Semiconductor Physics

Foreword
Preface to the Second Edition
Preface to the First Edition
Contents
About the Authors
Part I: Growth, Bonding and Structure
1 Properties and Growth of Semiconductors
1 Historic Development
2 Some General Properties of Semiconductors
2.1 Electrical Aspects
2.2 Structural Aspects
2.3 Chemical Aspects
3 Growth of Semiconductors
3.1 Driving Force and Nucleation
3.1.1 Equilibrium
3.1.2 Driving Force
3.1.3 Nucleation
3.1.4 Growth Modes
3.1.5 Kinetic Approach
3.1.6 Growth Habit
3.2 Growth of Bulk Single Crystals
3.2.1 Growth from the Liquid Phase
Growth from the Melt
Growth from a Solution
3.2.2 Growth from the Vapor Phase
Physical Vapor Deposition
Chemical Vapor Transport
3.2.3 Growth of Organic Crystals
3.3 Epitaxy of Layer Structures
3.3.1 Liquid-Phase Epitaxy
3.3.2 Molecular-Beam Epitaxy
Beam Sources
Kinetic Aspects
3.3.3 Metalorganic Vapor-Phase Epitaxy
Metalorganic Precursors
Precursor Supply
Growth Regimes
4 Summary
References
2 Crystal Bonding
1 Ionic and Covalent Bonding
1.1 Ionic Bonding
1.2 Covalent Bonding
1.3 Mixed Bonding
2 Metallic Bonding
3 Further Types of Bonding in Solids
3.1 Atomic and Ionic Radii
3.2 Bond-Length Relaxation in Alloys
3.3 Bonding in Organic Crystals
4 Summary
References
3 The Structure of Semiconductors
1 Structure and Symmetry in Crystalline Solids
1.1 Crystal Systems and Bravais Lattices
1.1.1 Crystal Systems
1.1.2 Bravais Lattices
1.1.3 The Primitive Unit Cell
1.2 Point Groups (Crystal Classes) and Space Groups
1.2.1 Point Groups
1.2.2 Space Groups
1.2.3 Crystallographic Notations
1.2.4 Morphology of Similar Crystals
1.3 The Reciprocal Lattice
1.3.1 Wigner-Seitz Cells and Brillouin Zones
1.4 Relevance of Symmetry to Semiconductors
1.4.1 Elemental Semiconductors and Binary Semiconducting Compounds
Elemental Semiconductors
Binary Semiconducting Compounds
1.4.2 Ternary and Quaternary Semiconducting Compounds
Ternary Chalcopyrites
Ternary Pnictides and ABC2 Compounds
Nowotny-Juza Compounds
The Adamantine AnB4-nC4 and Derived Vacancy Structures
Pseudoternary Compounds
1.5 Structure of Organic Semiconductors
2 Superlattices and Quantum Structures
2.1 Superlattice Structures
2.1.1 Mini-Brillouin Zone
2.1.2 Ultrathin Superlattices
2.1.3 Intercalated Compounds and Organic Superlattices
Intercalated Compounds
Organic Superlattices
2.2 Quantum Wells, Quantum Wires, and Quantum Dots
2.2.1 Quantum Wells
2.2.2 Quantum Wires
Epitaxial Quantum Wires
Nanowires
2.2.3 Quantum Dots
Epitaxial Quantum Dots
Colloidal Quantum Dots
3 Amorphous Structures
3.1 Building Blocks and Short-Range Order
3.1.1 Building Blocks
3.1.2 Short-Range Order
EXAFS and NEXAFS
3.2 Network Structures and Matrix Glasses
3.2.1 Network Structures
3.2.2 Matrix Glasses, α-Si:H
4 Quasicrystals
4.1 Quasiperiodicity and Properties of Quasicrystals
4.1.1 Quasiperiodicity
4.1.2 Quasicrystal Compounds
4.2 Modeling Quasicrystals
4.2.1 The Superspace Approach
4.2.2 Three-Dimensional Direct-Space Approach
5 Summary
References
Part II: Phonons
4 Elasticity and Phonons
1 Elastic Properties
1.1 Stress-Strain Relations
1.2 Elastic Stiffness Constants
1.2.1 Third-Order Elastic Constants
1.2.2 Temperature Dependence
1.2.3 Information from Elastic Stiffness Constants
2 Elastic Waves
2.1 Sound Waves in Crystals
2.1.1 Cubic Crystals
2.1.2 Hexagonal Crystals
2.1.3 Anharmonic Effects
3 Phonon Spectra
3.1 Oscillations of One-Dimensional Lattices
3.1.1 Longitudinal Lattice Oscillation
3.1.2 Transverse Lattice Oscillation
3.1.3 Transverse Oscillation in a Diatomic Lattice
3.1.4 Phonon Velocity
3.2 Phonons in a Three-Dimensional Lattice
3.2.1 Phonon Density of States
3.2.2 Local Phonon Modes
3.2.3 Phonon Modes in Mixed Crystals
3.2.4 Pressure Dependence of Phonons
3.2.5 Microscopic Force Models
3.3 Phonons in Superlattices, at Surfaces, in Organic Semiconductors, and in Amorphous Semiconductors
3.3.1 Phonons in Superlattices
3.3.2 Surface Phonons
3.3.3 Phonons in Organic Semiconductors
3.3.4 Phonons in Amorphous Semiconductors
3.3.5 Measurement of Phonon Spectra
4 Summary
References
5 Phonon-Induced Thermal Properties
1 Heat Capacity
1.1 Classical Models
1.1.1 Einstein Model
1.1.2 Debye Model
1.1.3 Validity Range of the Approximations
1.2 General Phonon-Distribution Function and Phase Changes
1.2.1 Phase Changes
1.3 Specific Heat of Amorphous Semiconductors
2 Thermal Expansion
2.1 Phenomenological Description
2.2 Lattice Dynamic Consideration
2.2.1 Negative Thermal Expansion
2.2.2 Photothermal Expansion
3 Thermal Conductivity
3.1 Diffusive Thermal Transport
3.2 Phonon-Scattering Mechanisms
3.2.1 Phonon-Phonon Scattering
3.2.2 Phonon Scattering at Lattice Defects
3.3 Phonon Scattering in Crystalline and Amorphous Semiconductors
3.3.1 Phonon Scattering in Crystalline Semiconductors
3.3.2 Thermal Conductivity by Free Carriers
3.3.3 Phonon Scattering in Amorphous Semiconductors
4 Thermal Transport in Nanostructures
4.1 Scattering at Crystal Boundaries
4.2 Mean Free Path
4.3 Thermal Transport Parallel to Boundaries
4.4 Thermal Transport Normal to Boundaries
5 Summary
References
Part III: Energy Bands
6 The Origin of Band Structure
1 Approaches for Modeling
1.1 The Proximity Approach
1.1.1 Formation of Energy Bands
1.1.2 Electronic Structure of Amorphous Semiconductors
1.2 The Periodicity Approach
1.2.1 The Kronig-Penney Model
1.3 Periodicity Versus Proximity Approach
1.3.1 Band-Edge Fluctuation
1.3.2 Discrete Defect Level in the Bandgap
2 The Reduced k Vector
2.1 Newtonian Description of a Quasi-Free Electron
2.2 The Effective Mass
3 The Proximity Approach in Organic Crystals
4 Summary
References
7 Quantum Mechanics of Electrons in Crystals
1 The Schrödinger Equation
1.1 Born-Oppenheimer Approximation
1.2 One-Electron Approximation
1.3 Pseudopotentials
2 Band-Structure Calculation
2.1 Noninteracting Electrons in Crystals
2.1.1 The kp Method
2.1.2 Hartree Approximation
2.1.3 Tight-Binding or LCAO Approach
2.1.4 Nearest-Neighbor Tight-Binding Model
2.1.5 Cellular Method
2.1.6 Augmented Plane-Wave Method
2.1.7 Green´s Function (KKR) Method
2.1.8 Linearized Muffin-Tin Orbital Method
2.2 Approaches Explicitly Containing Electron-Electron Interaction
2.2.1 Hartree-Fock Approximation
2.2.2 Density-Functional Theory
2.2.3 Quasiparticle GW Calculations
3 Relativistic Effects
4 Band Structure of Three-Dimensional Lattices
4.1 Empty and Nearly Empty Lattices
4.2 The Band Structure of Typical Semiconductors
4.2.1 Symmetry of E(k)
4.2.2 Density of States
4.3 Band Structure of Organic Crystals
5 Summary
References
8 Bands and Bandgaps in Solids
1 Valence and Conduction Bands
1.1 Insulators, Semiconductors, and Metals
1.1.1 Insulators and Semiconductors
Electrons and Holes
1.1.2 Metals
1.1.3 Semimetals and Narrow-Gap Semiconductors
1.1.4 The Shape of Valence and Conduction Bands in Semiconductors
1.2 The Effective Mass in Real Bands
1.2.1 The Conduction Bands
1.2.2 The Valence Band of Cubic Semiconductors
1.2.3 The Valence Band of Wurtzite Semiconductors
1.2.4 Probing Bands with Cyclotron Resonance
1.2.5 Measurement of Effective Masses with Cyclotron Resonance
1.2.6 The Conduction Band at Higher Energies
1.2.7 The Momentum Effective Mass
1.2.8 The Effective Mass at Higher Energies
2 The Bandgap
2.1 Bandgap of Alloys
2.2 Bandgap Dependence on Temperature and Pressure
2.3 Bandgap at High Doping Level
2.3.1 Fermi Level at High Doping Densities
3 Electronic States in Low-Dimensional Semiconductors
3.1 Quantum Wells and Superlattices
3.1.1 Quantum Wells
3.1.2 Superlattices
3.1.3 Ultrathin Superlattices
3.2 Dimensionality of the Density of States
3.3 Quantum Wires
3.4 Quantum Dots and Nanocrystals
4 Bands in Organic and Amorphous Semiconductors
4.1 Bands and Bandgap in Organic Semiconductors
4.2 Bands in Amorphous Semiconductors
5 Summary
References
9 Magnetic Semiconductors
1 Magnetic Interaction in Solids
1.1 Paramagnetic Ions
1.2 Magnetic Ordering in Semiconductors
1.2.1 Exchange Interactions
1.2.2 Ferromagnetic Domains
1.2.3 Ferromagnetic Susceptibility
1.2.4 Antiferromagnetic Susceptibility
2 Diluted Magnetic Semiconductors
2.1 II-VI Diluted Magnetic Semiconductors
2.1.1 Doping Regime
2.1.2 Low-Alloying Regime
2.1.3 High-Alloying Regime
2.2 III-V Diluted Magnetic Semiconductors
2.2.1 Mediation of Ferromagnetism by Holes
2.2.2 Stability of the Ferromagnetic State
2.3 Exchange Mechanisms in Diluted Magnetic Semiconductors
2.3.1 Superexchange
2.3.2 Double Exchange
2.3.3 p-d Exchange
3 Spintronics
3.1 Generation of a Spin Polarization
3.2 Spin-Polarized Transport
3.3 Optical Spin Detection
4 Summary
References
Part IV: Photons
10 Interaction of Light with Solids
1 Continuum Model of Solid-Light Interaction
1.1 Reflection, Transmission, and Absorption
1.1.1 Nonabsorbing Dielectrics
1.1.2 Metamaterials
1.1.3 Semiconductors with Optical Absorption
1.1.4 The Complex Electrical Conductivity
1.1.5 Dielectric Polarization
1.2 Measurement of Optical Parameters
1.2.1 Reflectance and Transmittance in Dielectrics
1.2.2 Reflectance and Transmittance in Semiconductors
1.2.3 Modulation Spectroscopy
1.2.4 Ellipsometry
1.3 Frequency Dependence of the Dielectric Function and Dielectric Screening
1.3.1 Longitudinal and Transverse Dielectric Constants
1.3.2 Spectral Ranges of the Dielectric Function
1.3.3 Dielectric Screening as Function of Wavevector
1.3.4 Empirical Screening Parameters
1.3.5 Screened Coulomb Potential
2 Photonic Bandgap Structures
2.1 Photonic Crystals
2.1.1 Scaling of Solutions
2.1.2 One-Dimensional Photonic Crystal
2.1.3 Two-Dimensional Photonic Crystals
2.1.4 Three-Dimensional Photonic Crystals
2.2 Localized Defect Modes and Microcavities
2.2.1 Optical Defects
2.2.2 Microcavity Effects
3 Nonlinear Optical Effects
3.1 Electronic and Mixing Effects
3.1.1 Nonresonant Effects of Valence Electrons
3.1.2 Nonlinear Polarization of Free Electrons
3.1.3 The Different Mixing Effects
3.1.4 Upconversion and Difference Mixing
3.1.5 Phase Matching
3.1.6 Mixing and dc Fields
3.1.7 Conversion Efficiencies
3.2 Electro-Optical Effects
3.2.1 The Pockels Effect
3.2.2 The Kerr Effect
4 Summary
References
11 Photon-Phonon Interaction
1 Lattice Polarization
1.1 Electric Fields and Polarizability
1.1.1 Ionic and Electronic Polarizability
1.1.2 Piezoelectricity and Electrostriction
1.2 Dielectric Response and Kramers-Kronig Relations
1.2.1 Kramers-Kronig Relations
1.2.2 Sum Rules
2 The Dielectric Function in the IR Range
2.1 Elementary Oscillators
2.1.1 Effective Charges
2.2 IR Reflection and Reststrahlen
3 Scattering of Photons with Phonons
3.1 The Phonon-Polariton
3.2 One- and Multiphonon Absorption
3.3 Brillouin and Raman Scattering
3.3.1 Elastic and Inelastic Scattering
3.3.2 Brillouin Scattering
3.3.3 Raman Scattering
3.3.4 Raman Scattering in Superlattices
3.3.5 Raman Scattering in Glasses
4 Summary
References
12 Photon-Free-Electron Interaction
1 Free-Electron Resonance Absorption
1.1 Electron-Plasma Absorption
1.2 Valence-Electron Plasma Absorption
1.3 Charge-Density Waves
2 Nonresonant Free-Carrier Absorption
2.1 Dispersion Relation for Free Carriers
2.2 Free-Electron Absorption
2.2.1 Effect of Scattering Mechanisms on Free-Electron Absorption
2.2.2 Free-Hole Absorption
3 Carrier Dispersion in Electric and Magnetic Fields
3.1 Magnetoplasma Reflection
3.2 Cyclotron-Resonance Absorption and Faraday Effect
3.2.1 Cyclotron-Resonance Absorption
3.2.2 Faraday Effect
4 Plasmon Dispersion in 2D Semiconductors
5 Summary
References
13 Band-to-Band Transitions
1 Optical Absorption Spectrum
1.1 The Joint Density of States
1.2 Absorption Coefficient and Dielectric Function
1.3 The Fundamental Absorption Edge
2 Direct and Indirect Transitions
2.1 Indirect Transitions
2.2 Allowed and Forbidden Transitions
2.3 Band-to-Band Magnetoabsorption
3 Transitions in Quantum Wells
3.1 Energy Levels in Multiple Quantum Wells
3.2 Absorption in Quantum Wells
4 Optical Bandgap of Amorphous Semiconductors
4.1 Intrinsic Absorption
4.2 Extrinsic Absorption in Glasses
5 Summary
References
14 Excitons
1 Optical Transitions of Free Excitons
1.1 Frenkel Excitons
1.1.1 Excitons in Alkali Halides
1.1.2 Excitons in Organic Crystals
1.2 Wannier-Mott Excitons
1.2.1 Direct-Gap Excitons
1.2.2 Complexity of Exciton Spectra
1.2.3 Indirect-Gap Excitons
1.3 Exciton-Polaritons
1.4 Trions and Biexcitons in Bulk Crystals
2 Excitons in Low-Dimensional Semiconductors
2.1 Excitons in Quantum Wells
2.2 Biexcitons and Trions in Quantum Wells
2.3 Excitons in Quantum Wires and Quantum Dots
2.3.1 Excitons in Quantum Wires
2.3.2 Excitons in Quantum Dots
Energy Levels of Excitons
Bright Excitons
Dark Excitons
3 Confined Excitons in Quantum Optics
3.1 Representation of a Qubit
3.1.1 The Qubit
Physical Implementations of Qubits
Qubits in Quantum Information Processing
3.1.2 Requirements for Qubit Photons
Different Sources of Radiation
Single and Entangled Photons
3.2 Qubit Photons from Semiconductor Quantum Dots
3.2.1 Single-Photon Emission from Bright and Dark Excitons
3.2.2 Generation of Entangled Photon Pairs
4 Summary
References
Part V: Defects
15 Crystal Defects
1 Classification of Defects
1.1 Defect Types
1.2 Defect Notation and Charged Point Defects
2 Point Defects
2.1 Density of Intrinsic Point Defects
2.2 Frozen-in Intrinsic Defect Density
2.3 Defect-Formation Energy
2.4 Defect Chemistry
2.5 Changing of Stoichiometry and Compensation
2.6 Brouwer Approximation
3 Diffusion of Lattice Defects
3.1 Fick´s Laws of Diffusion
3.2 Types of Diffusion
4 Line Defects
4.1 Edge and Screw Dislocations, Burgers Vector
4.1.1 Edge and Screw Dislocations
4.1.2 The Burgers Vector
4.1.3 Dislocation Imaging and Counting
4.2 Dislocations in Compound Semiconductors
4.3 Motion and Creation of Dislocations
4.3.1 Dislocation Kinks and Jogs
4.3.2 Dislocation Velocity
4.3.3 Dislocations and Electronic Defect Levels
5 Planar Defects
5.1 Stacking Faults and Antiphase Domains
5.2 Grain Boundaries
6 Summary
References
16 Crystal Interfaces
1 Structure of Heterointerfaces
1.1 Pseudomorphic Layers
1.2 Strain Relaxation
2 Electronic Properties of Heterointerfaces
2.1 Issues for Band Alignment
2.1.1 Experimental Results for Valence-Band Offsets
2.1.2 Space-Charge Regions
2.1.3 Classification of Interfaces
2.2 Band-Alignment Models
2.2.1 The Anderson Model for Heterojunctions
2.2.2 Linear Models for Band-Edge Offsets
2.2.3 The Harrison Valence-Band Offsets
2.2.4 Transition-Metal or Hydrogen Levels as Reference
2.2.5 The Frensley-Kroemer Model
2.3 Interface Dipole
2.3.1 Heterovalent Interfaces
2.3.2 Interface-Dipole Theory
2.3.3 Disorder-Induced Gap-State Model
2.4 Ab Initio Approaches
2.4.1 The Model-Solid Approach
2.4.2 Density-Functional Theory Combined With Many-Body Perturbation
2.4.3 The Neutral-Polyhedra Theory
3 Metal-Semiconductor Interfaces
3.1 Classification of Semiconductor-Metal Interfaces
3.2 The Classical Schottky-Mott Model
3.3 Experimental Results on Schottky Barriers
3.3.1 The Bardeen Model
3.3.2 Chemical Trends for Schottky Barriers
3.4 Interface-Dipol Models
3.4.1 Model of Interface-Induced States
3.4.2 An Initio Approaches on Schottky-Barrier Modeling
Modeling of MIGS
Modeling by Neutral Polyhedra
4 Summary
References
17 Optical Properties of Defects
1 Energy and Strength of Defect Absorption
1.1 Energy of Shallow Defects
1.2 Deep-Level Defects
1.2.1 Defect-Center Relaxation and Configuration Coordinates
1.2.2 The Huang-Rhys Factor and Relaxation Process
1.2.3 First-Principles Calculation of Model Parameters
1.2.4 Recombination-Center Relaxation
1.2.5 Oscillator Strength of Optical Absorption Lines
2 Line Shape of Electronic Defect Transitions
2.1 Homogeneous Lines
2.2 Inhomogeneous Broadening
2.2.1 Line Broadening by Electric Fields and Stress
2.2.2 Line Broadening with Compositional Disorder
2.3 Deep-Level Defect Line Broadening
2.3.1 Franck-Condon Principle and Lattice Relaxation
2.3.2 Strong, Medium, and Weak Lattice Coupling
2.3.3 Line Shape of Resonant States
2.4 Photoionization Edge Shape
2.4.1 Photoionization from Deep Centers
2.4.2 Photoionization from Shallow Centers
2.4.3 Phonon Broadening of the Ionization Edge
3 Optical Absorption of Disordered Crystals
3.1 Band Tailing
3.2 Heavy Doping and Burstein-Moss Effect
4 Summary
References
18 Shallow-Level Centers
1 Hydrogen-Like Defects
1.1 The Chemical Identity
1.2 Hydrogen-Like Donors in Indirect-Bandgap Semiconductors
1.3 Hydrogen-Like Ground State and Chemical Shift
1.3.1 Band Mixing
1.3.2 Short-Range Potential Corrections
1.3.3 Local Pseudopotentials and Model Potentials
1.4 Hydrogen-Like Acceptors
1.5 Shallow Defects in Compound Semiconductors
1.6 Donor-Acceptor Pair and Free-To-Bound Transitions
1.7 Higher Charged Coulomb Centers and Metal-Ion Interstitials
2 Excitons Bound to Impurity Centers
2.1 Excitons Bound to Ionized Donors or Acceptors
2.2 Excitons Bound to Neutral Donors or Acceptors
2.2.1 Two-Electron and Two-Hole Transitions
2.3 Excitons Bound to Isoelectronic Centers
3 Influence of External Fields on Defect Levels
3.1 Influence of Hydrostatic Pressure
3.2 Influence of Uniaxial Stress
3.3 Influence of an Electric Field
3.4 Influence of a Magnetic Field
3.4.1 The Zeeman Effect
3.4.2 Magnetic Resonances at Lattice Defects
4 Summary
References
19 Deep-Level Centers
1 Modeling of Deep-Level Centers
1.1 General Properties of Deep-Level Centers
1.1.1 Model of Square-Well Potential
1.1.2 Coulomb Tail and Deep-Center Potential
1.2 Theoretical Methods to Analyze Defect Centers
1.2.1 Perturbative Methods and Green´s Function Technique
1.2.2 Cluster Calculation and Supercell Technique
1.2.3 Semiempirical Tight-Binding Approximation
1.3 The Jahn-Teller Effect
1.4 Crystal-Field Theory
2 Deep Centers in Semiconductors
2.1 Defects in Alkali Halides
2.1.1 Anion Vacancy: The F Center
2.1.2 Other Centers in Alkali Halides
2.2 Vacancies in Semiconductors
2.2.1 Vacancies in Covalent Crystals
2.2.2 Vacancies in Compound Semiconductors
2.3 Self-lnterstitials and Antisite Defects
2.4 Hydrogen in Semiconductors
2.5 Substitutional Defects
2.6 Chalcogens in Semiconductors
2.7 The DX Center
2.8 Negative-U Centers
2.9 Instabilities of Shallow and Deep Centers
3 Transition-Metal Impurities
3.1 Effect of Site, Charge, Spin, and Excitation
3.2 The Energy of Levels
3.3 Optical Transitions of Transition-Metal Dopants
4 Summary
References
20 Defects in Amorphous and Organic Semiconductors
1 Tailing States in Disordered Semiconductors
1.1 The Anderson Model
1.2 Anderson and Anderson-Mott Localizations
1.3 Band Tails, Localization, and Mobility Edge
1.4 Simulation of Defect States in Amorphous Semiconductors
2 Defects in Amorphous Semiconductors
2.1 Classes of Amorphous Semiconductors
2.2 Defect Types in Amorphous Semiconductors
2.2.1 Strain-Related Defects
2.2.2 Under- and Overcoordinated Defects
2.2.3 Dangling and Floating Bonds
2.2.4 Deviation from Optimal Bonding Configuration
2.2.5 Doping in Semiconducting Glasses
2.2.6 Microcrystalline Boundaries and Voids
2.2.7 Spin Density of Defects
3 Defects in Organic Semiconductors
3.1 Classes of Organic Semiconductors
3.2 Structural Defects in Small-Molecule Crystals
3.2.1 Molecule Crystals Grown on Substrates
3.2.2 Point Defects in Molecule Crystals
3.3 Defects in Polymers
4 Summary
References
Part VI: Transport
21 Equilibrium Statistics of Carriers
1 The Intrinsic Semiconductor
1.1 Level Distribution Near the Band Edge
1.2 Statistical Distribution Functions
1.3 Intrinsic Carrier Densities in Equilibrium
1.4 Density-of-State Effective Mass and Fermi Energy
1.5 Intrinsic Carrier Generation
2 The Extrinsic Semiconductor
2.1 The Position of the Fermi Level
2.2 Temperature Dependence of the Fermi Level
2.3 Carrier Density in Extrinsic Semiconductors
2.4 Intrinsic and Minority Carrier Densities
2.5 Self-Activated Carrier Generation
2.6 Frozen-In Carrier Densities
3 Phase Transitions at High Carrier Densities
3.1 The Mott Transition
3.2 Electron-Hole Condensation
4 Summary
References
22 Carrier-Transport Equations
1 Carriers in Semiconductors
1.1 Bloch Electrons and Holes
1.2 The Polaron
1.2.1 Large Polarons and Fröhlich Coupling
1.2.2 Small Polarons and Criteria for Different Polarons
2 Conductivity and Mobility of Carriers
2.1 Electronic Conductivity
2.2 Electron Mobility
3 Currents and Electric Fields
3.1 Drift Current in an Electric Field
3.2 Diffusion Currents and Total Currents
3.3 Electrochemical Fields and Quasi-Fermi Levels
3.4 Carrier Distributions in External and Built-In Fields
4 The Boltzmann Equation
4.1 The Boltzmann Equation for Electrons
4.2 The Boltzmann Equation for Phonons
4.3 The Relaxation-Time Approximation
4.4 Carrier Scattering and Energy Relaxation
4.5 The Mobility Effective Mass
4.6 Momentum and Energy Relaxation
4.6.1 The Average Momentum Relaxation Time
4.6.2 The Average Energy Relaxation Time
4.7 Phonon and Electron Drag
5 Summary
References
23 Carrier Scattering at Low Electric Fields
1 Types of Scattering Centers
2 Electron Scattering with Phonons
2.1 General Properties of Scattering with Phonons
2.2 Scattering with Acoustic Phonons
2.2.1 Longitudinal Acoustic Phonon Scattering
2.2.2 Acoustic Phonon Scattering with Piezoelectric Interaction
2.3 Scattering with Optical Phonons
2.3.1 Optical Phonon Scattering in Nonpolar Compounds
2.3.2 Optical Phonon Scattering in Polar Semiconductors
3 Scattering at Coulomb Potentials
3.1 Ionized-Impurity Scattering
3.2 Coulomb Scattering in Anisotropic Semiconductors
3.3 Scattering at Dislocations
3.4 Carrier-Carrier and Carrier-Plasmon Scattering
3.4.1 Carrier-Carrier Scattering
3.4.2 Carrier Scattering on Plasmons
4 Scattering by Neutral Defects
4.1 Scattering by Neutral Lattice Defects, Intrinsic Point Defects, and Defect Clusters
4.2 Influence of External Surfaces
4.3 Influence of Microcrystallite Boundaries
4.4 Alloy Scattering
5 Multivalley Carrier Transport
5.1 Processes in Intervalley Scattering
5.2 Mobility for Intervalley Scattering
6 Summary
References
24 Carrier Scattering at High Electric Fields
1 Transport-Velocity Saturation
1.1 Drift-Velocity Saturation in External Fields
1.2 Carrier-Diffusion Saturation
1.3 High-Field Carrier Transport in Built-In Electric Fields
2 Distribution Function at Higher Electric Fields
2.1 Warm and Hot Carriers
2.2 Mobility Changes Induced by Optical Excitation
2.3 Numerical Solution of the Boltzmann Equation
3 Elastic and Inelastic Scattering at High Electric Fields
3.1 Intravalley Scattering at High Electric Fields
3.1.1 Scattering with Acoustic Phonons
3.1.2 Scattering with Optical Phonons
3.2 Intervalley Scattering at High Electric Fields
3.2.1 Equivalent-Intervalley Scattering
3.2.2 Intervalley Scattering into Nonequivalent Valleys
4 Summary
References
25 Carriers in Magnetic Fields and Temperature Gradients
1 Transport Equations and Thermoelectric Effects
1.1 The Boltzmann Equation in Magnetic Fields and Temperature Gradients
1.2 Transport Equations
1.2.1 Thermoelectric Effects
1.2.2 Magneto-Electric Effects
The Hall Effect
Transverse Magnetoresistance
1.3 Cyclotron Resonance
2 Quantum Effects in a Strong Magnetic Field
2.1 Quasi-Free Carriers in a Strong Magnetic Field
2.2 Diamagnetic and Paramagnetic Electron Resonance
2.3 Density of States and DeHaas-Type Effects
3 Ballistic Transport in Strong Magnetic Fields
3.1 The Integer Quantum-Hall Effect
3.2 The Fractional Quantum Hall Effect
4 Summary
References
26 Superconductivity
1 Low-Temperature Superconductors
1.1 Superconductive Solids
1.2 Cooper Pairs and Condensation
1.3 The Critical Temperature
1.4 Meissner-Ochsenfeld Effect and Type I or Type II Superconductors
1.5 Josephson Tunneling and SQUID
2 High-Temperature Superconductors
2.1 Ceramic High-Tc Superconductors
2.2 Normal-State Properties of High-Tc Superconductors
2.3 The Superconductive State of High-Tc Superconductors
2.4 Mediating-Partner Models for High-Tc Superconductors
3 Summary
References
27 Carrier Transport in Low-Dimensional Semiconductors
1 In-Plane Transport in Two-Dimensional Structures
1.1 The Two-Dimensional Electron Gas (2DEG)
1.2 Carrier Mobility in a 2D Electron Gas
2 Perpendicular Carrier Transport in 2D Structures
2.1 Tunneling Through a Planar Barrier
2.2 Tunneling Through a Double-Barrier Quantum Well
2.3 Perpendicular Transport in Superlattices
2.3.1 Wannier-Stark Ladder and Bloch Oscillations
2.3.2 Quantum-Cascade Laser and High-Field Domains
3 Transport in 1D Structures
3.1 Diffusive and Ballistic Transport
3.2 Quantization of Conductance
3.3 Landauer-Büttiker Formalism
4 Topological Insulators
4.1 Topological Band Theory
4.2 Quantum Spin Hall Insulator
4.3 3D Topological Insulators
5 Zero-Dimensional Transport
5.1 Single-Electron Tunneling
5.2 Coulomb Blockade in Few-Electron Dots
6 Summary
References
28 Carrier Transport Induced and Controlled by Defects
1 Impurity-Band Conduction
1.1 Concept of Impurity Bands
1.2 The Impurity Band
1.2.1 The Lifshitz-Ching-Huber Model
1.2.2 Coulomb Gap and Mott Transition
2 Phonon-Activated Conduction
3 Heavily Doped Semiconductors
3.1 Intermediate Doping Range
3.2 Degenerate and Highly Compensated Heavily Doped Semiconductors
4 Transport in Amorphous Semiconductors
4.1 The Mobility Edge
4.2 Diffusive Carrier Transport and Percolation
4.3 Activated Mobility
4.4 Temperature Dependence of the Conductivity
5 Charge Transport in Organic Semiconductors
5.1 Band Conductance in Organic Crystals
5.1.1 Single-Component and Two-Component Semiconductors
5.1.2 Carrier Mobility in Pure Organic Crystals
5.2 Hopping Conductance in Disordered Organic Semiconductors
6 Summary
References
Part VII: Generation - Recombination
29 Carrier Generation
1 Thermal and Optical Carrier Generation
1.1 Optical Carrier Generation
1.2 Thermal Ionization
1.2.1 Thermal Ionization Mechanism
1.2.2 Thermal Excitation Probability
2 Field Ionization
2.1 Frenkel-Poole Ionization
2.2 Impact Ionization
2.2.1 Impact Ionization Across the Bandgap
2.2.2 Avalanche Current and Multiplication Factor
2.2.3 Ionization via Energetic Particles
2.3 Electron Tunneling
2.3.1 Tunneling Through Triangular or Parabolic Barriers
2.3.2 Tunneling in a Three-Dimensional Crystal
2.3.3 Tunneling Spectroscopy
3 Summary
References
30 Carrier Recombination and Noise
1 Nonradiative Recombination
1.1 Energy Transfer to Phonons
1.1.1 Recombination at Coulomb-Attractive Centers
1.1.2 Nonradiative Recombination at Deep Centers
1.2 Energy Transfer to Electrons
1.2.1 Auger Recombination
1.2.2 Auger Recombination at High Carrier Densities
2 Statistics of Recombination
2.1 Trapping or Recombination
2.1.1 Electron and Hole Traps
2.1.2 Recombination Centers
2.2 Thermal Equilibrium, Steady State, and Shockley-Read-Hall Recombination
2.2.1 Thermal Equilibrium
2.2.2 The Shockley-Read-Hall Center
3 Radiative Recombination
3.1 Thermal Radiation
3.2 Intrinsic Luminescence
3.2.1 Band-to-Band Luminescence
3.2.2 Recombination of Free Excitons
3.2.3 Recombination of Exciton Molecules and of Electron-Hole Liquids
3.3 Extrinsic Luminescence
3.3.1 Band-Edge Luminescence in Heavily Doped Semiconductors
3.3.2 Free-to-Bound and Donor-Acceptor-Pair Transitions
3.3.3 Bound-Exciton Luminescence
3.3.4 Luminescence Centers
3.3.5 Quenching of Luminescence
3.3.6 Stimulated Emission
4 Noise
4.1 Description of Fluctuation
4.2 Noise in Equilibrium Conditions
4.3 Nonequilibrium Noise
4.3.1 Shot Noise or Injection Noise
4.3.2 Generation-Recombination Noise
4.4 The 1/f Noise
4.4.1 The Conventional Quantum 1/f Effect
4.4.2 The Coherent Quantum 1/f Effect
5 Summary
References
31 Photoconductivity
1 Basic Photoconductivity Processes
1.1 Carrier Generation
1.1.1 Wavelength Dependence of the Generation Rate
1.1.2 Photo-Ionization Cross Section
1.2 Intrinsic Photoconductivity
2 Extrinsic Photoconductivity
2.1 Effect of Traps on Photoconductivity
2.2 Effect of Recombination Centers
3 Persistent and Negative Photoconductivity
3.1 Persistent Photoconductivity
3.2 Negative Photoconductivity
3.2.1 Optical Quenching
3.2.2 Thermal Quenching
3.2.3 Field Quenching
4 Summary
References
32 Dynamic Processes
1 Carrier Transit and Relaxation
1.1 Transit Effects in Carrier Transport
1.1.1 Characteristic Transport Times and Lengths
1.1.2 Shockley-Haynes-Type Experiment
1.1.3 Dispersive Carrier Transport in Amorphous Semiconductors
1.2 Relaxation of Carriers
1.2.1 Momentum Relaxation of Electrons
1.2.2 Energy Relaxation of Electrons
1.2.3 Energy-Relaxation Mechanisms
1.3 Recombination in Electron-Hole Plasmas and Liquids
2 Phonon and Exciton Kinetics
2.1 Relaxation of Phonon Distributions
2.1.1 TO-Phonon Relaxation
2.1.2 LO-Phonon Relaxation
2.1.3 Phonon Relaxation in Quantum Wells
2.2 Exciton Kinetics
2.2.1 Dynamics of Bulk Excitons
2.2.2 Dynamics of Quantum-Well Excitons
3 Relaxation of the Spin Momentum
3.1 Measurement of Spin Relaxation
3.2 Spin-Relaxation of Free Electrons in Bulk Semiconductors
3.3 Spin-Relaxation of Free Carriers and Excitons in Quantum Wells
4 Summary
References
Appendix: High-Field Domains
Inhomogeneous Field or Current Distributions
Negative Differential Conductivity
Domain Instability
Phase-Space Analysis
Decrease of Carrier Density with Field
Field Quenching
Cathode- and Anode-Adjacent Domains
Franz-Keldysh Effect to Directly Observe High-Field Domains
Drift-Velocity Saturation
Workfunction Dependence on Photoconductivity
Moving High-Field Domains
Summary and Emphasis
References
Index