Showing papers on "Effective mass (solid-state physics) published in 1980"

Electron transport in compound semiconductors

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.

Electrical and optical properties of undoped and antimony‐doped tin oxide films

Abstract: Tin oxide films have been prepared on glass substrates by spray pyrolysis technique. The electrical and optical properties of undoped and antimony‐doped tin oxide films have been studied. The temperature dependence of electron mobility has been analyzed to establish the electron conduction mechanism. Optical properties near the plasma edge have been analyzed using Drude’s theory. The dependence of effective mass on carrier concentration has been explained on the basis of nonparabolicity of the conduction band. The shift in the Fermi energy, calculated on the basis of energy dependent effective mass, is consistent with the measured shift in the absorption edge.

Deep levels in semiconductors

Abstract: All defects which are dominated by short-range forces belong to the family of ‘deep’ impurities and exhibit distinctly different properties from the familiar shallow donors and acceptors, where the decisive term is the Coulomb potential. Whereas formation of the shallow states relates to a small part of the Brillouin zone and can be described within the effective mass theory, the opposite is true of the deep states. However, it has recently been shown that the formation of deep localized states in semiconductors can be described with speed and accuracy, and in a self-consistent manner, by exploiting the localized character of the main part of the defect potential. It is possible to project the interaction between the localized potential and the rest of the crystal upon a limited number of localized functions, spanning the range of the potential, with an uncertainty which is small compared to the magnitude of the forbidden gap. This is achieved without truncating proper characterization of the ele...

Theory of Superconductivity in Polar Semiconductors and Its Application to N-Type Semiconducting SrTiO 3

Abstract: By solving the gap equation numtaerically from the first principles, we have investigated the mechanism of superconductivity in n -type seumiconducting SrTiO 3 . The observed transition temperature as a function of the carrier density and the applied stress is reproduced quite well, when we take account of the plasmon and the polar optic phonon which relates to the stress-induced ferroelectric transition. In the calculation, the conduction band of SrTiO 3 is assumed to be the single-valley model proposed by Mattheiss and all the physical quantities such as the effective mass, the dielectric constant and the phonon dispersion relation are taken to be the values measured by experiments, so that there are no adjustable parameters in the theory. The effect of other phonons like the acoustic one is also evaluated and found to be small.

Cyclotron resonance and the magnetophonon effect in GaxIn1−xAsyP1−y

Abstract: Cyclotron resonance and the magnetophonon effect have been used to measure the effective mass as a function of alloy composition for GaxIn1−xAsyP1−y samples grown lattice matched to InP. Values of ωτ of up to 6 allow an accurate measurement of effective mass, which is found to depend linearly upon alloy composition y with the relation m*/m0=0.080−0.039y. The observation of shallow impurity transitions in a quaternary alloy is also reported.

Theory of a Polaron at Finite Temperatures

Abstract: In order to calculate the effective mass and free energy of a polaron at finite temperatures, Feynman's path-integral formalism is generalized in the following two points: (a) the most general quadratic form is used to fully optimize the partition function, and (b) the new definition of the effective mass is introduced such that the effective mass is determined from the acceleration rate against the fictitious driving force which is incorporated in the original Lagrangian. The use of (a) leads to a non-linear integral equation which determines the best trial form. This non-linear integral equation is solved analytically for the Frohlich polaron model to obtain the explicit expressions for the effective mass and free energy at finite temperatures.

Two‐dimensional hole gas at a semiconductor heterojunction interface

Abstract: We report the first observation of a two‐dimensional hole gas (2DHG) at a semiconductor heterojunction interface (GaAs/AlxGa1−xAs). Low‐temperature angular‐dependent Shubnikov‐de Haas measurements demonstrate the two dimensionality of the system and yield a carrier surface density of 7×1011 cm−2. From the temperature dependence of the magneto oscillations we derive an effective mass of 0.35±0.1m0 for the carriers. Hall measurements establish a He temperature mobility of μ≈1700 cm2/V sec.

Pressure Dependence of the Specific-Heat Jump at the Superfluid Transition and the Effective Mass of He 3

Abstract: The specific heat of liquid $^{3}\mathrm{He}$ has been measured from 1 to 10 mK between 0 and 32.5 bars. The values implied for the effective mass are considerably smaller than the currently accepted ones. Near zero pressure the specific-heat jump is close to the BCS value 1.43, and at 32.5 bars it has reached 1.90 in the $B$ phase and 2.04 in the $A$ phase. The temperature dependence of the specific heat in the $B$ phase agrees with a model of Serene and Rainer. The latent heat at the $A\ensuremath{-}B$ transition has been measured.

Self-energy, momentum distribution, and effective masses of a dilute Fermi gas

Abstract: The dependence upon momentum $k$ and upon energy $E$ of the self-energy of a dilute Fermi gas is studied up to terms of order ${({k}_{F}c)}^{2}$, where ${k}_{F}$ denotes the Fermi momentum and $c$ is the positive scattering length. Algebraic expressions are derived for the imaginary part $W(k;E)$ of the self-energy in the whole ($k$,$E$) plane. They are compared with a conjecture recently made by Orland and Schaeffer in their analysis of single-particle states in nuclei. The contributions of core polarization and of ground state correlations to the real part $V(k;E)$ of the self-energy are calculated with the help of subtracted dispersion relations which connect them with $W(k;{E}^{\ensuremath{'}})$. Algebraic expressions are derived for the momentum distribution in the correlated ground state. It is shown that the effective mass of a quasiparticle with momentum $k$ is equal to the bare particle mass at $k=0$ and reaches a local maximum for $k$ close to ${k}_{F}$. This maximum is ascribed to the dependence of $V(k;E)$ upon $E$, which is described in terms of an $E$ mass. We compute the contributions of core polarization and of ground state correlations to this $E$ mass. The dependence of $V(k;E)$ upon $k$ reflects the nonlocality of the self-energy. It is characterized by a $k$ mass that we also calculate. These results shed light on some nuclear matter properties and on the meaningfulness and limitation of nuclear matter calculations that have recently been performed in the framework of the Brueckner-Hartree-Fock approximation.

Superconductivity in graphite-alkali metal intercalation compounds

Abstract: Superconducting properties of pseudo-single crystals of C8K were mainly investigated by the low frequency AC magnetic susceptibility and the electrical resistivity. The measured values of Tc dispersed from 128 mK to 198 mK for 13 samples. The measurements of the superconducting transition under magnetic field revealed a remarkable anisotropy due to the field angle θ measured from the layer plane, i.e., a type I superconductivity was observed for 25°⪅¦θ¦≦ 90dg and a type II for 0°≦¦θ¦⪅25°. The angular dependences of Hc2 and Hc3 were fairly well explained by the effective mass model. The Hc2 versus T curve under magnetic field perpendicular to the c-axis showed a positive curvature in the temperature range near Tc.

Band structure and thermodynamic properties of He atoms near a graphite surface

Abstract: The energy-band structure and thermodynamic properties (in the noninteracting limit) of He atoms on graphite are calculated Bound-state eigenvalues epsilon/sub n/ and matrix elements obtained in scattering experiments are used as input The validity of the assumptions used to derive these quantities is verified for self-consistency The results of these calculations differ from earlier studies in that the binding energies are 15 percent smaller and the corrugation is 50 --100 percent larger The effective mass enhancement m*/m is 106 for /sup 4/He and 103 for /sup 3/He Agreement with adsorption-isotherm determinations of the chemical potential in the limit of low coverage and temperature is remarkably good for both isotopes These results, which are consistent with our previous analysis of the potential energy V(r), indicate that band-structure effects cannot be neglected in treating He films on graphite

Core excitons in solids.

Abstract: The theory of core excitons in insulators and semiconductors is reviewed, and the validity of the effective-mass approximation is discussed. It is shown that deep core excitons with binding energies of the order of 1 eV can only occur in semiconductors as the result of a breakdown of the effective mass approximation. A possible mechanism for such a breakdown is seen in dynamical correlation effects, which can be computed with the model of the electronic polaron. This may produce an effective electron-hole interaction much stronger than the fully screened interaction over a distance comparable with the exciton radius. It is shown, however, that the conditions for such an occurrence are not met in semiconductors because of their small electron mass and their large dielectric functions, so that effective mass theory should apply. It is hinted that in special cases additional effects due to interaction between equivalent minima or to time-dependent screening may produce an increase in binding energy that increases the electron-hole interaction and precipitates a shallow-deep instability in the binding energy. Only future detailed calculations will show if this is a realistic possibility. Experiments to check the theory are suggested.

Transport Properties of Ternary Compounds

Abstract: The Hall mobility, thermal conductivity and thermoelectric power of CuInTe2 and CuGaTe2 and the thermal conductivity and thermoelectric power of CuInSe2 between 80 K and room temperature have been studied. The temperature variation of the mobility has been explained by taking into account the scattering of the charge carriers by ionized and neutral impurities and due to the presence of the space charge defects. From the theoretical fit of the thermal conductivity data, the impurity concentration and the Gruneisen constant have been estimated. The density of states effective mass has been calculated from the Seebeck coefficient.

Effect of a varying density of states on superconductivity

Abstract: A microscopic treatment of the consequences for superconductivity of a nonconstant electronic density of states is presented. Generalized Eliashberg gap equations valid for a varying density of states are presented, from which the change of ${T}_{c}$ with static or thermal disorder can be calculated. The temperature dependence of the effective mass is shown to be altered by disorder. Use of these results provides a possible experimental approach for deducing the energy variation of the density of states of superconductors.

Semiclassical theory of vibrational, rotational and translational energy exchange in collisions of polyatomic molecules

Abstract: We derive a theory of inter- and intramolecular transfer of vibrational, rotational and translational energy in collisions of polyatomic molecules, in the case that only short range forces are important. Normal mode vibrations of molecules are treated quantum mechanically whereas translations and rotations are assumed to be classical degrees of freedom. We are able to show that, in case of short range forces, the energy exchange in binary collisions is essentially governed by an effective mass which is given by an algebraic function of the usual reduced mass and moments of inertia and depends also on the relative orientation of the two molecules. As an application of the theory, we calculated the probabilities for collision-induced 1 →0 transitions of the v 3 mode in pure CH3I, CH3Br and CH3Cl gases. The calculated values are close to the experimental vibrational deactivation probabilities.

Galvanomagnetic Effect of CoS2 Single Crystal

Abstract: Making use of a single crystal of ferromagnetic CoS 2 , the resistivity, the transverse and longitudinal magnetoresistances and the Hall effect were measured in the temperature range from 4.2 K to 130 K under magnetic field strength up to 15.3 kOe. The ordinary and extraordinary Hall coefficients were determined. By assuming an electron correlation effect on the effective mass and the relaxation time for the majority and minority spin band electrons, the anomalies of resistivity and magnetoresistance were explained. The electron configuration having dγ 1 was confirmed from the ordinary Hall coefficient. The extraordinary Hall coefficient resembles that of Fe. In appendix, determinations of the Curie point and the critical exponents of this crystal were shown.

Electron effective mass in InuGa1−uPvAs1−v for 0 ≤ v ≤ 1

Abstract: The electron effective mass in InuGa1−uPvAs1−v has been measured on seven samples lattice-matched to InP and evenly spaced in values of v between 0 and 1, using the temperature dependence of the amplitude of the Shubnikov-de Haas oscillations at high magnetic fields. Values of the carrier concentrations, Hall mobilities and Dingle temperatures measured on these samples are also reported.

Resonant donor-bound-exciton luminescence in semiconductors

Abstract: The authors report novel ultra-sharp satellite luminescence lines when excited states of neutral-donor bound excitons (BE) are resonantly excited in ZnTe by a narrow laser line. The spectral position and magnetic characteristics indicate 'two-electron' transitions, leaving the donor in a series of ns and np excited orbital states. Optical pumping of the inhomogeneously broadened lines in the best crystal provides an almost tenfold linewidth reduction compared with normal BE transitions, toward a value comparable with both the laser line and the homogeneous lifetime broadening of the BE. This narrowing is greatly advantageous in the difficult task of distinction between donor species in medium to narrow direct-gap semiconductors. Orbital and spin magnetic splittings provide accurate values for electron effective mass and g value. The intensity ratio of transitions to s and p orbital states yield information on the character of the BE excited states, in agreement with recently published data of Romestain and Magnea (1979).

Evidence for alloy scattering from pressure-induced changes of electron mobility in In1-xGaxAsyP1-y

Abstract: The electron mobility in the quaternary alloy In1-xGaxAsyP1-y has been measured at pressures up to 16 kbar which produce significant changes in the effective mass. Both the pressure dependence and the temperature dependence indicate that alloy scattering has a strong influence on the electron mobility.

Optical properties of liquid tin between 0.62 and 3.7 eV

Abstract: The optical constants of liquid tin at 261 /sup 0/C have been deduced from ellipsometric measurements for photon energies between 062 and 37 eV Liquid tin behaves like a nearly-free-electron metal over the measured range The Drude parameters were derived from the real part of the dielectric constant, giving tau=490 x 10/sup -16/ sec for the relaxation time and m*/m=098 for the ratio of the effective mass to free-electron mass Comparison is made with previous results for liquid tin and also with data for solid tin