Kane Model Research Articles

Theory of luminescence spectra fromδ-doping structures: Application to GaAs

A general procedure for calculating luminescence spectra from $\ensuremath{\delta}$-doping structures of semiconductors is developed. The electron and hole states are self-consistently calculated within the eight-band Kane model. Explicit results are obtained for $p$-type $\ensuremath{\delta}$-doping wells and superlattices in GaAs. For a prototype superlattice (SL) it is demonstrated how the luminescence spectra of $\ensuremath{\delta}$-doping structures depend on their self-consistent potentials, band structures, and oscillator strengths of radiative recombination processes between extended electron and confined hole states. Wave-vector conserving (direct) and nonconserving (indirect) transitions are considered. Luminescence spectra are calculated for a series of $p$-type $\ensuremath{\delta}$-doping SL's, varying their sheet doping concentrations, doping spreads, and periods. A comparison with experimental spectra shows that direct transitions may be ruled out. The indirect spectra are dominated by an emission band below the gap whose structures reflect the various occupied hole subbands. Increasing the temperature, the calculated hole emission bands become stronger, in contrast with experiment. This discrepancy is solved by means of a photoinduced electron confinement.

Parameters of the Kane Model from Effective Masses: Ambiguities and Instabilities

The problem of calculating the parameters of the Kane model from experimental effective masses is reinvestigated. Conditions for the applicability of the Kane and Luttinger-Kohn models are derived in terms of experimental effective masses. It is found that different definitions of the Luttinger parameters are used within the Kane model. Some of the parameters of the Kane model are very sensitive to small changes of effective masses. The reason for this unexpected instability is analyzed, and its effects on bulk band structures and energy levels from effective mass theory are discussed.

“Bare” and “polaron” band parameters of ZnSe and the energy spectrum of QWs in the (Zn,Cd)Se/(Zn,Mg)SSe heterosystem

Magneto-optical measurement of superthin (⩽ 1 μm) ZnSe samples have been carried out in magnetic fields up to 7.5 T at T = 1.7 K. Treatment of the obtained spectra gives two sets of band parameters of bulk ZnSe, “bare” and “polaron” ones. Optical properties of MQWs in (Zn,Cd)Se/(Zn,Mg)SSe heterostructures MBE grown on GaAs substrates have been studied. Absorption spectra of free samples etched from GaAs substrate have been obtained. The calculation of the carrier spectrum and exciton binding energies in strained QWs have been carried out in the framework of the eight-band Kane model. It is demonstrated that the best agreement between calculated and measured energy positions of the absorption maxima of ZnCdSe/ZnSSe MQWs can be obtained only using two sets of band parameters: “bare” one for the QW levels and “polaron” one for the exciton binding energies.

Electronic Structure and Transport Properties of CoSb3: A Narrow Band-Gap Semiconductor

AbstractWe report calculations which show that the band structure of CoSb3 is typical of a narrow band-gap semiconductor. The gap is strongly dependent on the relative position of the Sb atoms inside the unit cell. We obtain a band gap of 0.22 eV after minimization of these position. This value is more than four times larger than the result of a previous calculation which reported that the energy bands near the Fermi surface are unusual. The electronic states close to the Fermi level are properly described by a two-band Kane Model. The calculated effective masses and band gap are in excellent agreement with Shubnikov de Haas and Hall effect measurements. Recent measurements of the transport coefficients of this compound can be understood assuming it is a narrow band gap semiconductor, in agreement with our results.

Auger recombination in strained quantum well InAlAsSb/GaSb structures for 3–4 µm lasers

Thresholdless Auger recombination in InAlAsSb strained quantum wells is studied theoretically. Analytical formulas for the Auger transition matrix element have been derived in the framework of the Kane model. A detailed analysis of overlap integrals between initial and final states of carriers has shown that the strain and light–heavy hole mixing affect both qualitatively and quantitatively the overlap integral between the electron and hole states. The Auger recombination coefficient is found to have a strong dependence on strain, quantum well width and emission wavelength, but weak dependence on temperature. The Auger coefficient temperature dependence is shown to be very sensitive to the bandgap variation with temperature.

Determination of the Band Offset of GalnP- GaAs and AllnP- GaAs Quantum Wells by Optical Spectroscopy

We report the determination of band offset ratios, using photoluminescence excitation measurements, for GaInP/GaAs and AlInP/GaAs quantum wells grown by gas-source molecular beam epitaxy. To reduce the uncertainty related to the intermixing layer at heterointerfaces, the residual group-V source evacuation time was optimized for abrupt GalnP/GaAs (AlInP/GaAs) interfaces. Based upon thickness and composition values determined by double-crystal x-ray diffraction simulation and cross-sectional transmission electron microscopy, the transition energies of GalnP/GaAs and AlInP/GaAs quantum wells were calculated using a three-band Kane model with varying band-offset ratios. The best fit of measured data to calculated transition energies suggests that the valence-band offset ratio (γ band discontinuity) was 0.63 ± 0.05 for GalnP/GaAs and 0.54 ± 0.05 for AlInP/GaAs heterostructures. This result showed good agreement with photoluminescence data, indicating that the value is independent of temperature.

Concentration dependence of optical absorption in tellurium-doped GaSb

The optical absorption of molecular-beam-epitaxy-grown and Te-doped GaSb layers is measured in the spectral region of the fundamental absorption over a temperature range extending from 10 K to 300 K. In accordance with the Burstein - Moss description, a filling of the conduction-band states, resulting in a change of the shape and a shift of the absorption edge to higher energies, is observed in the absorption spectra of Te-doped n-type GaSb layers, with electron density ranging from to at room temperature. A quantitative description of the Burstein - Moss effect is performed and the Fermi-level energy and the electron density in the valley are obtained as a function of the temperature in two different ways: (i) by comparing absorption spectra of heavily doped and unintentionally or lightly doped GaSb samples; (ii) through a direct fit of absorption data performed in the framework of Kane's band model. The values of the Fermi level and of electron density in the valley which have been optically obtained resulted in satisfactory agreement with those obtained from electrical measurements. The bandgap narrowing and the perturbation of the conduction-band density of states due to heavy doping in small-effective-mass semiconductors, such as GaSb, is considered in the framework of some current theoretical models.

Observation of hot electron relaxation in GaAs/AlGaAs multiple quantum wells by excitation spectroscopy

Hot electron relaxation in GaAs/AlGaAs multiple quantum well (MQW) structure was studied with the use of photoluminescence excitation (PLE) spectroscopy. Oscillation due to the emission of confined longitudinal optical (LO) GaAs phonons, by photoexcited electrons were observed in the (6 K) excitation spectra. The period of the oscillation is different from that observed in bulk GaAs. The calculation from a four-band Kane model, describing the mixing of heavy- and light-hole bands at wave vector away from k=0, was used to interpret the difference of oscillation features between the GaAs/AlGaAs MQW structure and bulk GaAs. The recorded PLE spectrum and calculated results show that photoexcited electrons can directly cascade downwards to the exciton energy state by LO phonon emissions.

Spin-orbit splitting of electronic states in semiconductor asymmetric quantum wells

The spin-orbit splitting in the dispersion relation for electrons in III-V semiconductor asymmetric quantum wells is studied within the standard envelope-function formalism starting from the eight-band Kane model for the bulk. The Rashba spin-orbit splitting in the different subbands is obtained for both triangular and square asymmetric quantum wells. It is shown, for example, that the Rashba splitting in AlAs/GaAs/${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As square quantum wells is of the order of 1 meV and presents a maximum as a function of the well width. The splitting of the excited subband in square and triangular quantum wells is shown to be bigger and smaller than the splitting in the first subband, respectively. A simple single-band approach, employing spin-dependent boundary conditions and approximate coupling parameters, is also introduced and its range of validity assessed. The discussion presented clarifies the treatment of abrupt interfaces, the Ando argument against the splitting, and the use of common approximations such as neglecting the barrier penetration or the energy-dependent corrections to the parameters. Good agreement is found with available experimental data.

Phonon-assisted interband tunnelling in single-barrier structures with type II heterojunctions

The interband tunnelling processes assisted by longitudinal optical (LO) phonons in single-barrier structures with type II heterojunctions are investigated. Kane's model and multicomponent wavefunctions corresponding to the initial and final states are used to obtain the matrix element for interband transition by means of emission of LO phonon inside the barrier. It is shown the phonon-assisted interband tunnelling processes may be dominant even if the transitions without scattering are not forbidden.

Photoluminescence study of heavy doping effects in Te-doped GaSb

The photoluminescence (PL) of heavily Te-doped GaSb has been investigated for different free carrier concentrations. A careful line shape analysis of the dominant free-to-bound transition has been performed using nonparabolic bands and taking into account the band tailing through the Kane model. The Fermi level and the band edge position have been determined from the fit of the PL band. Our results show that the energy gap value is significantly lower than in lightly doped and undoped material. This band-gap narrowing can be well understood taking into account both manybody interaction (exchange) and the random impurity distribution, that induces a rigid shift of the bands toward each other and tail states into the forbidden gap, respectively. Measurements have been performed at different temperatures and excitation power densities to evidence the role of the acceptor fluctuation and of the minority carrier distribution in determining the optical emission energy. Simple relations connecting the band-gap narrowing and the PL linewidth to the free carrier concentration are proposed in GaSb.

Interband mixing between two-dimensional states localized in a surface quantum welland heavy-hole states of the valence band in a narrow-gap semiconductor

Theoretical calculations in the framework of Kane model have been carried out in order to elucidate the role of interband mixing in forming the energy spectrum of two-dimensional carriers, localized in a surface quantum well in narrow gap semiconductor. Of interest was the mixing between the 2D states and heavy hole states in the volume of semiconductor. It has been shown that the interband mixing results in two effects: the broadening of 2D energy levels and their shift, which are mostly pronounced for semiconductors with high doping level. The interband mixing has been found to influence mostly the effective mass of 2D carriers for large their concentration, whereas it slightly changes the subband distribution in a wide concentration range.

Tunneling and impact ionization at high electric fields in abrupt GaAs p-i-n structures

GaAs p-i-n structures with very abrupt doping transitions and different lengths of the quasi-intrinsic zone have been fabricated by molecular beam epitaxy technology. For structures with ultra-thin intrinsic zones, tunnel currents were determined experimentally up to electric fields of 1.9 MV/cm, in good agreement with a modified Kane model. The difference of calculated tunnel current and measured total current in structures which also perform impact ionization is used to fit a Monte Carlo simulation program at high electric fields. Resulting idealized homogeneous-field ionization rates are given which are experimentally verified up to fields of 1.3 MV/cm.

Intrinsic carrier concentration and electron effective mass in Hg1−xZnxTe

The intrinsic carrier concentrations, Fermi energies, and the electron effective masses are calculated for Hg1−xZnxTe with 0<x⩽0.4 and 50 K⩽T⩽400 K. The numerical calculations are based on the Kane k⋅p model and no further analytical simplification or approximation is made for the energy band structure beyond those inherent in the Kane model. The results are compared to the previous calculations.

Shubnikov-de Haas oscillations in HgSe〈Fe〉 and HgSe〈Co〉 under hydrostatic pressure

Shubnikov-de Haas oscillations have been studied in the gapless semiconductors HgSe〈Fe〉 and HgSe〈Co〉 under hydrostatic pressure. It is shown that in HgSe〈Fe〉 an increase in pressure results in a decrease in the electron density, which fits within the framework of the Kane model with constant Fermi energy. In contrast, in HgSe〈Co〉 the electron density is independent of the pressure, i.e., Fermi-level pinning is absent.

Modeling of Mid-Infrared Multi-Quantum Well Lasers

AbstractThreshold characteristics of mid-infrared MQW lasers have been studied theoretically. Auger recombination rates in strained quantum wells have been calculated in the framework of 8×8 Kane model taking account of spin-orbit interaction. It is demonstrated that the Auger coefficients of both CHCC and CHHS processes essentially depends on the QW parameters (strain, QW width, barrier bandgap), but have relatively weak (non-exponential) temperature dependence. It is shown that the laser characteristics can be improved for optimized laser structures, when the Auger rate is decreased.

Application of Green Function Method to the Calculation of Surface States in Semiconductors with Inverted Kane Spectrum

The energy spectrum of surface states in semiconductors with Kane spectrum has been calculated by Green function method. The generalized Kane model was used, which describes simultaneously the dispersion laws for light and heavy holes and electrons. It has been shown that the surface states of electrons exist in semimetallic phase, as well as in semiconductor phase in semiconductors with Kane spectrum.

Relaxation time for ionized impurity scattering in compensated n-type Hg1-xCdxTe near x=0.2

The electron relaxation time, τI, for ionized impurity scattering in heavily compensated Hg1-xCdxTe (x ∼ 0.2) is calculated. The Kane model of band structure is used. The τI expression differs from that of Szymanska–Dietl because in heavily compensated materials the Brooks–Herring scattering potential is not adapted. The relaxation time depends essentially on the pair correlation function between acceptors and donors. Acceptor and donor concentrations using the Szymanska–Dietl model and our model have been determined for two samples.

Calculation of the band structure of semiconductor quantum wells using scattering matrices

The transfer-matrix method widely used in the calculation of the band structure of semiconductor quantum wells is found to have limitations due to its intrinsic numerical instability. It is pointed out that the numerical instability arises from free-propagating transfer matrices. A new scattering-matrix method is developed for the multiple-band Kane model within the envelope-function approximation. Compared with the transfer-matrix method, the proposed algorithm is found to be more efficient and stable. A four-band Kane model is used to check the validity of the method and the results are found to be in good agreement with earlier calculations.

Regulatory competition and the efficiency of alternative derivative product margining systems

Although margin requirements would arise naturally in the context of unregulated trading of clearinghouse-guaranteed derivative contracts, the margin requirements on U.S. exchange-traded derivative products are subject to government regulatory oversight. At present, two alternative methodologies are used for margining exchange-traded derivative contracts. Customer positions in securities and securities options are margined using a strategy-based approach. Futures, futures-options, and securities-option clearinghouse margins are set using a portfolio margining system. This study evaluates the relative efficiency of these alternative margining techniques using data on S&P500 futures-option contracts traded on the Chicago Mercantile Exchange. The results indicate that the portfolio margining approach is a much more efficient system for collateralizing the one-day risk exposures of equity derivative portfolios. Given the overwhelming efficiency advantage of the portfolio approach, the simultaneous existence of these alternative margining methods is somewhat puzzling. It is argued that the co-existence of these systems can in part be explained in the context of Kane's (1984) model of regulatory competition. The efficiency comparison also provides insight into other industry and regulatory issues including the design of bilateral collateralization agreements and the efficiency of alternative schemes that have been proposed for setting regulatory capital requirements for market risk in banks and other financial institutions (This abstract was borrowed from another version of this item.)