Effect of carrier degeneracy on the diffusivity-mobility ratio in n-Cd3As2
01 Oct 1981-Czechoslovak Journal of Physics (Kluwer Academic Publishers)-Vol. 31, Iss: 10, pp 1138-1143
TL;DR: An attempt is made to study the dependence of the diffusivity-mobility ratio on carrier concentration in degenerate n-Cd3As2 according to the Bodnar model which has recently been shown in the literature from studies on magnetic quantization to be the most valid model for Cd 3As2.
Abstract: An attempt is made to study the dependence of the diffusivity-mobility ratio on carrier concentration in degenerate n-Cd3As2 according to the Bodnar model which has recently been shown in the literature from studies on magnetic quantization to be the most valid model for Cd3As2. The results obtained are then compared with those derived on the basis of the Kane model to indicate the amount of error that would be involved with the use of the same model since many authors have continued to use it for Cd3As2.
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01 Jan 2016
TL;DR: This chapter contains twenty eight applications of the DRs as presented for various HD materials and their quantized counterparts as investigated in this book.
Abstract: This chapter contains twenty eight applications of the DRs as presented for various HD materials and their quantized counterparts as investigated in this book. The Sect. 20.3 contains 1 multi dimensional open research problem, which form the integral part of this chapter.
1 citations
01 Jan 2021
TL;DR: In this article, the carrier statistics in quantized extremely degenerate III-V, ternary, quaternary and tetragonal compounds were studied and the influence of photo-excitation and electric field on the Fermi energy was investigated.
Abstract: In this chapter, we study the carrier statistics (CS) in quantized extremely degenerate III–V, ternary, quaternary and tetragonal compounds respectively. We have also investigated the influence of photo-excitation and electric field on the Fermi energy. We note by taking various types of opto-electronic materials as examples that the Fermi energy oscillates with inverse magnetic field due to SdH effect, changes with changing electric field, light intensity, wave length and alloy composition in different ways which are totally energy band constants dependent.
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TL;DR: The band structure of InSb is calculated using the k ·. p perturbation approach and assuming that the conduction and valence band extrema are at k = 0 as mentioned in this paper.
2,905 citations
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06 May 1980
TL;DR: In this paper, the Boltzmann Transport Equation is used to calculate the collision probability of the Sphalerite and the Chalcopyrite structures, and the Brillouin Zone is used for the Wurtzite structure.
Abstract: 1. Introduction.- 1.1 Historical Note.- 1.2 Applications.- 1.3 Transport Coefficients of Interest.- 1.4 Scope of the Book.- 2. Crystal Structure.- 2.1 Zinc-Blende Structure.- 2.2 Wurtzite Structure.- 2.3 Rock-Salt Structure.- 2.4 Chalcopyrite Structure.- 3. Energy Band Structure.- 3.1 Electron Wave Vector and Brillouin Zone.- 3.2 Brillouin Zone for the Sphalerite and Rock-Salt Crystal Structure.- 3.3 Brillouin Zone for the Wurtzite Structure.- 3.4 Brillouin Zone for the Chalcopyrite Structure.- 3.5 E-k Diagrams.- 3.5.1 Energy Bands for the Sphalerite Structure.- 3.5.2 Energy Bands for the Wurtzite Structure.- 3.5.3 Energy Bands for the Rock-Salt Structure.- 3.5.4 Band Structure of Mixed Compounds.- 3.6 Conclusion.- 4. Theory of Efiergy Band Structure.- 4.1 Models of Band Structure.- 4.2 Free-Electron Approximation Model.- 4.3 Tight-Binding Approximation Model.- 4.4 Energy Bands in Semiconductor Super!attices.- 4.5 The k-p Perturbation Method for Derivating E-k Relation.- 4.5.1 Single-Band Perturbation Theory.- 4.5.2 Two-Band Approximation.- 4.5.3 Effect of Spin-Orbit Interaction.- 4.5.4 Nonparabolic Relation for Extrema at Points Other than the r Point.- 4.6 External Effects on Energy Bands.- 4.6.1 Effects of Doping.- 4.6.2 Effects of Large Magnetic Fields.- 5. Electron Statistics.- 5.1 Fermi Energy for Parabolic Bands.- 5.2 Fermi Energy for Nonparabolic Bands.- 5.3 Fermi Energy in the Presence of a Quantising Magnetic Field.- 5.3.1 Density of States.- 5.3.2 Fermi Level.- 5.4 Fermi Energy and Impurity Density.- 5.4.1 General Considerations.- 5.4.2 General Formula.- 5.4.3 Discussion of Parabolic Band.- 5.4.4 Effect of Magnetic Field.- 5.5 Conclusions.- 6. Scattering Theory.- 6.1 Collision Processes.- 6.2 Transition Probability.- 6.3 Matrix Elements.- 6.4 Free-Carrier Screening.- 6.5 Overlap Integrals.- 6.6 Scattering Probability S(k).- 6.6.1 S(k) for Ionised Impurity Scattering.- 6.6.2 S(k) for Piezoelectric Scattering.- 6.6.3 S(k) for Deformation-Potential Acoustic Phonon Scattering.- 6.6.4 S(k) for Polar Optic Phonon Scattering.- 6.6.5 S(k) for Intervalley and Nonpolar Optic Phonon Scattering.- 6.7 Scattering Probabilities for Anisotropic Bands.- 6.7.1 Herring-Vogt Transformation.- 6.7.2 Scattering Integrals.- 6.8 S(k) for Neutral Impurity, Alloy, and Crystal-Defect Scattering.- 6.8.1 Neutral-Impurity Scattering.- 6.8.2 Alloy Scattering.- 6.8.3 Defect Scattering.- 6.9 Conclusions.- 7. The Boltzmann Transport Equation and Its Solution.- 7.1 The Liouville Equation and the Boltzmann Equation.- 7.2 The Boltzmann Transport Equation.- 7.3 The Collision Integral.- 7.4 Linearised Boltzmann Equation.- 7.5 Simplified Form of the Collision Terms.- 7.5.1 Collision Terms for Elastic Scattering.- 7.5.2 Collision Terms for Inelastic Scattering.- 7.6 Solution of the Boltzmann Equation.- 7.6.1 Relaxation-Time Approximation.- 7.6.2 Variational Method.- 7.6.3 Matrix Method.- 7.6.4 Iteration Method.- 7.6.5 Monte Carlo Method.- 7.7 Method of Solution for Anisotropic Coupling Constants and Anisotropic Electron Effective Mass.- 7.7.1 Solution for Elastic Collisions.- 7.7.2 Solution for Randomising Collisions.- 7.7.3 Solution for Nonrandomising Inelastic Collisions.- 7.8 Conclusions.- 8. Low-Field DC Transport Coefficients.- 8.1 Evaluation of Drift Mobility.- 8.1.1 Formulae for Relaxation-Time Approximation.- 8.1.2 Evaluation by the Variational Method.- 8.1.3 Evaluation by Matrix and Iteration Methods.- 8.1.4 Evaluation by the Monte Carlo Method.- 8.2 Drift Mobility for Anisotropic Bands.- 8.2.1 Ellipsoidal Band.- 8.2.2 Warped Band.- 8.3 Galvanomagnetic Transport Coefficients.- 8.3:1 Formulae for Hall Coefficient, Hall Mobility, and Magnetoresistance.- 8.3.2 Reduced Boltzmann Equation for the Galvanomagnetic Coefficients.- 8.3.3 Solution Using the Relaxation-Time Approximation Method.- 8.3.4 A Simple Formula for the Low-Field Hall Mobility.- 8.3.5 Numerical Methods for the Galvanomagnetic Coefficients for Arbitrary Magnetic Fields.- 8.3.6 Evaluation of the Galvanomagnetic Transport Coefficients for Anisotropic Effective Mass.- 8.4 Transport Coefficients for Nonuniform conditions.- 8.4.1 Diffusion.- 8.4.2 Thermal Transport Coefficients.- 8.4.3 Formula for Thermoelectric Power.- 8.4.4 Electronic Thermal Conductivity.- 8.5 Conclusions.- 9. Low-Field AC Transport Coefficients.- 9.1 Classical Theory of AC Transport Coefficients.- 9.1.1 Solution for the Relaxation-Time Approximation.- 9.1.2 Solution for Polar Optic Phonon and Mixed Scattering.- 9.1.3 Solution for Nonparabolic and Anisotropic Bands.- 9.2 AC Galvanomagnetic Coefficients.- 9.3 Cyclotron Resonance and Faraday Rotation.- 9.3.1 Propagation of Electromagnetic Waves in a Semiconductor in the Presence of a Magnetic Field.- 9.3.2 Cyclotron Resonance Effect.- 9.3.3 Faraday Rotation.- 9.4 Free-Carrier Absorption (FCA).- 9.4.1 Classical Theory of FCA.- 9.4.2 Quantum-Mechanical Theory of FCA.- 9.5 Concluding Remarks.- 10. Electron Transport in a Strong Magnetic Field.- 10.1 Scattering Probabilities.- 10.2 Mobility in Strong Magnetic Fields.- 10.3 Electron Mobility in the Extreme Quantum Limit (EQL).- 10.3.1 Electron Mobility for Polar Optic Phonon Scattering in the EQL.- 10.4 Oscillatory Effects in the Magnetoresistance.- 10.4.1 Shubnikov-de Haas Effect.- 10.4.2 Magnetophonon Oscillations.- 10.5 Experimental Results on Magnetophonon Resonance.- 10.6 Conclusions.- 11. Hot-Electron Transport.- 11.1 Phenomenon of Hot Electrons.- 11.2 Experimental Characteristics.- 11.3 Negative Differential Mobility and Electron Transfer Effect.- 11.4 Analytic Theories.- 11.4.1 Differential Equation Method.- 11.4.2 Maxwellian Distribution Function Method.- 11.4.3 Displaced Maxwellian Distribution Function Method.- 11.5 Numerical Methods.- 11.5.1 Iteration Method.- 11.5.2 Monte Carlo Method.- 11.6 Hot-Electron AC Conductivity.- 11.6.1 Phenomenological Theory for Single-Valley Materials.- 11.6.2 Phenomenological Theory for Two-Valley Materials.- 11.6.3 Large-Signal AC Conductivity.- 11.7 Hot-Electron Diffusion.- 11.7.1 Einstein Relation for Hot-Electron Diffusivity.- 11.7.2 Electron Diffusivity in Gallium Arsenide.- 11.7.3 Monte Carlo Calculation of the Diffusion Constant.- 11.8 Conclusion.- 12. Review of Experimental Results.- 12.1 Transport Coefficients of III-V Compounds.- 12.1.1 Indium Antimonide.- 12.1.2 Gallium Arsenide.- 12.1.3 Indium Phosphide.- 12.1.4 Indium Arsenide.- 12.1.5 Indirect-Band-Gap III-V Compounds.- 12.2 II-VI Compounds.- 12.2.1 Cubic Compounds of Zinc and Cadmium.- 12.2.2 Wurtzite Compounds of Zinc and Cadmium.- 12.2.3 Mercury Compounds.- 12.3 IV-VI Compounds.- 12.4 Mixed Compounds.- 12.5 Chalcopyrites.- 12.6 Conclusion.- 13. Conclusions.- 13.1 Problems of Current Interest.- 13.1.1 Heavily Doped Materials.- 13.1.2 Alloy Semiconductors.- 13.1.3 Transport Under Magnetically Quantised Conditions.- 13.1.4 Inversion Layers.- 13.1.5 Superlattices and Heterostructures.- 13.2 Scope of Further Studies.- Appendix A: Table of Fermi Integrals.- Appendix B: Computer Program for the Evaluation of Transport Coefficients by the Iteration Method.- Appendix C: Values of a. and b. for Gaussian Quadrature Integration. 417 Appendix D: Computer Program for the Monte Carlo Calculation of Hot-Electron Conductivity and Diffusivity.- List of Symbols.- References.
716 citations
TL;DR: In this article, the structure of the conduction and valence bands near the Brillouin-zone center of chalcopyrite compounds was calculated by using a model obtained by adding an anisotropic crystal potential to the Hamiltonian of the Kane model for III-V compounds.
Abstract: The structure of the conduction and valence bands near the Brillouin-zone center has been calculated for the II-IV-${\mathrm{V}}_{2}$ chalcopyrite compounds by using a model obtained by adding an anisotropic crystal potential to the Hamiltonian of the Kane model for III-V compounds. The model, reuiring only four readily obtainable parameters, is applied to CdGe${\mathrm{As}}_{2}$ to calculate effective masses and intervalence-band absorption cross sections. The theoretical results are in good agreement with experimental values.
117 citations
TL;DR: Using the Bodnar model, the effective mass, density of states, and g-factor of Cd3As2 are calculated in this paper, and it is found that the g-Factor is considerably more anisotropic than the effective Mass, but decreases sharply with energy in all directions.
Abstract: Using the Bodnar model, the effective mass, density of states, and g-factor of Cd3As2 are calculated. It is found that the g-factor is considerably more anisotropic than the effective mass, but decreases sharply with energy in all directions.
Nous avons calcule, a partir du modele de Bodnar, la masse effective, le densite d'etats et le facteur g de Cd3As2. Nous trouvons que le facteur g est beaucoup plus anisotrope que la masse effective, et diminue rapidement en fonction de l'eergie pour toutes les directions cristallographiques.
73 citations
TL;DR: In this article, the dispersion related for the conduction band has been obtained along with a ${\ensuremath{\Gamma}}_{8}$ energy gap of 0.19 eV.
Abstract: Electron effective-mass values obtained from room-temperature magneto-Seebeck and Hall measurements on ${\mathrm{Cd}}_{3}$${\mathrm{As}}_{2}$ have been gathered from the literature. Using Kane's model for an $\ensuremath{\alpha}\ensuremath{-}\mathrm{Sn}$-type inverted electronic energy band structure, the dispersion related for the conduction band has been obtained along with a ${\ensuremath{\Gamma}}_{8}\ensuremath{-}{\ensuremath{\Gamma}}_{6}$ energy gap of 0.19 eV. Combining these results with the available room-temperature optical data, the relative positions of other bands have been obtained. The heavy-hole valence band, whose maximum is displaced from $\ensuremath{\Gamma}$ by \ensuremath{\sim} 10% of the distance to the Brillouin-zone edge, has a possible small overlap with the conduction band. These two ${\ensuremath{\Gamma}}_{8}$ bands are split at $\ensuremath{\Gamma}$ by a residual gap of \ensuremath{\sim} 0.04 eV. There is a second conduction band whose minimum at $\ensuremath{\Gamma}$ is \ensuremath{\sim} 0.6 eV above the ${\ensuremath{\Gamma}}_{8}$ valence band and perhaps a third one \ensuremath{\sim} 0.4 eV above the latter.
61 citations