Electronic and Optoelectronic Properties of Semiconductor Structures
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1 Electronic and Optoelectronic Properties of Semiconductor Structures Jasprit Singh University of Michigan, Ann Arbor CAMBRIDGE UNIVERSITY PRESS
2 CONTENTS PREFACE INTRODUCTION xiii xiv 1.1 SURVEY OF ADVANCES IN SEMICONDUCTOR PHYSICS xiv I.2 PHYSICS BEHIND SEMICONDUCTORS xvi I.3 ROLE OF THIS BOOK XVÜi 1 STRUCTURAL PROPERTIES OF SEMICONDUCTORS INTRODUCTION CRYSTAL GROWTH Bulk Crystal Growth Epitaxial Crystal Growth Epitaxial Regrowth CRYSTAL STRUCTURE Basic Lattice Types Basic Crystal Structures Notation to Denote Planes and Points in a Lattice: Miller Indices Artificial Structures: Superlattices and Quantum Wells Surfaces: Ideal Versus Real Interfaces Defects in Semiconductors 24
3 1.4 STRAINED HETEROSTRUCTURES STRAINED TENSOR IN LATTICE MISMATCHED EPITAXY POLAR MATERIALS AND POLARIZATION CHARGE TECHNOLOGY CHALLENGES PROBLEMS REFERENCES 44 SEMICONDUCTOR BANDSTRUCTURE INTRODUCTION BLOCH THEOREM AND CRYSTAL MOMENTUM Significance of the k-vector METALS, INSULATORS, AND SEMICONDUCTORS TlGHT BDSfDING METHOD Bandstructure Arising From a Single Atomic s-level Bandstructure of Semiconductors SPIN-ORBIT COUPLING Symmetry of Bandedge States ORTHOGONALIZED PLANE WAVE METHOD PSEUDOPOTENTIAL METHOD k p METHOD SELECTED BANDSTRUCTURES MOBILE CARRIERS: INTRINSIC CARRIERS DOPING: DONORS AND ACCEPTORS Carriers in Doped Semiconductors Mobile Carrier Density and Carrier Freezeout Equilibrium Density of Carriers in Doped Semiconductors Heavily Doped Semiconductors TECHNOLOGY CHALLENGES PROBLEMS REFERENCES 107
4 3 BANDSTRUCTURE MODIFICATIONS 109 vii 3.1 BANDSTRUCTURE OF SEMICONDUCTOR ALLOYS GaAs/AIAsAlloy InAs/GaAsAlloy HgTe/CdTeAlloy Si/Ge Alloy InN.GaN.AIN System BANDSTRUCTURE MODIFICATIONS BY HETEROSTRUCTURES Bandstructure in Quantum Wells Valence Bandstructure in Quantum Wells SUB-2-DIMENSIONAL SYSTEMS STRAIN AND DEFORMATION POTENTIAL THEORY Strained Quantum Wells Self-Assembled Quantum Dots POLAR HETEROSTRUCTURES TECHNOLOGY ISSUES PROBLEMS REFERENCES 149 TRANSPORT: GENERAL FORMALISM INTRODUCTION BOLTZMANN TRANSPORT EQUATION Diffusion-Induced Evolution of ftfr) External Field-Induced Evolution of f k (r) Scattering-Induced Evolution of f k (r) AVERAGING PROCEDURES TRANSPORT IN A WEAK MAGNETIC FIELD: HALL MOBILITY SOLUTION OF THE BOLTZMANN TRANSPORT EQUATION Iterative Approach BALANCE EQUATION: TRANSPORT PARAMETERS TECHNOLOGY ISSUES PROBLEMS REFERENCES 177
5 DEFECT AND CARRIER-CARRIER SCATTERING IONIZEDIMPURITY SCATTERING ALLOY SCATTERING NEUTRAL IMPURITY SCATTERING INTERFACE ROUGHNESS SCATTERING CARRIER-CARRIER SCATTERING Electron-Hole Scattering Electron-Electron Scattering: Scattering of Identical Partides 5.6 AUGER PROCESSES AND IMPACT IONIZATION PROBLEMS REFERENCES LATTICE VIBRATIONS: PHONON SCATTERING LATTICE VIBRATIONS PHONON STATISTICS Conservation Laws in Scattering of Partides Involving Phonons POLAR OPTICAL PHONONS PHONONS IN HETEROSTRUCTURES PHONON SCATTERING: GENERAL FORMALISM LIMITS ON PHONON WAVEVECTORS Intravalley Acoustic Phonon Scattering Intravalley Optical Phonon Scattering Intervalley Phonon Scattering ACOUSTIC PHONON SCATTERING OPTICAL PHONONS: DEFORMATION POTENTIAL SCATTERING OPTICAL PHONONS: POLAR SCATTERING INTERVALLEY SCATTERING 251
6 ix 6.11 ELECTRON-PLASMON SCATTERING TECHNOLOGY ISSUES PROBLEMS REFERENCES VELOCITY-FIELD RELATIONS IN SEMICONDUCTORS LOW FIELD TRANSPORT HIGH FIELD TRANSPORT: MONTE CARLO SIMULATION Simulation of Probability Functions by Random Numbers Injection of Carriers Free Flight Scattering Times Nature of the Scattering Event Energy and Momentum After Scattering STEADY STATE AND TRANSIENT TRANSPORT GaAs, Steady State GaAs, Transient Behavior High Field Electron Transport in Si BALANCE EQUATION APPROACH TO HIGH FIELD TRANSPORT IMPACT IONIZATION IN SEMICONDUCTORS TRANSPORT IN QUANTUM WELLS TRANSPORT IN QUANTUM WIRES AND DOTS TECHNOLOGY ISSUES PROBLEMS REFERENCES 308 COHERENCE, DISORDER, AND MESOSCOPIC SYSTEMS INTRODUCTION ZENER-BLOCH OSCILLATIONS RESONANT TUNNELING 316
7 8.4 QUANTUM INTERFERENCE EFFECTS DLSORDERED SEMICONDUCTORS Extended and Localized States Transport in Disordered Semiconductors MESOSCOPIC SYSTEMS Conductance Fluctuations and Coherent Transport Columb Blockade Effects TECNOLOGY ISSUES PROBLEMS REFERENCES 343 OPTICAL PROPERTIES OF SEMICONDUCTORS INTRODUCTION MAXWELL EQUATIONS AND VECTOR POTENTIAL ELECTRONS IN AN ELECTROMAGNETIC FIELD INTERBAND TRANSITIONS Interband Transitions in Bulk Semiconductors Interband Transitions in Quantum Wells INDIRECT INTERBAND TRANSITIONS INTRABAND TRANSITIONS Intraband Transitions in Bulk Semiconductors Intraband Transitions in Quantum Wells Interband Transitions in Quantum Dots CHARGE INJECTION AND RADIATIVE RECOMBINATION Spontaneous Emission Rate Gain in a Semiconductor NONRADIATIVE RECOMBINATION Charge Injection: Nonradiative Effects Nonradiative Recombination: Auger Processes SEMICONDUCTOR LIGHT EMITTERS Light Emitting Diode Laser Diode CHARGE INJECTION AND BANDGAP RENORMALIZATION TECHNOLOGY ISSUES 396
8 xi 9.12 PROBLEMS REFERENCES EXCITONIC EFFECTS AND MODULATION OF OPTICAL PROPERTIES INTRODUCTION EXCITONIC STATES IN SEMICONDUCTORS OPTICAL PROPERTIES WITH INCLUSION OF EXCITONIC EFFECTS EXCITONIC STATES IN QUANTUM WELLS EXCITONIC ABSORPTION IN QUANTUM WELLS EXCITON BROADENING EFFECTS MODULATION OF OPTICAL PROPERTIES Electro-Optic Effect Modulation of Excitonic Transitions: Quantum Confined Stark Effect Optical Effects in Polar Heterostructures EXCITON QUENCHING TECHNOLOGY ISSUES PROBLEMS REFERENCES 437 SEMICONDUCTORS IN MAGNETIC FIELDS SEMICLASSICAL DYNAMICS OF ELECTRONS IN A MAGNETIC FIELD Semiclassical Theory of Magnetotransport QUANTUM MECHANICAL APPROACH TO ELECTRONS IN A MAGNETIC FIELD AHARNOV-BOHM EFFECT Quantum Hall Effect MAGNETO-OPTICS IN LANDAU LEVELS EXCITONS IN MAGNETIC FIELD 467
9 xii Contents 11.6 MAGNETIC SEMICONDUCTORS AND SPINTRONICS Spin Selection: Optical Injection Spin Selection: Electrical Injection and Spin Transistor TECHNOLOGY ISSUES PROBLEMS 474 A 11.9 REFERENCES 476 STRAIN IN SEMICONDUCTORS 478 A.1 ELASTIC STRAIN 478 B A.2 ELASTIC CONSTANTS 480 EXPERIMENTAL TECHNIQUES 484 B.1 HIGH RESOLUTION X-RAY DIFFRACTION 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 C B.4 OPTICAL PUMP PROBE EXPERIMENTS 494 QUANTUM MECHANICS: USEFUL CONCEPTS 498 C.1 C.2 C.3 DENSITY OF STATES STATIONARY PERTURBATION THEORY C.2.1 Nondegenerate Case C.2.2 Degenerate Case TIME DEPENDENT PERTURBATION THEORY AND FERMI GOLDEN RULE D C.4 BOUND STATE PROBLEM: MATRIX TECHNIQUES IMPORTANT PROPERTIES OF SEMICONDUCTORS INDEX 527
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