Basic Semiconductor Physics

Description

Preface Contents 1 Energy Band Structures of Semiconductors 1.1 Free-Electron Model 1.2 Bloch Theorem 1.3 Nearly Free Electron Approximation 1.4 Reduced Zone Scheme 1.5 Free–Electron Bands (Empty–Lattice Bands) 1.5.1 First Brillouin Zone 1.5.2 Reciprocal Lattice Vectors of fcc Crystal 1.5.3 Free Electron Bands 1.6 Pseudopotential Method 1.6.1 Local Pseudopotential Theory 1.6.2 Pseudopotential Form Factors 1.6.3 Nonlocal Pseudopotential Theory 1.6.4 Spin–Orbit Interaction 1.6.5 Energy Band Calculation by Local Pseudopotential Method 1.6.6 Energy Band Calculations by Nonlocal Pseudopotential Method with Spin–orbit Interaction 1.7 kcdotp Perturbation 1.7.1 kcdotp Hamiltonian 1.7.2 Derivation of the k cdotp Parameters 1.7.3 15–band k cdotp Method 1.7.4 Antisymmetric Potentials for Zinc Blende Crystals 1.7.5 Spin–Orbit Interaction Hamiltonian 1.7.6 30–band kcdotp Method with the Spin–Orbit Interaction 1.8 Density of States 1.9 Problems References 2 Cyclotron Resonance and Energy Band Structures 2.1 Cyclotron Resonance 2.2 Analysis of Valence Bands 2.3 Spin–Orbit Interaction 2.4 Non-parabolicity of the Conduction Band 2.5 Electron Motion in a Magnetic Field and Landau Levels 2.5.1 Landau Levels 2.5.2 Density of States and Inter Landau Level Transition 2.5.3 Landau Levels of a Non-parabolic Band 2.5.4 Effective g Factor 2.5.5 Landau Levels of the Valence Bands 2.5.6 Magneto–Optical Absorption 2.6 Luttinger Hamiltonian 2.7 Luttinger Parameters 2.8 Problems References 3 Wannier Function and Effective Mass Approximation 3.1 Wannier Function 3.2 Effective-Mass Approximation 3.3 Shallow Impurity Levels 3.4 Impurity Levels in Ge and Si 3.4.1 Valley–Orbit Interaction 3.4.2 Central Cell Correction 3.5 Electron Motion Under an External Field 3.5.1 Group Velocity 3.5.2 Electron Motion Under an External Force 3.5.3 Electron Motion and Effective Mass 3.6 Problems References 4 Optical Properties 1 4.1 Reflection and Absorption 4.2 Direct Transition and Absorption Coefficient 4.3 Joint Density of States 4.4 Indirect Transition 4.5 Exciton 4.5.1 Direct Exciton 4.5.2 Indirect Exciton 4.6 Dielectric Function 4.6.1 E0, E0+ Δ0 Edge 4.6.2 E1 and E1+Δ1 Edge 4.6.3 E2 Edge 4.6.4 Exciton 4.7 Piezobirefringence 4.7.1 Phenomenological Theory of Piezobirefringence 4.7.2 Deformation Potential Theory 4.7.3 Stress-Induced Change in Energy Band Structure 4.8 Problems References 5 Optical Properties 2 5.1 Modulation Spectroscopy 5.1.1 Electro-optic Effect 5.1.2 Franz–Keldysh Effect 5.1.3 Modulation Spectroscopy 5.1.4 Theory of Electroreflectance and Third-Derivative Form of Aspnes 5.2 Raman Scattering 5.2.1 Selection Rule of Raman Scattering 5.2.2 Quantum Mechanical Theory of Raman Scattering 5.2.3 Resonant Raman Scattering 5.3 Brillouin Scattering 5.3.1 Scattering Angle 5.3.2 Brillouin Scattering Experiments 5.3.3 Resonant Brillouin Scattering 5.4 Polaritons 5.4.1 Phonon Polaritons 5.4.2 Exciton Polaritons 5.5 Free–Carrier Absorption and Plasmon 5.6 Problems References 6 Electron–Phonon Interaction and Electron Transport 6.1 Lattice Vibrations 6.1.1 Acoustic Mode and Optical Mode 6.1.2 Harmonic Approximation 6.2 Boltzmann Transport Equation 6.2.1 Collision Term and Relaxation Time 6.2.2 Mobility and Electrical Conductivity 6.3 Scattering Probability and Transition Matrix Element 6.3.1 Transition Matrix Element 6.3.2 Deformation Potential Scattering (Acoustic Phonon Scattering) 6.3.3 Ionized Impurity Scattering 6.3.4 Piezoelectric Potential Scattering 6.3.5 Non–polar Optical Phonon Scattering 6.3.6 Polar Optical Phonon Scattering 6.3.7 Inter–Valley Phonon Scattering 6.3.8 Deformation Potential in Degenerate Bands 6.3.9 Theoretical Calculation of Deformation Potentials 6.3.10 Electron–Electron Interaction and Plasmon Scattering 6.3.11 Alloy Scattering 6.4 Scattering Rate and Relaxation Time 6.4.1 Acoustic Phonon Scattering 6.4.2 Non–polar Optical Phonon Scattering 6.4.3 Polar Optical Phonon Scattering 6.4.4 Piezoelectric Potential Scattering 6.4.5 Inter–Valley Phonon Scattering 6.4.6 Ionized Impurity Scattering 6.4.7 Neutral Impurity Scattering 6.4.8 Plasmon Scattering 6.4.9 Alloy Scattering 6.5 Mobility 6.5.1 Acoustic Phonon Scattering 6.5.2 Non–polar Optical Phonon Scattering 6.5.3 Polar Optical Phonon Scattering 6.5.4 Piezoelectric Potential Scattering 6.5.5 Inter–Valley Phonon Scattering 6.5.6 Ionized Impurity Scattering 6.5.7 Neutral Impurity Scattering 6.5.8 Plasmon Scattering 6.5.9 Alloy Scattering 6.6 Problems References 7 Magnetotransport Phenomena 7.1 Phenomenological Theory of the Hall Effect 7.2 Magnetoresistance Effects 7.2.1 Theory of Magnetoresistance 7.2.2 General Solutions for a Weak Magnetic Field 7.2.3 Case of Scalar Effective Mass 7.2.4 Magnetoresistance 7.3 Shubnikov–de Haas Effect 7.3.1 Theory of Shubnikov–de Haas Effect 7.3.2 Longitudinal Magnetoresistance Configuration 7.3.3 Transverse Magnetoresistance Configuration 7.4 Magnetophonon Resonance 7.4.1 Experiments and Theory of Magnetophonon Resonance 7.4.2 Various Types of Magnetophonon Resonance 7.4.3 Magnetophonon Resonance Under High Electric and High Magnetic Fields 7.4.4 Polaron Effect 7.5 Problems References 8 Quantum Structures 1 8.1 Historical Background 8.2 Two-Dimensional Electron Gas Systems 8.2.1 Two-Dimensional Electron Gas in MOS Inversion Layer 8.2.2 Quantum Wells and HEMT 8.3 Transport Phenomena of Two-Dimensional Electron Gas 8.3.1 Fundamental Equations 8.3.2 Acoustic Phonon Scattering and Non-Polar Optical Phonon Scattering 8.3.3 Inter-Valley Phonon Scattering 8.3.4 Polar Optical Phonon Scattering 8.3.5 Piezoelectric Potential Scattering 8.3.6 Ionized Impurity Scattering 8.3.7 Surface Roughness Scattering 8.3.8 Screening Effect 8.3.9 Remote Ionized Impurity Scattering 8.3.10 Mobility of a Two-Dimensional Electron Gas 8.4 Mesoscopic Phenomena 8.4.1 Mesoscopic Region 8.4.2 Definition of Mesoscopic Region 8.4.3 Landauer Formula and Büttiker–Landauer Formula 8.4.4 Research in the Mesoscopic Region 8.4.5 Aharonov–Bohm Effect (AB Effect) 8.4.6 Ballistic Electron Transport 8.5 Quantum Hall Effect 8.6 Problems References 9 Quantum Structures 2 9.1 Superlattices 9.1.1 Kronig–Penney Model 9.1.2 Effect of Brillouin Zone Folding 9.1.3 Tight Binding Approximation 9.1.4 sp3sast Tight Binding Approximation 9.1.5 Energy Band Calculations for Superlattices 9.1.6 Second Nearest-Neighbor sp3 Tight Binding Approximation 9.2 Quantum Dots 9.2.1 Addition Energy 9.2.2 Exact Diagonalization Method 9.2.3 Hamiltonian for Electrons in a Quantum Dot 9.2.4 Diagonalization of N Electrons Hamiltonian Matrix 9.2.5 Electronic States in Quantum Dots 9.2.6 Quantum Dot States in Magnetic Field 9.2.7 Electronic States in Elliptic and Triangular Quantum Dots 9.3 Coulomb Blockade and Single Electron Transistor 9.4 Surface modulation of Two-dimensional Electron Gas and Weiss Oscillation 9.5 Wannier–Stark Effect in Superlattices 9.6 Bloch Oscillation 9.7 Problems References 10 Light Emission and Laser 10.1 Einstein Coefficients A and B 10.2 Spontaneous Emission and Stimulated Emission 10.3 Band Tail Effect 10.4 Luminescence 10.4.1 Luminescence Due to Band to Band Transition 10.4.2 Luminescence Due to Excitons 10.4.3 Luminescence via Impurities 10.4.4 Luminescence in GaP and GaAsP via N Traps 10.4.5 Luminescence from GaInNAs 10.4.6 Light Emitting Diodes (LEDs) in Visible Region 10.5 Heterostructure Optical Waveguide 10.5.1 Wave Equations for Planar Waveguide 10.5.2 Transverse Electric Modes 10.5.3 Transverse Magnetic Modes 10.5.4 Effective Refractive Index 10.5.5 Confinement Factor 10.5.6 Laser Oscillations 10.6 Stimulated Emission in Quantum Well Structures 10.6.1 Confinement in Quantum Well 10.6.2 Optical Transition in Quantum Well Structures 10.6.3 Reduced Density of States and Gain 10.6.4 Strain Effect 10.6.5 Wurtzite Semiconductor Lasers 10.6.6 Optical Gain of Nitride Quantum Well Structures 10.7 Problems References 11 Wade Bandgap Semiconductor and Photonic Crystals 11.1 Energy Band Structures of Nitrides 11.1.1 Energy Band Calculations of GaN, AlN, and InN 11.1.2 Energy Band Structures of Ternary Alloys 11.1.3 Spin–Orbit–Interaction and Valence Band Structures 11.2 Electron and Hole Mobilities of GaN 11.2.1 Acoustic Deformation Potential Scattering 11.2.2 Piezoelectric Potential Scattering 11.2.3 Ionized Impurity Scattering 11.2.4 Polar Optical Phonon Scattering 11.2.5 Remote Impurity Scattering 11.2.6 Other Scatterings 11.2.7 Evaluation of Electron and Hole Mobility 11.3 SiC and Other Semiconductors 11.3.1 SiC 11.3.2 Electron Mobility in 4H-SiC 11.4 Photonic Crystals 11.4.1 One-Dimensional Photonic Crystal 11.4.2 Two-Dimensional Photonic Crystal 11.4.3 Defects in Photonic Crystal 11.4.4 FDTD Method 11.5 Problems References 12 Answers for Problems Appendix A Delta Function and Fourier Transform A.1 Dirac Delta Function A.2 Cyclic Boundary Condition and Delta Function A.3 Fourier Transform Appendix B Gamma Function Appendix C Uniaxial Stress and Strain Components in Cubic Crystals Appendix D Boson Operators Appendix E Random Phase Approximation and Lindhard Dielectric Function Appendix F Density Matrix Appendix G Spontaneous and Stimulated Emission Rates Appendix H Spin–Orbit Interaction References Index