# Band offset in inp/ga0.47in0.53as heterostructures

TL;DR: In this paper, the energy-band nonparabolicity of both conduction and valence bands was investigated and the required value of the ratio of the conduction-band and the valence-band discontinuities was found to be close to 2/3 in agreement with the value found by other methods.

Abstract: Energy levels in InP/Ga0.47In0.53As quantum wells are calculated after reformulating the energy‐dependent effective mass to be used for taking into account the energy‐band nonparabolicity of both constituents. The required value of the ratio of the conduction‐band and valence‐band discontinuities is found to be close to 2/3, in agreement with the value found by other methods. The value of the nonparabolicity factor is also found to be the same as that used in earlier transport studies.

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TL;DR: In this article, the authors reviewed the assumptions of conventional effective-mass theory, especially the one of continuity of the envelope function at an abrupt interface, and the need for a fresh approach becomes apparent.

Abstract: The assumptions of conventional effective-mass theory, especially the one of continuity of the envelope function at an abrupt interface, are reviewed critically so that the need for a fresh approach becomes apparent. A new envelope-function method, developed by the author over the past few years, is reviewed. This new method is based on both a generalization and a novel application to microstructures of the Luttinger-Kohn envelope-function expansion. The differences between this new method and the conventional envelope-function method are emphasized. An alternative derivation of the new envelope-function equations, which are exact, to that already published is provided. A new and improved derivation of the author's effective-mass equation is given, in which the differences in the zone-centre eigenstates of the constituent crystals are taken into account. The cause of the kinks in the conventional effective-mass envelope function, at abrupt effective-mass changes, is identified.

375 citations

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TL;DR: In this paper, the average sizes of Cd(S,Se) quantum dots in glasses have been measured for the same samples by using three methods: high-resolution transmission electron microscopy, low-frequency inelastic Raman scattering, and small-angle x-ray scattering.

Abstract: The average sizes of Cd(S,Se) quantum dots in glasses have been measured for the same samples by using three methods: high‐resolution transmission electron microscopy, low‐frequency inelastic Raman scattering, and small‐angle x‐ray scattering. Three samples with crystal sizes of 5.5–8, 9–12, and 17 nm have been studied. For each method the interaction mode and the underlying assumptions in measuring the size are discussed. The correlation between the measurements is good and points out a narrow size distribution. The discrepancies observed for the smallest sizes are discussed with respect to the probe and the interactions used by each technique. They may be ascribed to structural effects.

63 citations

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TL;DR: In this paper, the energy levels of 3D quantum confinement structures with finite potential barriers were investigated. But the authors focused on 3D systems and did not consider the effects of nonparabolicity.

Abstract: Energy levels are calculated for three-dimensional (3D) quantum-confinement structures with finite potential barriers. , and systems are considered. Analytic results are presented for spherical structures including the effects of nonparabolicity. A numerical method is also presented for the calculation of the energy levels in a 3D quantum-confinement structure in the shape of a cube or a parallelopiped. The method is applied for calculating the energy shift in a cylindrical dot of the system.

32 citations

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TL;DR: In this paper, energy eigenvalues for quantum wells of the GaAs/GaAlAs, GaInAs/AlInAs, and InAs/GAAlSb systems are given for widths ranging between 0.5 and 20 nm.

Abstract: Energy eigenvalues are given for quantum wells of the GaAs/GaAlAs, GaInAs/AlInAs, and InAs/GaAlSb systems, for widths ranging between 0.5 and 20 nm. The energy band nonparabolicity is shown to affect the values significantly particularly for wells with widths of about 2 nm. The InAs/GaAlSb wells are shown to have lowest energy levels with odd parity because of the negative effective mass in the barrier layer for energies below the mid-gap energy. Experiments are suggested for the detection of these levels.
Fur Quantenwells der Systeme GaAs/GaAlAs, GaInAs/AlInAs, und InAs/GaAlSb mit Dicken zwischen 0,5 und 20 nm werden die Energieeigenwerte angegeben. Diese Werte werden durch Abweichungen von parabolischen Energiebandern merklich beeinflust, insbesondere bei Dicken von etwa 2 nm. Die InAs/GaAlSb-Wells haben die niedrigsten Energieniveaus mit ungerader Paritat, weil die effektive Masse in der Barrierenschicht fur Energien unterhalb der Mitte der Bandlucke negativ ist. Experimente zur Auffindung dieser Niveaus werden vorgeschlagen.

21 citations

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TL;DR: In this article, the energy eigenvalues of cylindrical and elliptic quantum wires with finite potential barriers were derived for the Ga0.47 In0.53As/InP system and experimental results were explained.

Abstract: Formulae are derived for the calculation of the energy eigenvalues in cylindrical and elliptic quantum wires with finite potential barriers. Calculated values are given for quantum wires of the Ga0.47 In0.53As/InP system and experimental results are explained.

11 citations

##### References

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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

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IBM

^{1}TL;DR: In this paper, the band structure of HgTe-CdTe superlattices was investigated and it was shown that these materials can be either semiconducting or zero-gap semiconductors, i.e., behave exactly like the ternary Hg{1\ensuremath{-}x}{\mathrm{Cd{x}$ Te random alloys.

Abstract: We extend our previous investigations on the band structure of superlattices by applying the envelope-function approximation to four distinct problems. We calculate the band structure of HgTe-CdTe superlattices and show that these materials can be either semiconducting or zero-gap semiconductors, i.e., behave exactly like the ternary ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}$ Te random alloys. We analyze the superlattice dispersion relations in the layer planes (Landau superlattice subbands) and we compare the longitudinal and transverse effective masses of semiconducting InAs-GaSb superlattices. We calculate the general equation for the bound states due to aperiodic layers, taking account of the band structure of the host materials. We finally derive the dispersion relations of polytype ($\mathrm{ABC}$ or $\mathrm{ABCD}$) superlattices.

448 citations

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01 Jan 1990

TL;DR: In this article, the authors present a perspective on the evolution of quantum Semiconductor devices. But they do not discuss the theoretical foundations of these devices and do not provide a detailed analysis of them.

Abstract: 1. Introduction.- 1.1 A Perspective on the Evolution of Quantum Semiconductor Devices.- 1.2 Outline of the Book.- References.- 2. The Nature of Molecular Beam Epitaxy and Consequences for Quantum Microstructures.- 2.1 Dimensional Confinement and Device Concepts.- 2.2 Molecular Beam Epitaxy.- 2.2.1 Conceptual Picture.- 2.2.2 Reflection High Energy Electron Diffraction.- 2.2.3 Formation of Interfaces and Growth Interruption.- 2.3 The Surface Kinetic Processes and Computer Simulations of Growth.- 2.3.1 The CDRI Model.- 2.3.2 Growth Front Morphology.- 2.3.3 The CDRI Model and the Nature of GaAs/AlxGa1?xAs (100) Interfaces.- 2.4 Quantum Wells: Growth and Photoluminescence.- 2.5 Concluding Remarks.- 2.6 Recent Advances.- References.- 3. Nanolithography for Ultra-Small Structure Fabrication.- 3.1 Overview.- 3.2 Resolution Limits of Lithographic Processes.- 3.2.1 Lithography.- 3.2.2 Resolution Limits of Lithographic Methods.- 3.2.3 Photolithography and X-Ray Lithography.- 3.2.4 Ion Beams.- 3.2.5 Electron Beams.- 3.3 Pattern Transfer.- References.- 4. Theory of Resonant Tunnelling and Surface Superlattices.- 4.1 Tunnelling Probabilities.- 4.1.1 Single Barrier.- 4.1.2 Resonant Tunnelling Rates.- 4.2 Tunnelling Time.- 4.3 Pseudo-Device Calculations.- 4.3.1 The Wigner Function.- 4.3.2 Diode Response.- 4.4 Lateral Superlattices.- 4.4.1 Transport Effects.- 4.4.2 Bloch Oscillators.- 4.4.3 High Frequency Response.- References.- 5. The Investigation of Single and Double Barrier (Resonant Tunnelling) Heterostructures Using High Magnetic Fields.- 5.1 Background.- 5.2 LO Phonon Structure in the I(V) and C(V) Curves of Reverse-Biased Heterostructures.- 5.2.1 n-GaAs/(AlGa)As/GaAs Heterostructures.- 5.2.2 n-(InGa)As/InP/(InGa)As Heterostructures.- 5.2.3 Magnetocapacitance and Magnetic Freeze-out.- 5.3 Magnetotunnelling from the 2D Electron Gas in Accumulated (InGa)As/InP Structures Grown by MBE and MOCVD.- 5.4 Observation of Magnetoquantized Interface States by Electron Tunnelling in Single-Barrier n? (InGa)As/InP/n+ (InGa)As Heterostructures.- 5.5 Box Quantised States.- 5.6 Double Barrier Resonant Tunnelling Devices.- 5.6.1 Hybrid Magneto-electric States in Resonant Tunnelling Structures.- 5.6.2 Intrinsic Bistability in Resonant Tunnelling Devices.- 5.6.3 Magnetic Field Studies of Elastic Scattering and Optic Phonon Emission in Resonant Tunnelling Devices.- References.- 6. Microwave and Millimeter-Wave Resonant-Tunnelling Devices.- 6.1 Speed of Response.- 6.2 Resonant-Tunnelling Oscillators.- 6.3 Self-Oscillating Mixers.- 6.4 Resistive Multipliers.- 6.5 Variable Absolute Negative Conductance.- 6.6 Persistent Photoconductivity and a Resonant-Tunnelling Transistor.- 6.7 A Look at Resonant-Tunnelling Theory.- 6.7.1 Stationary-State Calculation.- 6.7.2 Temporal Behavior.- 6.7.3 Scattering.- 6.8 Concluding Remarks.- Note Added in Proof.- List of Symbols.- References.- 7. Resonant Tunnelling and Superlattice Devices: Physics and Circuits.- 7.1 Resonant Tunnelling Through Double Barriers and Superlattices.- 7.1.1 The Origin of Negative Differential Resistance.- 7.1.2 Coherent (Fabry-Perot-Type) Resonant Tunnelling.- 7.1.3 The Role of Scattering: Sequential Resonant Tunnelling Through Double Barriers and Superlattices.- 7.1.4 Ga0.47In0.53As/Al0.48In0.52As Resonant Tunnelling Diodes.- 7.1.5 Resonant Tunnelling Through Parabolic Quantum Wells.- 7.1.6 Resonant Tunnelling Electron Spectroscopy.- 7.2 Application of Resonant Tunnelling: Transistors and Circuits.- 7.2.1 Integration of Resonant Tunnelling Diodes and Their Circuit Applications.- a) Horizontal Integration of RT Diodes.- b) Vertical Integration of RT Diodes.- 7.2.2 Resonant Tunnelling Bipolar Transistors.- a) Circuit Applications of RTBTs.- b) Resonant Tunnelling Bipolar Transistors Operating at Room Temperature.- c) Alternative Designs of RTBTs.- d) RTBT with Multiple Peak Characteristics.- 7.2.3 Resonant Tunnelling Unipolar Transistors.- a) Resonant Tunnelling Gate Field Effect Transistor.- b) Quantum Wire Transistor.- c) The Gated Quantum Well Resonant Tunnelling Transistor.- References.- 8. Resonant-Tunnelling Hot Electron Transistors (RHET).- 8.1 RHET Operation.- 8.2 RHET Technology Using GaAs/AlGaAs Heterostructures.- 8.3 InGaAs-Based Material Evaluation.- 8.4 RHET Technology Using InGaAs-Based Materials.- 8.5 Theoretical Analyses of RHET Performance.- 8.6 Summary.- References.- 9. Ballistic Electron Transport in Hot Electron Transistors.- 9.1 Ballistic Transport.- 9.1.1 The Search for Ballistic Transport.- 9.1.2 Properties of GaAs.- 9.2 Hot Electron Transistors.- 9.2.1 Principles of Operation.- 9.2.2 Some History.- 9.3 Hot Electron Injectors.- 9.3.1 What is a Hot Electron Injector?.- 9.3.2 The Thermionic Injector.- 9.3.3 The Tunnel Injector.- 9.4 Energy Spectroscopy.- 9.4.1 Spectroscopy Defined.- 9.4.2 Band Pass Spectrometer.- 9.4.3 High Pass Spectrometer.- 9.4.4 Energy Resolution of the Square Type Barrier.- 9.4.5 Observation of Quasi Ballistic and Ballistic Electron Transport in GaAs.- 9.4.6 Observation of Ballistic Hole Transport in GaAs.- 9.5 Electron Coherent Effects in the THETA Device.- 9.5.1 Size Quantization Effects.- 9.5.2 Classical and Self-Consistent Well Potential.- 9.5.3 Tunnelling into a Well.- 9.5.4 Nonparabolicity Effects, Real and Resonant States.- 9.5.5 Interference Effects of Ballistic Holes.- 9.6 Transfer to the L Satellite Valleys.- 9.6.1 Spectroscopic Observations.- 9.6.2 Verification of the Intervalley Transfer.- 9.7 The THETA as a Practical Device.- 9.7.1 Gain Considerations.- 9.7.2 Speed Considerations.- 9.7.3 Final Comments.- References.- 10. Quantum Interference Devices.- 10.1 Background.- 10.2 Two-Port Quantum Devices.- 10.2.1 Conductance Formula.- 10.2.2 Quantum Interference Transistor.- 10.3 Multiport Quantum Devices.- 10.3.1 Conductance Formula.- 10.3.2 Quantum Reflection Transistor.- 10.3.3 Quantum Networks.- Appendix: Aharonov - Bohm Phase-shift in an Electric or Magnetic Field.- References.- Additional References.- 11. Carrier Confinement to One and Zero Degrees of Freedom.- 11.1 Experimental Methods.- 11.2 Discussion of Experimental Results.- 11.3 Conclusions.- References.- 12. Quantum Effects in Quasi-One-Dimensional MOSFETs.- 12.1 Background.- 12.2 MOSFET Length Scales.- 12.3 Special MOSFET Geometries.- 12.4 Strictly 1D Transport.- 12.4.1 Localization and Resonant Tunnelling.- 12.4.2 Hopping Transport.- 12.5 Multichannel Transport (Particle in a Box?).- 12.6 Averaged Quantum Diffusion.- 12.6.1 Weak Localization.- 12.6.2 Electron-Electron Interactions.- 12.7 Mesoscopic Quantum Diffusion (Universal Conductance Fluctuations).- 12.7.1 Universal Conductance Fluctuations at Scale Lo.- 12.7.2 Self-Averaging of Conductance Fluctuations at Larger Probe Spacings.- 12.7.3 Nonlocal Response of Conductance Fluctuations at Shorter Probe Spacings.- 12.7.4 Comprehensive Comparison Between Theory and Experiment.- 12.7.5 Internal Asymmetries of Mesoscopic Devices.- 12.8 Effect of One Scatterer.- 12.8.1 Interface Traps.- 12.8.2 Quantum Effect of One Scatterer.- 12.9 Conclusion.- References.

296 citations

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Bell Labs

^{1}TL;DR: In this article, an empirical two-band model for heterostructures is proposed, which provides a consistent energy-dependent effective mass characterization of nonparabolicity in quantum wells.

Abstract: We propose an empirical two-band model for heterostructures which provides a consistent energy-dependent effective-mass characterization of nonparabolicity in quantum wells We show that it predicts several surprising results Nonparabolicity has a very small effect on the lowest subband edge regardless of the well width and hence the energy of the state Nonparabolicity causes a raising of the lowest subband edge rather than the expected lowering Nonparabolicity causes a lowering of subband edge energies for higher subbands and the effect becomes substantial for the higherst subband edges We show that a large nonparabolicity lowering of a subband edge requires the state to have both a high-energy and a high occupancy probability in the well, ie, not in the barriers

291 citations

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TL;DR: In this paper, the steady state and transient electron drift velocities and impact ionization rate were derived for GaAs, InP and InAs based on a Monte Carlo simulation using a realistic band structure derived from an empirical pseudopotential.

Abstract: Calculations of the steady state and transient electron drift velocities and impact ionization rate are presented for GaAs, InP and InAs based on a Monte Carlo simulation using a realistic band structure derived from an empirical pseudopotential. The impact ionization results are obtained using collision broadening of the initial state and are found to fit the experimental data well through a wide range of applied fields. In InP the impact ionization rate is much lower than in GaAs and no appreciable anisotropy has been observed. This is due in part to the larger density of states in InP and the corresponding higher electron-phonon scattering rate. The transient drift velocities are calculated under the condition of high energy injection. The results for InP show that higher velocities can be obtained over 1000–1500 A device lengths for a much larger range of launching energies and applied electric fields than in GaAs. For the case of InAs, due to the large impact ionization rate, high drift velocities can be obtained since the ionization acts to limit the transfer of electrons to the satellite minima. In the absence of impact ionization, the electrons show the usual runaway effect and transfer readily occurs, thus lowering the drift velocity substantially.

225 citations