A simple theoretical analysis of the carrier contribution to the elastic constants in quantum wires of IV-VI semiconductors in the presence of a parallel magnetic field
TL;DR: In this paper, the carrier contribution to the elastic constants in quantum wires of IV-VI semiconductors under parallel magnetic field on the basis of a newly derived electron dispersion law was studied.
About: This article is published in Journal of Physics and Chemistry of Solids.The article was published on 1997-03-01. It has received 21 citations till now. The article focuses on the topics: Quantum wire & Magnetic field.
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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 paper, the influence of terahertz frequency on the elastic constants in extremely degenerate (ED) 2D systems taking quantized films (QFs) and accumulation layers (ALs) of nonlinear optical, tetragonal, ternary, quaternary, III-V, II-VI, IV-VI and strained compounds, respectively, was investigated.
Abstract: We investigate the influence of terahertz frequency on the elastic constants in extremely degenerate (ED) 2D systems taking quantized films (QFs) and accumulation layers (ALs) of nonlinear optical, tetragonal, ternary, quaternary, III–V, II–VI, IV–VI and strained compounds, respectively. It has been found taking ED QFs and ALs of specific materials of the important 2D electronic compounds as examples that the elastic constants (C1 and C2) change with nano-size of the said QFs and the two-dimensional carrier statistics per unit area in different oscillatory ways. The influence of electric field for both the limits in inversion layers of non-parabolic materials has also been studied. Besides, C1 and C2 are in nice agreement with our suggestive relationships for determining them experimentally.
01 Jan 2017
TL;DR: In this paper, the effect of strong photo excitation on the elastic constant (EC) in extremely degenerate nano-wires (NW) forming Gaussian band tails has been investigated by deriving a fundamental carrier statistics formula using NWs of Heavily Doped (HD) n-InSb, n-INAs, Hg1−xCdxTe and In 1−xGaxAsyP1−y y lattice matched to InP as examples.
Abstract: Effect of strong photo excitation on the elastic constant (EC) in extremely degenerate Nano-Wires (NW) forming Gaussian band tails has been investigated by deriving a fundamental carrier statistics formula using NWs of Heavily Doped (HD) n-InSb, n-InAs, Hg1−xCdxTe and In1−xGaxAsyP1−y y lattice matched to InP as examples. We observe that ΔC44 becomes invariant of the film thickness under the condition of relatively low values of the quantum thickness, indicating a very sharp fall at a particular value of the nano thickness manifesting the quantum size effect, in EC. The EC increases with decreasing light intensity, wavelength and alloy composition where the rate of change depends on the values of the band constants respectively. The EC can be experimentally determined by using the corresponding the experimental values of the thermo electric power.
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.
01 Jan 2012
TL;DR: The concept of the effective mass of the carriers of the conduction electrons in semiconductors is one of the basic pillars in the realm of solid state and related sciences as discussed by the authors, and it can be shown that it is the effective momentum mass which enters in various transport coefficients and plays the most dominant role in explaining the experimental results of different scattering mechanisms through Boltzmann's transport equation.
Abstract: The concept of the effective mass of the carriers in semiconductors is one of the basic pillars in the realm of solid state and related sciences [1]. It must be noted that among the various definitions of the effective electron mass (e.g effective acceleration mass, density-of-state effective mass, concentration effective mass, conductivity effective mass, Faraday rotation effective mass, etc) [2], it is the effective momentum mass that should be regarded as the basic quantity [3]. This is due to the fact that it is this mass which appears in the description of transport phenomena and all other properties of the conduction electrons in a semiconductor with arbitrary band nonparabolicity [3]. It can be shown that it is the effective momentum mass which enters in various transport coefficients and plays the most dominant role in explaining the experimental results of different scattering mechanisms through Boltzmann’s transport equation [4,5]. The carrier degeneracy in semiconductors influences the effective mass when it is energy dependent.
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Book•
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
01 Jan 1990
TL;DR: The proceedings of the NATO Advanced Research Workshop on the Science and Engineering of 1 and O-dimensional semiconductors held at the University of Cadiz from 29th March to 1st April 1989, under the auspices of theNATO International Scientific Exchange Program as discussed by the authors.
Abstract: This volume comprises the proceedings of the NATO Advanced Research Workshop on the Science and Engineering of 1- and O-dimensional semiconductors held at the University of Cadiz from 29th March to 1st April 1989, under the auspices of the NATO International Scientific Exchange Program. There is a wealth of scientific activity on the properties of two-dimensional semiconductors arising largely from the ease with which such structures can now be grown by precision epitaxy techniques or created by inversion at the silicon-silicon dioxide interface. Only recently, however, has there burgeoned an interest in the properties of structures in which carriers are further confined with only one or, in the extreme, zero degrees of freedom. This workshop was one of the first meetings to concentrate almost exclusively on this subject: that the attendance of some forty researchers only represented the community of researchers in the field testifies to its rapid expansion, which has arisen from the increasing availability of technologies for fabricating structures with small enough (sub - O. I/tm) dimensions. Part I of this volume is a short section on important topics in nanofabrication. It should not be assumed from the brevity of this section that there is little new to be said on this issue: rather that to have done justice to it would have diverted attention from the main purpose of the meeting which was to highlight experimental and theoretical research on the structures themselves.
104 citations
TL;DR: In this paper, an attempt is made to study the effective electron mass in strained layer superlattices of non-parabolic semiconductors with graded structures under sirong magnetic quantization and to compare the same with the bulk specimens of the constituent materials, by formulating the appropriate magneto-dispersion laws.
Abstract: An attempt is made to study the effective electron mass in strained layer superlattices of non-parabolic semiconductors with graded structures under sirong magnetic quantization and to compare the same with the bulk specimens of the constituent materials, by formulating the appropriate magneto-dispersion laws. It is found, taking InAs/GaSb superlattice as an example, that the effective electron mass oscillates with the inverse quantizing magnetic field due to the Shubnikov-de Hass effect. The dependence of the effective mass on the magnetic quantum number in addition to Fermi energy is an intrinsic property of such semiconductor heterostructures. The stress makes the mass quantum number dependent in bulk specimens and even in the presence of broadening, the effective masses in superlattices exhibit significant oscillations with enhanced numerical values from that of the constituent semiconductors. Besides the effective electron masses also increase in an oscillatory way with increasing electron c...
41 citations
TL;DR: In this paper, the photoemission from ultrathin films, quantum wires and quantum dots of degenerate Kane-type semiconductors, respectively, on the basis of a newly derived dispersion relation of the conduction electrons allowing all types of anisotropies of the band parameters within the framework of k⋅p formalism was investigated.
Abstract: An attempt is made to investigate the photoemission from ultrathin films, quantum wires and quantum dots of degenerate Kane‐type semiconductors, respectively, on the basis of a newly derived dispersion relation of the conduction electrons allowing all types of anisotropies of the band parameters within the framework of k⋅p formalism. It is found, taking n‐Cd3As2 as an example, that the photoemission increases with increasing photon energy in a ladderlike manner and also exhibits oscillatory dependences with changing electron concentration and film thickness, respectively, for all types of quantum confinement. The photoemitted current density is greatest for quantum dots and least for ultrathin films in all the cases. In addition, the well‐known results for bulk specimens of parabolic semiconductors have also been obtained from the generalized expressions under certain limiting conditions.
31 citations