Kane Type Semiconductors Research Articles

Influence of Parallel Electric and Magnetic Fields on the Carrier Contribution to the Elastic Constants in Kane Type Semiconductors

Influence of Parallel Electric and Magnetic Fields on the Carrier Contribution to the Elastic Constants in Kane Type Semiconductors

Elastic Scattering in Kane Type Semiconductor Circular Dots

In this paper we have investigated the scattering of electrons by a circular narrow penetrable δ-type potential barrier in AB type semiconductors by using three-band Kane model. By using the Kane equations with the continuous conditions of the wave functions and ux discontinuous at the interface of two circular dots, we have analytically calculated the total cross-section and the Boltzmann conductivity for the semiconductor quantum rings with delta potential barrier. It has been shown that the quasi-bound states appear as peaks in the cross-section.

Influence of Parallel Electric and Magnetic Fields on the Einstein Relation in Kane Type Semiconductors

Influence of Parallel Electric and Magnetic Fields on the Einstein Relation in Kane Type Semiconductors

Simple Theoretical Analysis of the Effective Electron Mass in Semiconductor Nanowires

In this paper we study the effective electron mass (EEM) in Nano wires (NWs) of nonlinear optical materials on the basis of newly formulated electron dispersion relation by considering all types of anisotropies of the energy band constants within the framework of k . p formalism. The results for NWs of III-V, ternary and quaternary semiconductors form special cases of our generalized analysis. We have also investigated the EEM in NWs of Bi, IV-VI, stressed Kane type materials, Ge, GaSb and Bi2Te3 by formulating the appropriate 1D dispersion law in each case by considering the influence of energy band constants in the respective cases. It has been found that the 1D EEM in nonlinear optical materials depend on the size quantum numbers and Fermi energy due to the anisotropic spin orbit splitting constant and the crystal field splitting respectively. The 1D EEM is Bi, IV-VI, stressed Kane type semiconductors and Ge also depends on both the Fermi energy and the size quantum numbers which are the characteristic features of such NWs. The EEM increases with increase in concentration and decreasing film thickness and for ternary and quaternary compounds the EEM increases with increase in alloy composition. Under certain special conditions all the results for all the materials get simplified into the well known parabolic energy bands and thus confirming the compatibility test.

On the two dimensional effective electron mass in quantum wells, inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures.

Kane-like electrons in type II/III heterostructures versus Dirac-like electrons in graphene

The propagation of charge carriers in graphene is compared to that in type II/III heterostructures for which a two-band Kane model is appropriate. In particular, conditions for a quantitative analogy between these two cases are searched for and found to be quite restrictive. The analysis in this paper shows that the essential property of graphene is not the spinor character of its wave function but the linear dispersion relation, which does not hold in finite-gap two-band Kane-type semiconductors. Therefore, Kane-like and Dirac-like charge carriers behave differently, except in zero-band gap semiconductor superlattices.

Ballistic conductance in kane type semiconductor quantum wire

The energy spectrum, ballistic conductance of an electron on the surface of a Kane type semiconductor hollow cylinder has been calculated by using the Kane equation with an additional term that takes into account the spin-orbit (SO) interaction. This term, known as Rashba term, occurs for asymmetric quantum wells, where two directions on the normal n are physically nonequivalent. If Rashba spin-orbital interaction is incorporated into energy spectrum, it leads to the emergence of new extrema. We obtained electron energy spectrum, which depends on the sign of the effective spin orbital constant. The energy spectrum of electrons has two branches when the magnetic field does not exist. One of these branches has only one minimum while the other branch has one maximum around k = 0 and two minima. The external magnetic field can control these extrema which occur in the event transport. The results were used to obtain the ballistic conductance at finite temperature of the Kane type hollow cylinder. It has been found that the presence of additional local extremum points in the subband of the electronic spectrum leads to a nonmonotonic dependence of the ballistic conductance of the system on the chemical potential. The g-factor of electrons was observed to depend on Rashba parameter in a linear manner. The effect of finite temperature smears out the sharp steps in the zero-temperature conductance.

Phase time in Kane type barrier tunneling

The behavior of Wigner phase delay time in the reflection mode is studied taking into account the real band structure of Kane type semiconductor quantum ring. It's calculated the analytical expression for the saturated delay time. It's shown that the saturated delay time is independent of the width of the opaque barrier.

Exact solutions of the Kane equations with scalar and vector Coulomb potentials

The exact solutions of the Kane equations with the Coulomb potential have been studied for the condition when the scalar potential is equal to the vector potential. The exact energy expressions and the wave functions for the bound states are presented. The results obtained can be used to describe the energy spectrum of hydrogenic impurity states for the Coulomb potential in Kane-type semiconductors.

Bound states in Kane-type semiconductor quantum dots

In the present study, the bound states of the electrons in spherical quantum dots of A3B5-type semiconductors are studied in the framework of the three-band Kane model. An analytical expression for the bound states has been found that takes into account the non-parabolicity of the spectrum. The system considered in this study consists of two concentric spheres with GaAs in the inner part and InAs in the outer part. The spherical potential barrier in the inner part of the sphere equals - V. The numerical results are given for the spherical heterostructure of InAs/GaAs. Unlike the parabolic model, in the frame of the Kane ones, the existence of intervals of ground state in InAs/GaAs quantum dots is investigated according to the values of spherical potential.

Electron Lande g-factor in GaAs/Al xGa 1−xAs quantum wires

Energy spectrum of charge carriers is researched with and without magnetic field in Kane-type semiconductor quantum nanostructures in case of finite potential barrier V. The model that is considered in the present study is composed of two concentric quantum wires. The inner part and outer part are made up of GaAs and Al x Ga 1− x As, respectively. In the first part, it is shown that energy spectrum of carriers depends on quantum wire radius for finite potential barrier without magnetic field by using Kane model. In the second part, energy spectra of charge carriers are calculated as the function of magnetic field by using Kane model in Al x Ga 1− x As/GaAs quantum wire and compared with results of parabolic approach. It is also shown that g-factors of electrons rely on radius. It is seen that g-factor of electrons is increasing while radius is decreasing. The applied model is also useful for obtaining the energy spectra of light holes and spin–orbit splitting holes.

Energy spectrum of carriers in Kane-type semiconductors in a certain magnetic field

We present compact analytical solutions for the energy spectrum of carriers in Kane-type semiconductors in a certain varying magnetic field. We find an analytical expression for the effective g-factor of electrons in the three-dimensional semiconductors in a certain magnetic field.

Energy spectrum of carriers in 2D Kane type semiconductors in an inhomogeneous magnetic field

We present compact analytical solutions for the energy spectrum of carriers, and local effective g-factor of electrons in two-dimensional Kane type semiconductors in a magnetic field B of constant direction with arbitrarily strong exponentially depending variation perpendicular to the field direction. It has been found as an analytical expression for the local effective electron g-factor as a function of the inhomogeneous parameter.

Hartman effect in a Kane-type semiconductor quantum ring

The Hartman effect for a tunnelling particle implies that group delay time is independent of the opaque barrier width. In the present study, the tunnelling delay time in the transmission mode is studied taking into account the real band structure of an InSb-type semiconductor quantum ring and compared with that of a parabolic band structure. The system considered in this study consists of a circular loop in the presence of Aharonov–Bohm flux. It is shown that while tunnelling through an opaque barrier, the group delay time for a given incident energy becomes independent of the barrier thickness as well as the magnitude of the flux.

Energy spectrum of carriers in Kane type quantum wells

The electronic states of a Kane type semiconductor quantum well with magnetic field are theoretically investigated and compared with those of a quantum wire of the same size. Calculations are performed for a hard-wall confinement potential and the size dependence of the effective g-values in bare InSb type quantum well for electrons and light holes are found, respectively. It has been seen that the effective g-value of the electrons and light holes are decreased with the increasing of quantum well thickness.

Simple theoretical analysis of the density-of-states function of Kane type semiconductors in the presence of an external electric field

We study theoretically the energy spectrum of conduction electrons and the corresponding density-of- states function (DOS) of III–V, ternary and quaternary semiconductors, whose unperturbed energy band structures are defined by the three band model of Kane, in the presence of an external electric field. It has been observed that the unperturbed isotropic energy spectrum becomes modified under external electric field and changes into an anisotropic dispersion relation with the energy-dependent mass anisotropy. Besides, the band gap of semiconductors increases with the electric field; a phenomenon never explained earlier either theoretically (Franz–Keldysh effect) or experimentally. In addition, from the study of the DOS, it indicates that the carriers disappear from the edge of the conduction band after certain values of the applied electric field. It has been found taking n-InSb, n-InAs, Hg 1− x Cd x Te and In 1− x Ga x As y P 1− y lattice matched to InP as examples of Kane-type semiconductors for numerical computation that the increase of band gap and disappearance of carriers from the edges of the conduction band do happen for all types of materials in the presence of external electric field. The well-known energy spectrum and the corresponding DOS for wide-gap semiconductors in the absence of electric field have been obtained under certain limiting conditions from the theoretical expressions. This compatibility is an indirect mathematical test of our generalized analysis.

Energy Spectrum of Carriers in a Kane-type Semiconductor Anti-wire

The electronic states of a Kane-type semiconductor anti-wire with and without a magnetic field are theoretically investigated. The eigenvalues and eigenstates of Kane’s Hamiltonian are obtained. The calculations are performed for a hard-wall confinement potential, and electronic states are obtained as functions of the magnetic field applied along the cylinder axis. The size dependences of the effective g-value in InSb for electrons and light holes are calculated. The effective g-values of the electrons and light holes decreased with decreasing anti-wire radius.

Barrier penetration in Kane type semiconductor nanostructures

Particle penetration through a square potential and a step potential barrier are studied with the eight-band Kane Hamiltonians. It has found expressions for transmission probability and reflection coefficients of electrons for both potentials. It is shown in the Kane model that the transmission probability will have a finite value that is different from the one-band model at the state where the barrier height is infinite. The Landauer formula for resistance is applied to the Kane type semiconductor heterostructures.

Rashba splitting in Kane type quantum disk

Electrons in Kane type semiconductor quantum disk in presence of Rashba spin–orbital interaction and external magnetic field parallel to axis of quantum disk are considered theoretically. A three-level model of the kp theory is used to describe electrons in weak Rashba spin–orbit coupling regimes and external magnetic field, taking into account the main features of the band structure in InSb-type semiconductors: a small energy gap, a strong spin–orbit interaction. We calculated the radii, thickness, coupling strength, and magnetic field dependence of Rashba splitting for electrons. It has been seen that the Rashba splitting of the electrons are decreased with the increasing of radius.

G-Factor of carriers in Kane-type semiconductor wire

The electronic states of a Kane-type cylindrical semiconductor quantum wire with and without magnetic field are theoretically investigated and compared with those of a quantum wire of the same size. The eigenstates and eigenvalues of the Kane's Hamiltonian are obtained. Calculations are performed for a hard-wall confinement potential and electronic states are obtained as a function of the magnetic field applied along the cylinder axis. We calculated the size dependence of the effective g-values in bare GaAs, InSb and InAs nanocrystals for electrons, light holes and spin–orbital splitting holes, respectively. It has been seen that the effective g-value of the electrons and light holes are decreased while that of the spin–orbit splitting holes is increased with the increasing of quantum wires radius. It is shown that the g-value for electrons in GaAs quantum wire changes sign as a function of quantum wire radius.