Semiconductor Alloys

1. Crystal Structures.- 1.1. Diamond, Zinc Blende, and Wurtzite Structures.- 1.2. Bulk Alloys.- 1.3. Alloy Structure Determined by EXAFS.- 1.4. Long-Range Ordered Semiconductor Alloys.- 1.4.1. ABC2 Structures.- 1.4.2. Bond Lengths.- 1.5. Concluding Remarks.- References.- 2. Bonding in Ordered Structures.- 2.1. Cohesive Energy in the Born—Oppenheimer Adiabatic Approximation.- 2.2. Density Functional Theory.- 2.3. Bonds and Bands from Local Density Functional Theory.- 2.4. Tight-Binding Approach.- 2.5. The Bond-Orbital Model.- 2.6. Polarity and Ionicity.- 2.7. Excess Energies of Ordered Alloys.- 2.8. Concluding Remarks.- References.- 3. Elasticity.- 3.1. Definitions and Analysis.- 3.2. Ab Initio Calculations.- 3.3. Valence-Force-Field Model.- 3.3.1. Diamond Structure.- 3.3.2. Zinc Blende Structure and Coulomb Force.- 3.4. “Exact” Tight-Binding Calculation.- 3.5. Analytical Expressions in the Bond-Orbital Model.- 3.6. Quantitative Tight-Binding Model.- 3.6.1. Full-Band-Structure Calculation.- 3.6.2. Quantitative Extended Bond-Orbital Model.- 3.7. Elasticity in Alloys.- 3.7.1. Ordered Alloys.- 3.7.2. Disordered Alloys.- 3.8. Concluding Remarks.- References.- 4. Alloy Statistics and Phase Diagrams.- 4.1. Mixing Free Energy, Miscibility Gap, and Order-Disorder Transitions.- 4.2. Analytical Models.- 4.2.1. Ideal-Solution Model.- 4.2.2. Zeroth Approximation.- 4.2.3. First Approximation—The Quasi-Chemical Approximation.- 4.3. Phase Diagram: Common Tangent Line and Activity Coefficient.- 4.4. Vieland’s Method and Binary Liquidus.- 4.5. Ternary Phase Diagrams.- 4.6. Phase Diagram Data and Simple Mixing Enthalpy Models.- 4.7. Generalized Quasi-Chemical Theory.- 4.8. Internal Strain and Cluster Energies.- 4.9. Sixteen-Bond Microclusters.- 4.10. Cluster Variational Method.- 4.11. Ab Initio Calculations.- 4.12. Concluding Remarks.- References.- Appendix 4A: Analytical Formulas of GQCA.- Appendix 4B: Critical Temperature in GQCA.- Appendix 4C: GQCA at Low Temperature.- 5. Band Structure Theory.- 5.1. Formation of Energy Bands.- 5.2. LCAO and the Empirical Tight-Binding Method.- 5.3. Plane-Wave Method and Empirical Pseudopotentials.- 5.4. Band Gaps and Effective Masses.- 5.5. Band Structure of Semiconductor Alloys: Problems and Applications.- 5.6. Green Function and Spectral Density of States.- 5.7. Perturbation Theory and Bowing of Fundamental Gaps.- 5.8. Multiple Scattering Theory and the Coherent Potential Approximation.- 5.9. A Single-Band Alloy Model.- 5.10. Molecular CPA for Zinc Blende Alloys.- 5.11. Effects of Diagonal and Off-Diagonal Disorder on Band-Edge Properties.- 5.12. Concluding Remarks.- References.- 6. Transport.- 6.1. Master and Boltzmann Equations.- 6.1.1. Master Equation for a Supersystem.- 6.1.2. Master Equation for a System in a Heat Bath.- 6.1.3. Single-Particle States.- 6.1.4. The Boltzmann Equation.- 6.2. Electron—Phonon Interaction and Single-Particle Master Equation.- 6.3. Low-Field Transport for Nondegenerate Electrons in Collision—Time Approximations.- 6.4. Mobilities in Alloys: Example, SixGe1-x.- 6.5. Hot-Electron v—E Characteristics: Comparison of Materials’ Merits.- 6.5.1. Example: In1-xGaxAs.- 6.5.2. Merits of Other Alloys Compared with GaAs.- 6.6. Scattering Mechanisms.- 6.6.1. Ionized Impurity Scattering.- 6.6.2. Bare Electron—Phonon Interaction.- 6.6.3. Polar Optical Phonon Scattering.- 6.6.4. Alloy Scattering.- 6.6.5. Electron—Electron Scattering.- 6.7. Expansion Solution of the Boltzmann Equation.- 6.8. Near-Ballistic Transport.- 6.9. Intervalley Scattering.- 6.10. Narrow-Gap Materials.- 6.11. Concluding Remarks.- References.- 7. Band Structures of Selected Semiconductors and Their Alloys.- 7.1. Hybrid Pseudopotential and Tight-Binding Model (HPT).- 7.2. Band Structures and Hamiltonian Parameters for III–V Constituent Compounds.- 7.2.1. A1P.- 7.2.2. A1As.- 7.2.3. A1Sb.- 7.2.4. GaP.- 7.2.5. GaAs.- 7.2.6. GaSb.- 7.2.7. InP.- 7.2.8. InAs.- 7.2.9. InSb.- 7.3. The HPT Model Applied to III–V Pseudobinary Alloys.- 7.4. Band Structures of Selected III–V Zinc Blende Alloys.- 7.4.1. Ga1-xA1xAs.- 7.4.2. Ga1-xA1xSb.- 7.4.3. Ga1-xA1xP.- 7.4.4. In1-xGaxP.- 7.4.5. Ga1-xInxAs.- 7.4.6. Ga1-xInxSb.- 7.4.7. In1-xA1xP.- 7.4.8. In1-xA1xAs.- 7.4.9. In1-xA1xSb.- 7.4.10. AlAs1-xPx.- 7.4.11. AlAs1-xSbx.- 7.4.12. AlP1-xSbx.- 7.4.13. GaAs1-xPx.- 7.4.14. GaAs1-xSbx.- 7.4.15. GaSb1-xPx.- 7.4.16. InAs1-xPx.- 7.4.17. InAs1-xSbx.- 7.4.18. InP1-xSbx.- 7.5. Band Structures and Hamiltonian Parameters for II–VI Zinc Blende Compounds.- 7.5.1. ZnS.- 7.5.2. ZnSe.- 7.5.3. ZnTe.- 7.5.4. CdS.- 7.5.5. CdSe.- 7.5.6. CdTe.- 7.5.7. HgSe.- 7.5.8. HgTe.- 7.6. II–VI Zinc Blende Pseudobinary Alloys.- 7.6.1. ZnS1-xSex.- 7.6.2. ZnSe1-xTex.- 7.6.3. ZnS1-xTex.- 7.6.4. CdS1-xTex.- 7.6.5. CdSe1-xTex.- 7.6.6. CdS1-xTex.- 7.6.7. HgSe1-xTex.- 7.6.8. Cd1-xZnxS.- 7.6.9. Cd1-xZnxSe.- 7.6.10. Cd1-xZnxTe.- 7.6.11. Hg1-xCdxSe.- 7.6.12. Hg1-xZnxSe.- 7.6.13. Hg1-xCdxTe.- 7.6.14. Hg1-xZnxTe.- 7.7. Concluding Remarks.- References.- Appendix 7A: Band Structure Calculation Using HPT.- Appendix 7B: VCA Hamiltonian, Alloy Disorder and Molecular ATA Calculation.- 7B.1. The Alloy Hamiltonian in HPT.- 7B.2. The VCA Hamiltonian.- 7B.3. Disorder Hamiltonian and ATA Calculation.- 7B.4. Band Calculation Using the Molecular ATA.- Problems.- 1.- 1. Bond Lengths and Relaxation Parameters of Pseudobinary Alloys.- 2. Crystal Diffraction and Miller Indices (hkl).- 3. Diffraction Patterns for Ordered and Disordered Alloys.- 2.- 1. Single-Particle Schrödinger Equation in the Local Density Approximation.- 2. Tight-Binding Matrix Elements in the Two-Center Approximation.- 3. The Bond-Orbital Model (BOM).- 4. Application of BOM to Impurity Formation Energies.- 5. Excess Energy of Ordered Alloys.- 3.- 1. Valence-Force-Field Model (VFF).- 2. Elastic Constants in the Bond-Orbital Model.- 3. Bulk Modulus in an Ordered Alloy.- 4. Bulk Modulus in a Disordered Alloy.- 4.- 1. Quasi-Chemical Approximation (QCA).- 2. Common Tangent Line and Equal Chemical Potentials in Equilibrium.- 3. Composition Diagram for Ternary Alloys.- 4. Liquidus Curves for III–V Compounds.- 5. Mixing Energy in Pseudobinary Alloy.- 6. Entropy of Mixing for Pseudobinary Alloys in GQCA and CVM.- 7. Special Solution for GQCA.- 5.- 1. Band Gaps in Semiconducting Polymers—The SSH Model.- 2. k·p Theory and Effective Mass.- 3. Green Function Applied to an Impurity.- 4. CPA Calculation for Binary Alloys.- 5. Tight-Binding Band Structures and Spin-Orbit Splitting.- 6.- 1. Master Equation, H-Theorem, and a priori Distribution.- 2. Time-Dependent Solution of the Supersystem Master Equation.- 3. Brooks’ Formula for Alloy Limited Mobility.- 4. Particle and Momentum Relaxation Time by Optical Phonon Scattering.- 5. Quantum Mechanical Basis of Transport Theory.- 6. Transient Solution to the Boltzmann Equation.