Influence of quantization of band states on the effective electron mass in quaternary alloys

Summary An attempt is made to study the effective electron mass in quaternary alloys, taking a In_1−x Ga _x As _y P_1−y lattice matched to InP, by using the three-band Kane model under different physical conditions,e.g. bulk specimens, magnetic quantization, cross-field configuration, quantum well, electric-field-aided quantum well, magnetic-field-aided quantum well, quantum well under cross fields, quantum well wires, electric-field-aided quantum well wires, magnetic-field-aided quantum well wires and quantum well wires under cross fields by formulating the respective expressions. We have plotted the effective Fermi level mass with various physical variables under different conditions. In the presence of a quantizing magnetic field the effective mass depends on the spin splitting of Landau levels due to the spin-orbit splitting parameter of the valence bands. Under cross-field configuration and the various quantum confined low-dimensional systems, the effective masses depend on the respective quantum numbers in addition to the Fermi energies even for parabolic models because of the inherent features of such systems. In addition, the corresponding results for relatively wide-gap materials have also been obtained from our generalized formulations under certain limiting conditions.     

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.     

Oscillatory effective mass in degenerate narrow-gap semiconductors in a quantizing magnetic field

An attempt is made to study the effect of a quantizing magnetic field on the effective electron mass in degeneraten-type narrow-gap semiconductors at low temperatures. It is found, takingn-Hg_1−x Cd _x Te as an example, that the effective electron mass shows an oscillatory magnetic-field dependence as is expected because of the dependence of the effective mass in degenerate non-parabolic bands on Fermi energy which oscillates with changing magnetic field. The amplitude of oscillations is, however, found to be significantly influenced by the alloy composition whereas the period is found to be independent of the band non-parabolicity, i.e. of the compositional parameter in ternary semiconductors.     

Tamm surface states of Hg1-xCdxTe

Using the Kane model, the wave functions and dispersion laws were obtained for Tamm surface states of electrons and holes arising on the ideal surface of Hg_1-xCd_xTe crystal in the parabolic and strong nonparabolic limits. The dependence of surface electrons and holes effective masses, in the parabolic limit, is determined from the parameters of the bulk states. The surface states of heavy holes is shown to be unsensitive to the degree of nonparabolicity of the electron spectrum.     

Influence of magnetic quantization on the effective mass in semiconductor superlattices

An attempt is made to study the effect of a quantizing magnetic field on the effective electron mass in a semiconductor superlattice at low temperatures. It is found on the basis of the tight-binding approximation, taking GaAs-Ga_1–x Al _x As an example, that the effective mass at the Fermi level depends on the magnetic quantum number due to the cosine dependence of the wave-vector in the superlattice direction. The mass also exhibits oscillatory features in the presence of magnetic quantization because of its dependence on Fermi energy which oscillates with changing magnetic field.     

Threshold and probability of impact ionization by electrons in narrow-gap p-type semiconductors with highly degenerate holes

The process of electron-initiated impact ionization of states in the heavy-hole band is investigated theoretically for a p-type narrow-gap semiconductor with energy bands governed by the Kane dispersion law, subject to the condition that the Fermi level of the holes lies in the valence band. The dependence of the minimum electron energy for ionization of a state at the Fermi level in the valence band on the heavy-hole Fermi momentum is determined. The probability of impact ionization for electrons with near-threshold energies is calculated for the case in which the heavy-hole Fermi momentum exceeds the hole threshold momentum for the given ionization process. Relations between the temperatures of holes and electrons with energies of the order of the threshold value are found, thereby establishing the validity domain of the final results. Fiz. Tverd. Tela (St. Petersburg) 39, 275–279 (February 1997)     

The effect of nonparabolicity on binding energy of ground and excited states in a corrugated quantum well

The binding energy of a hydrogenic impurity is calculated in a Ga_1−xAl_xAs/Ga_1−yAl_yAs corrugated quantum well within the single band effective mass approximation for different Al concentration. Binding energy of the ground state and the excited state of a donor is calculated, with the inclusion of 2D Hartree dielectric screening function. The effect of nonparabolicity of the conduction band is considered through the energy dependent effective mass. The effect of nonparabolicity on spin–orbit interaction energy is found. The oscillator strength coupling between the ground state and the excited state is calculated. The dependence of the donor binding energy on the well width and the Al-concentration is discussed. These results are discussed with the available data in the literature.     

Spin splitting in HgTe/CdHgTe (013) quantum well heterostructures

The electron transport and cyclotron resonance in a one-sided selectively doped HgTe/CdHgTe (013) heterostructure with a 15-nm quantum well with an inverted band structure have been investigated. The modulation of the Shubnikov-de Haas oscillations has been observed, and the spin splitting in zero magnetic field has been found to be about 30 meV. A large Δm _c/m _c ≃ 0.12 splitting of the cyclotron resonance line has been discovered and shown to be due to both the spin splitting and the strong nonparabolicity of the dispersion relation in the conduction band.     

Temperature dependence of the electron effective mass in MnxHg1−xSe

We have investigated the temperature dependence of the electron effective mass in Mn_xHg_1–xSe crystals (0 < x 0.1) in the T=90–300 K temperature range. We have determined that the temperature-dependent changes in the band gap (_g), in the band diagram nonparabolicity, and in the conduction band carrier concentration have a strong effect on the temperature dependence of the carrier effective mass at the Fermi level m ^*=f(T).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 5–9, November, 1987.     

Interface contributions to the spin-orbit interaction parameters of electrons at the (001) GaAs/AlGaAs interface

One-body mechanisms of spin splitting of the energy spectrum of 2D electrons in a one-side doped (001) GaAs/Al _x Ga_{1 ? x} As quantum well have been studied theoretically and experimentally. The interfacial spin splitting has been shown to compensate (enhance) considerably the contribution of the bulk Dresselhaus (Bychkov-Rashba) mechanism. The theoretical approach is based on the solution of the effective mass equation in a quasi-triangular well supplemented by a new boundary condition at a high and atomically sharp hetero-barrier. The model takes into account the spin-orbit interaction of electrons with both bulk and interfacial crystal potential having C _2v symmetry, as well as the lack of inversion symmetry and nonparabolicity of the conduction band in GaAs. The effective 2D spin Hamiltonian including both bulk and interface contributions to the Dresselhaus (α_BIA) and Rashba (α_SIA) constants has been derived. The analytical relation between these constants and the components of the anisotropic nonlinear g-factor tensor in an oblique quantizing magnetic field has been found. The experimental approach is based, on one hand, on the detection of electron spin resonance in the microwave range and, on the other hand, on photoluminescence measurements of the nonparabolicity parameter. The interface contributions to α_BIA and α_SIA have been found from comparison with the theory.     

Electron–hole symmetry and spin–orbit splitting in IV–VI asymmetric quantum wells

It is shown that, due to the electron–hole symmetry of the fundamental gap of the lead–salts (PbTe, PbSe and PbS), the Rashba spin splitting in their flat band asymmetric quantum wells is much reduced with the usual equal conduction and valence band-offsets. Different from the III–V case, we find that the important structure inversion asymmetry for the Rashba splitting in IV–VI quantum wells with different left and right barriers is not a material property (i.e., barrier height, effective mass or band gap) but results from the band alignment. This is shown by specific envelope function calculations of the spin-dependent subband structure of Pb_1−xEu_xTe/PbTe/Pb_1−yEu_yTe asymmetric quantum wells (x≠y), based on a simple but accurate four-band kp model for the bulk band structure near the gap, which takes into account band anisotropy, nonparabolicity and multi-valley effects.     

Electronic structure of p-type La1 ? xM x2+ MnO3 manganites in the ferromagnetic and paramagnetic phases in the LDA + GTB approach

The band structure, spectral intensity, and position of the Fermi level in doped p-type La_{1 − x} M _x/2+MnO₃ manganites (M = Sr, Ca, Ba) is analyzed using the LDA + GBT method for calculating the electronic structure of systems with strong electron correlations, taking into account antiferro-orbital ordering and using the Kugel-Khomskii ideas and real spin S = 2. The results of the ferromagnetic phase reproduce the state of a spin half-metal with 100% spin polarization at T = 0, when the spectrum is of the metal type for a quasiparticle with one spin projection and of the dielectric type for the other. It is found that the valence band becomes approximately three times narrower upon a transition to the paramagnetic phase. For the paramagnetic phase, metal properties are observed because the Fermi level is located in the valence band for any nonzero x. The dielectrization effect at the Curie temperature is possible and must be accompanied by filling of d _x orbitals upon doping. The effect itself is associated with strong electron correlations, and a complex structure of the top of the valence band is due to the Jahn-Teller effect in cubic materials.     

Theory of the electronic structure and spin susceptibility of La2−x SrxCuO4

We solve the problem of the effect of strong electron correlations on the homogeneous spin susceptibility of current carriers in CuO₂ planes. We show that the dependence of the spin susceptibility χ(T) of high-T _c superconductors of the La_2−x Sr_xCuO₄ type on temperature and the doping index x can be explained fairly well by the two-band model suggested earlier (the singlet-correlated oxygen band plus the lower Hubbard band of copper). The model has features in common with the phenomenological t-J model but cannot be reduced to the latter completely. In contrast to the t-J model, the density of states of the oxygen holes has a peak near the bottom of the band. It is the presence of this peak together with the non-Fermi-liquid properties that explain the unusual behavior of the spin susceptibility of La_2−x Sr_xCuO₄. Zh. éksp. Teor. Fiz. 112, 1763–1777 (November 1997)     

Magnetooptic measurements of the cyclotron mass and g-factor of light holes in GaAs

An emission line appearing in the hot-luminescence spectrum of GaAs at a frequency shifted from the laser line by the cyclotron energy of light holes is observed and investigated. Analysis of the magnetooscillations of the intensity of this line shows that the line is due to the recombination of a photoexcited electron and a light hole after the hole undergoes energy relaxation between Landau levels. The dependence of the cyclotron mass and g factor of light holes on the hole energy was measured directly and a very strong nonparabolicity of the valence band of GaAs, several times greater than the theoretical estimates, was observed. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 766–771 (10 December 1996)     

Binding energies of helium-like impurities in parabolic quantum wells under an applied electric field

We present a variational method to compute the binding energies of helium-like impurities in finite parabolic GaAs- Ga_1 − xAl_xAs quantum wells. The effects of band nonparabolicity in the conduction band are taken into account within the effective mass approximation. The dependence of the impurity binding energy on the applied electric field and the impurity position is also discussed together with the polarization effect for all cases.     

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.     

Application of band theory to experimental eigen-state energies of In0.53Ga0.47As quantum wells lattice-matched to InP

Nonparabolic band structure of InGaAs/InAlAs multi-quantum wells was studied theoretically and experimentally. The electron effective mass was derived even from eigen-states and this nonparabolicity was explicitly determined as a function of energy. Electron eigen-state energies applying Kane’s bulk band theory fitted very well with our experiments in the multi-quantum wells.     

AB initio energy band structure of polysulfur nitride, (SN)x

All electron energy band structure is reported for an infinite one-dimensional model of polysulfur nitride, (SN)_x, using the ab initio LCAO Hartree-Fock method. The calculated values of the effective mass and density of states at the Fermi level are ?0.72 m_e and 0.06 states/(eV spin molecule), respectively. An appreciable amount of charge transfer (0.30 e) from sulfur to nitrogen was obtained. Finally, comparison is made with the results of a semi-empirical version of the same method.     

Nonparabolicity corrections to the valence band energy levels of Si/GexSi1-x quantum wells

In earlier work, subband energies of Si/Ge_xSi_1-x quantum wells were obtained neglecting valence band nonparabolicity. Here we present an algorithm for solving for the energies and wavefunctions of the mixed light-hole and split-off subbands under stress, which incorporates the energy dependence of the effective mass exactly. We show that this gives corrections to the energies that are of the order of tens of meV, and results in small nonorthogonality corrections to the envelope wavefunctions. These corrections are discussed for several cases of physical interest and are compared to the results obtained assuming a constant bandedge effective mass.     

Influence of magnetic quantization on the Einstein relation in non-linear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestion for experimental determination

In this paper, we have investigated the Einstein relation for the diffusivity-to-mobility ratio (DMR) under magnetic quantization in non-linear optical materials on the basis of a newly formulated electron dispersion law by considering the crystal field constant, the anisotropies of the momentum-matrix element and the spin-orbit splitting constant, respectively, within the frame work of k·p formalism. The corresponding result for the three-band model of Kane (the conduction electrons of III-V, ternary and quaternary compounds obey this model) forms a special case of our generalized analysis. The DMR under magnetic quantization has also been investigated for II-VI (on the basis of Hopfield model), bismuth (using the models of McClure and Choi, Cohen, Lax and parabolic ellipsoidal, respectively), and stressed materials (on the basis of model of Seiler et al.) by formulating the respective electron statistics under magnetic quantization incorporating the respective energy band constants. It has been found, taking n-CdGeAs₂, n-Hg_1−xCd_xTe, p-CdS, and stressed n-InSb as examples of the aforementioned compounds, that the DMR exhibits oscillatory dependence with the inverse quantizing magnetic field due to Subhnikov de Haas (SdH) effect with different numerical values. The DMR also increases with increasing carrier degeneracy and the nature of oscillations are totally dependent on their respective band structures in various cases. The classical expression of the DMR has been obtained as a special case from the results of all the materials as considered here under certain limiting conditions, and this compatibility is the indirect test of our generalized formalism. In addition, we have suggested an experimental method of determining the DMR for degenerate materials under magnetic quantization having arbitrary dispersion laws. The three applications of our results in the presence of magneto-transport have further been suggested.