Holes In InSb Research Articles

Dimensional quantization in InSb and GaAs in three-zone model

Various cases of size quantization in narrow-gap crystals of cubic or tetrahedral symmetry in the three-band Kane approximation are analyzed. Expressions for the energy spectrum depending on the two-dimensional wave vector are obtained for two different cases, differing in the range of current carrier energy values. The size-quantized energy spectrum of electrons in the conduction band and holes in the subband of light holes in InSb and GaAs semiconductors is analyzed in the three-band Kane model.

To the Theory of Dimensional Quantization in Narrow-Gap Crystals

This article discusses studies of size quantization phenomena in zero-, one-, and two-dimensional semiconductor structures. The main attention is paid to the mechanisms of photon-kinetic effects in these structures. Despite many studies of the physical properties of low-dimensional systems of current carriers, the size quantization of energy spectra in narrow-gap semiconductors and the associated photonic-kinetic effects are still insufficiently studied. Therefore, this study focuses on the quantum mechanical study of size quantization in certain cases using Kane's multiband model. The insolvability of the 8×8 matrix Schrödinger equation in the Kane model for a potential well of arbitrary shape is analyzed. The dependence of the energy spectrum on the two-dimensional wave vector is studied for various cases. In particular, the energy spectra for InSb and GaAs semiconductors are considered, depending on the band parameters and the size of the potential well. Conclusions are presented on the analysis of various cases of size quantization in narrow-gap crystals with cubic or tetrahedral symmetry in the three-band approximation. It is shown that the energy spectrum corresponds to a set of size-quantized levels that depend on the Rabi parameter, band gap, and well size. The size-quantized energy spectra of electrons and holes in InSb and GaAs semiconductors are analyzed in a multiband model.

Prediction of an Excitonic Ground State inInAs/InSbQuantum Dots

Using atomistic pseudopotential and configuration-interaction many-body calculations, we predict an excitonic ground state in the InAs/InSb quantum-dot system. For large dots, the conduction band minimum of the InAs dot lies below the valence band maximum of the InSb matrix. Due to quantum confinement, at a critical size calculated here for various shapes, the gap E(g) between InAs conduction states and InSb valence states vanishes. Strong electron-hole correlation effects are induced by the spatial proximity of the electron and hole wave functions, and by the lack of strong (exciton unbinding) screening, afforded by the existence of discrete 0D confined energy levels. These correlation effects overcome E(g), leading to the formation of a biexcitonic ground state (two electrons in InAs and two holes in InSb) being energetically more favorable (by approximately 15 meV) than the dot without excitons.

Effective masses and g factors for 2D light holes in InSb

The light holes in InSb are characterised using a Shubnikov-de Haas technique by exploiting the type II band offset of an InAs0.15Sb0.85/InSb strained-layer superlattice. The data are analysed to determine the effective masses and g factors as a function of carrier concentration.

Electrons and holes in InSb under crossed magnetic and stress fields. IV. Stimulated Raman scattering in the valence bands.

Anticrossing of magnetic levels in InSb leads to high combined densities of states in the valence band at nonzero values of the longitudinal momentum ${k}_{B}$. Using pump laser radiation with photon energies near the band gap we observed stimulated Raman scattering due to transitions between repelling energy levels under uniaxial deformation. The stress was applied perpendicular to the magnetic field and perpendicular to the wave vector of the incident light (T?[100], B?[001], k?[010]). The energy levels involved in the scattering process could be identified as states with ${k}_{B}$\ensuremath{\ne}0 in the heavy-hole bands 3V (0,-1/2) and 6V (1,1/2). The range of frequency of the Raman radiation and of the magnetic field, where the observation is possible, depends very sensitively on stress. Detailed calculations of the valence-band structure show that the deformation shifts the anticrossing point in ${k}_{B}$ space and varies the energy difference of the levels 3V and 6V.

Electrons and holes in InSb under crossed magnetic and stress fields. I. Theory.

In a series of four papers magnetooptical transitions are presented for InSb crystals, which are subjected to uniaxial stress perpendicular to the magnetic field. Here, in the first paper, we establish an 8\ifmmode\times\else\texttimes\fi{}8 k\ensuremath{\cdot}p Hamiltonian matrix for stress T?[100] and field B?[001] and diagonalize it exactly. The dependence of valence and conduction states on stress and longitudinal momentum is discussed and compared with the geometry of parallel fields T?B?[001]. Characteristic features are extracted for inter- and intraband transitions. Under crossed fields, the levels are separated much stronger with stress, yielding more insight than in the parallel configuration.

Electrons and holes in InSb under crossed magnetic and stress fields. II. Recombination radiation.

Stimulated recombination radiation and spin-flip Raman scattering have been observed in InSb with uniaxial stress T applied perpendicular to a magnetic field B (T?[100], B?[001]). A k\ensuremath{\cdot}p Hamiltonian was established within an 8\ifmmode\times\else\texttimes\fi{}8 Kane model and diagonalized exactly for this particular geometry. Energy levels, transition energies, and corresponding oscillator strengths were calculated and compared to the experimental data.

Electrons and holes in InSb under crossed magnetic and stress fields. III. Magnetoreflection.

We have investigated the electronic interband transitions close to the band gap of InSb by observing magnetoreflectivity under uniaxial stress. The sensitivity of the experiment was increased by application of a magnetic-field-modulation technique. By this method we can resolve transitions from the conduction band to various valence-band Landau levels. The measurements were carried out with light polarized linearly along and perpendicular to the magnetic induction B (E?B and E\ensuremath{\perp}B). In addition to well-known electric dipole resonances we observed new transitions induced by stress. These additional lines are connected with transition matrix elements which arise from lowering the symmetry. The observed transition energies are compared with band-structure calculations.

Temperature dependence of intrinsic carrier concentration and density of states effective mass of heavy holes in InSb

From Hall measurements the temperature dependence of the intrinsic carrier concentration n i in InSb is determined between 200 K and the melting point of the compound (798 K). An empirical formula describing the temperature variation of n i is proposed. From the formula the temperature dependence of the density of states effective mass of heavy holes m d in InSb is determined. The effective mass increases from the minimum value of 0.37 m e at 225 K to a maximum value of 0.45 m e at 650 K. The obtained temperature variation of m d is smaller than found in earlier publications. The value of m d and its temperature dependence are also determined independently from the values of the valence band parameters and their temperature dependences. m d = 0.400 m e decreasing with temperature at the rate of about 10 −5deg −1 is obtained by this method. The discrepency of the results obtained by both methods is discussed and it is shown that the m d determined from the valence band parameters is more reliable. A by-product of the work is the determination of the valence band parameters which are: F = −97.8, H = −4.72 and G = −1.30.

Quantum mechanical treatment of polar optical mode mobility and application to InSb

Abstract A manifestly quantum mechanical calculation of the electrical conductivity for polar optical mode lattice scattering of carriers has been carried out by application of a Kubo formula. Frohlich's interaction Hamiltonian has been used in an S matrix approximation scheme. The resulting conductivity is then found to lie above the corresponding classical expression when the temperature is below the characteristic temperature, as expected. However, for temperatures above the characteristic temperature the conductivity lies below the classical expression and is contrary to expectation. When both calculations are compared to mobility data for heavy holes in InSb, the quantum calculation gives a better fit to the data. Experimentally it is found that the dominant lattice scattering for heavy holes is the polar mechanism for T ⩽ 300°K; above 300°K a second mechanism contributes to the scattering and is tentatively identified as non-polar optical mode scattering. The identification is complicated by the fact that the carrier-optical mode coupling constant and the optical mode characteristic temperature are both unknown.

Intrinsic Concentration and Heavy-Hole Mass in InSb

The intrinsic carrier concentration of holes in InSb has been redetermined from the temperature variation of the Hall coefficient without the assumption of acoustic mode scattering. Seven samples were used, three p type and four n type. The best statistical fit to the data yielded ni=5.76×1014T3/2exp(−0.129/kBT)over the temperature range 150°≤T≤300°K. Error analysis indicates ni is accurate to within one percent. The heavy-hole band structure proposed by Kane was used to derive a theoretical expression for the heavy-hole density of states mass which was then estimated from the value of ni determined experimentally. At low temperatures the mass was found to be 0.430 m0 and to increase with increasing temperature. When the mass value reported here was compared to cyclotron resonance data, agreement was obtained.

Conductivity Effective Mass of Holes in InSb

Conductivity Effective Mass of Holes in InSb

Landau Levels and Cyclotron Resonance of Holes in InSb

Landau levels and cyclotron resonance of holes in InSb are studied for the magnetic field along the direction on the basis of the effective mass theory. The effective Hamiltonian used for the envelope states is of the form \(\mathscr{H}\) ( k 0 + k ). Here \(\mathscr{H}\) is a 4×4 coupled Hamiltonian matrix about the center of the Brillouin zone (B. Z.) including the inversion asymmetry part ( k -linear term) in the valence band, and k 0 is one of the valence band extremu points which exist away from the center of B.Z. in the direction. Equally spaced Landau levels are obtained from the Hamiltonian, when \(|K/(\hbar^{2}/m)(eH/\hbar c)^{1/2}|\) is larger than about 2, where H is the magnetic field and K is Kane's coefficient of the k -linear term. Bagguley et al. 's valence band parameters are used in the Hamiltonian. The recent cyclotron resonance measurement reported by Robinson is well explained with the equally spaced Landau levels.

Effective Mass of Holes in InSb

Effective Mass of Holes in InSb