Kane Model Research Articles

Polarization Dependences of Two-Photon Absorption in Narrow-Gap InSb and HgCdTe Type Semiconductors

Two-photon absorption of light in narrow-gap semiconductors of InSb and HgCdTe type is considered in the framework of the two-band Kane model. The analytical expressions for the TPA coefficient in dependence on the energies of pumped radiation and band gap of semiconductor is obtained. All the possible nonequivalent geometries of experiment are considered. In the calculations the excitonic effects are neglected. The polarization dependences are discussed and the comparison with experiment is carried out. [Russian Text Ignored].

The diffusivity-mobility ratio in nonparabolic materials

An attempt is made to study the Einstein relation for the diffusivity mobility ratio of the carriers in III–V, II–VI, IV–VI materials and Bi by formulating the respective expressions in accordance with the Kane, Hopfield, Cohen, and McClure and Choi models, respectively, which have been stated in the literature as to be the best models in describing the carrier energy spectra in these nonparabolic materials. It is found, by taking various types of aforementioned samples and Bi, that the above ratio increases with increasing electron concentration in different manners and the rates of variations are totally band structure dependent. We have also suggested an experimental method of determining the Einstein relation in degenerate materials having arbitrary dispersion laws. In addition, the corresponding well-known results for relatively wide band gap materials have also been obtained as special cases of our generalized formulations.

Electron mobility evaluation in Hg 1−xCd xTe and Hg 1− xZnx Te with two-optical-mode dispersion

Electron mobility is calculated for narrow gap HgCdTe and HgZnTe taking into account scattering by the two optical modes. The calculation is done by an iterative method using a two-band Kane model. The results show that in the temperature range where optical scattering is dominant, the one-phonon description gives mobility values very near those obtained with two modes. The mobilities in HgCdTe and in HgZnTe of the same gap are also very close. Comparison with experimental results is difficult because of the strong variation of mobility with composition in both ternaries.

Analytical descriptions of the band structure of direct-band-gap zinc-blende-structure semiconductors in the k

In the framework of the well-known k\ensuremath{\cdot}p Kane band theory, accurate analytical approximations of conduction- and valence-band dispersion of direct-band-gap zinc-blende-structure semiconductors are derived when the spin-orbit-splitting energy does not exceed the band-gap energy. These approximations include the interactions with the remote bands. The expressions of the eigenfunctions are also obtained. The present analysis elucidates and unifies previous analytical band descriptions.

Band structure of indium phosphide from near-band-gap photoemission

Energy analysis of the electrons photoemitted from p-type doped (100) InP crystals is performed with 20-meV resolution, at 120 K. The samples are activated to low electron affinity. Laser excitation in the photon energy range 1.96\ensuremath{\le}h\ensuremath{\nu}\ensuremath{\le}3.53 eV is used. The locations of the subsidiary minima ${\mathit{L}}_{6}$ and ${\mathit{X}}_{6}$ of the first conduction band and ${\mathit{X}}_{7\mathit{c}}$ of the second one are unambiguously measured (respectively, 0.67, 0.90, and 1.18 eV above the bottom of the conduction band). The energy dispersion of the three upper valence bands and of the first conduction band is probed over a large portion of the Brillouin zone. These experimental results are accurately described in the framework of the k\ensuremath{\cdot}p Kane model and the value of the spin-orbit-split-band mass ${\mathit{m}}_{7}$=(0.19\ifmmode\pm\else\textpm\fi{}0.01)${\mathit{m}}_{0}$ (where ${\mathit{m}}_{0}$ is the free-electron mass) is directly obtained.

On the diffusivity-mobility ratio in small-gap semiconductors in the presence of a strong magnetic field: Theory and suggestion for experimental determination

An attempt is made to study the Einstein relation for the diffusivity-mobility ratio of the electrons in degenerate n-type small-gap semiconductors under strong magnetic field on the basis of three-band Kane model without any approximations of band parameters and incorporating the electron spin and broadening of Landau levels, respectively. It is found, taking n-Hg1−xCdxTe as an example, that the Einstein relation exhibits an oscillatory magnetic field dependence due to Shubnikov–de Haas effect and decreases with increasing alloy composition. Besides the same ratio increases with increasing electron concentration and is in close agreement with the suggested experimental method of determining the Einstein relation in degenerate semiconductors having arbitrary dispersion laws. In addition, the corresponding well-known results of parabolic semiconductors both in the presence and absence of magnetic field have been obtained from the generalized expressions under certain limiting conditions.

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

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-Hg1−xCdxTe 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.

Effect of crossed electric and magnetic fields on the gate capacitance in n-channel inversion layers of Kane-type semiconductors

We study the effect of cross-field configuration on the gate capacitance inn-channel inversion layers of Kane-type semiconductors by formulating the model expression within the framework of K·p formalism. It is found, takingn-channel inversion layers on CdGeAs2 as example, that the gate capitances oscillate with inverse quantizing magnetic field, increase with increasing surface fields and are in agreement with the experimental data, as reported elsewhere. The corresponding results for three band Kane model, two-band Kane model and that of parabolic energy band have been obtained as special cases of the generalized expressions.

The Einstein relation in quaternary alloys under different physical conditions

AbstractThe Einstein relation for the diffusivity—mobility ratio of the carriers in quaternary alloys is studied, taking the In1−xGaxAsyP1−y lattice matched to InP, by using the three‐band Kane model in bulk specimens, magnetic quantization, cross‐field configurations, and the low‐dimensional quantum confined structures of the same material under various quantization of band states by formulating the respective electron energy spectra. The same ratio is plotted with different physical variables in all the cases and the theoretical results are in agreement with the suggested experimental method of determining the Einstein relation in degenerate materials having arbitrary dispersion laws. In addition, the corresponding well‐known results of parabolic semiconductors are obtained from our generalized expressions as special cases under certain limiting conditions.

Interband electronic Raman scattering in semiconductors induced by nonparabolicity

AbstractThe interband electronic Raman scattering (IERS) of light in narrow‐gap semiconductors due to nonparabolicity is investigated in the framework of the two‐band Kane model. Bulk and size‐quantized thin film cases are considered in detail. The possibilities to determine the semiconductor parameters and also to investigate the semiconductor—semimetal (and vice‐versa) transition with the aid of IERS are discussed.

Magneto-optical study of Ga0.47In0.53As–InP under hydrostatic pressure

Far-infrared and interband photoconductivity measurements were carried out on high-purity Ga0.47In0.53As. All the measurements were performed at 4.2 K or below in magnetic fields up to 16 T. Hydrostatic pressure of up to 10 kbar (1 bar = 105 Pa) was also applied on the sample during the experiments, using the liquid clamp cell technique. Our work was mainly focussed on the study of conduction-band nonparabolicity. The dependence of the electron effective mass toward energy was accurately determined from our cyclotron resonance measurements and compared with a theoretical description that includes nonparabolicity and magnetopolaron effects. We find that the nonparabolicity coefficient and its variation with pressure are in agreement with the theoretical predictions based on the Kane model, when the contribution of magnetopolaron effect is included in the data analysis. These results are correlated with those obtained in the interband measurements, which have been analysed within a Pidgeon–Brown approach. Some interesting data concerning impurity states were also obtained in our far-infrared photoconductivity measurements. A much richer set of Zeeman-split impurity-related peaks were recorded, as compared with previously published results. The influence of pressure, nonparabolicity, and the magnetopolaron effect on the position of these peaks will be briefly discussed.

Temperature Damping of Plasmons in Nonparabolic Band

Collective excitations influence many effects observed in quantum free-carrier semiconductor plasmas, like, for example, the impurity scattering of carriers for radiation frequencies close to the plasma frequency. Recent studies on linear-conduction-band materials [1, 2] indicate that the free-carrier band nonparabolicity may have a strong impact on the plasmons behaviour. In the present paper the influence of the nonparabolic structure of the free-carrier band on the dispersion of plasmons and their temperature damping is considered. The temperature-dependent formfactor —Im[1/e(q, ω)], where e(q, ω) is the wavevectorand frequency-dependent RPA [3] longitudinal complex dielectric function, is used to examine the properties of the collective excitations. The nonparabolic energy band of the form E(k) = (1/2)[(E8 + 4Ρ2k2)1/2 — Eg] is assumed and the overlap integrals of the electronic wave functions calculated from the Kane model are taken into account in the free-carrier polarizability. The calculations were performed for the plasma in n-PbSe in isotropic approximation [4], with P 2 = ħ2Eg/2m*, where Eg is the energy gap and m* is the effective mass at the bottom of the conduction band. The dielectric function included also the optical-phonon contribution [e.g. 4] i.e. we account for the plasmon-phonon coupling. For the degenerate plasma the nonparabolicity of the free-carrier band was found to extend the range of the wavevectors and energies where the plasmons

Subband electron cyclotron resonance and spin resonance for p-HgCdTe MIS heterostructures

The subband electron cyclotron and spin resonance spectroscopy of the inversion layer on narrow gap semiconductors p-HgCdTe have been measured for different surface electron concentrations N s with photon energies of 3.6, 10.5, 12.7, and 17.5 meV at 4.2 K. The experimental data are used to verify the subband electron Landau level fan chart and the effective g ∗ factor which are derived from Kane's model, taking into account the surface electron spin-orbit interaction.

Generalized Kane model of the band spectrum of diamond-like semiconductors. Secular determinant and dispersion equations

Available experimental data indicates that the Kane models of the band structure of diamond-like semiconductors do not quite correctly describe anisotropy effects, and in particular, the nonparabolic character of the valence bands. In this paper, a uniform examination of the spectrum of all diamond-like semiconductors with a stype, lowest conduction band is presented in the framework of a generalization of both Kane four band models. A fourth-order dispersion equation (DE-4s) is obtained which permits one to state more precisely the limits of applicability of the Kane models for the realistic semiconductors under consideration. In the case of narrow gap semiconductors, the DE-4s transforms to a cubic DE possessing a number of advantages over the expression derived by the Kane theory. In this study it is shown that for a rather broad range of energies in the crystals examined the conduction and spinsplit hole bands are quite correctly described by Kane's theory (1957), that the heavy hole band is correctly described by Kane's equations (1956), but that for a description of the light hole bands it is necessary to employ the DE-4s equation.

On The Thermoelectric Power in Degenerate Narrow Gap Semiconductors in the Presence of a Strong Magnetic Field

ABSTRACTIn this paper we have studied the thermoelectric power under strong magnetic field in degenerate 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, taking n-Hg1-xCdxTe as an example, that the magneto-thermo power increases with decreasing electron concentration and increasing magnetic field respectively for both the models in an oscillatory way. The oscillations are due to SdH effects and the theoretical snelysis in accordance with fourth order in effective mass theory is in agreement with the experimental observation as reported elsewhere. In addition, the corresponding results for parabolic energy bands have also been obtained as special cases of our generalized foriulations.

DISPERSION RELATION AND LANDAU LEVELS OF INVERSION LAYER SUBBAND ON p-HgCdTe

Starting from Kane's model and taking into account the surface electron spin-orbit interaction, we have derived the dispersion relation and Landau levels of inversion layer subband on narrow-gap semiconductors. The capacitance-voltage spectroscopy, magnetoconductivity oscillations and cyclotron resonance spectroscopy for the p-Hg 1-x Cd x Te MIS structure sample at temperature 4.2 K have been measured. From the experimental data, the subband parameters and spin-orbit coupling intensity, which are involved in the expressions of subband dispersion relation and Landau levels, have been determined. As a result, the inversion layer electron subband dispersion relation and Landau level fan chart for HgCdTe as well as the zero field spin splitting effect, the shifting and the crossing effect of Landau levels have been described quantitatively.

Envelope-function approximation for nonrectangular Hg1-xCdxTe superlattices.

The standard eight-band Kane model envelope-function formalism for rectangular superlattices (SL's) is extended to compositionally graded and doping SL's with arbitrary potential profiles. SL band structures along the growth direction are described by a set of coupled differential equations that is easily solved numerically with use of Runge-Kutta methods. A detailed application of this approach to graded ${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Cd}}_{\mathit{x}}$Te SL's is presented. For a given period and a wide range of band offsets, the SL band gap increases as the composition profile changes from rectangular to sinusoidal to triangular (symmetric) to sawtooth (asymmetric). This and other effects of SL shape are discussed in terms of known quantum-well results and the inherent degree of ``interdiffusion'' in the SL. Calculated subband structures for ${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Cd}}_{\mathit{x}}$Te sawtooth SL's agree well with recent tight-binding calculations. An inconsistency in the limited experimental data available for this system is identified.

On a simplified analysis of the photoemission from quaternary alloys

An attempt is made to study the photo-emission from bulk specimens of quaternary alloys on the basis of three-band Kane model. It is found, taking In1−xGaxAsyP1−y lattice matched to InP as an example, that the photo-emission increases, with increasing carrier degeneracy and decreasing alloy composition respectively. The valence band splitting parameter influences significantly the numerical magnitude of the photo-emission in both cases. The corresponding well-known results of parabolic semiconductors having nondegenerate electron concentration have also been obtained as special cases from our generalized expressions, under certain limiting conditions.

On a Simplified Analysis of the Magnetic Susceptibilities of Electrons in Ultrathin Films of Non‐Parabolic Semiconductors in the Presence of a Quantizing Magnetic Field

AbstractAn attempt is made to formulate simplified expressions of the dia‐and paramagnetic susceptibilities of electrons in ultrathin films of non‐parabolic semiconductors under strong magnetic quantization, taking n‐CdGeAs2 as an example. It is found, on the basis of a newly derived magneto‐dispersion relations of ultrathin films, that both the susceptibilities oscillate with increasing film thickness and increase with increasing electron concentration in the quantum limit. In addition the corresponding results for the three‐band Kane model, two‐band Kane model, and parabolic energy bands are derived as special cases of our generalized expressions.

Interface States in Subband Structure of Semiconductor Quantum Wells

AbstractAn analytical investigation is made of semiconductor quantum‐well subband structures using the three‐band Kane model. The analysis is based on the assumption, that electron and light hole masses are much smaller than heavy hole mass in the heterostructure. It is demonstrated, that some anomalies in the subband spectrum are due to the interaction with interface states, others are generated by the repulsion between the subbands near the points of their quasiintersections. For the heterostructure, composed of the gapless layer in a finite‐gap bulk material, the interface state is found to cause a nonmonotonous dependence of the gap on the layer thickness.