Effect Of Band Non-parabolicity Research Articles

Effect of conduction band non-parabolicity on bound polaron fundamental state in GaN/InN core shell quantum dots

In this paper, we present a theoretical investigation on the polaronic, impurity position and quantum confinement effects on the ground state binding energy of single dopant confined in cubic GaN/InN core/shell quantum dots. Within the framework of the effective mass and non-parabolic approaches, the Schrödinger equation is numerically solved by using the Ritz variational method. The polaronic corrections are included via the renormalization of the effective mass and a phonon-modified electron-impurity Coulombic interaction. It is found that the influence of both electron-phonon interaction and the band non-parabolicity result in the reduction of the ground state binding energy. The inclusion of the non-parabolicity leads to stronger decrease of the magnitude of the impurity binding energy. This points at the importance of including such element for an appropriate quantitative description of the spectrum of coupled electron-donor-impurity systems in nitride core/shell quantum dots.

Intersubband Raman gain in strained zincblende III-nitride-based step asymmetric quantum wells: non-parabolicity effects

The conduction band states in step-like strained zincblende nitride-based quantum wells are theoretically investigated including effects of band non-parabolicity. In particular, the intersubband Raman gain is calculated in order to identify the possible use of this kind of structures as sources of THz Raman lasing. The theoretical procedure includes the use of the envelope function approximation, taking into account strain effects on the conduction band offset and position-dependent non-parabolic effective masses. Three-level Raman gain is reported for a group of possible intersubband transitions. The results are discussed in terms of the variation of the geometry of the heterostructure as well as the concentration of In in the well regions. It is shown that under a suitable geometric design and plausible detuning conditions it is possible to achieve–for certain intersubband transitions–values of the intersubband Raman gain above $$1000\,\hbox {cm}^{-1}$$ , quite larger than those previously reported in GaAs- and wurtzite GaN-based double asymmetric quantum wells. Besides, it is found that the band-nonparabolicity acts as a significant element that reduces the Raman gain response in this kind of systems, whereas strain affects it in the same way but the changes are mainly noticed for higher In contents. It turns out that it is necessary to take both effects into account for the better quantitative description on intersubband Raman response in zincblende nitride heterostructures.

Effect of electric field, dielectric screening and conduction band nonparabolicity of donor in a quantum dot

The effect of electric field, dielectric screening, conduction band nonparabolicity and effective mass mismatch of a hydrogenic donor in a GaAs/Ga[Formula: see text]Al[Formula: see text]As spherical quantum dot is investigated by assuming parabolic confinement using variational method. In the present work we obtain the increase of binding energy by decreasing the dot size for certain dot radii (50 Å) and the screening function gives uniformly larger values for smaller dot size. The effect of electric field and temperature decrease the donor binding energy whereas the conduction band nonparabolicity leads to increased binding energy.

Effect of conduction band non-parabolicity on the intersubband transitions in ZnO/MgxZn1-xO quantum well heterostructures

In this paper, we have calculated the electronic states and the coefficient of transmission in ZnO/MgxZn1-xO quantum well structures (QW), with 20% of Magnesium in both the parabolic and the non-parabolic cases. Our calculations are performed in the context of the approximation of the envelope function formalism, and using the finite difference method. The results show that the intersubband transition energy increases rapidly with well width until Lw=5nm and becomes almost constant (specially transitions E13 et E23). Wavelength λ23 decreases with well width until Lw=5nm and becomes constant. The non-parabolicity effect is more pronounced for small QW (Lw ≤ 5nm) and less marked in narrow and large QW. Also, we are studied the coefficient of transmission. We notice that when the height of barrier increases the coefficient of transmission decreases. It will be necessary to provide more energy to the electron so that it can cross the barrier. We also notice the variations related to a phenomenon of reflection quantum.

Effect of conduction band nonparabolicity on Aharonov-Bohm oscillations in n-type InAs/GaAs quantum ring

We study the effect of nonparabolicity of the conduction band on the energy spectrum of the off-axis donors in InAs crater-like quantum rings in framework of the Kane Hamiltonian. By using ta simple numerical procedure we find the low-lying energies dependencies on the radius, height and width of the ring and on the distance of the donor location from the axis. The comparison of our results with those obtained in one-band effective mass approximation reveals an essential influence of the non-parabolicity of the conduction band on the off-axis energy spectra in InAs/GaAs quantum rings. In addition, we analyse the effect of the external magnetic field applied along the symmetry axis on the Aharonov-Bohm oscillations of lower energy levels.

Effect of conduction band non-parabolicity on the optical gain of quantum cascade lasers based on the effective two-band finite difference method

We theoretically investigate the effect of conduction band non-parabolicity (NPB) on the optical gain spectrum of quantum cascade lasers (QCLs) using the effective two-band finite difference method. Based on the effective two-band model to consider the NPB effect in the multiple quantum wells (QWs), the wave functions and confined energies of electron states are calculated in two different active-region structures, which correspond to three-QW single-phonon and four-QW double-phonon resonance designs. In addition, intersubband optical dipole moments and polar-optical-phonon scattering times are calculated and compared without and with the conduction band NPB effect. Finally, the calculation results of optical gain spectra are compared in the two QCL structures having the same peak gain wavelength of 8.55 μm. The gain peaks are greatly shifted to longer wavelengths and the overall gain magnitudes are slightly reduced when the NPB effect is considered. Compared with the three-QW active-region design, the redshift of the peak gain is more prominent in the four-QW active-region design, which makes use of higher electronic states for the lasing transition.

Thermal Energy Diffusion Incorporating Generalized Einstein Relation for Degenerate Semiconductors

The currently used generalized Einstein relation for degenerate semiconductors with isotropic nonparabolic energy bands produces physically improper results, as well as losing numerical accuracy for large values of nonparabolicity parameters at room temperature. Therefore, a new generalized Einstein relation (a macroscopic equation and a formula) is derived from the semiclassical momentum balance equation based on a drift-diffusion approximation, by introducing a new concept of the effective temperature of a carrier gas for generalization of the classical kinetic theory for nonideal gases of carriers in semiconductors. The proposed formula takes into account the carrier thermal energy diffusion effect completely, so that it can accurately reflect the effect of band nonparabolicity on the ratio of the diffusion coefficient to the mobility for carriers in degenerate semiconductors. From the results evaluated with the formula, new and critically important nonparabolicity effects are observed. It is shown that the new generalized Einstein relation is valid for applied electrical fields of the full linear regime. In addition, useful figures are also presented, from which the ratio of the diffusion coefficient to mobility, as well as the Fermi energy, can be easily determined from the electron concentration, or doping density, for a given semiconductor material.

Optical rectification in quantum wells within different confinement and nonlinearity regimes

In this paper, we study the effect of conduction band non-parabolicity on optical rectification coefficients (ORCs) of quantum well systems by using compact density matrix approach. To investigate the non-parabolicity effect, we include a fourth derivative of the wave function in the Schrödinger equation. Our calculations are based on high accuracy 3, 5, 13 and 15 points finite difference methods that are developed by an interpolation approach. We show that, in some situations, the conduction band non-parabolicity can considerably affect the optical properties. Thus, it is necessary to include the conduction band non-parabolicity effects. We compare three different structures GaAs/AlxGa1-xAs (weak confinement & medium nonlinearity), GaN/AlN (strong confinement & weak nonlinearity) and InSb/GaSb (medium confinement & strong nonlinearity). We show that the non-parabolicity is very important for systems with smaller system lengths. For fixed geometrical parameters, the ORC of Al0.3Ga0.7As/GaAS quantum wells is greater than that of GaN/AlN quantum wells and the ORC of GaN/AlN quantum wells is greater than that of InSb/GaSb quantum wells. The behavior of the ORC under the influence of the applied electric field is different for the three above-mentioned quantum well systems. The red or blue shift of the ORC peak positions is more observable for systems with larger Leff.

Compact Modeling of Gate Capacitance in III–V Channel Quadruple-Gate FETs

In this paper, we present a compact model for charge density and gate capacitance for low effective mass channel material based quadruple-gate FETs (QGFETs). The proposed model accounts for the effect of quantum capacitance and conduction band non-parabolicity, which are important in FETs comprised of the low effective mass channel material. In modeling of QGFET, we propose and use a new form of Fermi–Dirac integral of order $-$ 1/2, which matches closely with the numerical data. Our model for the charge density and gate capacitance is compared with three-dimensional technology computer aided design (TCAD) simulations data, and shows excellent match. The proposed explicit compact model can be easily employed in efficient exploration of circuits based on the low effective mass QGFET nanowires.

Compact Modeling of Charge, Capacitance, and Drain Current in III–V Channel Double Gate FETs

In this paper, we present a surface potential based compact modeling of terminal charge, terminal capacitance, and drain current for III–V channel double gate field-effect transistor (DGFET) including the effect of conduction band nonparabolicity. The proposed model is developed accounting for the two-dimensional density of states and includes the effect of quantum capacitance associated with the low density of states channel material. In addition, model incorporates contribution of the first two sub-bands and efficiently captures the step like behavior appearing in the gate capacitance and transconductance with population of the higher sub-bands. The behavior of bias-dependent terminal capacitances and drain current is verified with the numerical simulation data of InGaAs channel DGFET and shows a close agreement with the simulation data.

The effects of polaronic mass and conduction band non-parabolicity on a donor binding energy under the simultaneous effect of pressure and temperature basing on the numerical FEM in a spherical quantum dot

Basing on the numerical Finite Element Method (FEM), we have investigated the influences of polaronic mass and conduction band non-parabolicity on the binding energy of the ground state of an on-center hydrogenic donor impurity in a spherical GaAs/Ga1−xAlxAs quantum dot structure. The calculations have been made with a realistic potential barrier height in the framework of the effective mass approximation including the combined effect of hydrostatic pressure and temperature. The donor binding energy is computed as a function of dot size, Al concentration x, hydrostatic pressure and temperature both in the absence and presence of polaronic mass and conduction band non-parabolicity effects. We have taken into account the electronic effective mass, dielectric constant, and conduction band offset between the dot and barriers varying with pressure and temperature. It has been found that the binding energy is strongly affected by the effect of polaronic mass and conduction band non-parabolicity for narrow quantum dot and large Al concentration x. The results show again that the donor binding energy increases linearly with the pressure in direct gap regime and its variation is larger for narrower dots only and drops slightly with the temperature. A good agreement is obtained with the existing literature values.

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.

Dispersion of nonresonant third-order nonlinearities in Silicon Carbide

In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region.

Polaronic effects on diamagnetic susceptibility of a hydrogenic donor in nanostructures

The binding energy and diamagnetic susceptibility of a hydrogenic donor in nanostructures like quantum well, quantum wire and quantum dot have been calculated for the finite and infinite barrier square well potential and are computed using variational technique. The binding energy of cubic nanostructures formed by GaAs/Ga1−x Al x As has also been obtained using conduction band non-parabolicity and polaronic correction. Our results demonstrate that the effect of polaronic mass and band non-parabolicity which exhibits effective binding energy and diamagnetic susceptibility for the nanostructures having narrow width sizes and it is not significant to the low dimensional nanostructures.

Effect of Temperature and Band Nonparabolicity on Density of States of Two Dimensional Electron Gas

The analysis of the density of states for electrons in single quantum well, the conduction band nonparabolicity take is account. It is shown that the degree of conduction band nonparabolicity pronounces depending on the energy density of states. With increasing temperature, a step change in the density of states smoothes and at high temperatures is completely blurred. Nonparabolicity dispersion law manifests itself in a wide range of temperatures. Calculations are carried out for the example of the quantum wells in InAs and InSb.

An Improved Virtual-Source-Based Transport Model for Quasi-Ballistic Transistors—Part I: Capturing Effects of Carrier Degeneracy, Drain-Bias Dependence of Gate Capacitance, and Nonlinear Channel-Access Resistance

In this paper, an improved physics-based virtual-source (VS) model to describe transport in quasi-ballistic transistors is discussed. The model is based on the Landauer scattering theory, and incorporates the effects of: 1) degeneracy on thermal velocity and mean free path of carriers in the channel; 2) drain-bias dependence of gate capacitance and VS charge, including the effects of band nonparabolicity; and 3) nonlinear resistance of the extrinsic device region on $g_{m}$ -degradation at high drain currents in the channel. The improved charge model captures the phenomenon of reduction in VS charge under nonequilibrium transport conditions in a quasi-ballistic transistor.

Modeling source-drain tunneling in ultimately scaled III–V transistors

Intraband source-drain tunneling is predicted to limit leakage current in sub-10 nm field-effect transistors (FETs). We use non-equilibrium Green's function simulations to study this effect in III-V multigate FETs and derive simple, accurate intraband tunneling formulas suitable for use in compact models or semiclassical device simulators. Band nonparabolicity effects are shown to be quantitatively important and incorporated using band gap scaling. We also supply a general subthreshold electrostatic model including source and drain depletion effects for analytical modeling. Our results enable rapid modeling and simulation of ultimately scaled III-V FETs for device evaluation and optimization.

Cubic GaN/AlGaN based quantum wells optimized for applications to tunable mid-infrared photodetectors

We propose a method which delivers optimal cubic GaN/AlGaN quantum well profiles such that both the Stark effect and peak intersubband absorption from the ground to the first excited electronic state, in a prescribed range of bias electric fields, are maximized. Our method relies on the Genetic Algorithm which finds globally optimal structures with a predefined number of embedded layers. We investigate simple rectangular quantum wells with embedded step layers for applications in tunable mid-infrared photodetectors. The effects of band nonparabolicity are taken into account to refine our model.

Simultaneous Effects of External Electric Field and Conduction Band Nonparabolicity on Optical Properties of a GaAs Quantum Dot Embedded at the Center of a GaAlAs Nano-Wire

An investigation of the optical properties of a GaAs spherical quantum dot which is located at the center of a Ga1−xAlxAs cylindrical nano-wire has been performed in the presence of an external electric held. The band nonparabolicity effect is also considered using the energy dependent effective mass approximation. The energy eigenvalues and corresponding wave functions are calculated by finite difference approximation and the reliability of calculated wave functions is checked by computing orthogonality. Using computed energy eigenvalues and wave functions, the linear, third-order nonlinear and total optical absorption coefficients and refractive index changes are examined in detail. It is found that (i) Presence of electric field causes both blue and red shifts in absorption spectrum; (ii) The absorption coefficients shift toward lower energies by taking into account the conduction band nonparabolicity; (iii) For large values of electric field the effect of conduction band nonparabolicity is less dominant and parabolic band is estimated correctly; (iv) In the presence of electric field and conduction band nonparabolicity the nonlinear term of absorption coefficient rapidly increases by increasing incident optical intensity. In other words, the saturation in optical spectrum occurs at lower incident optical intensities.

Theory of band warping and its effects on thermoelectronic transport properties

Optical and transport properties of materials depend heavily upon features of electronic band structures in proximity to energy extrema in the Brillouin zone (BZ). Such features are generally described in terms of multi-dimensional quadratic expansions and corresponding definitions of effective masses. Multi-dimensional expansions, however, are permissible only under strict conditions that are typically violated by degenerate bands and even some non-degenerate bands. Suggestive terms such as "band warping" or "corrugated energy surfaces" have been used to refer to such situations and ad hoc methods have been developed to treat them. While numerical calculations may reflect such features, a complete theory of band warping has not been developed. We develop a generally applicable theory, based on radial expansions, and a corresponding definition of angular effective mass. Our theory also accounts for effects of band non-parabolicity and anisotropy, which hitherto have not been precisely distinguished from, if not utterly confused with, band warping. Based on our theory, we develop precise procedures to evaluate band warping quantitatively. As a benchmark demonstration, we analyze the warping features of valence bands in silicon using first-principles calculations and we compare those with previous semi-empirical models. We use our theory and angular effective masses to generalize derivations of tensorial transport coefficients for cases of either single or multiple electronic bands, with either quadratically expansible or warped energy surfaces. From that theory we discover the formal existence at critical points of transport-equivalent ellipsoidal bands that yield identical results from the standpoint of any transport property. Additionally, we illustrate the drastic effects that band warping can induce on thermoelectric properties using multi-band models.