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Physical Properties of Iii-V Semiconductor Compounds PHYSICAL PROPERTIES OF III-V SEMICONDUCTOR COMPOUNDS Physical Properties of III-V Semiconductor Compounds. Sadao Adachi Copyright © 1992 by John Wiley & Sons, Inc. ISBN: 0-471-57329-9 PHYSICAL PROPERTIES OF m-V SEMICONDUCTOR COMPOUNDS InP, InAs, GaAs, GaP, InGaAs, and InGaAsP SADAO ADACHI Department of Electronic Engineering Gunma University Kiryu-shi, Gunma 376, Japan A Wiley-Interscience Publication JOHN WILEY & SONS New York • Chichester • Brisbane • Toronto • Singapore ANOTE TO THE READER This book has been electronically reproduced from digital information stored at John Wiley & Sons, Inc. We are pleased that the use of this new technology will enable us to keep works of enduring scholarly value in print as long as there is a reasonable demand for them. The content of this book is identical to previous printings. In recognition of the importance of preserving what has been written, it is a policy of John Wiley & Sons, Inc., to have books of enduring value published in the United States printed on acid-free paper, and we exert our best efforts to that end. Copyright © 1992 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. Library of Congress Cataloging in Publication Data: Adachi, Sadao, 1950- Physical properties of III-V semiconductor compounds: InP, InAs, GaAs, GaP, InGaAs, and InGaAsP / Sadao Adachi. p. cm. "A Wiley-Interscience publication." Includes bibliographical references and indexes. ISBN 0-471-57329-9 (cloth : acid-free) 1. Gallium arsenide semiconductors. 2. Indium alloys. 3. Indium phosphide. I. Title. QC611.8.G3A33 1992 537.6'226-dc20 92-7286 Printed in the United States of America 10 987654321 To Yuki, Mai, and Koya PREFACE The ln{ _^Ga^ As^ -y/lnP heterostructure system is potentially useful for optoelectronic, high-speed digital, and high-frequency microwave device applications. Even though the basic In, _^Ga^As^P, _y/InP heterostructure concept is understood at this time, some practical device parameters in this system have been hampered by a lack of definite knowledge of many ma- terial parameters. The purpose of this book is twofold: (1) to discuss key properties of InP, ln{_xGaxA^yPi,y quaternary, and In0^Ga^yAs ternary; and (2) to pre- sent various material parameters and constants of these semiconductors for a variety of basic research and device applications. A set of the material properties and parameters of these semiconductors are considered in this book. The host of effects associated with the presence of specific impurities and defects is, however, omitted from the coverage. The model used in some cases is based on an interpolation scheme and, therefore, necessitates known values of the material parameters for the related binaries InP, In As, GaAs, and GaP. Emphasis is, therefore, also placed on tnaterial properties not only of InP but also of In As, GaAs, and GaP binaries. It is hoped that the book will be useful to both beginning and advanced specialists as well as to workers in related fields, thus contributing to the further development of III-V semiconductor devices. SADAO ADACHI Gunma, Japan May 1992 vii ACKNOWLEDGMENTS The author wishes to thank the editors and authors of the following journals and symposium paper for permission to reproduce previously published figures: Journal of Applied Physics for Figs. 2.3, 3.1, 4.6, 8.18, 8.19, 8.21, 8.22, 8.25, 8.26, 9.4, 9.5, 9.9, 9.11, 9.12, 9.14, 9.15, 10.13, and 11.4; Canadian Journal of Physics for Fig. 3.10; Zeitschrift fur Naturfor- schung for Fig. 4.1; Physical Review for Figs. 6.1, 6.2, 8.5, 8.8, 8.9, 8.16, and 8.17; Solid State Communications for Fig. 6.13; Journal of Elec- tronic Materials for Figs. 8.6 and 10.7; Applied Physics Letters for Figs. 8.30 and 11.3; Journal of Crystal Growth for Figs. 8.31 and 10.3; IEEE Journal of Quantum Electronics for Figs. 8.33 and 8.35; and Institute of Physics Conference Series (Gallium Arsenide and Related Compounds) for Fig. 10.2. ix CONTENTS Principal Symbols xv 1 Introduction 1 References, 3 2 Structural Properties 4 2.1 Crystal Structure and Lattice Constant, 4 2.2 Binding and Cleavage Properties, 8 2.3 Molecular and Crystal Densities, 11 2.4 Ordered Alloys, 13 References, 14 3 Mechanical, Elastic, and Lattice Vibrational Properties 17 3.1 Knoop Hardness, 17 3.2 Elastic Properties and Sound Velocities, 20 3.2.1 Elastic Stiffness and Compliance Constants, 20 3.2.2 Young's Modulus, Poisson's Ratio, and Similar, 24 3.2.3 Sound Velocities and Mode Griineisen Parameters, 26 3.2.4 Surface Acoustic Waves, 29 xi xii CONTENTS 3.3 Lattice Vibrational Properties, 31 3.3.1 Dispersion Curves and Phonon Density of States, 31 3.3.2 Phonon Spectra and Mode Griineisen Parameters, 33 3.3.3 Long-Wavelength Optical Phonons in InGaAsP, 37 3.3.4 Phonon Deformation Potentials, 39 References, 44 4 Thermal Properties 48 4.1 Specific Heat and Debye Temperature, 48 4.2 Thermal Expansion Coefficient, 51 4.3 Lattice Thermal Conductivity, 55 References, 60 5 Collective Effects and Some Response Characteristics 63 5.1 Static and High-Frequency Dielectric Constants, 63 5.2 Piezoelectricity, 66 5.2.1 Piezoelectric Stress and Strain Constants, 66 5.2.2 Electromechanical Coupling Constant, 70 5.3 Frohlich Coupling Constant, 71 References, 72 6 Electronic Energy-Band Structure 75 6.1 Fundamental Absorption Edge and Optical Transition Energies, 75 6.1.1 E0 and E0 + A0 Gaps, 79 6.1.2 E{ and El + A{ Gaps, 82 6.1.3 E'Q Triplet Region, 82 6.1.4 Lowest Indirect Band Gaps, 84 6.1.5 Energy Gaps in In053Ga0.47As, 86 6.2 Electron and Hole Effective Masses, 86 6.2.1 Electron Effective Mass, 86 6.2.2 Hole Effective Mass, 91 6.3 Conduction- and Valence-Band Offsets, 96 6.3.1 In, .^Ga^As^Pi _3,/InP Heterojunction System, 96 6.3.2 In053Gao.47As/InP and In053Ga047As/ In0 52A10 48As Heteroj unction Systems, 98 CONTENTS xiii 6.3.3 Lattice-Mismatched Heterojunctions Based on In^Ga^As, 99 6.4 External Perturbation Effects on Band Parameters, 100 6.4.1 Effects of Temperature, 100 6.4.2 Effects of Pressure, 106 References, 109 7 Electron and Hole Deformation Potentials 118 7.1 Deformation Potentials for Holes at the T Point, 118 7.2 Deformation Potentials for Electrons, 126 References, 131 8 Optical Properties 135 8.1 Optical Dispersion Relations, 135 8.2 The Reststrahlen Region, 136 8.3 The Interband Transition Region, 143 8.3.1 Model Dielectric Function, 143 an (a) £0 d EQ + A0 Transitions, 147 (b) £*! and E\ + Aj Transitions, 148 (c) Eo(£2) Transitions, 150 (d) Indirect-Band-Gap Transitions, 152 (e) Excitons and Exciton Parameters, 153 8.3.2 Experimental et and c2 Spectra, 160 8.3.3 Dispersion of the Refractive-Index, Extinction, and Absorption Coefficients, 165 8.4 Free-Carrier Effects on Optical Properties, 174 8.4.1 Optical Absorption, 174 8.4.2 Carrier-Induced Change in Refractive Index, 179 8.5 Intervalence-Band Absorption, 182 8.6 Nonlinear Index of Refraction and Absorption, 186 References, 187 9 Elastooptic and Electrooptic Effects 193 9.1 Elastooptic Effect, 193 9.1.1 Model Representation, 193 9.1.2 Analyses, 195 9.2 Linear Electrooptic Effect, 201 9.2.1 Model Representation, 201 9.2.2 Analyses, 205 xiv CONTENTS 9.3 Quadratic Electrooptic Effect, 211 9.3.1 Model Representation, 211 9.3.2 Analyses, 216 9.4 Franz-Keldysh Effect, 218 References and Note, 220 10 Carrier Transport Properties 223 10.1 Low-Field Mobility, 223 10.1.1 Electrons, 223 10.1.2 Holes, 232 10.2 High-Field Transport, 239 10.2.1 Velocity-Field Characteristics, 239 (a) Electrons, 239 (b) Holes, 246 10.2.2 Gunn Phenomena, 248 10.3 Minority-Carrier Transport, 250 10.3.1 Electron Mobility, 250 10.3.2 Electron Drift Velocity, 252 References, 254 11 Strain Problems in InGaAs(P)-Based Heterostructures 263 11.1 Strain Effects on Crystallographic Properties, 263 11.1.1 Elastic Strain in Heterostructures, 263 11.1.2 Misfit Dislocations and Defect Etchants, 267 11.1.3 Critical Layer Thickness, 271 11.2 Strain Effects on Physical Properties, 273 11.2.1 Theoretical Consideration, 273 11.2.2 InGaAs(P)/InP System, 275 11.2.3 InGaAs/GaAs Lattice-Mismatched System, 277 References, 280 12 Concluding Remarks 287 Appendix: Summary of Interpolation Scheme 289 Index to Tables of Physical Constants 293 Author Index 295 Subject Index 315 PRINCIPAL SYMBOLS A isotropy factor a, b, d hydrostatic (a) and shear deformation potentials (b, d) for holes at the F-point valence-band maximum # BD(a|D) three-dimensional (two-dimensional) exciton Bohr radius aQ lattice constant B binary material parameter, magnetic field strength B0 Born ratio Bu bulk modulus 5u pressure derivative of the bulk modulus Ca Caucy ratio Cy second-order elastic stiffness constant Cijk third-order elastic stiffness constant C0 elastic compressibility Cp, Cv specific heats at constant pressure and constant volume C, deformation potential for electrons at the F-point conduc- tion-band minimum c bowing parameter, velocity of light D(j intervalley deformation potential constant d interatomic spacing dy piezoelectric strain constant, nonlinear optical coefficient d0 optical-phonon deformation potential E energy, electric field strength Eac phenomenologic acoustic deformation potential £g band-gap energy XV xvi PRINCIPAL SYMBOLS L V C Ef, El E g indirect-gap energy, T 8 -> X 6(££), r$ -> L£ (££) EgX lasing emission energy Enpo phenomenologic optical deformation potential Eth threshold electric field (Gunn oscillation) EQ, EI, .
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