline GaAs regions, increasing only at the border with the nitride mask (Fig. 29). Porous silicon has also been proposed as seed pads for GaAs on Si growth. But the improvement so far achieved in epilayer quality is not impressive(Lin et al., 1987). Improvement of the quality of GaAs on Si has also been obtained with growth on sapphire. A misorientation away from (100) was introduced and two sets of samples were compared: those grown directly on Si, and those grown on Si on sapphire (SOS). Low-temperature GaAs buffer layers were grown on both samples. In the samples grown on 6" misoriented SOS, the photoluminescence intensity increased 30 times, compared to the samples grown directly on Si. This was explained by stress relief. Reduction of stress for GaAs on SOS was expected because of the closer match of thermal expansion coefficients between GaAs and sapphire. Metal-semiconductor field effect transistors (MESFETs) fabricated on these materials had device characteristics comparable to those of GaAs on GaAs (Metzger et al., 1990).

7. DEFECT REDUCTION FOR OTHER III/v HETEROEPITAXIAL LAYERS Although the feasibility of InGaAs/InAlAs HBTs and MODFETs on GaAs substrates was demonstrated (Won et al., 1988), the problem of the lattice mismatch between epilayers and substrates was left unsolved. More recently, it was shown that the use of a graded In,Ga,-,As buffer layer grown at a relatively low temperature of about 400°Cimproves the electron mobility in this lattice-mismatched system. The electron mobility at 300 K increases monotonically with an increase in In composition, from 7000cm2/Vs at x = 0.2, to 10,500cm2/Vs at x = 0.53,and to 20,000cmZ/Vs at x = 1.0. At 77K 118,000cm2/vs was obtained at x = 0.8. These high mobility values indicate that the dislocations created to relieve the strain are efficiently confined in the buffer layer, and the propagation of threading dislocations into the active layer is minimal (Inoue et al., 1991). Successful InGaAs/InAlAs modulation-doped heterostructures that are latticemismatched to GaAs substrates for a full In composition range have been demonstrated. A highly perfect InGaAslInP strained layer superlattice has been obtained by using gas-source molecular-beam epitaxy (Vanderberg et al., 1989). The advantage of this method is a capability for excellent control of composition and layer thickness, which makes it possible to grow very closely matched layers as well as strained-layer superlattices(SLSs). The layers with a nominal In concentration as low as x = 0.075 and a thickness of -2nm were

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obtained. High crystal perfection was reported based on high-resolution xray diffraction. It has been shown that interface structure of AlGaAs/GaAs heterostructures is affected by surface segregation of impurities in the AlGaAs layer. Interface smoothness was improved by using substrates 2-4" off (100)toward (1 11) GaAs, and by incorporating thin layers of GaAs at regular intervals in AlAs (Chand and Chu, 1990). Incorporation of these GaAs smoothing layers increased photoluminescence three times.

V.

Conclusions

This review makes it clear that there are many factors that influence defect formation in epitaxial layers. Defects are often formed because of impurities present on the substrate. This source of defects is common for homoepitaxial and heteroepitaxial layers. In many cases these defects can be avoided by proper cleaning procedures. Another class of defects is related to the growth parameters, such as growth temperature and the flux ratio of the elements used to the growth. This has been observed for homoepitaxial growth such as GaAs grown at low temperature on GaAs. These defects can often be avoided by choosing optimum growth parameters. However, there are defects related to lattice mismatch and difference in thermal expansion coefficient that cannot be easily avoided, where they are detrimental for device performance. Methods to avoid their propagation into the active areas of the devices need to be applied. Reduction of dislocation density in difficult heteroepitaxial systems such as GaAs grown on Si has been possible to some extent. Controlled growth of antiphase domain-free GaAs/Si has been achieved. The cleaning of the Si substrates has been improved, but is not yet completely satisfactory. Of special interest should be development of cleaning procedures that avoid the high-temperature substrate annealing currently used. Such high annealing temperatures result in roughening of the Si surface and are generally incompatible with patterned epitaxy. Further dislocation density reduction strategies, such as thermal cycling during growth, post-growth annealing, and the use of buffer layers such as strained-layer superlattices, still have to be optimized. Combined use of some of these methods together with use of patterned epitaxy should lead to higher-quality growth of lattice-mismatched heterostructures such as GaAs/Si and InGaAs/GaAs for practical application in minority carrier devices, the feasibility of which has already been demonstrated with GaAs/Si heteroepitaxy and other ternary compounds grown on GaAs or InP substrates.

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Acknowledgment This review includes work supported by the Materials Science Division of the U.S. Department of Energy under Contract No. DEAC03-76SF00098. The part concerning GaAs epilayers grown at low temperature was supported by the Air Force Office of Scientific Research under the contract AFOSR-ISSA-90-0009. The authors thank Prof. E. R. Weber for many fruitful discussions, The technical assistance in TEM sample preparation and in photographic work of W. Swider is greatly appreciated. Use of the electron microscopes at the National Center for Electron Microscopy of Lawrence Berkeley Laboratory is acknowledged.

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SEMICONDUCTORS AND SEMIMETALS, VOL. 38

CHAPTER 10

Defects in Metal/III/V Heterostructures William E. Spicer Srandord University Stanford, Calfirnia

I.

INTRODUCnON

. . . . . . . . . . . . . . . . . . . . . . . .

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11. MOV~MENT OF THE FERMI LEVELAND DEPARTURES FROM GaAs STOICHIOMETRY . . 451 1. Schottky Diodes . . . . . . . . . . . . . . . . . . . . . . . 451 2. Interfacial Chemistry and Departures from GaAs Stoichiometry . . . . . . . 454 111. A MODELTO EXPLAINFERMI LEVELMOVEMENT.. . . . . . . . . . . . 461 3. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 461 4. Native Defects and the Antisite Defect Model ( A D M ) . . . . . . . . . . 463 5. Fermi b e 1 Movement Due to Excess As . . . . . . . . . . . . . . 466 6. Ohmic Contacts on n-GaAs . . . . . . . . . . . . . . . . . . . 416 I . Fermi Level Movement Due to Excess Ga . . . . . . . . . . . . . . 418 8. Measurements of Departuresfrom Stoichiometry at the Interface and Their Relation to the ADM . . . . . . . . . . . . . . . . . . . 480 Iv. GaAs/INSULAToR INTERFACES. . . . . . . . . . . . . . . . . . . 483 V. CONCLUSIONS AND DISCUSSION . . . . . . . . . . . . . . . . . . . 481 ACKNOWLEDGM. . . . . . . . . . . . . . . . . . . . . . . 488 REFFXENCES . . . . . . . . . . . . . . . . . . . . . . . . . 488

I. Introduction Since Bardeen’s 1947 paper, we have become accustomed to the thinking of Fermi levels at metal/semiconductor interfaces as being highly pinned or fixed in energy. During the 1970s and early 1980s, a literature developed that established that for GaAs it was difficult to move the interface Fermi level throughout the band gap (i.e., achieve inversion) at the hative oxide interface. All of this has tended to fix in our mind the idea of a highly fixed and unmovable Fermi level at GaAs interfaces with either metals or insulators. Similar but less extreme effects were found for InP. However, in recent years there has been an increasing number of papers that report changes in the Fermi level position at GaAs and InP interfaces with accompanyingchanges

449 Copyright 0 1993 by Academic Press Inc. All rights of reproduction in any form reserved. ISBN 0-12-7521384

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in interface parameters of importance to devices and their application. These papers go back as far as 10 years. Among the pioneers in this type of work were Grant and Waldrop at the Rockwell Science Center and Bachrach and Bauer at the Xerox Palo Alto Research Center. The purpose of this paper is to focus on work in which the Fermi level position at GaAs interfaces has been changed, and to provide a possible atomic-level model as to what produces these changes. It is not difficult to see the importance of Fermi level motion for device applications. If some degree of control can be obtained in the Fermi level at the interface, Efi, this can be applied to ohmic contacts as well as Schottky barriers. For nonmetallic interfaces, it could also lead to reduced surface recombination and even MIS devices. These are just some examples; there are many more. Ohmic contacts would be improved by moving Efi to near the appropriate band edge. For Schottky barrier gates, the height of the barrier is important. if one can develop some degree of control of this height, devices and ICs can be made more optimally. For such applications, stability and predictability are also essential. This will be most easily obtained if we understand the interactions at the interface which cause Fermi level motion. Another area of importance is the semiconductor/insulator interface. At the lowest level of sophistication one may worry about surface recombination where such interfaces form boundaries of active areas of devices. Very large effects on device performance have been demonstrated in specially designed devices (Sandroff et al., 1987a; Yablanovitch et al., 1987). A more sophisticated level would be the demonstration of a viable MIS device using GaAs. This has never been done. On InP, such devices have been demonstrated; however, time instabilities have kept them from being useful (Meiners and Wieder, 1988). In the next section, several examples of Fermi level shifts due to various types of treatment of GaAs will be presented. Other examples could be given (see, for example, Spicer et al., 1988a; however, for brevity, only a few will be examined in detail here. In many cases of E,, change, a correlation with changes in Ga to As stoichiometry near the interface has been found. We also discuss this and interfacial metal/GaAs chemistry in Section 11. In Section 111 we discuss several models for Fermi level “position” at the interface and concentrate on a model that gives reasonable qualitative correlations with the changes in Efi position and changes in stoichiometry. This model is based on a wide range of experimental data (Spicer et al., 1988a, 1989). For example, certain pinning positions correspond almost exactly with the AsGa antisite defect energy levels (Weber et al., 1982; Weber and Schneider, 1983). The model makes it possible to make a connection between shifts in the Fermi level and the GaAs/metal chemistry at the interface. Section IV touches briefly on recent

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work on GaAs insulator interfaces. This article closes with a section giving a summary, conclusions, and discussion.

11. Movement of the Fermi Level and Departures from GaAs Stoichiometry

1. SCHOTTKY DIODES

Newman and co-workers (1985a, 1985b, 1987)have performed very careful experiments in which reproducible changes in barrier height were obtained by thermal annealing. Results are indicated in Figs. 1 and 2. In order to reduce the number of variables, the diodes were formed on atomically clean GaAs surfaces formed by cleaving in ultrahigh vacuum (UHV). The atmosphere in which the annealing was done was found to be important for some metals. The usual procedure was to anneal the diodes in a N, atmosphere. (For Au/GaAs diodes different results were obtained when the annealing was done in vacuum.) It also proved important to separate out electrical leakage effects at the perimeter of the diode from change in the barrier height itself. This has been done for the data presented in Figs. 1 and 102

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v

10.7 10-8

v (mv) FIG. 1. I-V data from the thick-film n-type-GaAs diode. All measurements were performed at room temperature after annealing at various temperatures. The barrier height and ideality factor are determined from the equation I = S A . TZe-4b’”l(eY-’R~””~ - 1).

452

W. E. SPICEX

FIG. 2. I-V data from the thick-film A1 n-type-GaAs(ll0) diode. These diodes were fabricated on a clean cleaved GaAs(l10) surface under UHV conditions. All measurements were performed at room temperature after annealing to various temperatures. The barrier height is determined from the equation in Fig. 1. It is a measure of the energy separation between the Efi and the CBM at the interface.

2. Careful studies were made of Au (Newman et al., 1985a, 1985b), A1 (Newman et al., 1985a), Ti (McCants et a/., 1988, Ag (Newman et al., 1985a), and Cr (Liliental-Weber et al., 1989). The results are summarized in Table I (Spicer et al., 1990). Examining Figs. 1 and 2, which are typical of those published by Newman and co-workers, it is important to realize that the shifts in the I - V curves (and thus in barrier height) are well beyond experimental uncertainty and that they are highly reproducible. A detailed discussion of reproducibility and experimental uncertainty is given by Newman et al., (1987). From the Schottky barrier heights, (Pb, quoted in Figs. 1 and 2, one can obtain Efi.The zero for E,, is taken at the VBM. Figure 3 gives the relevant energy level diagrams. The barrier height is the energy difference between the Fermi level at the interface, Efi,and the conduction band minimum (valence band maximum) for n-type (p-type). Thus, for n-type material, as was used for the data of Figs. 1 and 2 and Table I. Efiis obtained from the barrier height by the relation

(n-typ)

Efi

= Eg

- (Pb.

(1)

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES

FERW

453

TABLE I LEWLMOTIONAND METAL/GaAs INTERFACIAL CHEMISTRY ______

Fermi Level (Ef) Position Metal Ag Au

Al Ti Cr

Before Anneal

After Anneal

0.5 0.5 0.65 0.7 0.15

0.5

none

0.6 0.55 0.6 0.75

+0.1 -0.1

none Au+GaAs+AuGa+As A1 +GaAs-tAIAs+ Ga Ti + GaAs-tTiAs +Ga Cr + GaAs-tGaCr + CrAs

-0.1 none

n-type

Semiconductor

where:

Interfacial Chemistry Expected for Annealing

Ef

Movement with Respect to VBM

I-

Reaction Product (As or Ga) none As Ga Ga neither

+b.n

+b,n = Eg

Efi

Schottky Barrier Height on n-type Schottky Barrier Hewight on p-type Efi = position of Fermi level at interface (same on n- and p-type) and +b,n + +b,p = Eg

+b,n

I

+b,p

3

FIG. 3. Relationship between Eli position and Schottky barrier heights on n- and psemiconductors. Efi is measured from the VBM. See Eq. (1) and (2) in the text.

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W. E. SPICER

For p-type semiconductors, the relation is

Using these equations, the changes in (P, given in Figs. 1 and 2 can at once be translated into values of Efi. The key point here is that the Fermi level can be reproducibly changed by a processing step, thermal annealing, and that the details of movement depend on the metal used to form the Schottky barrier. Note that A1 and Ti move Efi toward the VBM, whereas Au moves it toward the CBM. No movement is seen for Ag and Cr. What is the mechanism that determines this movement, and how can the movement be controlled? In the next section, we will explore the relationship between interface chemistry, stoichiometry, and Fermi level motion. The purpose is to see if there are systematics which might help us begin to answer these questions. 2. INTERFACIAL CHEMISTRY AND DEPARTURES FROM GaAs STOICHIOMETRY There is considerable literature concerning equilibrium reactions between GaAs and metals (Mayer and Lau, 1990). These data are extremely important, but are still insufficient because they are thermodynamical data for the metal in equilibrium with the semiconductor. By definition, an interface is the boundary between two chemical systems, which may or may not be in equilibrium. For example, living organisms (including human beings) are made up principally of carbon and exist in a world where they are surrounded by oxygen. Equilibrium thermodynamics tells us that the carbon should be oxidized to form COz. In layman’s terms, this means that each human being should become a flaming torch until all of the carbon in our body is oxidized. Yet we are not unduly worried. The reason is that there are kinetic barriers to this oxidation that keep it from occurring. One can think of our skin as forming an interface with the oxidizing atmosphere surrounding us. There is a kinetic bamer between the O2molecules in the atmosphere and the carbon of our skin that prevents equilibrium being reached at room temperature. If the temperature is high enough, this barrier is overcome and we become, in reality, torches so that equilibrium can be achieved. In a similar way, it is important to look not only at the thermodynamics, i.e., equilibrium chemistry, between metals and GaAs, but also at the real interfaces and the effects of kinetic barriers on the chemistry and intermixing that takes place. Experimentally,it is well established that one can determine phase diagrams and the equilibrium chemistry by reacting the components to

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES

455

completion and analyzing the resulting compounds. It is much more complicated to examine interfaces in situations where kinetic barriers control the interface and equilibrium is not reached, as is usually the case with semiconductor interfaces. In this article, we will concentrate on two types of experimental techniques to attack this problem: photoemission spectroscopy (PES) and electron microscopy (EM). To apply photoemission spectroscopy,one evaporates a metal onto a clean GaAs surface in UHV and uses principally core-level spectroscopy to follow the reactions taking place between the metal and semiconductor. PES and related electron spectroscopies are highly surface-sensitive. Moreover, the depth probed can be changed by varying either the energy of the photoelectron (this can be done by varying the energy of the exciting photon), or the

70

1

65

-

60

-

55 50

-

45 40

-

35

-

5

I

Cu, Ag, Au

2

Au A1 Al A1

A1203

C

w w ~ O B Mo K

cs Sr

Ba Y Ce

Gd Gd Y Ni Fe Si Si

Cd Te Na K Sb

3

/

ELECTRON ENERGY ABOVE THE FERMl LEVEL (eV) FIG.4. Experimentally obtained elastic scattering lengths in various solids. Data points 1 through 28, see Lindau and Spicer (1974); 29 and 30 from Evans et nl., (1979); 31 from Jacobi and Hold (1971); “Our work” is derived from carbon 1s surface core level shifts of diamond (111) 2 x 2f2 x 1 as described in Section 1.7.

456

W. E. SPICER

angle of escape of the photoelectron with respect to the surface normal (Weaver, 1987). Figure 4 gives curves of electron escape depth versus electron energy for various solids. These data are for electrons emitted normally to the surface. The depth probed is reduced with angle by cos 8, where 8 is the angle between the normal and the direction of escape of the electron. Using PES from the atom core levels, one can obtain quantitative or semiquantitative analysis of the chemical composition near the surface. Assuming an escape depth of 5 A (typical for 60eV electrons in GaAs), one typically examines the first two or three atomic layers at the surface. If there were no reaction and if the deposited metal formed a uniform overlayer, one would exponentially decrease the electrons from the semiconductor that escape as more and more metal is deposited. A first-order equation for the

(a) FIG. 5. (a)As 3d (1) and Ga 3d (2) core level spectra for the room temperature Ti/GaAs (110) interface. The dots represent the raw data, the solid line through the dots is the curve fit to the data, and the various components are labeled according to the shading: the wide cross-hatching represents the surface-shifted component, the light and dark cross-hatchings represent the reacted components, and no shading represents the substrate component. Photon energy is equal to 70eV (1) and 50eV (2).

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES

457

4

m’ ?z

6

Kinetic Energy (eV)

25

26

21

28

Kinetic Energy (eV)

(b) FIG.5. (b) As3d(l) and Ga 3d(2) core level spectra for the room temperature Ti/GaAs(llO) interface for higher Ti coverages. In (2), no emission is observed for coverages higher than 17.3.ML.

probability of a photoelectron traversing uniform layer of deposited metal is

where P(x) is the probability of transmission through a thickness x of the overlayer. By examining the core level energies of the metal and semiconductor atoms, one can determine what chemical reactions have taken place. By measuring the intensity of the various atoms as a function of the amount of metal deposited, one can determine the spatial distribution of the various atoms involved and thus determine whether diffusion, intermixing, surface segregation,etc., are taking place. In this way insight can be obtained into the reactions taking place even in nonequilibrium, i.e., kinetically limited, situations.

450

W. E. SPICER

Figure 5 presents spectra of Ga and As 3d cores as a function of Ti coverage from the work of McCants (1988). Earlier studies for Ti can be found in the literature (Ruckman et al., 1987; Ludeke and Landgren, 1986). By deconvoluting the core spectra into surface-shifted (clean GaAs) or reacted (due to Ti on surface)and bulk components, one can examine how the reaction goes with increasing amounts of Ti deposited on the GaAs. One can see by the large amount of reacted As and Ga produced that a strong reaction takes place even at room temperature. The amount of Ti deposited is given in terms of monolayers (ML)in Fig. 5. A monolayer is taken to be 5.2 x l O I 4 atoms/cm* or 1.3 A of Ti. The core levels of the substrate can only be detected with 5.3 ML (6.9 A) or less of Ti deposited. For the next thickness of 10.7 ML (13.9A), no signal from the substrate is detected. This is consistent with an overcoating (Ti plus reacted Ga and As) that uniformly covers the GaAs (see Fig. 4). Note that the amount of Ga seen within the probing depth of the experiment decreases strongly with the highest coverages, whereas the As intensity does not. This indicates that the reacted Ga is being buried below the surface of the overlayer, whereas the reacted As is not; i.e., the As is moving toward the free surface as the amount of Ti deposited is increased. The deconvoluted As curves give evidence of two As-Ti compounds; however, only one broad peak is obtained for Ga. This Ga peak is consistent with Ga alloyed with Ti (Nogami et al., 1986). Note that the ratio of Ga and As peak strengths vanes with coverage. This argues against the formation of stoichiometric compounds containing Ga, As, and Ti. Rather, the lack of correlation for the higher Ti coverages indicates that reacted As and Ga are not distributed uniformly. Above all, one can draw the following conclusions: 0

0

On a monolayer scale, a very strong reaction takes place at room temperature. The reaction products are complex and not uniformly distributed. The nonuniform distribution of the As and Ga gives evidence that equilibrium has not been reached within the reaction products.

These results are consistent with what might be expected from thermodynamics, including heats of reaction or alloying, when it is recognized that equilibrium has not been achieved. Many data exist from photoemission studies done before high-resolution and deconvolution schemes and other more sophisticated data analysis became available. To illustrate what may be obtained even from such studies, we will next examine spectra from several metals deposited on GaAs in Fig. 6. These spectra are for for the As 3d and Ga 3d core levels. Core spectra are given for various metal coverages. Changes in binding energy with metal deposition indicate As or Ga in a chemical site other than that for GaAs. In

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES

459

BINDING ENERGY (eV) FIG. 6. Chemistry or lack thereof due to noble and transition metals on GaAs as seen through the Ga and As 3d levels.

many cases better data are now available; however, these spectra (all taken with approximately the same resolution) allow a quick overview and illustrate the differencein interfacial chemistry without the complication of deconvolution (Kendelewicz et al., 1984, 1985; Petro et al., 1983; Pan et al.,

460

W. E. SPICER

1984; Williams et al., 1985). In the raw binding energy PES data, there can be

shifts due to chemistry and to band bending. Since we are only interested in the chemical shifts, the band bending shifts have been removed from the curves of Fig. 6. Ludeke et al., (1983) have found that Ag does not react with GaAs. This is the only metal study to date for which this is the case. From the data of Fig. 6, there is clear evidence of a reaction for each of these metals. For Au the Ga peak moves to a lower binding energy, as one would expect (Nogami et al., 1986) if the GaAu alloying expected from thermodynamics is taking place and the Ga is alloying with Au. Note that the Ga intensity decreases faster than for As. This indicates that the near-surface region of the deposited Au is As-rich. The binding energy shift of the As peak is small, but toward high binding energy. This is consistent with the formation of elemental As and/or As weakly dissolved in Au and suggests that the reacted As is segregating to the surface. From bulk thermodynamics (p. 301 in Mayer and Lau, 1990), one would expect a saturated ternary solution (i.e., Au-saturated, with about 1% Ga and As) provided that one has a closed system (i.e., no As can escape). If As can escape, then the Ga can alloy with Au up to about 10% or the AuGa, and AuGa, phases with higher Ga content can be produced. The PES data (open system but at room temperature so that the As vapor pressure is below torr) suggests the presence of much more As than one would expect from thermodynamics. This is not surprising, since with room-temperature deposition it is unlikely that equilibrium would be reached. Cu is similar to Au; however, Ni and Pd show strong shifts to higher binding energy for the reacted As. This is suggestive of formation of strongly bonded PdjAs and Ni/As phases, as well as the Ga/Ni or GajPd phases. Again, one would expect this from bulk thermodynamics (Mayer and Lau, 1990). However, the As density still has a tendency to be higher near the surface than for Ga. This suggests phase separation with surface segregation of As. For Al, the reaction with GaAs has been well characterized by PES (Skeath et al., 1980, 1981; Duke et al., 1981; Bachrach and Bauer, 1979; Kahn et al., 1981). The reaction may be written schematically as GaAs + A1 3 AlAs

+ Ga,

(4)

i.e., the A1 replaces the Ga in the lattice, forming AlGa and liberating Ga. If any As is liberated into the Al, it will quickly react to form AIAs. Operationally this means that the GaAs near the interface is transformed into an alloy, All -xGaxAs,with either A1 or Ga on the metal sites in the covalent

10. DEFECTs IN METAL/III/VHETEROSTRUCTURES

461

lattice. For our future considerations here the key point is that free Ga but not As is produced at the interfaces. Ti and Cr are included in the metals of Table I. They fall into the class of Pd and Ni in Fig. 6, i.e., the class where both Ga and As compounds or alloys are formed. Fortunately, Weaver’s group has studied both Cr and Ti using PES. Importantly, they did in-situ thermal annealing and found that Ga but not As is expelled toward the free surface (UHV conditions) for Ti (McCants, 1988; Yu et al., 1987; McCants et al., 1988),whereas both As and Ga are held in the metal near the interface for Cr (Xu et al., 1987; McCants et al., 1988; McCants, 1988). Thus, that Ga may move out of the reactive phase, leaving excess As for Ti but not Cr. For Cr, the annealing may not change the stoichiometry near the interface. In Table I, we have indicated whether excess As or Ga might be expected from the reaction of each metal with the GaAs. This is based on the PES studies discussed earlier. The reactions of Table I are those for the situation where one has a thick (order 1OOOA) layer of metal on the GaAs. The condition of a lo00 A metal layer plus the N2 annealing gives a closed system. For Ag, Au, and Al, the reactions are very clear-cut and the conclusions straightforward. For Cr and Ti, they are much more tentative and should be considered as reasonable possibilities until more data is available. If annealing were done in an open system so that the excess As can leave, different results would be expected for Au. Such experiments were done and it was found that no change in the Fermi level occurred. Next, it is necessary to relate the changes in barrier height with annealing to reaction at the interface. The question is whether excess As or Ga at the interface is produced by the annealing. Such excess could serve as a source to modify the GaAs stoichiometry near the interface. Since we have a closed system, it will be the component that does not bind strongly with the metal that will be available to affect the GaAs stoichiometry. This is called the reaction product in Table I. For example, since As doesn’t react strongly with Au, it is the reaction product for Au/GaAs. Conversely the reaction product for Al/GaAs is Ga, since A1 reacts so much more strongly with As.

In. A Model to Explain Fermi Level Movement 3. INTRODUCTION

There is no consensus as to the mechanism that gives rise to Fermi level “pinning” and Schottky barrier formation. In fact, there is growing thought that more than one mechanism may be important, depending on the manner

462

W. E. SPICER

of Schottky barrier formation (Spicer et af., 1989; Batra, 1989).The proposed mechanisms can be placed in two classes. In the first or intrinsic class, the mechanism is operative for a perfect metal/semiconductor interface, i.e., it does not depend on defects or other departure from the ideal. A mechanism popularly called “metal-induced gap states” (MIGS) is the most widely accepted intrinsic mechanism (Spicer et af., 1989; Heine, 1965; Louie and Cohen, 1976; Tejedor et al., 1977; Tersoff, 1984; Rhoderick and Williams, 1988).In some cases it is reported that the original Schottky model (Brillson and Chiaradia, 1989) applies for specific GaAs surfaces (Spicer et al., 1979, 1980a, 1980b). This is also an intrinsic mechanism. The second class of mechanisms (Spicer et al., 1989; Heine, 1965; Louie and Cohen, 1976; Tejedor et af., 1977;Tersoff, 1984)depends on a departure from ideality at the interface, i.e., formation of interface levels due to a defective interface. The Unified Defect Model (UDM) (Spicer, 1989) and its recent embodiment, the Advanced Unified Defect Model (AUDM) or Antisite Defect Model (ADM) (Spicer et al., 1988% 1989; Batra, 1989), are based on native defects. The effective Work Function Model (EWF) (Freeouf and Woodall, 1981)depends on the work function of elemental As at the interface determining the barrier height via a Schottky mechanism (Brillson and Chiaradia, 1989). Ludeke (1989) has emphasized models that involve movement of the metal into the semiconductor forming doping levels and/or the changes in extrinsic and intrinsic levels at the interface. These various mechanisms will now be considered in order to see if they can explain the observed changes in Fermi level pinning due to annealing. It is difficult to see how intrinsic mechanisms could explain this if the interface remains perfect. To be specific, the MIGS model as it has been presented to date does not appear able to explain this. In fact, Tersoff (1984) has argued that the pinning due to MIGS is so strong that it is relatively independent of details of the interfacial region and depends mainly on the semiconductor alone. In response to these assertions of Tersoff, Zhang et al., (1985) have shown theoretically that the MIGS are insufficient to screen out strong local interface potential effects on Schottky barrier heights. In particular, using Si they showed that by replacing the first Si layer at the interface with a layer of “donor” atoms (modeled on column V atoms), they could move the Fermi level by 0.28eV toward the conduction band. In contrast, by removing the first layer of Si to create a potential barrier, they were able to shift the Fermi level by 0.27 toward the valence band maximum. Note that the total Fermi level motion by the two interface configurations is half the Si band gap. The work of Zhang et al., to our knowledge, is the first that demonstrated that MIGS and extrinsic or defect mechanisms could work together to determine the barrier height. It is also important to recognize that it was the introduction of a nonideal interface that caused the Fermi level movement.

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES

463

This reinforces one's intuition in concluding that extrinsic mechanisms must be introduced to explain Fermi level motion due to thermal annealing. In this paper we will attempt to explain Efi movement in terms of defects. However, we do not reject the possibility that MIGS may also be playing a role in conjunction with the defects. As mentioned earlier, a Schottky model has been suggested for certain specific GaAs surfaces (Brillson and Chiaradia, 1989). However, to date this has not been found to be the case for practical GaAs contacts. Let us examine extrinsic models of Schottky barrier formation. The systematics shown by the data of Table I are that the Fermi level moves toward the valence band when excess Ga is produced, and toward the conduction bacd when excess As is produced. With this is mind, let us explore the extrinsic mechailism discussed earlier. First consider the EWF model (Spicer et al., 1979; 1980a, 1980b).The basis of the model is the suggestion that the barrier height is set by work function difference between elemental As and the metal. If changes are observed as a result of changes in the As excess, we only explain them in terms of changing the fraction of the surface covered by As. One would expect the reduction of As to make the metal work function more important. A1 and Ti have low work functions compared to As (Freeouf and Woodall, 1981). Thus, for these metals one would, in the spirit of the EWF model, expect the barrier on ntype GaAs to be reduced on annealing (i.e., Efi would move toward the CBM). This is the opposite of the experimental results. Since the work function of Au used in this model is equal to or larger than that of As (Spicer et al., l979,1980a, 1980b),it does not appear possible to explain a decrease of barrier height for Au on n-GaAs due to annealing by this model. Thus, the EWF model is not attractive to explain the annealing results. The approaches of Ludeke do not, by themselves, seem capable of explaining the data at this time. However, as they become more highly developed, they may become more applicable, either independently or in conjunction with other models.

4. NATIVE DEFECTS AND THE ANTISITE DEFECT MODEL(ADM) Spicer suggested in 1979 (Spicer et al., 1979) that native defects determine the Fermi level at the interface. Allen and Dow (1982), using a theoretical approach, first pointed out that the antisite defects (i.e., an As or Ga atom on the wrong lattice site) had properties that made them strong candidates for being the dominant defects in the interfacial region. Independently, Weber et al., (1982;Weber and Schneider, 1983)found the energy levels due to the AsGa (As on a Ga site) antisite defect and reported that they corresponded

464

W. E. SPICER

remarkably well with the pinning positions found experimentally by Spicer et al., (1979, 1980%1980b) using PES and associated with native defects. Later, Monch (1984; Monch and Gant, 1983)published a detailed analysis of GaAs pinning data and identified the importance of the GaAsantisite. In 1987, Newman et al. showed that annealing data for AI/GaAs (see Section 11.1 of t h s article) could be explained in terms of antisite defects. This led to the Advanced Unified Defect Model (ADM) (Spicer et al., 1988a, 1989; Spicer, 1989). The energy levels of the ADM are given in Fig. 7. Near mid-gap are the donor levels of the AsGs antisite. In Fig. 8 is given a plot of the pinning positions found by Spicer et al., in 1979 (Spicer, 1989) and the AsGa antisite levels found by Weber et al. in 1982. As can be seen, there is strong agreement between these sets of levels (Spicer et al., 1988a).It should be noted that these AsGaantisites are now generally accepted as the levels responsible for the EL2 center in semi-insulating GaAs (see other articles in this volume). Just as for EL2, there must be a compensating deep acceptor in order for the mid-gap donor to affect n-type GaAs. We believe these levels to be the GaAsantisites near the interface. For the Fermi level to lie near mid-gap, as is usually the case, the AsGa antisites must outnumber the GaAsantisites, i.e., the GaAs must be slightly As-rich at the interface. GaAs is usually grown under As-rich conditions' so that one expects the bulk to be As-rich, and in fact there is

CBM

t

ASGA antisite

E9 = 1.4 eV

-0- -0-

Double Donor

-__

0.75 eV

-_

ADVANCED UNIFIED DEFECT MODEL FIG.7. Energy level diagram for the Antisite Defect Model (ADM). The As,, antisite double donor with levels of 0.76 and OSeV and the compensating acceptor (probably the Ga,, antisite) with energy levels below 0.5eV are shown. Both defects are located in the same spatial region near the surface. The surface Fermi level position, E,, for the free surface will be determined by the relative densities of the two defects in the near surface region. In the usual case where E f i > 0.5 eV, the density of As,, is greater than that of Ga,,.

* Hurle (1988) gives a good discussion for melt, LPE-, and VPE-grow material. MBE is grown under As-rich conditions.

465

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES PES RESULTS

F E R N MI. PINNINQ

1

N 1.2

-

PHOTO-SPIN RESONANCE RESULTS

on A ~ ANTISITE G ~

AP

7 GeAs (110) 1.00 eV

0.75 eV

Spicer et al., 1979

Weber et al., 1982

FIG. 8. The diagram to the left is taken from Spicer et al. (1979, 1980%1980b). This energy level diagram indicates the pinning positions obtained on n- and p-GaAs with very low coverages (order 1ML or less) of the indicated element measured at room temperature (Eg-1.42eV). The pinning positions are identical within experimental error to those obtained in the present work for Al, Ga, In, and Sb. The vertical lines through those data points indicate defect energy levels deduced in 1979. The right-hand diagram indicates the energy of the As,, antisite levels from the VBM measured at 8 K (E, = 1.52 eV) by Weber et al. in 1982. As can be seen, the two sets of levels are found to agree.

notable evidence that this is the case. Evidence for excess As in LEC-grown GaAs is given by the ubiquitous presence of the EL2 center (Baraff and Schluter, 1987a, 1987b). Evidence for excess As near the interfaces is given by the As inclusion on cleaved surfaces as reported by Bartels et al. (1983). It is also interesting to note that clouds of EL2 (and, therefore, of AsGa point defects) form around dislocations in GaAs (Martin et al., 1980).This suggests that the AsGa antisites find a lower energy state in the distorted lattice near the dislocation and raises the question as to whether a similar lower-energy state exists near free surfaces where the lattice is also distorted. For practical surfaces it should also be noted that As oxide is unstable in the presence of GaAs. In equilibrium, the As oxide will be transformed into Ga oxide with liberation of elemental As (Thurmund et al., 1980). This can provide an additional source of As. The differencein pinning positions of Al, In, Ga, and Cs found in 1979(Fig. 8) for n- and p-type GaAs (Fig. 8) was important because it allowed the two energy levels of AsGaantisites to be identified. In 1979 those pinning positions were thought to be those under a metal, since in each case they were found after enough metal to form a monolayer had been deposited. However, in 1983 Zur et al. found that the pinning position must be the same for n- and p type GaAs, and experimental work with thick (order lo00 A) metals on GaAs gave the same pinning positions on n- and p-type materials (Newman et al.,

466

W. E. SPICER

1987; Waldrop, 1984). Spicer et al. (Miyano et al., in preparation) have recently argued that the pinning observed in 1979 for Al, Ga, In, and Cs was that on nonmetalized surfaces.

5.

FERMI LEVELMOVEMENT DUETO EXCESS As

One value of the ADM is that it gives a mechanism by which movement of the Fermi level at the interface, Eri, can be explained. As can be seen from Fig. 7, the position of En will be determined by the relative number of AsG, double dotiors and Ga, double acceptors. Based on this, let us examine how changing the ratio of AsGato GaA, antisite densities can change the Fermi level position. The probability that an available quantum state at energy (E) is filled with an electron is given by the Fermi-Dirac function,

Note that E, is the energy at which the probability of a state being filled is one-half. At T = OK, P(E) reduces to a step function with all of the states above E , empty and those below E , filled (see for example, Kittel, 1986). Since the Fermi level will lie between the lowest-lying empty state and the highestlying filled state, we can easily find its approximate position by counting states. For example, let us assume that the density of GaAsantisites is just half of that of the As,,. The upper AsGPdonor will be empty and the lower full. As a result, Efi will lie halfway between them. If we increase the density of GaAs acceptors, electrons will move from the bottom AsG, donor level into these acceptor states, and the Eli will move toward the VBM because of the reduced occupancy of the AsGa states. At OK, Efi would move into the lower level since it would become partially empty; at higher temperatures, it would be above the lower level, but closer to the lower than the upper level. If the density of GaAsbecame larger than that of the AsGa donors, the E,, would move below the lower donor level at 0.5eV. In contrast, if the AsGadensity increased, the Fermi would move toward the CBM. Thus, the ADM gives a possible connection between Fermi level motion and departures from stoichiometry of GaAs at the interface. One thing that led to the ADM (Spicer et al., 1988a, 1989; Spicer, 1989; Weber et al., 1988) was evidence in the literature of a correlation between Fermi level motion and departures from stoichiometry. For example, Bachrach et al., (1981; Weber et al., 1988), when studying MBE GaAs with PES, found a shift in energies of approximately 0.5 eV toward the VBM when

10. DEFECTS IN METAL/III/VHETEROSTRUCTVRES

467

the conditions in their MBE growth chamber were changed from As excess to Ga excess. Svensson et al. (1984a)made measurements of Efi on MBE grown under the usual As-rich conditions. Figure 9 shows the Fermi level positions they found on n- and p-type samples. The n- and p-type samples have different pinning positions similar to those found by Spicer et al. for Al, Ga, In, and Cs deposition (Fig. 8). In addition, Svensson et al. found that by increasing the amount of excess As at the surface of the GaAs, the En could be moved toward the CBM for both n- and p-type GaAs, as the ADM predicts. Workers at the Optoelectronics Joint Research Laboratory in Japan studied Schottky barriers of LaB, on GaAs (Yokotsuka et al., 1987; Uchida et al., 1987) because the lack of strong chemical reactions of LaB, with GaAs makes it of interest for self-aligned gate technology. Studies were made of LaB, on both MBE and chemically prepared (100) surfaces. In the case of MBE, in-situ measurements of the Fermi level position at the surface were performed on thin layers (up to a few monolayers) of LaB, deposited and thermally annealed. Thick (1,800A) films were deposited on both the MBE and chemically prepared surfaces, and electrical measurements were performed to determine the Schottky barrier height as a function of annealing.

1.0 I

I

I

I

I

1

GaAs(001)

5> 0.75

0.75 0.6 0.5

w

0.4

2

0.2

> w

Annealing 0 0 Deposition 0 H n P

L

0'

I I I (4x6) C(2x8) C(4x4) RECONSTRUCTION

J

INCREASING As

FIG. 9. The surface E, of the free (100) surface grown by MBE for n-type and p-type GaAs. The three surface reconstructions are indicated on the horizontal axis. All the surfaces are Asrich, with the amount of excess As increasing from (4 x 6) to C(4 x 4). The energy levels of the AUDM model are shown. Note that these are the same as the pinning levels found on cleaved GaAs(ll0) surfaces due to metal or nonmetal depositions. (From Svensson et al., 1984a).)

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W.E. SPICER

For both the MBE thin-film studies and the thick studies, the effects of annealing were related to As loss. The results of these studies are shown in Fig. 10. Here the data on Efi are plotted as CBM-E,,, i.e., the reference point is taken as the CBM, not the VBM as in the rest of this article. In Fig. 10a, one has E,, for the MBE samples. (CBM and VBM are the conduction band minimum and valence MBE-In

Situ Annealing (Vacuum)

CBM-E,, (APProx.)

s

.-

- 0.9eV

.,%

m

- 0.7 eV 1

C(4x4) 1

2

LaS, Coverage

I

I

I

I

300 400 500 600 700 800 Annealing Temperature (“c)

IMLl Thick (leoO% LaBd Diodes I-V Measuremem

CBM-E,,

-

E

0.9eV

L.

aadepo. 300

500

700

900

Annealing Temperature (T.) T. Yokatsuka. el al., Appl. PhyJ. Lett. 50. 591 (1987) Y. Uchida. et al.. Appl. Phys. Lett. 50, 670 (1967)

FIG. 10. Surface or interface Fermi level position E,, for LaB, on GaAs. Upper panel-The Ga 2p core level position on MBE (100) GaAs due to LaB, deposition and/or annealing. The lefthand scale was obtained by assuming a 0.9 eV position after annealing. The arrows (l),(2), and (3) indicate changes due to LaB, deposition on different starting surfaces. Lower panel-The Schottky bamer heights as a function of annealing for 1,8001( or LaB, on GaAs. Open circles indicate MBE, and closed circles, chemically etched (100) GaAs surfaces.

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES

469

band maximum, respectively.) As grown, the surface is As-rich, and the E,, lies near the upper AsGaantisite level of Fig. 7. When As is removed, either by annealing or by deposition of the metal, Efi moves toward the VBM (i.e., CBM-Efi gets larger). For thick LaB, layers (1,800&, the same effect was observed on annealing for MBE (As-rich) or chemically etched samples, with the difference that the MBE samples took more annealing to produce the Fermi level motion than did the chemically etched sample. This is reasonable since a greater As excess would be expected in the starting MBE than the chemically etched samples. The systematics of the Fermi level moving toward the CBM with excess As and toward the VBM as this excess is reduced was once again found. Very important experiments have been performed by Waldrop and Grant (1987; Grant and Waldrop, 1987) in which they were able to move Efi from below mid-gap to within 0.2 eV of the CBM. The key was the evaporation of 6 to 14A of Ge in an As, atmosphere onto a clean GaAs(100) surface held at elevated temperature (200°C to 325°C). If the Ge was deposited without the As, over pressure, the Fermi level movement did not take place. The rate of arrival of Ge and As, at the GaAs surface seemed to be comparable. A LEED pattern was obtained after the Ge(As) was deposited showing that it was crystalline. In-situ studies were made of the band bending using PES. Samples were also made with thick Au or Ni overlayers for electrical measurements. PES results were compared to those obtained from I - V measurements. Figure 11 shows the E,, position (E: in the terminology of Grant and Waldrop) obtained by PES for various layers on GaAs. Without excess As (i.e., and As overpressure), Efi is in a typical position for a GaAs interface, (i.e., near mid-gap); however, with As the Fermi level position typically rose to between 1.0 and 1.2eV above the VBM (Waldrop and Grant, 1987). Once again we see a correlation with movement of Efi toward the CBM and excess As. Here E,, gets much closer to the CBM than in the cases we have discussed previously. A possible reason for this will be given presently. Figure 12 reproduces the I-V curves obtained by Waldrop and Grant (1987). The curves for Au-NiAs-9 A Ge(As) and Au-100A Te-7 A GeAs are believed to correspond to the PES films of Ge(As). The Te or NiAs layers were added to keep the Au or Ni from reacting with the Ge. For these films the Schottky barrier height on n-GaAs was approximately 0.25 to 0.4 eV, i.e., Efi was 1.0 to 1.15eV above the VBM, in agreement with the PES studies. However, without the Ge(As) layer a much different En position was found. Note the Au-GaAs case shown in Fig. 12 where Au was deposited directly on a clean GaAs surface; the barrier height was 0.89 eV, corresponding to an Efi 0.51eV above the VBM. Thus, the Ge(As) layer gives an En upward movement of over 0.5 eV.

470

W. E. SPICER GaAs

Ec 1.4 1.2

.- LL ILJ

0.6

0.4 0.2

E;aAs

8s -1

0

m

+

0

0

v)

cu

v)

cu

0

8

h h

v)

5

8 8

a 8

FIG. 11. Summary of several E; measurements. Overlayer characteristics are given at bottom of figure. Unless noted otherwise, overlayer thicknesses are nominally lOA and depositions intended to incorporate As or P in the overlayer were carried out in a lO-'torr background pressure of As, or P,. (a) Ge overlayers deposited in vacuum; (b)Ge overlayers deposited in As,; (c) Ge overlayers initially deposited in vacuum but completed with deposition in P,; (d) Ge overlayer deposited in P,; (e) Si overlayer deposited in As,. (From Grant and Waldrop, 1987).

-

An earlier example of Erimovement due to excess As and Ge is given by the work of Chiaradia et al., (1984). Using MBE techniques, the Fermi position on a GaAs(100) surface was first studied as a function of As or Ga excess in the starting GaAs(100) surface. The results are shown in Fig. 13. For a C(4 x 4) reconstructed surface (corresponding to at least a monolayer of excess As), Eri is approximately 0.7 eV above the VBM, whereas for a C(4 x 6) reconstruction (at least 2 of a monolayer of Ga), Eriis located at about 0.45 eV above the VBM. Note that these positions are close to the upper (0.75 eV) and lower (0.5eV) levels of the defect model and the AsGa antisite defect, with excess As putting Efi near the upper level and excess Ga putting En near the lower level.

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES

471

10-3 >200A NiAs -108,Ge

10-4

10-5

-5 lo-’ v)

10-6

-10081 Te -1 OA Ge

10-8

-1 OA Ge

n

10-9

10-10

10-11 I

v (volts) FIG. 12. Representative I - V data for a selection of contacts to GaAs that have a variety of structures (contact area = 5.07 x cm’).Multilayered contact structures are shown schematically on the right. (From Waldrop and Grant, 1987.)

Also shown in Fig, 13 is Efifor a C(8 x 2) reconstruction that has excess As, but less than the C(4 x 4) surface. As can be seen, the Fermi level on this free surface is near but lower than that on the C(4 x 4) surface. The difference is in agreement with the prediction of the ADM. There are also data in Fig. 13 for an n-type GaAs(l10) cleaved surface. Here the original position of the Fermi level is at the CBM. This is because of the perfection of this surface, which contains few defects, and the fact that it reconstructs so that the dangling band surface states are swept out of the band gap (Spicer et al., 1976;van Laar and Huijser, 1976), thus leaving insufficient surface states to move Efi from the bulk position. In Fig. 13, the effect of adding Ge to the various GaAs surfaces is also shown. For all GaAs(100) surfaces, the movement is toward the CBM, however, the more As excess present in the starting surface, the greater the movement. These results are summed up in Fig. 14, which gives a band

W.E. SPICER

472

O(ll0)

0

3

6

9

12

Ge Thickness (A)

FIG. 13. Fermi level movement due to adding Ge along to the surface. The greater the amount of excess As in the surface (seetext), the greater the Fenni level movement.

FIG. 14. Schematic of the energy bands and the Fermi-level position at the interface on a 10-A scale. The valence-band discontinuity is the same at the interface between the various surface reconstructions of GaAs(100)surface and Ge. However, the Fermi level position at the interface depends on the surface stoichiometry. This observation clearly demonstrates the independence of the interfacial Fermi level and the valence-band discontinuity.

diagram for the GaAs/Ge interface including the E,, positions for the three different starting GaAs(100) faces. In Fig. 15 we show the Fermi level development for Ge deposition in an As, ambient. The data in Fig. 15 suggested to Chiaradia et al. that the Fermi level movement with Ge deposition was associated with As moving into and doping the Ge. The work of Monch et al., (1982) indicates that such As

10.

DEFECTS IN

METAL/III/VHETEROSTRUCTURES

1

-----

GaAs (100)IGe

- - - - E,

/lf-*

1.o

A

473

0

1

-2 w

0.5 0 C(4x6)

A C(Px8)

0 C(4X4)

----------------_-_E"

0 0

I

I

I

I

3

6

9

12

Ge Thickness (A)

FIG. 15. The evolution of the Fermi level during the interface formation with Ge. The difference between this figure and Fig. 13is that Ge is deposited with As. The As source was open. The figure when compared with Fig. 13 shows that the presence of As influences the final E, position. Effor the Ga-rich, (4 x 6) surfaces moved closer to the conduction band by more than O.lOeV. E, for the As-rich, 44 x 4) only slightly moved toward the conduction band because E, is already close to the top of the Ge conduction band in Fig. 13 (Mahowald and Spicer, 1988).

diffusion (and to a much lesser extent Ga) takes place even without the presence of excess As at the original surface. The preceding material gives additional strong empirical correlation between excess As and movement of the Fermi level. We suggest that this might be explained in detail by the ADM; however, the reader should remember that these empirical correlations are experimental results that are independent of any model. Furthermore, even though I show that these results can qualitatively be explained by the ADM, I do not show this explanation to be unique. Figures 16a and b indicate our suggestions for the interpretation of the data of Waldrop and Grant (1987; Grant and Waldrop, 1987)and Chiaradia et al., (1984). Because of the lattice match between Ge and GaAs, the defect density near the interface may be reduced. However, as long as Ga,, antisites or other low-lying acceptors are present, the Fermi level can not move much above the upper AsGa antisite level. Even if the population of AsGaantisites is much larger than that of the GaAsantisite, there will be a density of holes in the upper (0.75eV) AsGa antisite level equal to twice the density of GaAs antisites (assuming that these antisites are double acceptors).Because of this, it will be difficult for the Fermi level to move much above the upper AsGalevel (see Eq. (5)) unless there is a source of electrons to fill these states (as shown in Fig. 16a). For the free surface, a clear source of such electrons are the donors

474

W.E. SPICER Partially filled AsGastates

0.75 eV Fermi Level

Empty Ge Donor Slater

Fermi level

FIG. 16. An explanation of Fermi level motion in terms of the Antisite defect Model. The upper and lower panels give band diagrams before and after adding an N-doped Ge overlayer and strong ndoping of the GaAs adjacent to the interface. The Fermi level moves upward because the interfacial states near mid-gap are filled by electrons from the new depleted region and the ndoped Ge. For simplicity the band bending in the upper panel is not shown. The lower panel sbows schematically the change in band bending.

that are emptied to produce band bending and the depletion, n d . In addition, if an n-doped Ge layer is present as in the experimentsjust discussed, then it also may contribute electrons, nd, to fill the empty interfacial states. The density of empty AsGastates, n,, will be given by n, = 2N(Ga,,) - n d - ?I,,

(6)

where N(GaAs) is the density of GaAs antisites and n, is the density of electrons donated from the doped Ge overlayer. nd

= JhssqNd

%b

(7)

in MKS units. Here ess is the permittivity of the semiconductor (ess = Ke,, where K is the dielectric constant and e, is the permittivity of free space), Nd

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES

475

is the density of uncompensated donors (for n-GaAs), 4 is the magnitude of the electron charge, and V , is the magnitude of the voltage drop across the depletion region, i.e., the amount of band bending, If n, in Eq. (6) is less than zero, it simply means that all of the available defect states have been filled with electrons, and E,, will move above the highest-lying defect level toward the CBM. In order to find the exact position of Efi, one would have to solve properly Poisson's equation with the correct parameters. This situation is shown schematically in Fig. 16b. Studies similar to those of Ge on GaAs have been performed by Mahowald et al. (Mahowald and Spicer, 1988; Marshall et al., 1989; Lau et al., 1990) on InP. There is an important difference,however. No P was added to the Ge for n-type doping. Rather, the PES studies (Yokotsuka et al., 1987; Uchida et al., 1987; Mahowald, 1987; Mahowald et al., 1987) suggested that the Ge slightly attacked the InP, producing primarily P in the InP and In segregated to the surface. The P in the Ge is believed to leave it highly n-doped. Experimental data for the Efi position as a function of Ge coverage are presented in Fig. 17. The starting InP surface was (1 10)cleaved. As can be seen for both n- and pInP, Efiinitially moves to a position about 0.4eV below the CBM. Then, for higher coverages, Efi moves toward the CBM. Mahowald et al. (Mahowald, 1987; Mahowald and Spicer, 1988; Mahowald et al., 1987) modeled these results in terms of Poisson's equation, charge neutrality, and certain assumptions. We will now outline the principal assumptions. For the first 0.5 A of Ge deposition, the defect concentration in the InP is assumed to increase at a linear rate of 3 x 10' defects/A of Ge. For Ge thickness greater than 0.5 A, it is assumed that no new defects are formed near the InP/Ge interface. For Ge coverages greater than this amount, it is assumed that P donors are added to the Ge at a rate of 3 x IOl3 donors A-' cmW2,which is equivalent to 21.5 x lozodonors/cm3. The defects were 1

w

>

!-- >

o

zg -0.4 k!g

Lut

0 5 -0.8 +

z

Maximum

GellnP (1 10)

-1.2 0

1

2

3

4

COVERAGE (ML Ge)

FIG.17. The data (dots and heavy solid line) for the Ge/InP fermi energy are shown above. The shaded line is the model evaluatedwith the donor and acceptor energies appropriate for InP (1.1 and 0.9eV from the VBM).The defect density is 3 x 1013cm-2A-' (same as for GaAs), and the doping donor density is f013cm-2A-1.These values were chosen to fit the data.

476

W.E. SPICER

taken to be a donor at 1.1 eV and an acceptor at 0.9eV above the valence band maximum. In the AUDM this will be equivalent to column V antisites outnumbering the column 111 antisites by two to one, so that the highest antisite donor state would be completely empty and the lowest completely filled. The shaded line in Fig. 17 indicates the calculated Fermi level position as a function of Ge coverage based on these assumptions. As can be seen, the calculated Efi positions closely follow the experimental data. This at least demonstrates that such data can be modeled in terms of a defect model such as the ADM. Preliminary work indicates that this model also works for GaAs. 6. OHWCCONTACTS ON n-GaAs

The reader has probably realized, as did the authors quoted, the importance of this work to development of ohmic contacts on n-GaAs. We will now address this question. Ohmic contacts on both n- and p-GaAs have always presented a problem. In recent years this has become more serious for some GaAs ICs because of reduced dimensions. Through most of the history of GaAs, the approach to ohmic contacts was almost solely empirical. It is only in recent years that a more scientific approach has been taken for ohmic contacts. The work of Waldrop and Grant (1987; Grant and Waldrop, 1987) referred to earlier is a good example of this. The work of S. S. Lau and his coworkers (Marshall et al., 1989; Lau et al., 1990)on the Pd/Ge/GaAs contact is another example of this, which has been carried forward to establish a new ohmic contact technology on n-GaAs. The contact often being replaced by Pd/Ge/GaAs is the NijAu/Ge/GaAs contact. One difficulty with that contact is that the metal/GaAs interface is not atomically smooth but contains irregular protrusions that can extend hundreds of angstroms into the GaAs. These protrusions not only can penetrate and thus destroy thin device structures, but they also make it very difficult to use electron microscopy and related tools to study the interface. One of the advantages of the Pd/Ge/GaAs contact is that it forms smooth interfaces without the protrusions. This makes it possible to analyze the interface in detail (see Fig. 18). It has been established that the GaAs within about 40A of the interface is regrown and is highly doped with Ge (Marshall et al., 1987, 1989; Lau et al., 1990) after the contact has been thermally processed. The top panel in Fig. 18 shows the structure of this contact. There are arguments against the Ge layer being highly doped with As (Marshall et al., 1989; Lau et al., 1990); however, we believe that it is best to keep this possibility open for the purpose of this discussion. The bottom panel in Fig. 18 gives a band diagram for this contact. The

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES PdlGelGaAs

411

Ohmic Contacts and alloys

~

*#$ Regv;:$A ;s

E,

- 0.3 ev ~

/

-

Tunneling Region

Thermionic Emmision over Barrier c

1ll

+

,- 0.3 ev

FIG. 18. The Pd/Ge/GaAs ohmic contact. The upper panel shows the locations of the various parts of this contact. The middle panel gives a schematic of the contact resistivity data of Lau et a!. This indicates a barrier height of about 0.3 eV. The lower panel indicates the suggested band diagram for this contact.

Schottky barrier between the GaAs and the Ge is shown to be 0.3eV, in agreement with the data of Lau and co-workers for the resistivity of the contact as a function of temperature (see the middle panel of Fig. 18 for schematic drawing of this). This means that the Fermi level has moved from its typical position near mid-gap to within 0.3eV of the CBM. Thus, the ohmic behavior is due to both the heavy doping of the GaAs giving a tunnel junction (see the middle panel of Fig. 18) and to a reduced barrier height due to the Fermi level movement. Previously, it has usually been assumed that the Fermi level was well pinned near mid-gap and that the tunneling had to be thought a much larger barrier than that reported for Pd/Ge/GaAs. The results and arguments given here indicate that this is not the case and that Ef, can be moved if the optimum conditions are achieved. (Recent work by Herrera-Gomez, et ul., J . Vuc. Sci. Technol. A 1029- 1034 (1992), shows that the flat region in log P vs. 1/T can’t be explained simply in terms of tunneling.) We would explain this contact in terms of the mid-gap interface states being completely filled by electrons from the strongly doped GaAs in the depletion region and As doped Ge in accordance with Eq. (6). On an atomic level, we would use the ADM to explain this. Since Ge and GaAs have an

478

W. E. SPICER

almost perfect lattice match and the heavily doped GaAs next to the Ge has been regrown in the process of forming the contact, we suggest that the density of interfacial defects has been reduced, i.e., n, in Eq. (6) has been reduced, by lowering the density of antisites. Further, we assume that enough electrons go into these interface states from the depletion region, nd, and the doped Ge, region n,, to completely fill the mid-gap interface states. As a result, Ef1moves up to near the Ge CBM, which is about 0.2eV from the GaAs CBM. Note that in Eq. (6),it is the density of GaAsantisites, N(GaAs), not the total density of antisite defects, which determines n,. One would expect a reduction in this density if the GaAs regrowth took place under strongly Asrich conditions. This may be case here for two reasons. First, since the bulk GaAs is As-rich and, as discussed earlier, excess As seems to segregate to interfaces, this will also produce a source of excess As. A second source may be produced because the Pd (which is originally in contact with the GaAs thermal anneal) appears to react with GaAs, releasing As. The reader’s attention is also directed to the relationship of this contact to the work of Waldrop and Grant and the Xerox group on the motion of the Fenni level due to As-doped Ge on GaAs. This gives direct evidence that the Fermi level can be moved in a closely related system. Note also that in this previous work, one depended solely on the doped Ge to provide the electrons to generate the Fermi level movement. However, with the ohmic contact, one has not only this source of electrons, but also the electrons from the highly doped depletion region that is formed during the thermal anneal (see Eq. (7)). It is reassuring that so much concerning the Pd/Ge/GaAs contact is consistent with the ADM; however, one must always remember that we have established consistency and not uniqueness. Other studies are now underway to test the application of the model to this ohmic contact more quantitatively and to test materials parameters critical to the explanations given earlier. The attractiveness of the ADM lies not in its ability to explain one contact or observation, but in its ability to explain a large range of behavior, not only at metal-GaAs interfaces but also at insulator-GaAs interfaces. We will examine one such situation in a later section.

7.

FERMI LEVELMOVEMENT DUETO EXCESS Ga

The last set of experimental data we would like 1 discuss in this sectia is that relating to Ga on GaAs. If Ga deposition could lead to an increase in GaAsantisite acceptor density, it would move Efi toward the VBM. Strong movement of E,, toward the VBM due to evaporation of the thin Ga layers for PES studies has not been observed. However, the studies of Cao (1989; the Ga data can also be found in Spicer et al., 1989; Heine, 1965; Louie and

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES

479

Cohen, 1976; Tejedor et al., 1977; Tersoff, 1984) show a trend in that direction. Bolmont el al. (1982) has reported that new states below the Ef are created by Ga deposition. This is consistent with GaAsantisite formation. However, the situation is quite different for thick layers of Ga deposited in various ways on GaAs. Table I1 summarizes results from five electrical studies of barrier heights for thick Ga on GaAs. Four of these indicate Ef positions surprisingly close to the VBM. This data is striking in that the barrier heights on n-GaAs are perhaps the highest (about 1.1eV) reported for any metal on GaAs. In the past, changes in barrier with metals have been found to correlate with electronegativity, i.e., E,, positions well away from the VBM for electropositive materials. On n-GaAs, lower electronic negativity is found to correlate with low eIectronegativity. Metals such as A1 and In are very close to Ga in electronegativity and have barrier heights of about 0.8 eV on n-GaAs. This is in contrast to the values near 1.1 eV for the thick Ga/GaAs samples. The highest-electronegativity metals such as Au and Pd have lower barrier heights (0.9- 1.0 eV). However, a word of warning is necessary. Problems of leakage plagued I- V measurements for the Ga/GaAs Schottky barrier, and some of the results in Table I1 are from C-V measurements, which are not as reliable. The I-V curves of Reinke and Meming are excellent; however, their evidence for excess Ga is not direct. MBE techniques may be the best suited for such studies. In fact, the studies of Svensson et al., (1984b) are perhaps the most satisfying of those included in Table I1 because their methods of forming the Ga/GaAs seemed most cleancut. However, in order to understand Ga/GaAs more completely, it is necessary that well-controlled experiments be done in which both the electrical properties of the contacts and the arrangement of atoms near the interface are sufficiently well specified. TABLE I1 VARIOUSREPORTS OF THE ELECTRICAL CHARACTEIU~TIC~ OF Ga CONTACTS ON GaAs" Ohmic contact on p-GaAs: R. Z. Bachrach and A. Bianconi, J. Vuc. Sci. Technol. 15,525 (1978). Ohmic contact on n-GaAs: J. Woodall and C. L a w , J. Vac. Sci. Technol. 15, 1436 (1978). 1.05eV Schottky barrier height on MBE, As-rich, (100) n-GaAs for thick Ga layers: S. P. Svensson, J. Kanski, and G. Anderson, Phys. Rev. B 30,6033 (1984). 1.15-1.2 eV Schottky barrier height for electrochemical metal depositions on n-GaAs: Related to metallic Ga which they believe is formed: R. Reinke and Meming, Sutf Sci. 192, 66 (1987). 1.0-l.leV Schottky barrier height for thick Ga on GaAs (110): A. B. McLean and R. H. Williams, Semicond. Sci. 7'echnol. 21, 654 (1987). "A summary of published results on Ga/GaAs contacts: By comparison with other metals of comparable electronegativity, one would expect a barrier height of only about 0.8 eV on n-GaAs (Stirland et ul., 1985). In contrast, the reported barrier heights are about l.leV. This is higher than those reported for any other metal.

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The data presented in Table I1 and discussed above can be explained in terms of the ADM (see Fig. 7). If Ga is deposited in such a way that the population of GaAsantisites is sufficiently enhanced, then it is reasonable that the Fermi level would move into the vicinity of the GaAsantisite levels, i.e., near the VBM as observed. In this section we have outlined the ADM and shown some of the data that seem to be consistent with it. In the next section we will examine evidence for departures from stoichiometry at the interface and see how this relates to “predictions” of the ADM. We put predictions in quotes because some of the data in the next section played a role in development of the ADM.

8. MEASUREMENTS OF DEPARTURES FROM STOICHIOMETRY AT THE INTERFACE AND THEIR RELATIONTO THE ADM The ADM predicts certain departures from stoichiometry at the GaAs interface. For Efi to lie above approximately OSeV, one needs a greater density of AsGnthan GaAsantisites and, thus, an As excess. In order for the AsGspopulation to dominate, it is likely that a much larger As excess exists at the interface than is represented just by the excess As in antisites. This is a situation similar to the enhanced As and EL2 (i.e., As antisite) densities at dislocations (Stirland et a/., 1985). Earlier in this article, changes in Schottky barrier height, and thus Efi on annealing, have been correlated with changes in stoichiometry expected in terms of interfacial chemistry. (See, for example, Table 1.) It is important to test experimentally whether such correlations actually exist. Liliental-Weber and co-workers have used energy dispersive xray (EDX) analysis to examine the interfacial stoichiometry (Liliental-Weber et al., 1986, 1989; Liliental-Weber, 1987) for several metals (see Table 111). Pallix et al. (1987) have used a new technique, surface analysis with laser

ARSENIC

Metal Au Al Cr TiSi,

TABLE 111 EXCESS AT THE SCHOTTKY BARRIER INTERFACE

As Excess after Metal Deposition, EDX Result

Yes Yes Yes Yes

Changes in As Excess Due to Annealing Predicted

Observed

increase increase decrease decrease none none not done

AND CHANGFS WITH

ANNEALING

Direction of Movement of Fermi Level Predicted

Observed

toward CBM toward CBM toward VBM toward VBM none none not done

10. DEFECTS IN METALPIIFHETEROSTRUCTURES

481

ionization (SALI), to study the stoichiometry of GaAs/Au interfaces before and after annealing. Let us first examine the SALI results. There is a great difficulty in examining interfaces for excess As if that As is not firmly tied into the lattice. The reason for this is the low vapor pressure of As combined with its high energy of ionization. As a result, excess As that may be loosely bound to the GaAs is easily desorbed without ionization. Unfortunately, the tools of surface analysis that might be used to detect the excess As impart energy into the surface region, which can cause such desorption. The key to the SALI technique is that it ionizes any atoms that leave the surface by means of a laser. Thus, it is peculiarly sensitive to loosely bound As. The SALI results for the GaAs/Au system are given in Fig. 19 (Pallix et al., 1987).As can be seen, a strong As build-up at the interface after the annealing is found, in qualitative agreement with expectations from the ADM. The EDX method used by Liliental-Weber is based on using a very fine, high-current-density electron beam to excite the core levels of atoms so that they emit characteristic x-rays. It has a lateral resolution of about 100 A. One would expect such a beam to cause desorption of loosely bound As. In essence this is what was found. Excess As was found, but this decreased as the electron beam was left on one spot. The key parameter is the ratio of As to Ga x-ray luminescence intensity. When the beam was placed at the GaAs/Au interface, an increase in the As/Ga ratio was seen over that for the GaAs away from the interface. The excess As signal decayed with time until it returned to the value seen from the GaAs away from the interface. As Table I11 shows, excess As was always found at the interface after metal deposition (in agreement with the ADM). After annealing, the increase or decrease of As excess was found to correlate with Fermi level movement in a way consistent with the ADM (see Table 111).There is an unexplained discrepancy between the SALI GaAs/Au and the EDX results. EDX showed an As excess after Au deposition but before annealing. However, as can be seen from Fig. 19, there is no clear evidence of this from the SALI results. This may be due to detailed differences in the two techniques. However, it emphasizes the fact that much more work should be done in studying departures from stoichiometry at GaAs interfaces in order to be certain of the results. In this section we have shown an experimental correlation between departures from stoichiometry at GaAa/metal interfaces and Fermi level movement. This strengthens the suggestion that Fermi level position, and thus the electrical properties at interfaces, may be controlled by departures from stoichiometry. However, it must be recognized that the presence of excess As or Ga at the interfaces alone is insufficient to explain Fermi level movement in terms of antisite defects. One must assume that the excess leads to an increase of As, or Ga,, in the interface region of the GaAs crystal. This

482

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I

I

I

I

I

SPUlTERING TIME (sec)

G+--

0

&-

750

150

SPUlTERING TIME (sec)

FIG. 19. SALI analysis of Pallix, Becker, and Newman (1987) for 1,OOOA of Au on GaAs. Note in particular the region at the Au/GaAs interface. The upper panel gives the results for an unannealed sample. There is little As or Ga in the Au. The lower panel gives the results after thermal annealing. The most striking change is the large increase in As as the sputtering approaches the Au/GaAs interface (indicated by the arrow). G a and, to a less extent, As are also seen in the Au and at the outside surface.

means that As or Ga must be incorporated in the GaAs as antisite defects. The kinetics of this is an important question that has not been addressed in this paper but that must be addressed in the future. It is easier to understand how this incorporation can take place in the annealing experiments, rather than experiments in which Ga is simply deposited on a GaAs surface held at room temperature. This may explain some of the difficulties in studying such

10. DEFECTS IN METAL/III/VHETEROSTRUCTURE~

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deposition of Ga on GaAs. MBE is very important, since it provides a way of more directly incorporating excess As or Ga into the lattice. The limited number of results with this method provide one of the best sets of evidence of Fermi level motion associated with departures from stoichiometry. Much more work is needed on the kinetics of antisite inclusion in the interface region.

IV. GaAslInsulator Interfaces Two types of interfaces are critical in order to bring GaAs devices and integrated circuits under control. The first, the GaAs/metal interface, has been treated in the previous sections. In this section we will touch on the second type of interface-the GaAs/insulator interface. In this category we include all GaAs surfaces not covered by metals, whether the insulator is consciously deposited or is a result of GaAs oxidation. In the 1970s a strong effort was made to develop a MOS technology for GaAs similar to that of Si. This failed. It became clear that the chemistry between GaAs and its oxides did not lead to a chemically stable, defect-free interface (Wieder, 1985; Thurmond and Schwartz, 1980; Spicer et al., 1980a).As a result, the hope of a GaAs MOS technology was abandoned and work concentrated on a field effect transistor (FET) technology in which a Schottky barrier or a p - n junction provided the control element for the device. However, even with these technologies, there are GaAs surfaces not covered by the control structures. These surfaces plague GaAs devices and ICs for several reasons. For example, they usually have a very high surface recombination, which can degrade device operations. In addition, it is hard to control this potential and this can lead to “sidegating” and other unpleasant occurrences that disrupt device and/or IC operation. In recent years three new and promising approaches have come forward to provide better control at such surfaces. These may also lead to MIS technologies. In the first of these a heterojunction is made with a higher bandgap semiconductor that has a sufficiently good lattice match so that a good heterojunction is formed. Al,Ga, - .As/GaAs and GaAs/ZnSe are examples (Qian et al., 1989). Here, it has been shown that interface (surface) state density can be kept relatively low. The main difficulty with such an approach is the difficulty in forming a sufficiently ideal heterojunction and the limitation due to the relatively low band gap of the “capping” semiconductor. A second approach is just in its early stages (Fountain et al., 1989).This starts with the deposition of a Si layer on the GaAs. Then an insulator (for example, SiOz or Si,N,) is grown. Again, this shows promise, but it is in the early

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stages of development and testing. In the third approach, striking success in reducing surface recombination has been achieved (Yablanovitch et al., 1989; Sandroff et al., 1987b) by treating GaAs surfaces with the sulfur compounds Na2S H 2 0or (NH&S. We will discuss this in more detail, since a number of measurements have been made of the Fermi level position and changes therein due to such treatments. Use of the sulfur passivation approach has recently been reviewed by Spindt and Spicer (1990). As emphasized in that paper, the principal criterion for passivation by this approach is the reduction of surface recombination by more than two orders of magnitude. It was first suggested that the treatment removed interface states so that the Fermi level at the interface moved from mid-gap to the bulk Fermi level position (Qian et al., 1989)near the CBM. However, measurements of Fermi level position using a number of different techniques showed that this was not the case (Besser and Helms, 1988, 1989; Liu et al., 1988a, 1988b; Hasegawa et al., 1988; Spindt et al., 1989a, 1989b). Rather the treatment moves the Fermi level closer to the VBM on n-GaAs. Spindt and Spicer(1990b)have suggested a model to explain this behavior. This model is based on the ADM and suggests that the sulfur treatment removes excess As and thus AsGa antisites from the surface. As we established in a previous section, if the AsGa density is reduced relative to the Ga, antisite density, the Fermi level must move toward the VBM in accord with the experimental observations. Results from Besser and Helms (1988,1989;Besser 1989)for the Fermi level position as a function of surface treatment are shown in Fig. 20. As can be seen, the Fermi level moves from the vicinity of the upper (0.75 eV) level of the AsGa antisite level to the vicinity of the lower (0.5eV) AsGa antisite level CBM

VBM

FIG. 20. Results for the Fermi level position as a function of sulfur treatment. Surface Fermi level position (labeled "surface Potential" in the figure) of GaAs after various treatments as obtained by Besser and Helms (1988,1989). The Na,S and (NH4),S treatmentsmove the Fermi level toward the valence band, i.e., increase the band bending rather than produce flat band conditions,

10. DEFECTS IN METAL/III/V HETEROSTRUCTURES

485

because of the sulfur treatment. As Spindt and Spicer noted, this results not only in the change in band bending, but also in the AsGa antisites becoming positively charged. With the interface Fermi level near OSeV, one has the bands bending upward with a barrier of about 0.9eV that electrons must overcome to reach the surface. Holes will be swept into the interface by the band bending, but they will be inhibited from recombining with electrons on the mid-gap AsGa states, since this double donor is compensated so that it has a single positive charge and will repel them. Thus, surface recombination will be reduced. Figure 21 shows the change in band bending found by a number of workers Before Sulfur Treatment

E, -E,,,M-0.7eV

-Large density of AS,.

antisites

-Upper AsGl level filled

-As,,

-4 After Sulfur treatment

are nuetral-good hole trap

A

...........\.............

Ef-Em-0.5%V

I 0

-Reduced As,, Density and A s G a l G ~ , ratio -Most AsGl are positively charged-poor hole trapping.

FIG. 21. Changes in band bending and Fermi level position due to sulfur treatment. Note that the treatment produces an about 0.2 eV increase in band bending. An explanation of this in terms of the ADM is also shown. A decrease in the number of Aso, relative to GaAsantisites moves Ef to near the lower As, level at 0.5eV. This inhibits surface recombinations by increasingthe band bending and charging the Aso, recombination centers positively so that they will repel electrons.

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using diverse experimental approaches (Spindt and Spicer, in press) and indicates how this is explained in terms of ADM. The key to application of the ADM is the assumption (supported by some experimental findings-see Spindt and Spicer, in press) that the AsGa to GaAsratio is reduced by the sulfur treatment’s preferential removal of As from the GaAs surface region. As explained in Section 111, this will cause the Fermi level to move toward the VBM because of depletion of electrons from the AsGa donors by the GaAs acceptors. The fact that Efi moves approximately to the lower AsGa level at 0SeV indicates that the AsGa is a little more than half-compensated. This results in the AsGa defect having a positive charge, which repels holes and thus inhibits the surface recombination as discussed earlier. Figure 22 shows surface DLTS results from Liu et af. (1988a) before and after the sulfur treatment. Note that before treatment there is a large density of states centered near 0.85 eV. This we associate with the upper AsGa level. After the treatment, the dominant levels are at 0.3 eV above the VBM. This we associate with the GaAslevels. Much more must be done before the “free” and/or insulator/GaAs surfaces and interfaces can be brought under sufficient control. However, the sulfur example illustrates the importance of Fermi level movement in this. We would argue that one must measure and understand the physics and chemistry driving Fermi level motion at the interface and the consequences of

c

E T - EvBM= 0.85eV

0.3eV

100

200

300

400

Temperature (K) FIG. 22. Surface DLTS for (100) GaAs after Liu et al., (1988b).The untreated sample shows a trap at about 0.85eV (dashed curve). In the treated sample (solid curve) the 310K signal disappeared and a new, weaker signal at about 0.3eV above the V B M was found.

10. DEFECTS IN METAL/III/VHETEROSTRUCTURES

487

such movement before control can be obtained of these interfaces. We also note that interface properties such as recombination can be improved without obtaining ideal passivation, which includes a flat band condition.

V. Conclusions and Discussion This article gives strong evidence that the Fermi level at GaAs metal interfaces can be varied by a good fraction of the band gap. For instance, Waldrop and Grant (1987; Grant and Waldrop, 1987)were able to move the Fermi level with about 0.3 eV of the CBM, and Svensson et al. (1984b) were able to move it to within about 0.3eV of the VBM. Many other examples have been given here of Fermi movement associated with special deposition conditions, thermal annealing, or other treatment. A surprisingly consistent thread runs through most of the work described. This is a correlation of the change of GaAs stoichiometry at the interface with the direction of motion of the Fermi level. When the Fermi level moves toward the CBM, an increase in As excess is found. Fermi level movement toward the VBM is associated with an increase in the relative amount of Ga at the interface. Using this, the interfacial chemistry between the metal and GaAs can be used to predict Fermi level movement due to thermal annealing. A model for the electrical properties of the interface, the Antisite Defect Model (ADM) (Spicer et al., 1988a) has been introduced to explain the changes in Fermi level. This model is based on the conclusions that AsGa antisites and GaAsantisites provide the energy levels that are dominant in determining the Fermi level position (Fig. 7). The AsGais a double donor with levels at 0.75 and 0.5eV above the VBM. The GaAsantisite is a double acceptor with levels near 0.3 eV. If we assume that the relative numbers of these two defects change in accordance with changes of stoichiometry near the interface, a large number of experimental results can be explained. Much more work must be done to fully test the correlations made here. The ADM must also be tested further. However, the agreements with experiments are sufficiently strong that one might use the correlations and/or the ADM to attempt to solve practical problems. Ohmic contacts are one such problem for GaAs device and IC development and applications. It is the ohmic contact that limits many devices. Most work developing ohmic contacts to date has been strongly empirical. Perhaps the ideas presented might be applied in an attempt to develop better ohmic contacts. Ohmic contacts on GaAs are usually thought to be tunneling, i.e., even though a large Schottky barrier is present, the doping of the GaAs near the interface is so high that a narrow depletion layer is formed through which the carriers

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can tunnel. This demands very high doping due to contact formation. However, if the Fermi level can be moved in a favorable direction, the ease of tunneling will increase exponentially. Thus, a combination of Fermi level movement and doping may be essential for developing a better ohmic contact technology. This approach does offer the possibility of new ways to think about and develop ohmic contacts. As indicated in Section 111.4, this approach seems to explain the Pd/Gd/GaAs ohmic contact on n-GaAs. Most of this article has concentrated on metal/GaAs interfaces. Another set of systems in which better control is needed are the GaAs/insulator interfaces. These were briefly discussed, and it was shown that data on sulfurtreated interfaces could also be qualitatively explained by antisites and the ADM. There is a need for much more work on such interfaces to bring them under control and stop them from limiting the usefulness of GaAs. Above all, there is a need to move from strongly empirical approaches to approaches in which sufficient characterization is done to allow us to understand and model these interfaces.

Acknowledgment Useful discussions with Nate Newman, Eicke Weber, Zuzanna LilientalWeber, Ken Miyano, Renyu Cao, Tom Kendelewicz, Christ Spindt, Paul Meissner, and S. S. Lau are gratefully acknowledged. This work was partially supported by DARPA and ONR through Contract # NOOO14-89-5-1083and by AFOSR through Contract # AFOSR-86-0263, and ONR through Contract # NW14-92-J- 1280.

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Kittel, Charles (1986). Introduction to Solid State Physics, 6th Ed. Wiley, New York. Lau, S . S., et al. (1990).Mat. Res. SOC,Symposium, Spring, 1990. Liliental-Weber, Z. (1987). J. Vac. Sci. Technol. B5, 1007, and references therein. Liliental-Weber, Z., Weber, E. R., Newman, N., Spicer, W. E., Gronsky, R., and Washburn, J. (1986). Defects in Semiconductors (J. von Bardeleben, ed.), Materials Science Forum, Vol. 1012, pp. 1223-1228. Liliental-Weber, Z., Newman, N., Washburn, J., and Weber, E. R. (1989). Appl. Phys. Lett. 54, 356.

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Liu, D., Larkins, E. C., Zhang, T., Chiang, T. T., LaRue, R. A., Sigmon, T., Spicer, W. E., and Hams, J. S., Jr. (1988b). Proc. 15th Int. Symp. on GuAs and Related Compounds, Atlanta. Institute of Physics, Bristol. Louie, G., and Cohen, M. L. (1976). Phys. Rev. B 13, 2461. Ludeke, R.(1989). Metallization and Metal-Semiconductor Interfaces, NATO AS1 Series, Series B, Physics, Vol. 195 (I. B. Batra, ed.), p. 39. Plenum Press, New York. Ludeke, R., and Landgren, G. (1986). Phys. Reo. B 33,5526. Ludeke, R., Chiang, T. C., and Miller, T. (1983). J . Vac. Sci. Technol. B1, 581. Mahowald, P. H. (1987). Ph.D. dissertation, Stanford University. Mahowald, P. H., and Spicer, W. E. (1988). J. Vac. Sci. Technol. B6, 1539. Mahowald, P. H., Kendelewicz,T., Bertness, K. A., McCants, C. E., Williams, M. D., and Spicer, W. E. (1987). J. Vac. Sci. Technol. Bs, 1258. Marshall, E. B., Zang, B., Wan& L. C., Jiao, P. F., Chen, W. X.,Sawada, T., and Lau, S. S. (1987). J . Appl. Phys. 62, 942. Marshall, E. B., Laq S. S.,Pamstrom, C. J., Sands, T., Schwartz, C. L., Swartz, S. A., Harbison, J. P., and Florez, L. T. (1989). Mat. Res. SOC.Symp. Proc. 148, 163. Martin, G. M., Farges, J. P., Jacob, G., and Hallais, J. P. (1980). J. Appl. Phys. 51, 2840.

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Index

A Acceptors, 93 Acceptor passivation, 161-163 Ag impurities acceptor level, 218,221-223 solubility limits, 190 AlAs deep states, 364 AlGaAs deep level defects, 366-369 DX centers, 237-285 growth defects, 414 AlGaInAs deep level defects, 375 AlGaInP deep level defects, 375 DX centers, 238 AlInAs deep level defecrs, 373 DX centers, 238 AlInP deep level defects, 373 Antiphase domains, 385 Antisite defect model, 463-465 Annealing GaAs on Si, 434ff semi-insulating GaAs, 110 site switching of impurities in GaAs, 179 Arsenic antisite defects (see also EL2), 26, 31, 72ff, 109, 176 EPR studies, 72ff annealing, 49.62, 179 metastability in, 37,38,43,50,68ff ODENDOR studies, 74 photocapacitancequenching, 68 photoluminescence,66 zero-phonon line, 65,76,77

As interstitials in GaAs, 28, 33, 168 As-precipitate model, 113 As vacancy, 24,30, 168 Au impurities acceptor level, 218,221-223 donor level, 221-223

B BEl, 109 Band offset, 378 Be in GaAs, 136 H-passivation of, 138, 161, 167 Born-Oppenheimerapproximation,6 B impurities in GaAs, 94, 141 BAS acceptors, 141f BAS bistability, 145 BAS donor paris, 146,160 electron irradiation, 142, 169, 172 negative-U, 146 stoichiometry 142, 145 B impurities in GaP B, defects, 144 B, donor pairs, 146 BGa-P,pairs, 170

c C impurities in GaAs, 138 electron irradiation, 140 - As, complexes, 170 CAq Cathodoluminescence,384 Chemical potentials, 32 Cohesive energies, 15 Compensation of GaAs, 92-1 14

493

494 CdF, DX centers, 238 CdTe DX centers. 238 Go impurities absorption spectra. 212,214,224-227 acceptor level, 21 I , 221-223 complexes. 213,221 double acceptor level. 21 1.221-223 EPR measurements, 212 luminescence spectra, 213.224-227 Cr tmpurities absorption spectra. 203J 224-227 acceptor level. 199.221-223 complexes, 206.224-227 donor level, 199.221-223 double acceptor level, 199,221-223 EPR measurements, 202,204,207 luminescence spectra. 203f.206,224-227 Critical layer thickness, 399ff.43Of Cross hatches, 4235 Cqstal field. 192 Cu impurities acceptor level, 221-223 complexes. 213 double acceptor level, 221-223

INDEX chemical shifts, 266f configuration coordinate diagrams, 2408 deep level transient spectroscopy (DLTS).

248-255 density functional calculations, 508 electron paramagnetic resonance (EPR),

216,284 emission barrier. 248,253 extended X-ray absorption fine structure (EXAFS), 2698 extrinsic self-trapping, 264-266 GaAsP. 237.250f.265f.284 GaAs. 181,255J272 Hall effect measurements, 243 compensation, 244-245,279 deep donor, 243,263 nonequilibrium, 243 magnetic propenies, 274-280 MODFETS, 2808 Mossbauer effect, 269-271 negative U, 53,158,274-280 photoionization, 256f PbSnTe. 280 persistent photoconductivity, 2458 photoluminescence, 258f semiconductors, table of DX in, 238 ZnCdTe, 250,260f.265s Dislocations (see also mechanical properties),

293-341.382-386,408442

Deep states AIAs. 364 Deep level transient spectroscopy (DLTS). IW#, 119. 168,486 alloy broadening. 2SOfl capture. 248 DX centers, 248-256 EL?,63 emission, 248 epitaxial films, 349ff transition metals. 22Iff DLOS measurements. 1985 2038 Delta-doping in GaAs, I59 Density-functional theory, 2-58 Donor passivation. 164-166 DX centers, 50-54. 155159,235-291 ballistic phonons, 272 capture barrier. 248,253

effect on device performance, 321 generation, 310 glide set, 297

loops,311.331 misfit dislocations, 321,4098 nonradiative recombination, 322 shuffle set. 297f threading dislocations, 425 threshold voltage, 332 velocity, 301,308,329,335 Dislocation density contour map, 3I3 distribution, 314 methods to reduce bulk crystals, 315ff heteroepitaxial layers, 431-441 Dislocation generation bulk crystals. 31&3 15 heteroepitaxial layers, 407425 Dyson equation, 23

INDEX

E EL2 (see also AsGaantisite), 4249,59-84,77, 92,97. 109, 138 annealing, 62 EL2 around dislocations in GaAs, 465 Franck-Condon shift, 48 luminescence properties, 66f metastability, 42J 68,84 models of, 77-78 ODENDOR measurements, 84 optical properties, 64ff EL6.108 Electrical reversibility, 111 Electron paramagnetic resonance (EPR), 72, 104, l09J 119J 167, 1758 276ff ENDOR, 42,119h 177 Energy dispersive x-ray (EDX) analysis, 480 Electron beam induced current (EBIC), 384 Er impurities luminescence spectra, 224-227 Exchange correlation functional, 3f Exchange correlation potential, 14

Ga(1) defect, 174 Ga interstitial, 28, 33 Ga vacancy, 24.30, 167, 179 GaAs (most topics under respective headers) compensation, 92-1 14,218ff growth bulk grown, 61f, 93fi 310-321 low-temperature MBE grown, 62, 83, 113, 153J 401ff GaAs on Si, 382ff, 416ff SbGacenter, 40 stoichiometry, 12J 34,60,96-98 GaAsP, 238,243ff, 276,370 GaInAs, 370,415 GaInAsP, 238,374 GaInP, 238,265,372 GaP

deep levels, 361-364 transition metal levels, 222, 226 intrinsic defects, 174ff GaSb, 238,265 GeIGaAs, 4 11,472 Glide set of dislocations, 297f. 300 Glide syslem, 299 Greens’ function methods, 23

F Fe impurities absorption spectra, 209-210,224-227 acceptor level, 207,221-223 double acceptor level, 207,221-223 EPR measurements, 207,212 luminescence spectra, 207,209-2 10,

224-227 FR 1 in GaAs, 109 FR2 in GaAs, 109 FR3 in GaAs, 109 Franck-Condon shift, 17J 27,48,256 Formation energies of defects, 30ff Fourier transform infrared (FTIR) absorption, 121ff Frenkel pairs, 12, 167, 170, 174 Frozen-core approximation, 6, 16,21

G Ga antisite, 26, 31

495

Hall measurements, 104ff,154, 243ff Hartree potential, 14 Helmholtz free energy, 7 Horizontal Bridgman growth, 93 Horizontal gradient freeze growth, 93 Hydrogen passivation, 161ff

InAs, 180 InP deep level defects, 27,357-361 transition metals, 198,205.21 1,223 Infrared absorption 121-181 EL2,64ff InSb, 180,238 Insulator/GaAs interfaces, 483ff Inversion boundaries, 4208 426ff

496

INDEX

Impurity hardening. 306.318

Jahn-Teller effect. 29,438, 192, 204

Kohn-Sham equation, 14

L LaBJGaAs, 468 Liquid encapsulated Czochralski crystals, 95. 3 I4 Local density approximation (LDA), 2, 16 Localized vibrational mode spectroscopy (LVM), 106, 118-181,271 Low-temperature growth of GaAs on Si, 401fi 43 1 Low-temperature MBE grown GaAs, 62.83, 113, lS3f.4018

Magnetic circular dichroism. 75 mechanical properties, 299 critical resolved shear stress. 304 cross-slip, 303 deformation stages. 303 glide, 299 impurity hardening, 306 microhardness, 309 primary slip system, 300 stress-strain curve, 300 transport equation. 301 yield point, 301 Metal-induced gap states, 462 MetalflIIN heterostntctures, 449ff electron microscopy, 455 Fermi level movement. 45 Iff annealing, 1 1 I , 453f elastic scattering lengths, 455 models antisite defect model (ADM). 463ff

advanced unified defect model, 464 effective work function model, 462f metal-induced gap states, 462 departures from stoichiometry, 454ff ohmic contacts on n-GaAs, 4 7 6 8 photoemission spectroscopy, 4558 Schottky barrier heights, 450,453 Schottky diodes, 45 1 4 5 4 I-V data, 45 If. 47 I , 479 Microhardness, 309 Misfit dislocations. 321,4098,424f Mn impurities absorption spectra, 214,215,224-227 acceptor level, 21 I , 221-223 EPR measurements, 207 luminescence spectra, 21 8 Mo impurities luminescence spectra. 2 i 8 MODFET, 280fl Modulation enhanced epitaxy. 433

N Native defects, 23, 3 0 8 Native defects model, 4638 Nb impurities acceptor level, 221-223 luminescence spectra, 21 8,224-227 Nd impurities luminescence spectra, 224ff Negative4 systems. 2, 18, 136, 158,274ff Ni impurities absorption spectra, 214, 215.224-227 acceptor level, 21 1,221-223 complexes, 215-216.224-227 double acceptor level, 21 I. 221-223 EPR measurements, 212, 215 luminescence spectra, 21 5,224-227

0 Ohmic contacts, 476f Oval defects, 399f. 430f Oxygen in GaAs. 94, 106 0,.133 OA,,134 negative-U center, 136

INDEX

P interstitial in GaP, 172 Patterned substrates, 438f PbSnTe, 238 Pd impurities luminescence spectra, 218 Pd/Ge/GaAs ohmic contact, 477f Peierls force, 299 Phase diagram of GaAs, 96 Phonon-induced current transient spectroscopy (PICTS), l05ff Photocapacitance,63ff, 107 Photoconductivity,63, 107, 157 Photoemission spectroscopy,455ff Photoluminescence,66, 109, 119,347,353ff Plastic deformation, 300 Si doped GaAs, 148 Pr impurities luminescence spectra, 224ff Pseudopotentials,21 Pyramidal defects, 403-40

Q

497

Semi-insulating (see also compensation) Cr-doped, 2 18,220 Fe doped, 220 Ti doped, 220-1 V-doped, 2 19 Shockley diagrams, 103, 112 Shuffle set of dislocations, 297J 300 Si in GaAs (see also DX centers in GaAs), 1478 Si-H in GaAs, 164 Site switching B in GaAs, 179 Si in GaAs, 179 Slip system, 300,313 Sn-H in GaAs, 164 Spark source mass spectroscopy (SSMS), 105 Stacking faults, 298,42ff Stoichiometry, 12J 34,60,96ff departures from, 402ff, 454461,480-483 Strain rate, 300 Stress-straincurve, 3008.335 Strained-layersuperlattices,437ff Supercell methods, 22 Superlattice, 376ff Surface analysis with laser ionization, 480ff

Quantum wells, 376ff, 414

R Raman scattering, 120, 132f Radiation damage, 1678 Rare earth impurities (see under respective element) Recombination-enhanced glide, 330

S compounds on GaAs, 484 SbGain GaAs, 40 Sc impurities, 195 Schmid factor, 304 Schottky diodes, 45 Iff Schottky mechanism, 462 Secondary ion mass spectroscopy (SIMS), 119, 154,219 Self interstitials,28.33

Ta impurities acceptor level, 221-3 luminescence spectra, 218,224-227 Thermal expansion coefficient,416ff Thermal stress, 312,416ff Thermal treatments (see also annealing),434ff Thermally stimulated capacitance, 349 Thermally stimulated current (TSC), 105, 349 Thermodynamics of defects, 5ff Threading dislocations, 425ff Threshold voltage distribution, 332ff variation with annealing, 336 Ti impurities absorption spectra, 196,201,224-7 acceptor level, 196,221-223 complexes, 224-227 donor level, 196,221-223 EPR measurements, 196,200 luminescence spectra, 196,201,224-227

498 Tm impurities luminescence spectra, 224ff Transition energies, 47,99 Transition metals, 189-233 compensation by TM-doping, 2188 Transition metal impurities (see under r-esprcrive rlemenr) Twinning. 299,3 I7

V Vertical gradient freeze. 93 Vacancies in GaAs VGA,24,30. 167. 179 vA\.24.30. i6x Vacancies in GaP V&. 174,175 V,, 176 Vibrational fine structure. 124 BA\in GaAs, 143 C,< in GaAs. 125. 140 C,\-As, in GaAs, 171 GeA;SiGain GaAs, 127 Keating cluster model. 122 0 in GaAs. 135 SiA< in GaAs. 147

INDEX

W impurities acceptor level, 22 1-223 donor level, 22 1-223 luminescence spectra, 201,224-227 W-shaped dislocation distribution, 314 Workfunction model, 462

Y Yb impurities luminescence spectra, 224ff Yield point, 301,305

Z ZnCdTe DX centers, 238,250,260,265 Zr impurities luminescence spectra, 2I8

Contents of Volumes in This Series

Volume 1 Physics of III-V Compounds C. Hilsum, Some Key Features of 111-V Compounds

Franco Bassani, Methods of Band Calculations Applicable to 111-V Compounds E. 0. Kane, The k p Method V. L.Bonch-Brueoich, Effect of Heavy Doping on the Semiconductor Band Structure Donald Long, Energy Band Structures of Mixed Crystals of 111-V Compounds Laura M. Roth and Petros N. Argyres, Magnetic Quantum Effects S. M. Puri and T. H. Geballe, Thermomagnetic Effects in the Quantum Region W. M. Becker, Band Characteristics near Principal Minima from Magnetoresistance E. H. Putley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity in InSb H. Weiss, Magnetoresistance Betsy Ancker-Johnson, Plasmas in Semiconductors and Semimetals

-

Volume 2 Physics of 111-V Compounds M. G. Holland, Thermal Conductivity S . I. Nookooa, Thermal Expansion U. Piesbergen, Heat Capacity and Debye Temperatures G. Giesecke, Lattice Constants J. R. Drabble, Elastic Properties A. U.Mac Rae and G. W. Gobeli, Low Energy Electron Diffraction Studies Robert Lee Mieher, Nuclear Magnetic Resonance Bernard Goldstein, Electron Paramagnetic Resonance T. S. Moss, Photoconduction in 111-V Compounds E. AntonEik and J. Tauc, Quantum Efficiency of the Internal Photoelectric Effect in InSb G. W. Gobeli and F. G. Allen, Photoelectric Threshold and Work Function P. S. Pershan, Nonlinear Optics in 111-V Compounds M. Gershenzon, Radiative Recombination in the 111-V Compounds Frank Stern, Stimulated Emission in Semiconductors

Volume 3 Optical Properties of 111-V Compounds Marvin Hass, Lattice Reflection William G. Spitzer, Multiphonon Lattice Absorption D. L . Stierwalt and R. F. Potter, Emittance Studies H. R. Philipp and H. Ehrenreich, Ultraviolet Optical Properties Manuel Cardona, Optical Absorption above the Fundamental Edge Earnest J. Johnson, Absorption near the Fundamental Edge John 0. Dimmock, Introduction to the Theory of Exciton States in Semiconductors

CONTENTS OF VOLUMES IN THISSERIES B. Lax and J . G. Mauroides, Interband Magnetooptical Effects H. Y. Fan, Effects o f Free Carries on Optical Properties Edward D.Palik and George B. Wright, Free-Carrier Magnetooptical Effects Richard H. Bube, Photoelectronic Analysis 8 . 0 .S e r a p h and H. E. Bennett, Optical Constants

Volume 4 Physics of 111-V Compounds N. A. Goryunoua, A. S. Borscheuskii, and D. N. Tretiakov, Hardness N. N.Sirora, Heats of Formation and Temperatures and Heats of Fusion of Compounds A"'BV Don L. Kendall, Diffusion A. G. Chynoweth, Charge Multiplication Phenomena Robert W. Keyes,The Effects of Hydrostatic Pressure on the Properties of 111-V Semiconductors L. W. Aukerman, Radiation Effects N. A. Goryunoua, F. P. Kesamanly, and D. N.Nasledoo, Phenomena in Solid Solutions R. T. Bate, Electrical Properties of Nonuniform Crystals

Volume 5 infrared Detectors Henry Leuinstein, Characterization of Infrared Detectors Paul W. Kruse, indium Antimonide Photoconductive and PhotoelectromagneticDetectors M. B. Prince, Narrowband Self-Filtering Detectors Iuars Melngailis and T. C. H a r m n , Single-Crystal Lead-Tin Chalcogenides Donaid Long and Joseph L. Schmit, Mercury-Cadmium Telluride and Closely Related Alloys E. H. Purley, The Pyroelectric Detector Norman B. Stevens, Radiation Thermopiles R. J. Keyes and T. M. Quist, Low Level Coherent and Incoherent Detection in the Infrared M. C. Teich, Coherent Detection in the Infrared F. R. A r m , E. W.Sard, B. J. Peyton, and F. P. Pace, Infrared Heterodyne Detection with Gigahertz IF Response H. S. Sommers, Jr., Macrowave-Based Photoconductive Detector Robert Sehr and Rainer Zuleeg, Imaging and Display

Volume 6 injection Phenomena Murray A. Lampert and Ronald E. Schilling, Current Injection in Solids: The Regional Approximation Method Richard Williams, Injection by Internal Photoemission Allen M. Barnett, Current Filament Formation R. Baron and J . W. Mayer, Double Injection in Semiconductors W. Ruppel, The Photoconductor-Metal Contact

Volume 7 Application and Devices PART A John A. Copeland and Stephen Knight, Applications Utilizing Bulk Negative Resistance F. A. Padovani, The Voltage-Current Characteristics of Metal-Semiconductor Contacts P. L. Hower, W. W. Hooper, B. R. Cairns, R. D. Fairman, and D. A. Tremere, The GaAs Field-Effect Transistor Maroin H. White, MOS Transistors G. R. Anrell, Gallium Arsenide Transistors T. L. Tansley, Heterojunction Properties

CONTENTS OF VOLUMES IN THISSERIES

PART B T. Misawa, IMPATT Diodes H. C. Okean, Tunnel Diodes Robert B. Campbell and Hung-Chi Chang, Silicon Carbide Junction Devices R. E. Enstrom, H. Kressel, and L. Krassner, High-Temperature Power Rectifiers of GaAs,-,P,

Volume 8 Transport and Optical Phenomena Richard J . Stirn, Band Structure and Galvanomagnetic Effects in 111-V Compounds with Indirect Band Gaps Roland W. Ure, Jr., Thermoelectric Effects in 111-V Compounds Herbert Piller, Faraday Rotation H. Barry Bebb and E. W. Williams, Photoluminescence 1: Theory E. W. Williams and H. Barry Bebb, Photoluminescence 11: Gallium Arsenide

Volume 9 Modulation Techniques B. 0.Seraphin, Electroreflectance R. L. Aggarwal, Modulated Interband Magnetooptics Daniel F.Blossey and Paul Handler, Electroabsorption Bruno Batz, Thermal and Wavelength Modulation Spectroscopy lvar Balsleu, Piezooptical Effects D.E. Aspnes and N. Bottka, Electric-Field Effects on the Dielectric Function of Semiconductors and Insulators

Volume 10 Transport Phenomena R. L.Rode, Low-Field Electron Transport J. D. Wiley, Mobility of Holes in 111-V Compounds C. M. Wove and G. E. Stillman, Apparent Mobility Enhancement in Inhomogeneous Crystals Robert L. Peterson, The Magnetophonon Effect

Volume 11 Solar Cells Harold J. Hovel, Introduction; Carrier Collection, Spectral Response, and Photocurrent; Solar Cell Electrical Characteristih; Efficiency; Thickness; Other Solar Cell Devices; Radiation Effects; Temperature and Intensity; Solar Cell Technology

Volume 12 Infrared Detectors (11) W. L. Eiseman, J. D. Merriam, and R. F. Potter, Operational Characteristics of Infrared Photodetectors Peter R. Bratt, Impurity Germanium and Silicon Infrared Detectors E. H. Putley, InSb Submillimeter Photoconductive Detectors G. E. Stillman, C. M. Wove, and J. 0. Dimmock, Far-Infrared Photoconductivity in High Purity GaAs G. E. Stillman and C. M. Wove, Avalanche Photodiodes P. L.Richards, The Josephson Junction as a Detector of Microwave and Far-Infrared Radiation E. H. Putley, The Pyroelectric Detector-An Update

Volume 13 Cadmium Telluride Kenneth Zanio, Materials Preparation; Physics; Defects; Applications

CONTENTS OF VOLUMEs IN

THISSERIES

Volume 14 Lasers, Junctions, Transport N. Holonyak, Jr. and M.H. Lee, Photopumped 111-V Semiconductor Lasers Henry Kressel and Jerome K. Butler, Heterojunction Laser Diodes A. Van der Ziel, Space-Charge-Limited Solid-state Diodes Peter J . Price, Monte Carlo Calculation of Electron Transport in Solids

Volume 15 Contacts, Junctions, Emitters B. L. Shurma. Ohmic Contacts to 111-V Compound Semiconductors Allen Nussbaum, The Theory of Semiconducting Junctions John S. Escher. NEA Semiconductor Photoemitters

Volume 16 Defects, (HgCd)Se, (HgCd)Te Henry Kressel, The Effect of Crystal Defects on Optoelectronic Devices C. R. Whitsett,J . G. Broerman, and C. J. Summers, Crystal Growth and Properties of Hg,-,Cd,Se Alloys M.H. Werler, Magnetooptical Properties of Hg,-,Cd,Te Alloys Paul W . Kruse and John G. Ready, Nonlinear Optical ElTects in Hg,-,Cd,Te

Volume 17 CW Processing of Silicon and Other Semiconductors James F. Gibbons, Beam Processing of Silicon Arto Lietoila, Richard B. Gold, James F. Gibbons, and Lee A. Christel, Temperature Distributions and Solid Phase Reaction Rates Produced by Scanning CW Beams A r m Lietoila and James F. Gibbons, Applications of CW Beam Processing to Ion Implanted Crystalline Silicon N . M.Johnson, Electronic Defects in CW Transient Thermal Processed Silicon K . F. Lee, T. J. Stultz, and James F. Gibbons, Beam Recrystallized Polycrystalline Silicon: Properties, Applications, and Techniques T. Shibata, A. Wakita, 7'.W. Sigmon, and James F. Gibbons, Metal-Silicon Reactions and Silicide Yoes f. Nissim and James F. Gibbons, CW Beam Processing of Gallium Arsenide

Volume 18 Mercury Cadmium Telluride Paul W . Kruse, The Emergence of (Hg,-,Cd,)Te as a Modern Infrared Sensitive Material H. E. Hirsch, S. C. Liang, and A. G. White, Preparation of High-Purity Cadmium, Mercury, and Tellurium W. F. H. Micklefhwaite, The Crystal Growth of Cadmium Mercury Telluride Paul E. Petersen, Auger Recombination in Mercury Cadmium Telluride R. M. Broudy and V. J . Mazurczyck, (HgCd)Te Photoconductive Detectors M. B. Reine, A. K . Sood, and T.J . Tredwell, Photovoltaic Infrared Detectors M.A. Kinch, Metal-Insulator-Semiconductor Infrared Detectors

Volume 19 Deep Levels, GaAs, Alloys, Photochemistry G. F. Neumark and K . Kosai, Deep Levels in Wide Band-Gap 111-V Semiconductors Daoid C. Look, The Electrical and Photoelectronic Properties of Semi-Insulating GaAs R. F. Brebrick, Ching-Hua Su, and Pok-Kai Liao, Associated Solution Model for Ga-In-Sb and Hg-Cd-Te Yu. Ya. Gureuich and Yu. V. Pleskou, Photoelectrochemistry of Semiconductors

CONTENTS OF VOLUMES IN THIS SERIES

Volume 20 Semi-Insulating GaAs R. N . Thomas, H. M. Hobgood, G. W . Eldridge, D. L.Barrett, 7'. T. Braggins, L. B. Ta, and S. K . Wang, High-Purity LEC Growth and Direct Implantation of GaAs for Monolithic Microwave Circuits C. A. Stolte, Ion Implantation and Materials for GaAs Integrated Circuits C. G. Kirkpatrick, R. T.Chen, D. E. Holmes, P. M. Asbeck, K . R. Elliott, R. D. Fairman, and J. R. Oliver, LEC GaAs for Integrated Circuit Applications J. S. BIakemore and S. Rahimi, Models for Mid-Gap Centers in Gallium Arsenide

Volume 21 Hydrogenated Amorphous Silicon Part A Jacques I. Pankove Introduction Masataka Hirose, Glow Discharge; Chemical Vapor Deposition Yoshiyuki Uchida, dc Glow Discharge T. D.Moustakas, Sputtering Isao Yamada, Ionized-Cluster Beam Deposition Bruce A. Scott, Homogeneous Chemical Vapor Deposition Frank J. Kampas, Chemical Reactions in Plasma Deposition Paul A. Longeway, Plasma Kinetics Herbert A. Weakliem, Diagnostics of Silane Glow Discharges Using Probes and Mass Spectroscopy Lester Guttman, Relation between the Atomic and the Electronic Structures A. Cheneuas-Paule, Experiment Determination of Structure S.Minomura, Pressure Effects on the Local Atomic Structure David Adler, Defects and Density of Localized States

Part B Jacques 1. Pankove, Introduction G. D. Cody, The Optical Absorption Edge of a-Si :H Nabil M. Amer and Warren B. Jackson, Optical Properties of Defect States in a-Si: H P. J. Zanzucchi, The Vibrational Spectra of a-Si :H Yoshihiro Hamakawa, Electroreflectance and Electroabsorption Jeffrey S. Lannin, Raman Scattering of Amorphous Si, Ge, and Their Alloys R. A. Street, Luminescence in a-Si :H Richard S. Crandall, Photoconductivity J. Tauc, Time-Resolved Spectroscopy of Electronic Relaxation Processes P. E. Vanier, IR-Induced Quenching and Enhancement of Photoconductivity and Photoluminescence H. Schade, Irradiation-Induced Metastable Effects L. Ley, Photoelectron Emission Studies

Part C Jacques I. Pankove, Introduction J. David Cohen, Density of States from Junction Measurements in Hydrogenated Amorphous Silicon P. C. Taylor, Magnetic Resonance Measurements in a-Si :H K. Morigaki, Optically Detected Magnetic Resonance J. Dresner, Carrier Mobility in a-Si: H

CONTENTS OF VOLUMESIN THIS SERIES T. Tiedje, lnformation about Band-Tail States from Time-of-Flight Experiments Arnold R. Moore, Diffusion Length in Undoped a-Si :H W. Beyer and J. Ouerhof, Doping Effects in a-Si :H C. R. Wronski, The Staebler-WronskiEffect R. J. Nemanich, Schottky Bamers on a-Si :H B. Abeles and T.Tiedje, Amorphous Semiconductor Superlattices

Part D Jacques 1. Pankove, Introduction D. E. Carlson, Solar Cells G. A. Swartz, Closed-Form Solution of I-V Characteristic for a-Si: H Solar Cells Isamu Shimizu, Electrophotography Sachio Ishioka, Image Pickup Tubes P. G. LeComber and W. E. Spear,The Development of the a-Si :H Field-Effect Transitor and Its Possible Applications D. G. Ast, a-Si :H FET-Addressed LCD Panel S. Kaneko, Solid-state Image Sensor Masakiyo Mutsumura, Charge-Coupled Devices M. A. Bosch, Optical Recording A. D’Amico and G. Fortunato, Ambient Sensors Hiroshi Kukimoto, Amorphous Light-Emitting Devices Robert J. Phelan, Jr., Fast Detectors and Modulators Jacques I. Pankoue, Hybrid Structures P. G. LeComber, A. E. Owen, W.E. Spear, J. Hajto, and W. K. Choi, Electronic Switching in Amorphous Silicon Junction Devices

Volume 22 Lightwave Communications Technology Part A Kazuo Nakajima, The Liquid-Phase Epitaxial Growth of InGaAsP W. T. Tsang, Molecular Beam Epitaxy for 111-V Compound Semiconductors G. B. Stringfellow, Organometallic Vapor-Phase Epitaxial Growth of 111-V Semiconductors G. Beuchet, Halide and Chloride Transport Vapor-Phase Deposition of InGaAsP and GaAs Manijeh Razeghi, Low-Pressure Metallo-Organic Chemical Vapor Deposition of Ga,In,-,As,P,-, Alloys P. M . Petrofl, Defects in III -V Compound Semiconductors

Part B J . P. van der Ziel, Mode Locking of Semiconductor Lasers Kom Y. Lau and Amnon Yariu, High-Frequency Current Modulation of Semiconductor Injection Lasers Charles H.Henry, Spectral Properties of Semiconductor Lasers Yasuhanc Suematsu, Katsumi Kishino, Shigehisa Arai, und Fumio Koyama, Dynamic Single-Mode Semiconductor Lasers with a Distributed Reflector W. T.Tsang, The Cleaved-Coupled-Cavity(C3)Laser

Part C R. J. Nelson and N. K. Dutta, Review of InGaAsP/InP Laser Structures and Comparison of Their Performance

CONTENTS OF VOLUMES IN THIS SERIES N. Chinone and M. Nakamura, Mode-Stabilized Semiconductor Lasers for 0.7-0.8- and 1.1-1.6pm Regions Yoshiji Horikoshi, Semiconductor Lasers with Wavelengths Exceeding 2 pm B. A. Dean and M. Dixon, The Functional Reliabilty of Semiconductor Lasers as Optical Transmitters R. H . Saul, T. P.Lee, and C.A. Burus, Light-Emitting Device Design C. L. Zipfel, Light-Emitting Diode Reliability Tien Pei Lee and Tingye Li,LED-Based Multimode Lightwave Systems Kinichiro Ogawa, Semiconductor Noise-Mode Partition Noise

Part D Federico Capasso, The Physics of Avalanche Photodiodes T.P. Pearsall and M. A. Pollack, Compound Semiconductor Photodiodes Takao Kaneda, Silicon and Germanium Avalanche Photodiodes S. R. Forrest, Sensitivity of Avalanche Photodetector Receivers for High-Bit-Rate LongWavelength Optical Communication Systems J. C. Campbell, Phototransistors for Lightwave Communications

Part E Shyh Wang, Principles and Characteristics of Integratable Active and Passive Optical Devices Shlomo Murgalit and Amnon Yariu, Integrated Electronic and Photonic Devices Takaaki Mukai, Yoshihisa Yamamoto, and Tatsuya Kimura, Optical Amplification by Semiconductor Lasers

Volume 23 Pulsed Laser Processing of Semiconductors R. F. Wood, C. W. White, and R. T. Young, Laser Processing of Semiconductors: An Overview C. W. White, Segregation, Solute Trapping, and Supersaturated Alloys G. E. Jellison, Jr., Optical and Electrical Properties of Pulsed Laser-Annealed Silicon R. F. Wood and G. E. Jellison, Jr., Melting Model of Pulsed Laser Processing R. F. Wood and F. W. Young, Jr., Nonequilibrium Solidification Following Pulsed Laser Melting D. H. Lowndes and G. E. Jellison, Jr., Time-Resolved Measurements During Pulsed Laser Irradiation of Silicon D.M, Zehner, Surface Studies of Pulsed Laser Irradiated Semiconductors D.H. Lowndes, Pulsed Beam Processing of Gallium Arsenide R. B. James, Pulsed CO, Laser Annealing of Semiconductors R. T. Young and R. F. Wood, Applications of Pulsed Laser Processing

Volume 24 Applications of Multiquantum Wells, Selective Doping, and Superlattices C. Weisbuch, Fundamental Properties of 111-V Semiconductor Two-Dimensional Quantized Structures: The Basis for Optical and Electronic Device Applications H. Morkoc and H. Unlu, Factors Affecting the Performance of (Al, Ga)As/GaAs and (Al, Ga)As/InGaAs Modulation-Doped Field-Effect Transistors: Microwave and Digital Applications N. T.Linh, Two-Dimensional Electron Gas FETs: Microwave Applications M. Abe et al., Ultra-High-speed HEMT Integrated Circuits D.S. Chemla, D. A. B. Miller, and P. W.Smith, Nonlinear Optical Properties of Multiple Quantum Well Structures for Optical Signal Processing

CONTENTS OF VOLUMES IN THIS SERIES

F. Capasso, Graded-Gap and Superlattice Devices by Band-gap Engineering W.T. Tsang, Quantum Confinement Heterostructure Semiconductor Lasers G . C . Osbourn et al., Principles and Applications of Semiconductor Strained-Layer Superlattices

Volume 25 Diluted Magnetic Semiconductors W. Giriar and J . K . Furdyna, Crystal Structure, Composition, and Materials Preparation of Diluted Magnetic Semiconductors W.M. Becker. Band Structure and Optical Properties of Wide-Gap AI'-,Mn,BV' Alloys at Zero Magnetic Field Saul Oserofl and Pieter H. Keesom, Magnetic Properties: Macroscopic Studies T. Giebulrowicz and T. M . Holden, Neutron Scattering Studies of the Magnetic Structure and Dynamics of Diluted Magnetic Semiconductors J . Kossut, Band Structure and Quantum Transport Phenomena in Narrow-Gap Diluted Magnetic Semiconductors C. Riqaux, Magnetooptics in Narrow Gap Diluted Magnetic Semiconductors J . A. Gaj, Magnetooptical Properties of Large-Gap Diluted Magnetic Semiconductors J . Mycielski, Shallow Acceptors in Diluted Magnetic Semiconductors: Splitting, Boil-off, Giant Negative Magnetoresistance A. K . Ramdas and S . Rodrique:, Raman Scattering in Diluted Magnetic Semiconductors P. A. Wolfl, Theory of Bound Magnetic Polarons in Semimagnetic Semiconductors

Volume 26 111-V Compound Semiconductors and Semiconductor Properties of Superionic Materials Zou Yuanxi, 111-V Compounds H . V. Winston, A. T. Hunter, H. Kimura, and R. E . Lee, InAs-Alloyed GaAs Substrates for Direct Implantation P. K. Bhattacharya and S . Dhar, Deep Levels in 111-V Compound Semiconductors Grown by MBE Yu. Yu. Gureuich and A. K . Iuanov-Shits, Semiconductor Properties of Superionic Materials

Volume 27

High Conducting Quasi-One-Dimensional Organic Crystals

E . M . Conweli, Introduction to Highly Conducting Quasi-One-Dimensional Organic Crystals 1. A. Howard, A Reference Guide to the Conducting Quasi-One-Dimensional Organic Molecular Crystals J . P. Pouget, Structural Instabilities E. M . Conwelf,Transport Properties C . S. Jacobsen, Optical Properties J . C. Scott, Magnetic Properties L. Zugpiroli, Irradiation Effects: Perfect Crystals and Real Crystals

Volume 28 Measurement of High-speed Signals in Solid State Devices J . Frey and D . Ioannou, Materials and Devices for High-speed and Optoelectronic Applications H . Schumacher and E . Strid, Electronic Wafer Probing Techniques D. H. Auston, Picosecond Photoconductivity: High-speed Measurements of Devices and Materials J . A. Valdmanis, Electro-Optic Measurement Techniques for Picosecond Materials, Devices, and Integrated Circuits J . M. Wiesenfeld and R. K . Join, Direct Optical Probing of Integrated Circuits and High-speed Devices

CONTENTS OF VOLUMES IN THIS SERIES G. Plows, Electron-Beam Probing A. M. Weiner and R. B. Marcus, Photoemissive Probing

Volume 29 Very High Speed Integrated Circuits: Gallium Arsenide LSI M. Kuzuhara and T. Nozaki, Active Layer Formation by Ion Implantation

H. Hashimoto, Focused Ion Beam Implantation Technology T. Nozaki and A. Higashisaka, Device Fabrication Process Technology M. In0 and T. Takada, GaAs LSI Circuit Design M. Hirayama, M . Ohmori, and K . Yamasaki, GaAs LSI Fabrication and Performance

Volume 30 Very High Speed Integrated Circuits: Heterostructure H. Watanabe, T. Mizutani, and A. Usui,Fundamentals of Epitaxial Growth and Atomic Layer Epitaxy S. Hiyamizu, Characteristics of Two-Dimensional Electron Gas in 111-V Compound Heterostructures Grown by MBE T. Nakanisi, Metalorganic Vapor Phase Epitaxy for High-Quality Active Layers T. Mimura, High Electron Mobility Transistor and LSI Applications T. Sugeta and T. Ishibashi, Hetero-Bipolar Transistor and Its LSI Application H. Matsueda, T. Tanaka, and M . Nakamura, Optoelectronic Integrated Circuits

Volume 3 1 Indium Phosphide: Crystal Growth and Characterization J . P. Farges, Growth of Discoloration-free InP M. J . McCollum and G. E. Stillman, High Purity InP Grown by Hydride Vapor Phase Epitaxy T. Inada and T. Fukuda, Direct Synthesis and Growth of Indium Phosphide by the Liquid Phosphorous Encapsulated Czochralski Method 0.Oda, K.Katagiri, K.Shinohara, S. Katsura, Y. Takahashi, K.Kainosho, K.Kohiro, and R. Hirano, InP Crystal Growth, Substrate Preparation and Evaluation K . Tada, M. Tatsumi, M. Morioka, T. Araki, and T. Kawase, InP Substrates: Production and Quality Control M. Razeghi, LP-MOCVD Growth, Characterization, and Application of InP Material T. A. Kennedy and P. J . Lin-Chung, Stoichiometric Defects in InP

Volume 32 Strained-Layer Superlattices: Physics T. P. Pearsall, Strained-Layer Superlattices Fred H. Pollack, Effects of Homogeneous Strain on the Electronic and Vibrational Levels in Semiconductors J . Y. Marzin, J . M. Gerdrd, P. Voisin, and J. A. Brum, Optical Studies of Strained 111-V Heterolayers R. People and S. A. Jackson, Structurally Induced States from Strain and Confinement M. Jaros, Microscopic Phenomena in Ordered Superlattices

Volume 33 Strained-Layer Superlattices: Materials Science and Technology R. Hull and J. C. Bean, Principles and Concepts of Strained-Layer Epitaxy William J. Schaff, Paul J . Tasker, Mark C. Foisy, and Lester F. Eastman, Device Applications of Strained-Layer Epitaxy S. T. Picraux, B. L. Doyle, and J . Y. Tsao, Structure and Characterization of Strained-Layer Superlattices

CONTENTS OF VOLUMESIN THIS SERIES E. Kasper and F. Schafler, Group IV Compounds Dale L , Martin, Molecular Beam Epitaxy of IV-VI Compound Heterojunctions Robert L. Gunshor, Leslie A. Kolod:iejski, Arto V. Nurmikko, and Nobuo Otsuka, Molecular Beam Epitaxy of 11- VI Semiconductor Microstructures

Volume 34 Hydrogen in Semiconductors J . 1. Pankoue and N. M . Johnson, Introduction to Hydrogen in Semiconductors C. H. Seager, Hydrogenation Methods J . I. Pankoue, Hydrogenation of Defects in Crystalline Silicon J. W. Corhett, P. Deak, U.V. Desnica, and S. J. Pearton, Hydrogen Passivation of Damage Centers

in Semiconductors S. J . Pearton, Neutralization of Deep Levels in Silicon J . I. Pankoue, Neutralization of Shallow Acceptors in Silicon N. M. Johnson, Neutralization of Donor Dopants and Formation of Hydrogen-Induced Defects in n-Type Silicon M . Stauola and S. J. Pearton, Vibrational Spectroscopy of Hydrogen-Related Defects in Silicon A. D. Marwick, Hydrogen in Semiconductors: Ion Beam Techniques C . Herring and N. M.Johnson, Hydrogen Migration and Solubility in Silicon E. E. Haller, Hydrogen-Related Phenomena in Crystalline Germanium J . Kakalios, Hydrogen Diffusion in Amorphous Silicon J . Cheuallier, E . Clerjuud, and B. Pajot, Neutralization of Defects and Dopants in 111-V Semiconductors G. G. DeLeo and W. B. Fowler, Computational Studies of Hydrogen-Containing Complexes in Semiconductors R. F. K e g and T. L . Estle, Muonium in Semiconductors C. G. Van de Walle, Theory of Isolated Interstitial Hydrogen and Muonium in Crystalline Semiconductors

Volume 35 Nanostructured Systems M. Reed, Introduction H. van Houren, C. W. J. Beenakker. and B. J. van Wees, Quantum Point Contacts G. Timp, When Does a Wire Become an Electron Waveguide? M. Blirtiker, The Quantum Hall Effect in Open Conductors W , Hansen, J. P. Kotthaus, and U.Merkt, Electrons in Laterally Periodic Nanostructures

Volume 36 Spectroscopy of Semiconductors D. H e i m n , Laser Spectroscopy of Semiconductors at Low Temperatures and High Magnetic Fields A. V Nurmikko, Transient Spectroscopy by Ultrashort Laser Pulse Techniques A. K. Ramdas and S. Rodriguez, Piezospectroscopy of Semiconductors 0.J. Glembocki and B. I! Shanabrook, Photoreflectance Spectroscopy of Microstructures D. G. Seiler, C. L Littler and M. H. Weifer, One- and Two-Photon Magneto-Optical Spectroscopy of InSb and Hg, -,Cd,Te

Volume 37 The Mechanical Properties of Semiconductors k - B . Chen, A. Sher and W Z Yost, Elastic Constants and Related Properties of Semiconductor Compounds and Their Alloys D. R. Clarke, Fracture of Silicon and Other Semiconductors

CONTENTS OF VOLUMES IN

THIS

SERIES

H . Siethox The Plasticity of Elemental and Compound Semiconductors S . Guruswamy, K. T Faber and J . P. Hirth, Mechanical Behavior of Compound Semiconductors S. Mahajan, Deformation Behavior of Compound Semiconductors J. P. Hirth, Injection of Dislocations into Strained Multilayer Structures D.Kendall, C. B. Fleddermann, and K . J . Malloy, Critical Technologies for the Micromachining of Silicon I . Matsuba and K . Mokuya, Processing and Semiconductor Thermoelastic Behavior

Volume 38 Imperfections in III/V Materials U. Scherz and M . Scheffler, Density-Functional Theory of spBonded Defects in III/V Semiconductors M . Kaminska and E . R. Weber, EL2 Defect in GaAs D.C. Look, Defects Relevant for Compensation in Semi-Insulating GaAs R. C. Newman, Local Vibrational Mode Spectroscopy of Defects in I I I P Compounds A. M . Hennel, Transition Metals in I I I P Compounds K. J. Malloy and K . Khachaturyan, DX and Related Defects in Semiconductors Z Swaminathan and A. S . Jordan, Dislocations in I I I P Compounds K. W Nauka, Deep Level Defects in the Epitaxial I I I P Materials 2. Liliental-Weber, H . Sohn, and J . Washburn, Structural Defects in Epitaxial I I I P Layers W E. Spicer, Defects in Metal/III/V Heterostructures

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SEMICONDUCTORS & SEMIMETALS V38, Volume 38 (Semiconductors and Semimetals)

Semiconductors and Semimetals Volume 72 Silicon Epitaxy (Semiconductors and Semimetals)