Semiconductor Alloys

In the first comprehensive treatment of these technologically important materials, the authors provide theories linking the properties of semiconductor alloys to their constituent compounds. Topics include crystal structures, bonding, elastic properties, phase diagrams, band structures, transport, ab-initio theories, and semi-empirical theories. Each chapter includes extensive tables and figures as well as problem sets.

Contenu

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.