Modern Semiconductor Physics and Device Applications

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Authors
1 Quantum Electron States and Energy Bands
	1.1 Crystal Structures
	1.2 Bravais Lattices
	1.3 Schrödinger Equation for an Electron in a Periodic Crystal Lattice Potential
		1.3.1 Symmetry and Classification of Electron Energy States
		1.3.2 Reciprocal Lattice and Brillouin Zone
	1.4 The Nearly-Free Electron Approximation
	1.5 The Kronig-Penney Model
	1.6 The Tight-Binding Approximation
	1.7 The k-p Method
	1.8 Effective Mass of an Electron
	1.9 Electron Density of States
	1.10 Korringa-Kohn-Rostoker and Ab-Initio Methods
	1.11 Spin–Orbit Interaction
	1.12 Luttinger-Kohn Band Structure: Si, Ge, and GaAs
	1.13 Energy Bands in Graphene
	1.14 Narrow-Gap Semiconductors
	1.15 Inverted Bands. Semimetals and Berry Field
	References
2 Quantum Confinement in Semiconductors
	2.1 Size Quantization
		2.1.1 Envelope Functions and Effective Hamiltonian
	2.2 Electrons in Quantum Wells
	2.3 Quantum Well States in the Valence Band
	2.4 2D-Semiconductors
	2.5 Quantum Wires and 1D-Semiconductors
	2.6 3D-Confinement: Quantum Dots
	2.7 Electrons States on Surfaces and Interfaces: Tamm States
	2.8 Topological Insulator and Surface States. Gapless Dirac Fermions
	References
3 Impurities and Disorder in Semiconductors
	3.1 Single Impurity: Donors and Acceptors
	3.2 Screening of Impurity Potential by Free Electrons
	3.3 Electron in the Field of Impurity Potential
	3.4 Model of Short-Range Impurity Potential
	3.5 T-Matrix Approximation
	3.6 Electron States of an Impurity Atom in the Crystalline Lattice: Tight-Binding Approach
	3.7 Magnetic Impurity
	3.8 Anderson Model for Magnetic Impurity
	3.9 Heavily Doped Semiconductors: Disorder Potential
	3.10 Impurity Bands. Impurity Band Tail
	3.11 Semiconductor Alloys
		3.11.1 Virtual Crystal and CPA Approximation
	3.12 Electron in a Smooth Disorder Potential
	References
4 Statistics of Electrons in Semiconductors
	4.1 Statistical Physics: Gibbs Distribution
	4.2 Metals and Semiconductors
	4.3 Intrinsic Semiconductors
	4.4 Electron Distribution in Doped Semiconductors
		4.4.1 Simple Donors and Acceptors
		4.4.2 Degenerate Impurities
		4.4.3 Multivalent Impurities and Electron Interaction
		4.4.4 Amphoteric Impurities
	References
5 Electrons in a Magnetic Field
	5.1 Lorentz Force
	5.2 Circular Motion in a Magnetic Field
		5.2.1 Cyclotron Mass in Anisotropic Semiconductors
	5.3 Landau Quantization
		5.3.1 Landau Levels: Degeneracy and Density of States
	5.4 Landau Levels in Symmetric Gauge
	5.5 Ladder Operators
	5.6 Localized States and Extended Chiral Modes
	5.7 Dirac Electrons in a Magnetic Field
	5.8 Chiral Anomaly
	5.9 Landau Spectrum in a Narrow-Gap Semiconductor
	5.10 Landau Levels in Rashba Electron Gas
	5.11 Aharonov–Bohm Effect
	References
6 Phonons and Electron–Phonon Interaction
	6.1 Types of Chemical Bonds
	6.2 Born-Oppenheimer Approximation
	6.3 Lattice Dynamics
		6.3.1 Phonons
		6.3.2 One-Dimensional Chain: Acoustical Vibrations
		6.3.3 One-Dimensional Chain: Optical Vibrations
		6.3.4 Optical Vibrations in Ionic Dielectric Crystals: Lyddane–Sachs–Teller Relation
	6.4 Thermodynamics of Lattice Vibrations. Heat Capacity
		6.4.1 The Density of States
	6.5 Phonon–Phonon Interaction
		6.5.1 Thermal Expansion
		6.5.2 Thermal Conductivity and Resistance
	6.6 Electron–Phonon Interaction
		6.6.1 Deformation Potentials
		6.6.2 Electron–Phonon Interaction in Ionic Crystals
			6.6.2.1 FrÖhlich Hamiltonian
			6.6.2.2 Piezoelectric Interaction
	References
7 Transport Properties
	7.1 Electrons in Electric and Magnetic Fields
	7.2 Nonequilibrium State under Electric Field or Temperature Gradient
	7.3 Electric Current: Conductivity Tensor
	7.4 Drude Theory
	7.5 Hall Effect
	7.6 Thermoelectric and Thermo-Electromagnetic Effects
	7.7 Kinetic Equation
	7.8 Kinetic Coefficients
	7.9 Symmetry of Kinetic Coefficients: Onsager’s Principle
	7.10 Macroscopic Equations
	7.11 Electron Wave Packet in Electric and Magnetic Fields
	7.12 Quantum Transport: Green’s Functions and Feynman Diagrams
		7.12.1 Green’s Function Technique at T = 0
		7.12.2 Green’s Function Technique at Finite Temperatures
	7.13 Quantum Transport Approach to Conductivity
	7.14 Quantum Hall Effect: Hall Conductivity as a Berry Phase: Thouless-Kohmoto-Nightingale-Nijs (TKNN) Theory
	7.15 Laughlin and Halperin Explanation of QHE
	7.16 Fractional QHE
	7.17 Anderson Localization
	7.18 Theory of Weak Localization
	7.19 Minimum Metallic Conductivity and Mott Transition
	References
8 Impurity Band Conductivity
	8.1 Low-Temperature Conductivity and Electron Hopping
	8.2 Variable-Range Hopping
	References
9 Spin-Resolved Transport in Semiconductors
	9.1 Spin Transport and Spin Current
	9.2 Anomalous Hall Effect
	9.3 Mechanism of AHE Related to the Spin-Orbit Scattering from Impurities
	9.4 Intrinsic Mechanism of AHE: Quantization of AHE
	9.5 Spin Hall Effect
	9.6 Current-Induced Spin Polarization and Spin Torque
	References
10 Electron Scattering
	10.1 Elements of Scattering Theory
	10.2 Electron Scattering in Solids
	10.3 Impurity Scattering: Momentum Relaxation Time
		10.3.1 Electron Scattering by a Screened Coulomb Potential
		10.3.2 Unscreened Coulomb Potential
	10.4 Neutral Impurity Scattering
	10.5 Phonon Scattering
		10.5.1 Transport Relaxation Time
	10.6 Simultaneous Action of Several Scattering Mechanisms
	10.7 Spin-Dependent Scattering and Spin Relaxation Time
	10.8 Kondo Effect
	References
11 Magnetic Semiconductors
	11.1 Direct and Indirect Interactions between Magnetic Impurities
	11.2 RKKY Interaction
	11.3 Indirect Exchange in Dielectrics: Bloembergen–Rowland Mechanism
	11.4 Ferromagnetic Ordering of Magnetic Impurities
	11.5 Magnetic Order and Percolation
	11.6 Spin Glass
	11.7 Diluted Magnetic Semiconductors
	11.8 GaMnAs Magnetic Semiconductor
	11.9 Stoner Ferromagnetism
	References
12 Optical Properties
	12.1 Coupling to Electromagnetic Field and Gauges
	12.2 Phenomenological Approach to Wave Propagation
		12.2.1 Quasi-Static Fields
		12.2.2 Energy Flux
		12.2.3 Electromagnetic Waves in a Conductive Media
		12.2.4 Negative Refraction
		12.2.5 Intraband Free Carrier Absorption
	12.3 Interband Absorption in Semiconductors
		12.3.1 Momentum Conservation in Direct Interband Transitions
		12.3.2 Absorption Due to Allowed and Forbidden Transitions
		12.3.3 Indirect Optical Transitions
	12.4 Exciton Transitions
	12.5 Impurity-Band Optical Transitions
	12.6 Electroabsorption and Franz–Keldysh Effect
	12.7 Lattice Absorption
	12.8 Optical Spin Orientation and Spin-Galvanic Effect
		12.8.1 Spin Relaxation
		12.8.2 Spin-Galvanic Effect
	References
13 Nonequilibrium Electrons and Holes
	13.1 Lifetime of Nonequilibrium Carriers: Phenomenological Approach
		13.1.1 Direct Band-to-Band Recombination
		13.1.2 Schokley–Read–Hall Recombination
		13.1.3 Auger Recombination
	13.2 Recombination: Microscopic Approach
		13.2.1 Radiative Recombination
		13.2.2 Auger Recombination: Bulk Semiconductors
		13.2.3 Auger Recombination. Quantum Wells
	References
14 Schottky Contacts and p–n Junctions
	14.1 Contacts Metal-Semiconductor
		14.1.1 Energy Band Diagram
		14.1.2 Rectifying Contacts
		14.1.3 Weak Band Bending
		14.1.4 Strong Band Bending
		14.1.5 Inverse Contact
		14.1.6 Current–Voltage Characteristics
		14.1.7 Thermionic Emission Model
		14.1.8 Drift-Diffusion Model
		14.1.9 Barrier Height Lowering
		14.1.10 Transmission Modes and Ohmic Contacts
		14.1.11 Equivalent Circuit and Frequency Response
	14.2 P–n Junctions
		14.2.1 Depletion Region
		14.2.2 Carrier Distributions
		14.2.3 Forward Bias
		14.2.4 Reverse Bias
			14.2.4.1 Diode Breakdown
		14.2.5 Frequency Response
	References
15 Field-Effect Transistors
	15.1 Energy Band Diagrams
	15.2 Accumulation Regime
		15.2.1 Current–Voltage Characteristics
	15.3 Depletion Regime
		15.3.1 Current–Voltage Characteristics
	15.4 FET Extrinsic Parameters
	15.5 High-Electron Mobility Transistors
		15.5.1 Remote Doping
		15.5.2 Polarization Doping in III-Nitride HEMTs
	15.6 Frequency Response and Power Characteristics
		15.6.1 Switching Time
		15.6.2 Output Power, Power Gain, and Power-Added Efficiency
	References
16 Semiconductor Lasers
	16.1 Quasi-Fermi Levels and Population Inversion
	16.2 Diode Laser Design
	16.3 Resonant Cavity and Longitudinal Modes
		16.3.1 Distributed Mirrors and Mode Selectivity
	16.4 Modal Gain and Threshold Condition
	16.5 Recombination Currents
	16.6 Light-Current Characteristics and Efficiency
	16.7 Temperature Sensitivity of the Threshold Current
		16.7.1 Threshold Carrier Density
		16.7.2 Radiative Recombination Current
		16.7.3 Auger Recombination Currents
		16.7.4 Threshold Current
	16.8 Light-Emitting Diodes
	16.9 Material Choice and Engineering in III–V Semiconductor Heterojunctions
	16.10 Quantum Cascade Laser
	References
17 Semiconductor Photodetectors
	17.1 Photoconductors
		17.1.1 Generation Rate and Distribution of Carriers
		17.1.2 Uniform Illumination, Photoresponse, and Relaxation Times
		17.1.3 Steady-State Illumination. Photoconductive Gain and Responsivity
		17.1.4 Rectangular Pulse Illumination
		17.1.5 Frequency Response
		17.1.6 The Noise in Photodetectors
		17.1.7 Specific Detectivity
		17.1.8 Background Limited Performance
	17.2 Photodiodes
	17.3 Quantum Well Photodetectors
		17.3.1 Intersubband Absorption
		17.3.2 Responsivity and Gain
		17.3.3 The Noise and Detectivity
	17.4 Concluding Remarks
	References
18 Device Applications of Novel 2D Materials
	18.1 Graphene
		18.1.1 Field-Effect Transistors
	18.2 Topological Insulators
		18.2.1 Contacts and Gating
		18.2.2 Heterojunctions
		18.2.3 Photodetectors
		18.2.4 Field-Effect Transistors
		18.2.5 Magnetic Devices
		18.2.6 Optoelectronics
	References
Index