PHYSICS OF SEMICONDUCTORS AND THEIR HETEROSTRUCTURES
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1 PHYSICS OF SEMICONDUCTORS AND THEIR HETEROSTRUCTURES Jasprit Singh University of Michigan McGraw-Hill, Inc. New York St. Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico Milan Montreal New Delhi Paris San Juan Singapore Sydney Tokyo Toronto
2 CONTENTS PREFACE INTRODUCTION THE FREE ELECTRON PICTURE 1.1 Atoms in Solids 1.2 The Drude Model 1.3 Quantum Mechanics and Electrons 1.4 The Density of States 1.5 Filling of Electronic States 1.6 For the Technologist in You 1.7 Problems 1.8 References PERIODICITY: CRYSTAL STRUCTURES 2.1 Periodicity of a Crystal 2.2 Basic Lattice Types 2.3 The Reciprocal Lattice 2.4 Artificial Structures: Superlattices 2.5 Surfaces: Ideal Versus Real 2.6 Interfaces 2.7 For the Technologist in You 2.8 Problems 2.9 References xvii xxi WAVE DIFFRACTION IN PERIODIC STRUCTURES Bragg's Law Laue Conditions Diffraction from Random Scatterers Diffraction Methods Temperature Dependent Effects For the Technologist in You Problems References 89 ix
3 X ELECTRONS IN PERIODIC STRUCTURES Periodicity and Bloch's Theorem Significance of k: Crystal Momentum Electron States in a Weak Periodic Potential A Simple Description of Band Filling Holes in Semiconductors For the Technologist in You Problems References 125 SEMICONDUCTOR BANDSTRUCTURE The Tight Binding Method The Spin-Orbit Coupling Symmetry of Conduction Bandedge States Symmetry of Valence Bandedge States The Orthogonalized Plane Wave Method The Pseudopotential Method The k p Method Selected Bandstructures Density of States in Semiconductors For the Technologist in You Problems References 176 BANDSTRUCTURE MODIFICATIONS: ALLOYS AND HETEROSTRUCTURES Bandstructure of Semiconductor Alloys Bandstructure Modifications by Heterostructures Bandstructure in Quantum Wells Bandstructure in Superlattices For the Technologist in You Problems References 215 BANDSTRUCTURE MODIFICATIONS THROUGH STRAIN Critical Thickness Elastic Strain The Elastic Constants Strain Tensor in Lattice Mismatched Epitaxy Deformation Potential Theory Bandgap Alteration Built-in Electric Fields in Strained Quantum Wells For the Technologist in You 248
4 XI 7.9 Problems References DOPING OF SEMICONDUCTORS Intrinsic Carrier Concentration The EfFective Mass Equation for Shallow Levels Extrinsic Camers Population of Impurity Levels, Carrier Freeze-out Heavily Doped Semiconductors Modulation Doping Hydrogenic Impurities in Quantum Wells For the Technologist in You Problems References LATTICE VIBRATIONS: PHONONS Considerations for Crystal Binding Crystal Vibrations for a Monatomic Basis Crystal Vibrations for a Diatomic Basis Phonons: Quantization of Lattice Vibrations Polar Optical Phonons Optical Phonon-Photon Interactions Phonon Statistics Models for Phonon Energy Phonon Dispersion Measurement Techniques Phonons in Heterostructures For the Technologist in You Problems References TRANSPORT: GENERAL FORMALISM Relaxation Times The Boltzmann Transport Equation Averaging Procedures Mobility Measurement Techniques Hall Mobility Solution of the Boltzmann Transport Equation For the Technologist in You Problems References DEFECT AND CARRIER-CARRIER SCATTERING Ionized Impurity Scattering Alloy Scattering Carrier-Carrier Scattering 374
5 11.4 Auger Processes and Impact Ionization For the Technologist in You Problems References 394 PHONON SCATTERING General Formalism Limits on Phonon Wavevectors Selection Rules for Phonon Scattering Acoustic Phonon Scattering Deformation Potential Optical Phonon Scattering Polar Optical Phonon Scattering Electron-Plasmon Scattering Piezoelectric Scattering Intervalley Scattering The Polaron For the Technologist in You Problems References 432 THE VELOCITY-FIELD RELATIONS Low Field Transport High Field Transport Monte Carlo Simulation of Carrier Transport Electron Transport Monte Carlo Calculations High Field Electron Transport in Si Hole Transport Monte Carlo Calculations Balance Equation Approach to High Field Transport Impact Ionization in Semiconductors Zener-Bloch Oscillations For the Technologist in You Problems References 492 TRANSPORT IN HETEROSTRUCTURES Parallel Transport in Quantum Wells and MODFETs Mobility in a MODFET Quantum Well High Temperature / High Field Transport Effect of Strain on Transport Transport in Quantum Wires Real Space Charge Transfer Avalanche Processes in Quantum Well Structures Quantum Transport Resonant Tunneling 524
6 14.10 Tunneling in Heterostructures with Spatially Varying Central Cell Symmetry Perpendicular Transport in Superlattices Quantum Interference Effects Density Matrix Formalism For the Technoligist in You References INTERACTIONS OF PHOTONS WITH SEMICONDUCTORS Maxwell Equations, Vector Potential, and Gauge Transformations Drude-Zener Theory Optical Modes in Ionic Crystals Kramers-Kronig Relation Electrons in an Electromagnetic Field Selection Rules for Optical Processes Interband Transitions Optical Processes in Semiconductor Lasers Indirect Interband Transitions Intraband Transitions For the Technologist in You Problems References OPTICAL PROPERTIES IN SEMICONDUCTORS: EXCITONIC TRANSITIONS 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 Excitonic Transitions: Quantum Confined Stark Effect Exciton Quenching Refractive Index Modulation Due to Exciton Modulation Strain Induced Electric Fields for Enhanced Optical Modulation Radiative Recombination from Excitonic States For the Technologist in You Problems References 665 xiü
7 XIV 17 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 The Aharonov-Bohm Effect The De Haas-Van Alphen Effect The Shubnikov-De Haas Effect The Quantum Hall Effect Magneto-optics in Landau Levels Excitons in Magnetic Field Shallow Impurities in Magnetic Fields Magnetic Semiconductors For the Technologist in You References DEFECTS AND DISORDER IN SEMICONDUCTORS Point Defects in Semiconductors Trapping and Recombination Dislocations and Lattice Mismatched Epitaxy Disordered Semiconductors Extended and Localized States Mesoscopic Structures For the Technologist in You References AND NOW SOMETHING OF REAL CONSEQUENCE: DEVICES Some Recent Trends Requirements for Successful Devices A Summary of Some Important Devices References 782 A THE WAVE PACKET PICTURE 783 A.l Motion of a Wavepacket 784 B ELECTRON IN A QUANTUM WELL 788 C THE HARMONIC OSCILLATOR PROBLEM 791 D COMBINATION OF ANGULAR MOMENTUM STATES 795
8 XV E STATIONARY PERTURBATION THEORY 797 E.l Nondegenerate Case 798 E.2 Degenerate Case 799 F EIGENVALUE METHOD TO SOLVE COUPLED EQUATIONS 801 G THE ZEEMAN EFFECT 804 H THE VARIATIONAL METHOD 807 I TIME DEPENDENT PERTURBATION THEORY AND THE FERMI GOLDEN RULE Transition Probability 813 J GAUSSIAN AND MKSA UNITS 815 K NUMERICAL EVALUATION OF SOME PHYSICAL PARAMETERS 819 K.l Density of States 819 K.2 Mobility 820 K.3 Cyclotrori Resonance Frequency 820 K.4 Bohr Radius and Binding Energies of Dopants or Excitons 821 K.5 Effective Density of States and Intrinsic Carrier Concentration 821 K.6 Absorption Coefficient and Emission Rate 822 K.7 Recombination Times 823 L SELECTED PROPERTIES OF SEMICONDUCTORS 824 L.l Tabulated Values 824 L.2 References 827 M EVALUATION OF SCATTERING RATES FOR A MONTE CARLO PROGRAM 828 M.l Polar L-0 Phonon Scattering 828 M.2 Acoustic Phonon Scattering 830 M.3 Equivalent Intervalley Scattering 831 M.4 Non-equivalent Intervalley Scattering 832 M.5 Ionized Impurity Scattering 833 M.6 Alloy Scattering 835 N WIDE BANDGAP SEMICONDUCTORS 836 N.l References 841 INDEX 843
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