Kane Model Research Articles

Model Hamiltonian and time reversal breaking topological phases of antiferromagnetic half-Heusler materials

In this work, we construct a generalized Kane model with a new coupling term between itinerant electron spins and local magnetic moments of anti-ferromagnetic ordering in order to describe the low energy effective physics in a large family of anti-ferromagnetic half-Heusler materials. Topological properties of this generalized Kane model is studied and a large variety of topological phases, including Dirac semimetal phase, Weyl semimetal phase, nodal line semimetal phase, type-B triple point semimetal phase, topological mirror (or glide) insulating phase and anti-ferromagnetic topological insulating phase, are identified in different parameter regions of our effective models. In particular, we find that the system is always driven into the anti-ferromagnetic topological insulator phase once a bulk band gap is open, irrespective of the magnetic moment direction, thus providing a robust realization of anti-ferromagentic topological insulators. Furthermore, we discuss the possible realization of these topological phases in realistic anti-ferromagnetic half-Heusler materials. Our effective model provides a basis for the future study of physical phenomena in this class of materials.

Theoretical investigation of the phonon-assisted tunneling in TFET with an indirect band gap semiconductor

There are intense recent interests in quantum tunneling transistor as a way to go beyond the metal-oxide-semiconductor transistors. Phonon-assisted tunneling (PAT) plays the dominating role in tunneling field effect transistors with an indirect band gap semiconductor. In this work, we provide a convenient expression based on Fermi gold rule to study the electron tunneling assisted by phonon from the valence band top to the conduction band bottom. Through the comparison with different phonon modes, the transverse acoustic phonon mode provides the largest contribution to PAT. The results of the transfer matrix model predict slightly higher tunneling current compared to the Wentzel–Kramers–Brillouin approximation which ignores the effect of the reflection wave. However, the current density calculated by using our method shows that there is about an order of the magnitude lager than Kane's model. Additionally, the temperature enhances the phonon-assisted Zener tunneling current densities. Our results shed some light on understanding the PAT in indirect band gap semiconductors.

Resonant electronic excitation energy transfer by exchange mechanism in the quantum dot system

A microscopic theory of nonradiative resonance energy transfer between spherical A3B5 semiconductor quantum dots by the exchange mechanism is suggested. The interdot Coulomb interaction is taken into consideration. It is assumed that the quantum dot-donor and the quantum dot-acceptor are made from the same A3B5 compound and are embedded in the matrix of another material that produces potential barriers for electrons and holes. The dependences of the energy transfer rate on the quantum-dot system parameters are found in the frame of the Kane model that provides the most adequate description of the real spectra of A3B5 semiconductors. The analytical treatment is carried out with using the density matrix method, which enabled us to perform an energy transfer analysis both in the weak-interaction approximation and in the strong-interaction approximation. The numerical calculations showed the saturation of the energy transfer rate at the distances between the donor and the acceptor approaching the contact one. The contributions of the exchange and direct Coulomb intractions can be of the same order at the small distances and can have the same value in the saturation range.

Band nonparabolicity effect on spectral properties of quantum ring

We study the effect of the non-parabolicity of the conduction band and of the interband mixing, on the Aharonov Bohm oscillations of the energy levels of a volcano-shaped thin layer, made of InAs material and deposited on the GaAs substrate, by using the Kane model. We derive a simple interpolative relationship between geometrical parameters of the layer and the confinement potential governing the in-plane electron's movement, which allows us to separate the non-linear energy confinement problem in a volcano-shaped structure with a special geometry. Our results show that the nonparabolicity of dispersion of the conduction band, given by the Kane formula, conduces to a significant lowering of the charge carriers' energies and their stronger localization inside the ring. On the contrary, the nonparabolicity almost does not change neither the amplitude nor the period of the Aharonov Bohm oscillations. Additionally, we analyze the interplay between the localization and tunneling of the charge carriers, generated by the external magnetic field in structures with radially directed single, double and quadruple valleys.

NUMERICAL MODELING OF THE EFFECTIVE MASS OF AN ELECTRON IN THE QUANTUM WELL MINIBANDS InAs/AlSb

The paper studies the effective mass and statistics of two-dimensional electrons in the InAs / AlSb heterostructure in the quantum well approximation of finite depth, and takes into account the nonparabolicity of the conduction band in the two-band Kane model. Moreover, the author proposes an approximate method for calculating the dispersion and the effective mass of an electron at the Fermi level for a two-dimensional electron gas depending on the total concentration and width of the quantum well. Numerical results were obtained for QWs based on the InAs / AlSb heterojunction. Some characteristics of the two-dimensional electron gas are calculated with the help of this dispersion. A simplified approximation of the dispersion is proposed. Based of the derived approximation, simpler formulas were obtained for the effective electron mass at the Fermi level and the equation for the concentration. For QWs (based on InAs / AlSb) with a width L> 50 nm, the approximate formulas are completely satisfactory. This statement is supported by the graphs, where the approximations obtained are compared with more accurate results and experimental data. This approximation makes it possible to study the kinetic, optical, and magnetic properties of two-dimensional electron gas.

Analytic evaluation of Kane fermion magneto-optics in two and three dimensions

We calculate and present an analytic form of the magneto-optical conductivity for the gapped low-energy Kane model in two and three dimensions separately. The two-dimensional case maps onto the $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}_{3}$ model at a particular value of $\ensuremath{\alpha}=1/\sqrt{3}$. In two dimensions, two chiral sectors exist, between which there are no optically activated transitions. In three dimensions, the extra dimension of dispersion mixes the two sectors so that intra- and intersector transitions can occur. The latter type of transition can be separated out via circular polarizations of light, and it shows a distinct signature in the transverse conductivity.

Resonant electronic excitation energy transfer by Dexter mechanism in the quantum dot system

In present work the energy transfer between quantum dots by the exchange (Dexter) mechanism is analysed. The interdot Coulomb interaction is taken into consideration. It is assumed that the quantum dot-donor and the quantum dot-acceptor are made from the same compound A3B5 and embedded in the matrix of other material creating potential barriers for electron and holes. The dependences of the energy transfer rate on the quantum-dot system parameters are found using the Kane model that provides the most adequate description spectra of semiconductors A3B5. Numerical calculations show that the rate of the energy transfer by Dexter mechanism is comparable to the rate of the energy transfer by electrostatic mechanism at the distances approaching to the contact ones.

Intersubband light absorption by holes in InAsSb/AlSb quantum well heterostructures

The absorption coefficients of intersubband optical transitions in the valence band of the AlSb/InAs0.84Sb0.16/AlSb quantum wells in framework of the four-band Kane model. It is established that the light absorption by holes may lead to the laser generation breakdown. It is shown that we need to decrease the quantum well width to range a<6 nm to neutralize the negative influence of this effect.

Electron g factor anisotropy in asymmetric III–V semiconductor quantum wells

The electron effective g factor tensor in asymmetric III–V semiconductor quantum wells (AQWs) and its tuning with the structure parameters and composition are investigated with envelope-function theory and the Kane model. The spin-dependent terms in the electron effective Hamiltonian in the presence of an external magnetic field are treated as a perturbation and the g factors and , for the magnetic field in the QW plane and along the growth direction, are obtained analytically as a function of the well width L. The effects of the structure inversion asymmetry (SIA) on the electron g factor are analyzed. For the g-factor main anisotropy in AQWs, a sign change is predicted in the narrow well limit due to SIA, which can explain recent measurements and be useful in spintronic applications. Specific results for narrow-gap and AQWs are presented and discussed with the available experimental data; in particular InAs QWs are shown to not only present much larger g factors but also a larger g-factor anisotropy, and with the opposite sign with respect to GaAs QWs.

Effect of the spin–orbit interaction on intersubband electron transition in GaAs/AlGaAs quantum well heterostructures

We have calculated matrix elements for the electron intersubband transitions in rectangular, triangular and double quantum wells using 8×8 Kane model that takes into account the spin–orbit interaction, the contribution of which is due to the lack of a center of inversion in the GaAs/AlGaAs heterostructures. It is shown that this contribution determines the value of the intersubband transition probability in a rectangular quantum well for normal incidence absorption. We also show that large errors occur if the transition matrix elements are calculated in a single-band model that takes into account only the dependence of electron effective mass on the semiconductor compound without including the electron spectrum nonparabolicity.

Consequences of the thermal dependence of spin orbit coupling in semiconductors

The $\vec{k}.\vec{p}$ perturbation theory in semiconductor modifies some spin related parameters of the semi-conducting system. Furthermore, renormalization of the Kane model parameters occurs when temperature appears in the scenario. In this paper, we have analysed the consequences of this renormalized Kane parameters on some spin transport issues. It is noteworthy to study that the temperature corrected scenario, explained here can open up a new direction towards the spin calorimetric applications in semiconductors.

Electric control of inverted gap and hybridization gap in type-II InAs/GaSb quantum wells

The quantum spin Hall effect has been predicted theoretically and observed experimentally in InAs/GaSb quantum wells as a result of inverted band structures, for which electron bands in InAs layers are below heavy hole bands in GaSb layers in energy. The hybridization between electron bands and heavy hole bands leads to a hybridization gap away from k=0. A recent puzzling observation in experiments is that when the system is tuned to more inverted regime by a gate voltage (a larger inverted gap at k=0), the hybridization gap decreases. Motivated by this experiment, we explore the dependence of hybridization gap as a function of external electric fields based on the eight-band Kane model. We identify two regimes when varying electric fields: (1) both inverted and hybridization gaps increase and (2) inverted gap increases while hybridization gap decreases. Based on the effective model, we find that light-hole bands in GaSb layers play an important role in determining hybridization gap. In addition, a large external electric field can induce a strong Rashba splitting and also influence hybridization gap.

Theoretical evaluation of maximum electric field approximation of direct band-to-band tunneling Kane model for low bandgap semiconductors

The two-band Kane model has been popularly used to calculate the band-to-band tunneling (BTBT) current in tunnel field-effect transistor (TFET) which is currently considered as a promising candidate for low power applications. This study theoretically clarifies the maximum electric field approximation (MEFA) of direct BTBT Kane model and evaluates its appropriateness for low bandgap semiconductors. By analysing the physical origin of each electric field term in the Kane model, it has been elucidated in the MEFA that the local electric field term must be remained while the nonlocal electric field terms are assigned by the maximum value of electric field at the tunnel junction. Mathematical investigations have showed that the MEFA is more appropriate for low bandgap semiconductors compared to high bandgap materials because of enhanced tunneling probability in low field regions. The appropriateness of the MEFA is very useful for practical uses in quickly estimating the direct BTBT current in low bandgap TFET devices.

A low-temperature study of manganese-induced ferromagnetism and valence band convergence in tin telluride

SnTe is renowned for its promise in advancing energy-related technologies based on thermoelectricity and for its topological crystalline insulator character. Here, we demonstrate that each Mn atom introduces ∼4 μB (Bohr magneton) of magnetic moment to Sn1−xMnxTe. The Curie temperature TC reaches ∼14 K for x = 0.12, as observed in the field dependent hysteresis of magnetization and the anomalous Hall effect. In accordance with a modified two-band electronic Kane model, the light L-valence-band and the heavy Σ-valence-band gradually converge in energy with increasing Mn concentration, leading to a decreasing ordinary Hall coefficient RH and a favorably enhanced Seebeck coefficient S at the same time. With the thermal conductivity κ lowered chiefly via point defects associated with the incorporation of Mn, the strategy of Mn doping also bodes well for efficient thermoelectric applications at elevated temperatures.

Magnetic anisotropy control in [formula omitted] magnetic semiconductors

Using the six-band Kane model of the electron energy spectrum in the valence band of GaMnAs magnetic semiconductor we investigate the dependence of the crystalline magnetic anisotropy on the magnitude of magnetization and on the doping with holes. Our main focus is on the difference between two possible models related to the constraint on the total hole number or on the chemical potential. Our results show that the theoretical results for magnetic anisotropy can change dramatically with the use of different constraints.

Electronic properties of unstrained unrelaxed narrow gap InAsxSb1−x alloys

The electronic properties of unstrained unrelaxed InAsxSb1−x alloys have been determined in a wide range of alloy compositions using IR magnetospectroscopy, magnetotransport and IR photoluminescence. All studied alloys have n-type background doping with electron concentration decreasing with the Sb content. The composition dependence of the background doping concentration follows an empirical exponential law in a wide range of compositions. Both bandgap and electron effective mass dependence on alloy composition exhibit negative bowing reaching lowest values at x = 0.63: Eg = 0.10 eV, m* = 0.0082 m0 at 4.2 K. The bowing coefficient of 0.038 m0 obtained for the electron effective mass is in good agreement with that obtained from the Kane model.

On the Thermodynamics of a Two-Dimensional Electron Gas with Non-Parabolic Dispersion

A thermodynamic density of states, electron density in the subband and the entropy of the gas as function of the temperature and the total two-dimensional electron density are studied. Semiconductor conduction band dispersion is described by the simplified Kane model. Numerical simulation shows that with an increase in the total electron concentration, thermodynamic density of states at low temperatures changes abruptly and smoothes jumps at high temperatures. This change manifests itself in the peculiar thermodynamic characteristics. The results are used to interpret existing experimental data.

A Theoretical Model of Thermoelectric Transport Properties for Electrons and Phonons

A generic theoretical model for five bulk thermoelectric materials (PbTe, Bi2Te3, SnSe, Si0.7Ge0.3, and Mg2Si) has been developed based on the semiclassical model incorporating nonparabolicity, the two-band Kane model, the Hall factor, and the Debye–Callaway model for electrons and phonons. It is used to calculate thermoelectric transport properties, viz. the Seebeck coefficient, electrical conductivity, and electronic and lattice thermal conductivities, in the temperature range from room temperature up to 1200 K. The present model differs from others in the following regards: Firstly, thorough verification of modified electron scattering mechanisms is carried out by comparison with reported experimental data; Secondly, extensive verification of the model is presented, with concomitant agreement between calculations and reported measurements of effective masses, electron and hole concentrations, Seebeck coefficient, electrical conductivity, and electronic and lattice thermal conductivities; Thirdly, the present model provides the Fermi energy as a function of temperature and doping concentration; Fourthly, the velocities of sound are calculated using the Debye model rather than taken from literature. After verification of the present model, we were able to examine the recently attractive material SnSe, indicating a significant improvement in the dimensionless figure of merit.

Atomistic k ⋅ p theory

Pseudopotentials, tight-binding models, and k ⋅ p theory have stood for many years as the standard techniques for computing electronic states in crystalline solids. Here, we present the first new method in decades, which we call atomistic k ⋅ p theory. In its usual formulation, k ⋅ p theory has the advantage of depending on parameters that are directly related to experimentally measured quantities, however, it is insensitive to the locations of individual atoms. We construct an atomistic k ⋅ p theory by defining envelope functions on a grid matching the crystal lattice. The model parameters are matrix elements which are obtained from experimental results or ab initio wave functions in a simple way. This is in contrast to the other atomistic approaches in which parameters are fit to reproduce a desired dispersion and are not expressible in terms of fundamental quantities. This fitting is often very difficult. We illustrate our method by constructing a four-band atomistic model for a diamond/zincblende crystal and show that it is equivalent to the sp3 tight-binding model. We can thus directly derive the parameters in the sp3 tight-binding model from experimental data. We then take the atomistic limit of the widely used eight-band Kane model and compute the band structures for all III–V semiconductors not containing nitrogen or boron using parameters fit to experimental data. Our new approach extends k ⋅ p theory to problems in which atomistic precision is required, such as impurities, alloys, polytypes, and interfaces. It also provides a new approach to multiscale modeling by allowing continuum and atomistic k ⋅ p models to be combined in the same system.

Kane model parameters and stochastic spin current

The spin current and spin conductivity is computed through thermally driven stochastic process. By evaluating the Kramers equation and with the help of $\vec{k}.\vec{p}$ method we have studied the spin Hall scenario. Due to the thermal assistance, the Kane model parameters get modified, which consequently modulate the spin orbit coupling(SOC). This modified SOC causes the spin current to change in a finite amount.