Electronic and Optoelectronic Properties of Semiconductor Structures

Electronic and Optoelectronic Properties
of Semiconductor Structures
Jasprit Singh
University of Michigan, Ann Arbor
  
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
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- ----
© Cambridge University Press 2003
2003
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PREFACE
INTRODUCTION
I.1 SURVEY OF ADVANCES IN SEMICONDUCTOR
PHYSICS
xiv
I.2 P
HYSICS BEHIND SEMICONDU
CTORS
xvi
I.3 R
OLE OF THIS BOOK
xviii
STRUCTURAL PROPERTIES
OF SEMICONDUCTORS
1.1 INTRODUCTION 1
1.2 CRYSTAL GROWTH
2
1.2.1 Bulk Crystal Growth 2
1.2.2 Epitaxial Crystal Growth 3
1.2.3 Epitaxial Regrowth 9
1.3 C
R
YSTAL STRUCTURE
10
1.3.1 Basic Lattice Types 12
1.3.2 Basic Crystal Structures 15
1.3.3 Notation to Denote Planes and Points in a Lattice:
Miller Indices
16
1.3.4 Artificial Structures: Superlattices and Quantum Wells 21
1.3.5 Surfaces: Ideal Versus Real 22
1.3.6 Interfaces 23
1.3.7 Defects in Semiconductors 24
CONTENTS
xiii
xiv
1
1
1.4 STRAINED HETEROSTRUCTURES 26
1.5 S
TRAINED TENSOR IN LATTICE MISMATCHED EPITAXY
32
1.6 P
OLAR MATERIALS AND POLARIZATION CHARGE
35
1.7 T
ECHNOLOGY CHALLENGES
41
1.8 P
ROBLEM
S
41
1.9 R
EFERENCES
44
SEMICONDUCTOR BANDSTRUCTURE
2.1 INTRODUCTION 46
2.2 BLOCH THEOREM AND CRYSTAL MOMENTUM 47
2.2.1 Significance of the k-vector 49
2.3 MET
ALS
, INSULATORS, AND
SEMICONDUCTORS
51
2.4 T
IGHT BINDING METHOD
54
2.4.1 Bandstructure Arising From a Single Atomic s-Level 57
2.4.2 Bandstructure of Semiconductors 60
2.5 S
PIN-ORBIT COUPLING
62
2.5.1 Symmetry of Bandedge States 68
2.6 O
RTHOGONA
LIZED PLANE WAVE METHOD
70
2.7 P
SEUDOPOTENTIAL METHOD
71
2.8 k
• p METHOD
74
2.9 S
ELECTED BANDSTRUCTURES
80
2.10 M
OBILE CARRIERS: INTRINSIC CARRIERS
84
2.11 D
OPING: DONORS AND ACCEPTORS
92
2.11.1 Carriers in Doped Semiconductors 95
2.11.2 Mobile Carrier Density and Carrier Freezeout 96
2.11.3 Equilibrium Density of Carriers in Doped Semiconductors 97
2.11.4 Heavily Doped Semiconductors 99
2.12 TECHNOLOGY CHALLENGES
102
2.13 PROBLEMS
104
2.14 R
EFERENCES
107
Con
tents
2
46
vi
BANDSTRUCTURE MODIFICATIONS
3.1 BANDSTRUCTURE OF SEMICONDUCTOR ALLOYS
109
3.1.1 GaAs/AlAs Alloy 113
3.1.2 InAs/GaAs Alloy 113
3.1.3 HgTe/CdTe Alloy 116
3.1.4 Si/Ge Alloy 117
3.1.5 InN, GaN, AlN System 117
3.2 B
ANDSTRUCTURE MODIFICATIONS BY HETEROSTRUCTURES
118
3.2.1 Bandstructure in Quantum Wells 119
3.2.2 Valence Bandstructure in Quantum Wells 123
3.3 SUB-2-DIMENSIONAL SYSTEMS
124
3.4 STRAIN AND DEFORMATION POTENTIAL THEORY 129
3.4.1 Strained Quantum Wells 137
3.4.2 Self-Assembled Quantum Dots 140
3.5 P
OLAR HETEROSTRUCTURES
142
3.6 TECHNOLOGY ISSUES
145
3.7 PROBLEMS 145
3.8 REFERENCES
149
TRANSPORT: GENERAL FORMALISM
4.1 INTRODUCTION
152
4.2 B
OLT
ZMANN TRANSPORT EQUATION
153
4.2.1 Diffusion-Induced Evolution of f
k
(r)
155
4.2.2 External Field-Induced Evolution of f
k
(r)
156
4.2.3 Scattering-Induced Evolution of f
k
(r)
156
4.3 A
VERAGING PROCEDURES
163
4.4 TRANSPORT IN A WEAK MAGNETIC FIELD:HALL MOBILITY 165
4.5 S
OLUTION OF THE BOLTZMANN TRANSPORT EQUATION
168
4.5.1 Iterative Approach 168
4.6 BALANCE EQUATION: TRANSPORT PARAMETERS 169
4.7 T
ECHNOLOGY ISSUES
175
4.8 P
ROBLEMS
176
4.9 R
EFERENCES
177
3
109
Contents vii
4
152
DEFECT AND CARRIER–CARRIER SCATTERING
5.1 IONIZED IMPURITY SCATTERING
181
5.2 ALLOY SCATTERING
191
5.3 N
EUTRAL IMPURITY SCATTERING
194
5.4 INTERFACE ROUGHNESS SCATTERING
196
5.5 C
ARRIER–CARRIER SCATTERING
198
5.5.1 Electron–Hole Scattering 198
5.5.2 Electron–Electron Scattering: Scattering of Identical Particles
201
5.6 AUGER PROCESSES AND IMPACT IONIZATION 205
5.7 PROBLEMS 213
5.8 REFERENCES 214
LATTICE VIBRATIONS: PHONON SCATTERING
6.1 LATTICE VIBRATIONS
217
6.2 P
HONON
STATISTICS
223
6.2.1 Conservation Laws in Scattering of Particles Involving
Phonons
224
6.3 POLAR
OPTICAL PHONONS
225
6.4 P
HONONS IN HETEROSTRUCTURES
230
6.5 P
HONON SCATTERING: GENERAL FORMALISM
231
6.6 L
IMITS ON PHONON WAVEVECTORS
237
6.6.1 Intravalley Acoustic Phonon Scattering 238
6.6.2 Intravalley Optical Phonon Scattering 239
6.6.3 Intervalley Phonon Scattering 240
6.7 A
COUSTIC PHONON SCATTERING
241
6.8 OPTICAL PHONONS: DEFORMATION POTENTIAL SCATTERING
243
6.9 O
PTICAL PHONONS: POLAR SCATTERING
246
6.10 INTERVALLEY SCATTERING
251
Contentsviii
5
179
6
217
6.11 ELECTRON–PLASMON SCATTERING 252
6.12 TECHNOLOGY ISSUES 253
6.13 PROBLEMS 254
6.14 REFERENCES
257
VELOCITY-FIELD RELATIONS
IN SEMICONDUCTORS
7.1 LOW FIELD TRANSPORT
261
7.2 HIGH FIELD TRANSPORT:MONTE CARLO SIMULATION 264
7.2.1 Simulation of Probability Functions by Random Numbers 265
7.2.2 Injection of Carriers 266
7.2.3 Free Flight 269
7.2.4 Scattering Times 269
7.2.5 Nature of the Scattering Event 271
7.2.6 Energy and Momentum After Scattering 272
7.3 S
TEADY STATE AND TRANSIENT TRANSPORT
288
7.3.1 GaAs, Steady State 288
7.3.2 GaAs, Transient Behavior 290
7.3.3 High Field Electron Transport in Si 291
7.4 B
ALANCE EQUATIO
N APPROACH TO HIGH FIELD T
RANSPORT
292
7.5 IMPACT IONIZATION IN SEMICONDUCTORS 295
7.6 T
RANSPORT IN QUANTUM WELLS
296
7.7 TRANSPORT IN QUANTUM WIRES AND DOTS 303
7.8 T
ECHNOLOGY ISSUES
305
7.9 PROBLEMS 306
7.10 R
EFERENCES
308
COHERENCE, DISORDER, AND
MESOSCOPIC SYSTEMS
8.1 INTRODUCTION
312
8.2 ZENER-BLOCH OSCILLATIONS 313
8.3 RESONANT TUNNELING 316
7
260
Conten
ts
ix
8
312
Contents
8.4 QUANTUM INTERFERENCE EFFECTS
323
8.5 DISORDERED SEMI
CONDUCTORS
324
8.5.1 Extended and Localized States 326
8.5.2 Transport in Disordered Semiconductors 328
8.6 MESOSCOPIC SYSTEMS 334
8.6.1 Conductance Fluctuations and Coherent Transport 335
8.6.2 Columb Blockade Effects 337
8.7 TECNOL
OGY ISSUES
340
8.8 PROBLEMS 342
8.9 REFERENCES 343
OPTICAL PROPERTIES OF SEMICONDUCTORS
9.1 INTRODUCTION
345
9.2 MAXWELL EQUATI
ONS AND VECTOR POTENTIAL
346
9.3 ELECTRONS IN AN ELECTROMAGNETIC FIELD 351
9.4 INTERBAND TRANSI
TIONS
358
9.4.1 Interband Transitions in Bulk Semiconductors 358
9.4.2 Interband Transitions in Quantum Wells 361
9.5 INDIRECT INTERBAND TRANSITIONS 364
9.6 INTRABAND TRANSITIONS 370
9.6.1 Intraband Transitions in Bulk Semiconductors 371
9.6.2 Intraband Transitions in Quantum Wells 371
9.6.3 Interband Transitions in Quantum Dots 374
9.7 CHARGE INJECTION AND RADIATIVE RECOMBINATION 376
9.7.1 Spontaneous Emission Rate 376
9.7.2 Gain in a Semiconductor 378
9.8 NONRADIATIVE RECOMBINATION 381
9.8.1 Charge Injection: Nonradiative Effects 381
9.8.2 Nonradiative Recombination: Auger Processes 382
9.9 SEMICONDUCTOR LIGHT EMITTERS 385
9.9.1 Light Emitting Diode 386
9.9.2 Laser Diode 387
9.10 CHARGE INJECTION AND BANDGAP RENORMALIZATION 395
9.11 TECHNOLOGY ISSUES
396
9
345
x
9.12 PROBLEMS 396
9.13 REFERENCES 400
EXCITONIC EFFECTS AND MODULATION OF
OPTICAL PROPERTIES
10.1 INTRODUCTION 402
10.2 EXCIT
ONIC STATES
IN SEMICONDUCTORS
403
10.3 OPTICAL PROPERTIES WITH INCLUSION OF EXCITONIC EFFECTS 408
10.4 EXCITONIC STATES IN QUANTUM WELLS 413
10.5 EXCITONIC ABSORPTION IN QUANTUM WELLS 414
10.6 EXCITON BR
OADENING EFFECTS
416
10.7 MODULATION
OF OPTICAL PROPERTIES
420
10.7.1 Electro–Optic Effect 421
10.7.2 Modulation of Excitonic Transitions:
Quantum Confined Stark Effect
426
10.7.3 Optical Effects in Polar Heterostructures 431
10.8 EXCITON QUENCHING 432
10.9 TECHNOLOGY ISSUES 434
10.10 PROBLEMS 436
10.11 REFERENCES 437
SEMICONDUCTORS IN MAGNETIC FIELDS
11.1 SEMICLASSICAL DYNAMICS OF ELECTRONS
IN A MAGNETIC FIELD
441
11.1.1 Semiclassical Theory of Magnetotransport 447
11.2 QUANTUM MECHANICAL APPROACH TO E
LECTRONS
IN A MAGNETIC FIELD
451
11.3 AHARNOV-BOHM EFFECT 457
11.3.1 Quantum Hall Effect 460
11.4 MAGNETO-OPTICS IN LANDAU LEVELS 465
11.5 EXCITONS IN MAGNETIC FIELD 467
10
402
Contents xi
441
11
11.6 MAGNETI
C SEMICOND
UCTORS AND
SPINTRONI
CS
469
11.6.1 Spin Selection: Optical Injection 470
11.6.2 Spin Selection: Electrical Injection and Spin Transistor 471
11.7 TECHNOLOGY ISSUES 474
11.8 PROBLEM
S
474
11.9 REFERENCES 476
STRAIN IN SEMICONDUCTORS
A.1 ELASTIC STRAIN
478
A.2 ELASTIC CONSTANTS 480
EXPERIMENTAL TECHNIQUES
B.1 HIGH RESOLUTI
ON
X-RAY DIFFRACTI
ON
484
B.1.1 Double Crystal Diffraction 487
B.2 DRIFT MOBILITY
AND
HALL MOBILITY 487
B.2.1 Haynes-Schockley Experiment 488
B.2.2 Hall Effect for Carrier Density and Hall Mobility 490
B.3 PHOTOLUMINESCENCE (PL) AND EXCITATION
PHOTOLUMINESCENCE (PLE)
490
B.4 OPTICAL PUMP PROBE EXPERIMENTS 494
QUANTUM MECHANICS: USEFUL CONCEPTS
C.1 DENSITY OF STATES
499
C.2 STATIONARY PERTURBATION THEORY 504
C.2.1 Nondegenerate Case 504
C.2.2 Degenerate Case 507
C.3 TIME DEPENDENT PERTURBATION THEORY AND FERMI
GOLDEN RULE
509
C.4 BOUND STATE PROBLEM: MATRIX TECHNIQUES 511
IMPORTANT PROPERTIES OF SEMICONDUCTORS
INDEX
Contentsxii
A
478
B
484
C
498
D
514
527

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