Physics of Quantum Well Devices

308 Pages·2002·4.604 MB·English

by  B. R. Nag (auth.)

PHYSICS OF QUANTUM WELL DEVICES
SOLID-STATESCIENCE AND TECHNOLOGYLIBRARY
VOLUME7
Editorial Advisory Board
L. R. Carley,Carnegie Mellon University, Pitsburgh, USA
G.Declerck,IMEC, Leuven, Belgium
F. M. Klaassen,University of Technology, Eindhoven, The Netherlands
AimsandScope of the Series
Theaimofthis seriesistopresentmonographs onsemiconductormaterials processinganddevice
technology, discussing theory formation and experimental characterization of solid-state devices in
relation to their application in electronic systems, their manufacturing, their reliability, and their -
limitations (fundamental or technology dependent). This area is highly interdisciplinary and
embraces the cross-section of physics of condensed matter, materials science and electrical enginee-
ring.
Undisputedly during the second half of this century world society is rapidly changing owing to the
revolutionary impact of new solid-state based concepts. Underlying this spectacular product
developmentis a steady progress in solid-stateelectronics, an area ofapplied physics exploiting
basic physical concepts established during the first half of this century. Since their invention,
transistors of various types and their corresponding integrated circuits (ICs) have been widely
exploited covering progress in such areas as microminiaturization, megabit complexity, gigabit
speed, accurate data conversion and/or high power applications. In addition, a growing number of
devices are being developed exploiting the interaction between electrons and radiation, heat,
pressure, etc., preferably by merging with ICs.
,
Possible themes are (sub)micron structures and nanostructures (applying thin layers, multi layers
and multi-dimensional configurations); micro-optic and micro-(electro)mechanical devices; high-
temperature superconducting devices; high-speed and high-frequency electronic devices; sensors and
actuators; and integrated opto-electronic devices (glass-fibre communications, optical recording and
storage, flat-panel displays).
The texts will be of a level suitable for graduate students, researchers in the above fields, practitioners,
engineers, consultants, etc., with an emphasis on readability, clarity, relevance and applicability.
The titles publislied in this series are listed at the end of this volume.
Physics of Quantum
Well Devices
by
B.R.Nag
INSASenior Scientist,
InstituteofRadio Physics and Electronics,
Calcutta University, Calcutta, India
KLUWER ACADEMICPUBLISHERS
NEW YORK / BOSTON / DORDRECHT / LONDON / MOSCOW
eBook ISBN: 0-306-47127-2
Print ISBN: 0-792-36576-3
©2002 Kluwer Academic Publishers
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Print ©2000 Kluwer Academic Publishers
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CONTENTS
Preface xi
Acknowledgments xiii
1. INTRODUCTION 1
1.1. Quantum Well Devices 1
1.2. Scope of the Book 6
2. HETEROSTRUCTURE GROWTH 8
2.1. Molecular Beam Epitaxy 8
2.2. Metalorganic Chemical Vapour Deposition 10
2.3. Chemical Beam Epitaxy 12
2.4. Other Techniques 13
2.4.1.HOT-WALL EPITAXY 13
2.4.2.GS-MBE 14
2.4.3.LASER-ASSISTED MBE 14
2.4.4. ATOMIC LAYER EPITAXY 15
2.4.5. RF-ECR MBE 16
2.5. 1D Structures 16
2.5.1. ETCHING AND REGROWTH 16
2.5.2. GROWTH ON VICINAL SUBSTRATES 17
2.5.3. INTERDIFFUSION OF GROUP-III ELEMENTS 18
2.5.4 GROWTH ON PATTERNED NON-PLANAR SUBSTRATES 18
2.6. 0D Structures 20
2.6.1. ETCHING OR ION MILLING 20
2.6.2. SELECTIVE ETCH TECHNIQUE 20
2.6.3. SELF-ORGANIZED GROWTH 20
2.7. Conclusion 21
3. BAND OFFSET 22
3.1. Types of Heterostructures 24
3.2. Empirical rules 26
V
vi CONTENTS
3.2.1. ELECTRON AFFINITY RULE 26
3.2.2. COMMON-ANION RULE 26
3.3. Theoretical Methods 27
3.3.1. TERSOFF METHOD 27
3.3.2. VAN DE WALLE-MARTIN METHOD 27
3.4. Experimental Methods 29
3.4.1.ABSORPTION MEASUREMENT 29
3.4.2.PHOTOLUMINESCENCE MEASUREMENT 30
3.4.3.X-RAY CORE LEVEL PHOTOEMISSION
SPECTROSCOPY (XPS) 32
3.5. Values of Band Offset 33
3.6. Conclusion 34
4. ELECTRON STATES 36
4.1. Effective-mass Approximation 37
4.1.1. EFFECTIVE-MASS APPROXIMATION FOR DEGENERATE
EXTREMA 38
4.1.2. ENVELOPE-FUNCTION EQUATION FOR ELECTRONS 39
4.1.3. ENVELOPE'-FUNCTION EQUATION FOR HOLES 41
4.1.4. ENVELOPE-FUNCTION EQUATION FOR HIGH-ENERGY
ELECTRONS 44
4.1.5. BOUNDARY CONDITIONS 47
4.2. Energy Levels of Electrons 49
4.2.1. QUANTUM WELL 50
4.2.2. SUPERLATTICE 53
4.2.3. SINGLE HETEROJUNCTION 57
4.2.4. QUANTUM WIRES AND QUANTUM DOTS 63
4.3. Energy Levels of Holes 67
4.4. Energy Levels in Strained-layer Wells 71
4.4.1.EFFECT OF STRAIN ON THE CONDUCTION BAND 73
4.4.2. EFFECT OF STRAIN ON THE VALENCE BAND 73
4.5. Conclusion 76
5.OPTICAL INTERACTOION PHENOMENA 77
5.1. Optical Interaction in Bulk Materials 77
5.2. Interaction in Quantum Wells 86
5.2.1. INTERBAND TRANSITIONS 86
5.2.2. INTERSUBBAND ABSORPTION 87
5.3.Excitons 89
5.3.1. EXCITED-STATE WAVE FUNCTION 90
5.3.2. EXCITONIC WAVE FUNCTIONS 93
5.3.3. EXCITONIC OPTICAL INTERACTION MATRIX ELEMENT 96
CONTENTS vii
5.3.4. EXCITONS IN QUANTUM WELLS 97
5.3.5. EXCITONIC OPTICAL MATRIX ELEMENT FOR
QUANTUM WELLS 99
5.4. Bound and Localized Excitons 101
5.5. Absorption 102
5.5.1. INTERBAND ADSORPTION 104
5.5.2. EXCITONIC ABSORPTION 107
5.5.3. ABSORPTION SPECTRUM 109
5.5.4. INTERSUBBAND ABSORPTION 112
5.6. Quantum-Confined Stark Effect 114
5.7. Nonlinear Effects 122
5.7.1.NONRESONANT NONLINEARITY 123
5.7.2. RESONANT NONLINEARITY 125
5.8. Photoluminescence 131
5.9. Photoluminescence Spectrum 136
5.10. Conclusion 138
6. TRANSPORT PROPERTIES 139
6.1. Scattering Processes for 2DEG 140
6.2. Matrix Elements for 2DEG 141
6.3. Form Factor 145
6.4. Screening by 2DEG 146
6.5. Collision Integral for 2DEG 148
6.6. Scattering Rate for 2DEG 149
6.7. Solution of the Transport Equation for 2DEG 152
6.8. Mobility 155
6.8.1. ELECTRON MOBILITY IN AlGaAs/GaAs AND AlGaAs/InGaAs
SINGLE HETEROJUNCTION AND InP/GaInAs QW’s 158
6.8.2. ELECTRON MOBILITY IN InGaP/GaAs QW’s 159
6.8.3. ELECTRON MOBILITY IN AlGaN/GaN QW’s 160
6.8.4. GENERALIZED EXPRESSION FOR MOBILITY 160
6.9. High-field Velocity OF 2DEG 160
6.9.1. THEORY 162
6.9.2. EXPERIMENTAL RESULTS 165
6.10. Scattering-induced Broadening of
Photoluminescence Spectrum 166
6.11. Ballistic Transport 171
7. HIGH ELECTRON MOBILITY TRANSISTOR 173
7.1. Structure and Principle of Operation 173
viii CONTENTS
7.2. Potential Distribution and
Accumulated Charge Density 175
7.3. Current-Voltage Characteristic 178
7.4. Experimental Results 182
7.5. Current Researches on HEMT’s 184
7.5.1. TEMPERATURE DEPENDENCE OF CHARACTERISTICS 184
7.5.2. THEORETICAL MODELS AND SIMULATORS 185
7.5.3. HIGH-POWER MICROWAVE HEMT’S 185
7.5.4. CONTROL OF HEMT’s BY LIGHT 187
7.6. Conclusion 187
8. RESONANT TUNNELING DIODE 188
8.1. Introduction 188
8.2. Tunneling Characteristic 191
8.3. Current-Voltage Characteristic 194
8.4. Experiments 198
8.5. Applications 199
9. QUANTUM WELL LASER 202
9.1. Operating Principle 202
9.2. Laser Equation 204
9.3. Operating Characteristics 205
9.4. Threshold Current 207
9.4.1. CONFINEMENT FACTOR 208
9.4.2. GAIN 210
9.4.3. ESTIMATION OF THRESHOLD CURRENT 213
9.4.4. EQUIVALENT CIRCUIT MODEL 214
9.5. Experimental Results 215
9.5.1. GaAs/AlGaAs QWL 215
9.5.2. InGaAsP QWL 215
9.5.3. STRAINED-LAYER LASERS 216
9.5.4. VISIBLE MQWL 217
9.5.5. SURFACE-EMITTING LASERS 218
9.5.6. QUANTUM WIRE LASER 219
9.5.7. QUANTUM DOT LASER 221
9.6. Conclusion 222
10. QUANTUM WELL DETECTOR, MODULATOR
AND SWITCH 223
10.1. Quantum Well Detector 223
10.1.1. PRINCIPLE OF OPERATION 223
10.1.2. EXPERIMENTAL RESULTS 233
CONTENTS ix
10.1.3. QUANTUM DETECTOR SYSTEMS UNDER
EXPERIMENTATION 235
10.2. Quantum Well Modulator 236
10.2.1. TRANSVERSE TRANSMISSION MODULATOR 239
10.2.2. WAVEGUIDE MODULATOR 240
10.2.3. FABRY-PEROT MODULATOR 241
10.3. Quantum Well Switch 243
10.3.1. R-SEED 243
10.3.2. D-SEED 245
10.3.3. S-SEED 246
10.4. Optical Bistable Device(OBD) 247
10.4.1. ABSORPTION-BASED OBD 249
10.4.2. DISPERSION-BASED 249
10.5. Waveguide all-optic switch 251
10.6. Conclusion 253
References 255
Appendix 287
Index 289
PREFACE
Quantum well devices have been the objects of intensive research during the last
two decades. Some of the devices have matured into commercially useful products
and form part of modern electronic circuits. Some others require further devel-
opment, but have the promise of being useful commercially in the near future.
Study of the devices is, therefore, gradually becoming compulsory for electronics
specialists. The functioning of the devices, however, involve aspects of physics
which are not dealt with in the available text books on the physics of semiconduc-
tor devices. There is, therefore, a need for a book to cover all these aspects at an
introductory level. The present book has been written with the aim of meeting
this need. In fact, the book grew out of introductory lectures given by the author
to graduate students and researchers interested in this rapidly developing area of
electron devices.
The book covers the subjects of heterostructure growth techniques, band-offset
theory and experiments, electron states, electron-photon interaction and related
phenomena, electron transport and the operation of electronic, opto-electronic and
photonic quantum well devices. The theory as well as the practical aspects of the
devices are discussed at length.
The aim of the book is to provide a comprehensive treatment of the physics
underlying the various devices. A reader after going through the book should find
himself equipped to deal with all kinds of quantum well devices.
The book may serve as a text-book for advanced level graduate courses. New
entrants into researches or developments in the area should also find the book
useful.
Indian National Science Academy helped the author to complete the book by
awarding him the position of INSA Senior Scientist for three years (1998-2000).
B. R. Nag
Calcutta
June, 2000
xi