Generalized Kane model for the band spectrum of diamond-like semiconductors. Nonparabolicity and anisotropy of the dispersion relations

Available experimental data indicate that the Kane models for the band structure of diamond-like semiconductors do not sufficiently correctly describe the effects of the anisotropy and nonparabolicity of the valence bands. In [1], we carried out parallel examinations of the spectrum for all diamond-like semiconductors with a lower conduction band of the s-type within the four-band kp model, which is a generalization of both Kane models. We obtained a dispersion equation of fourth degree (DE-4s), allowing us to refine the range of applicability of the Kane models. This paper is a continuation of [1] in which we do a detailed analysis of the nonparabolicity and anisotropy of the dispersion relations for the holes. We show that neither of the Kane models correctly describe the state of the light-hole band over a broad energy range. At the same time, the heavy-hole band is correctly described by the Kane equation (1956); the conduction band and the split-off hole band are correctly described by the Kane theory (1957).Ukrainian Engineering Institute for Utilization and Control of Water. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 109–114, November, 1992.     

On the electron energy spectrum in heavily doped non-parabolic semiconductors

An attempt is made to present a simple theoretical analysis of the energy-wave vector dispersion relation of the conduction electrons in heavily doped non-parabolic semiconductors forming band tails. We observe that the complex energy spectrum in doped small-gap materials whose unperturbed conduction band is described by the three band model of Kane is due to the interaction of the impurity atoms in the tail with the spin-orbit splitting constant of the valence band (Δ), For band-gap (E_g)<Δ the imaginary part predominates which tails in to the conduction band. For the opposite inequality the real part comes in to play which tails in to the split-off band. In the absence of the band tailing effect, the imaginary part of the complex energy spectrum vanishes and the same is also true for doped two-band Kane-type and parabolic energy bands respectively. The present formulation helps us in investigating the Boltzmann transport equation dependent transport properties of degenerate semiconductors and are expected to agree better with experiments. The well-known results of unperturbed three and two band models of Kane together with wide-gap parabolic energy bands have been obtained as special cases of our generalized analysis under certain limiting conditions.     

Influence of magnetic quantization on the effective electron mass in Kane-type semiconductors

Summary We study the effective electron mass at the Fermi level in Kane-type semiconductors on the basis of fourth order in effective mass theory and taking into account the interactions of the conduction electrons, heavy holes, light holes and split-off holes, respectively. The results obtained are then compared to those derived on the basis of the well-known three-band Kane model. It is found, takingn-Hg_1−x Cd _x Te as an example, that the effective electron mass at the Fermi level in accordance with fourth-order model depends on the Fermi energy, magnetic quantum number and the electron spin respectively due to the influence of band nonparabolicity only. The dependence of effective mass on electron spin is due to spin-orbit splitting parameter of the valence band in three-band Kane model and the Fermi energy due to band nonparabolicity in two-band Kane model. The same mass exhibits an oscillatory magnetic-field dependence for all the band models as expected since the origin of oscillations in the effective mass in nonparabolic compounds is the same as that of the Shubnikov-de Hass oscillations. In addition, the corresponding results for parabolic energy bands have been obtained from the generalized expressions under certain limiting conditions.     

Optical verification of the valence band structure of cadmium arsenide

Optical absorption measurements were performed on thin single crystalline samples of Cd₃As₂ at temperatures of 300 K and 10 K. At low temperature the interband absorption coefficient shows clearly two steps due to direct transitions from the heavy hole and light hole valence bands to the conduction band. The absorption coefficient can be interpreted quantitatively in an isotropic inverted Kane band model with a modified heavy hole band with its maximum shifted from the Λ-point.     

On the photoemission from III–V, ternary and quaternary materials: Simplified theory and relative comparison

We study theoretically the electron energy spectrum and the photoemission from III–V, ternary and quaternary materials in the presence of light waves, whose unperturbed energy band structures are defined by the three-band model of Kane. The band gap of semiconductors increases as a consequence of incident light waves and we have suggested two new experimental methods of determining the band gap of semiconductors in the presence of photoexcitations. The solution of the Boltzmann transport equation on the basis of this newly formulated electron dispersion law will introduce new physical ideas and experimental findings in the presence of external photoexcitation. It has been found taking n-InAs, n-InSb, n-Hg_1−xCd_xTe and n-In_1−xGa_xAs_yP_1−y lattice matched to InP, as examples that the photoemission increases with the increase in electron concentration and decreases in increasing intensity, wavelength and alloy composition, respectively, in various manners. The numerical values of the photoemission in the presence of light waves is less than that of the same for unperturbed three- and two-band models of Kane together with parabolic energy bands for all types of external variables. The strong dependence of the photoemission on the light intensity reflects the direct signature of light waves on the dispersion relation of the conduction electrons, which is in contrast when compared with the corresponding bulk specimens for the unperturbed band models. The rate of change is totally band structure dependent and is significantly influenced by the presence of the different energy band constants. The well-known result of the photoemission from non-degenerate wide gap materials has been obtained as a special case of the present analysis under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. Besides, we have suggested six important applications of our results in this context.     

Subband states inn-inversion layers on small-gap semiconductors

Subband states inn-inversion layers on small-gap semiconductors are subject to the coupling between valence and conduction band (nonparabolicity effects). In order to account for this coupling we study different models: two of them are based on Kane's 6×6 and 8×8 bulk-Hamiltonians, the third one takes into account higher order terms of the electron momentum in a 2×2 conduction band Hamiltonian. We perform selfconsistent calculations for these models with parameters characteristic for InSb and HgCdTe and electron concentrationsN _S , for which up to two subbands are occupied. The calculated subband separations and Fermi energies are independent of the models only if the same energy band dispersion is used and depend strongly on the applied boundary conditions.Work supported in part by the Deutsche Forschungsgemeinschaft     

Effect of Band Nonparabolicity on the Inter Band Tunneling in Semiconductors

A simple yet generalized theory is developed to study inter band tunneling property of narrow band gap III–V compound semiconductors. The band structures of these low band gap semiconductors with sufficiently separated split-off valance band are usually described by the three energy band model of Kane, so this has been adopted here for the analysis of interband tunneling property in the case of InAs, InSb, and In_1-xGa_xAs_yP_1-y lattice matched to InP as representative direct band gap semiconductors having varied split-off valence band compared to their bulk state band gap energy. It has been found that the magnitude of tunneling rate from heavy hole decreases with increasing band nonparabolicity and the impact is more significant at high electric field in the three-band model of Kane than those with simple parabolic energy band approximations reflecting the direct influence of energy band parameters on inter band tunneling transitions. With proper consideration of band nonparabolicity, the results of the analysis of tunneling rate of these narrow gap materials show significant deviations from the results when simple parabolic band approximation is considered. The exact physical basis of the sources of deviation in the nonparabolic case from the corresponding parabolic band approximations is discussed in association to band coupling effect, transverse energy dependence, and the interplay between them. Moreover, under certain limiting conditions, our results reduce to the well-known results of parabolic band approximation and thus providing an indirect test to the accuracy of our generalized formulations.     

sp3sTight-binding parameters for transport simulations in compound semiconductors

A genetic algorithm approach is used to fit orbital interaction energies of sp3s* tight-binding models for the nine binary compound semiconductors consistent of Ga, Al, In and As, P, Sb at room temperature. The new parameters are optimized to reproduce the bandstructure relevant to carrier transport in the lowest conduction band and the highest three valence bands. The accuracy of the other bands is sacrificed for the better reproduction of the effective masses in the bands of interest. Relevant band edges are reproduced to within a few meV and the effective masses deviate from the experimental values typically by less than 10%.     

Effective mass of heavy holes in diamond-like semiconductors

Nonparabolicity of the heavy hole band in diamond-like semiconductors, which occurs within the framework of the three band model with the perturbation from the other bands taken into account to the Löwdin prucedure, is studied. A direct dependence of nonparabolicity on the band anisotropy (caused by the different effect of _15c and _12c bands) and the inverse dependence on the magnitude of the spin-orbit splitting is established. A connection between the effective mass of heavy holes and their energy is obtained, which is valid for the majority of diamond-like semicondactors, except for materials with very strong nonparabolicity of the band of silicon type.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1987.     

Spin-orbit symmetries of conduction electrons in silicon

We derive a spin-dependent Hamiltonian that captures the symmetry of the zone edge states in silicon. We present analytical expressions of the spin-dependent states and of spin relaxation due to electron-phonon interactions in the multivalley conduction band. We find excellent agreement with experimental results. Similar to the usage of the Kane Hamiltonian in direct band-gap semiconductors, the new Hamiltonian can be used to study spin properties of electrons in silicon.     

Auger recombination in diamond-like narrow-gap semiconductors

In the calculation of the transition rate of Auger recombination in the Kane model the overlap integral between the wave functions of the conduction and heavy hole bands is equal to zero at the threshold. As a result the preexponential function has a different temperature dependence in comparison with the case of simple parabolic bands. The theoretical value of the recombination lifetime is in agreement with experimental data for InSb at 300 K. Estimates of the overlap integral given earlier are analyzed.     

Hydrides as materials for semiconductor electronics

Systematic studies using density functional theory have shown that some hydrides possess the features of semiconductors. These features include larger fundamental band gap, well dispersed bottom-most conduction band and/or top-most valence band, small electron/hole effective masses and small intrinsic carrier concentration. It is demonstrated that depending upon the composition, hydrides possess a wide range of band gap values and hence they can be regarded as materials for narrow to wide band gap semiconducting applications. The possibility of designing hydride-based p–n junctions, and also their advantages as well as deficiencies compared to existing oxide semiconductors, are discussed. Replacing oxide-based semiconductors by hydrides can help to avoid problems such as formation of an oxide layer, band offsets, large concentration of defect states at the interface between the oxide and semiconductor, etc. Moreover, hydrides can be regarded as an alternative to conventional semiconductors and hence can be used in future-generation electronic devices called “hydride electronics”.     

Host structure dependence of light yield and proportionality in scintillators in terms of hot and thermalized carrier transport

Several outstanding questions, including why complex halide scintillator host structures allow higher light yield and flatter electron energy response than simple monovalent metal halides, have remained unanswered by current models of luminescence in dense ionization tracks. Our measurements of nonlinear quenching kinetic order, recent literature on hot‐electron transport in scintillators, and calculations presented here of hot‐electron velocity from band structure of SrI₂ and NaI, lead us to expand our previously described diffusion and nonlinear quenching model to include hot‐electron transport. Trends in multivalent versus monovalent metal halides, heavier versus lighter halides, and halides versus oxides versus semiconductors can be predicted based on optical phonon frequency, thermalized band edge mobilities, velocity in the upper conduction bands, and hole self‐trapping. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonparabolicity and warping in the conduction band of GaAs

The dispersion of the conduction band in GaAs is calculated using k·p models which in different ways take into account the coupling to the p-bonding and p-antibonding states. Nonparabolicity, warping and spin-splitting are accurately described up to energies about 50 meV above the conduction band minimum by the 8×8 Kane model. For higher energies a 14×14 matrix is required.     

Theory of 1f noise in medium and far infrared photodetectors

The present report is denoted to the theory of infrared photodiode low frequency noise based on homogeneous and nondegenerate semiconductors. The results of the theoretical calculation are extended to include photodiodes made of elementary semiconductors, as well as of chalcogenides and solid solutions band structures which are described through a two-band Kane model. The kinetic equations of Boltzmann for the system of electrons and phonons are used to calculate the spectral density noise. In the calculation, only the electron-phonon interactions have been taken into consideration. For low frequency noise spectrum an expression is obtained which is well matched with the experimental formula Hooge.     

Electron and hole spectra of silicon quantum dots

In the framework of perturbation theory, the first several one-particle energies and wave functions for electrons and holes (six for each) in spherical silicon quantum dots are obtained in the envelope function approximation (kp method). It is shown that the model of an isotropic dispersion relation with the mean reciprocal effective mass is applicable for the ground state of holes in the valence band. Anisotropy of the dispersion relation, which takes place for bulk semiconductors, becomes significant for the electron ground state in the conduction band as well as for all excited (both electron and hole) states.     

Excitons in organic semiconductors

In this article, excitonic effects in organic semiconductors investigated within the framework of many-body perturbation theory are reviewed. As an example for this technologically relevant class of materials the oligoacene series is studied. The electron–hole interaction is included by solving the Bethe–Salpeter equation for the electron–hole Green's function. This approach allows for the evaluation of the exciton binding energies, which are of major interest concerning the application in organic opto-electronic devices. We start the discussion with a comparison of the Kohn–Sham band structure with recent angular resolved photo-emission data. Starting from this one-electron band structure we focus on the impact of the electron–hole interactions on the optical properties by solving the Bethe–Salpeter equation. We demonstrate the dependence of the exciton binding energy on the molecular size and emphasize the effect of the intermolecular interaction on the exciton binding energies by means of pressure investigations. To cite this article: P. Puschnig, C. Ambrosch-Draxl, C. R. Physique 10 (2009).     

硅酸锌的电子结构

采用局域密度泛函理论和第一性原理的方法,计算四方结构和六角结构硅酸锌的平衡晶格常数、电子态密度和能带结构。计算结果表明,四方结构硅酸锌的平衡晶格常数为0.71048nm,六角结构为1.40877nm,两者与实验值的误差均在1%左右。态密度图显示,主要电子态分布在-7.18～0.00eV和2.79～10.50eV两个能量区域;同时,不同元素电子对导带和价带有不同贡献,其中氧的p态电子对价带顶贡献最大,锌的s态电子对导带底贡献最大。能带计算表明,四方与六角结构硅酸锌均为直接带隙半导体,禁带宽度分别为2.66,2.89eV。