Effect Of Conduction Band Non-parabolicity Research Articles

Room temperature two-dimensional electron gas scattering time, effective mass, and mobility parameters in AlxGa1−xN/GaN heterostructures (0.07 ≤ x ≤ 0.42)

AlxGa1−xN/GaN high-electron-mobility transistor (HEMT) structures are key components in electronic devices operating at gigahertz or higher frequencies. In order to optimize such HEMT structures, understanding their electronic response at high frequencies and room temperature is required. Here, we present a study of the room temperature free charge carrier properties of the two-dimensional electron gas (2DEG) in HEMT structures with varying Al content in the AlxGa1−xN barrier layers between x=0.07 and x=0.42. We discuss and compare 2DEG sheet density, mobility, effective mass, sheet resistance, and scattering times, which are determined by theoretical calculations, contactless Hall effect, capacitance-voltage, Eddy current, and cavity-enhanced terahertz optical Hall effect (THz-OHE) measurements using a low-field permanent magnet (0.6 T). From our THz-OHE results, we observe that the measured mobility reduction from x=0.13 to x=0.42 is driven by the decrease in 2DEG scattering time, and not the change in effective mass. For x<0.42, the 2DEG effective mass is found to be larger than for electrons in bulk GaN, which in turn, contributes to a decrease in the principally achievable mobility. From our theoretical calculations, we find that values close to 0.3m0 can be explained by the combined effects of conduction band nonparabolicity, polarons, and hybridization of the electron wavefunction through penetration into the barrier layer.

Quadrupole assisted optical rectification and corresponding refractive index change in GaAs quantum dot in THz range

We investigate the optical rectification (OR) process and the corresponding refractive index change (RIC) in single electron charged GaAs spherical quantum dot. The effective mass approximation is used with the finite potential including the effect of conduction band nonparabolicity. The OR and the RIC processes are studied including dipole plus quadrupole effects within the framework of the density matrix approach for different dot radii and outside arsenide, nitride and oxide matrix in the terahertz range.

Efficient strain-modified improved nonparabolic-band energy dispersion model that considers the effect of conduction band nonparabolicity in mid-infrared quantum cascade lasers.

Intersubband polar-optical-phonon (POP) scattering plays an important role in determining the population inversion and optical gain of mid-infrared (mid-IR) quantum cascade lasers (QCLs). In particular, the nonparabolicity of the conduction band (CB) significantly affects the energy dispersion relation and intersubband POP scattering time. However, the currently used parabolic-band (PB) and nonparabolic-band (NPB) energy dispersion models are not appropriate for mid-IR QCLs because they are unsuitable for high electron wave vectors and do not consider the effect of applied strain on the energy dispersion relation of the CB. The eight-band k·p method can provide a relatively accurate nonparabolic energy dispersion relation for high electron wave vectors but has the disadvantages of high computational complexity and spurious solutions to be discarded. Consequently, we propose a strain-modified improved nonparabolic-band (INPB) energy dispersion model that has no spurious solution and acceptable accuracy, compared to the eight-band k·p method. To demonstrate the accuracy and efficiency of our proposed INPB model compared with those of the PB, NPB, and eight-band k·p models, we calculate the energy dispersion relations and intersubband POP scattering times in a strain-compensated QCL with a lasing wavelength of 3.58 µm. Calculation results reveal that our proposed model is almost as accurate as the eight-band k·p model; however, it enables much faster calculations and is free from spurious solutions.

Effects of conduction band non-parabolicity and matrix material on THG process in GaAs QD

We investigate theoretically the third harmonic generation (THG) process in the singly charged GaAs quantum dot (QD). The effective mass approximation is used to obtain the energy levels and the wavefunctions. The potential is considered to be of finite type, with and without the effect of non-parabolicity of the conduction band. The effect of the conduction band nonparabolicity is included using the Kane’s model. Within the framework of the density matrix approach, THG nonlinear optical process is investigated in THz region for different dot radii of GaAs QD embedded in three different matrices, viz: Ga1-yAlyAs, Al2O3 and Si3N4.

A SPICE compatible physics-based intrinsic charge and capacitance model of InAs-OI-Si MOS transistor

In this work, we present a core model of terminal charge and intrinsic capacitances of InAs-on-Si MOS transistors. The eigenenergy and corresponding wavefunctions are deduced by solving time independent Schrödinger wave equation inside the finite potential well. A second-order non-parabolic correction to the sub-band energy, effective mass of electron, and conduction band density of states have been employed and incorporated into the core model. The developed model effectively captures the variation in gate capacitance and reproduce the staircase like capacitance-voltage characteristics. Effect of conduction band nonparabolicity on gate capacitance is studied for different band-nonparabolicity factor. The model is validated with self-consistent Schrödinger-Poisson solver predicted result for different drain bias and channel thicknesses. The model calculated results are in a reasonable agreement with numerical simulation data. The SPICE compatibility of our model is demonstrated through Verilog-AMS implementation of the model and SPICE simulation of two benchmark circuits. • We propose a core model for intrinsic charge and capacitances of InAs-on-insulator MOS Transistor over Silicon substrate. • The model is derived from explicit solution of Schrödinger and Poisson equations without using any empirical parameters. • The model includes conduction band nonparabolicity effect on sub-band energy, terminal charges and capacitances. • Inversion charge present inside buffer region and its effect on capacitance is modeled using a semi analytical approach. • The model is developed using Verilog-AMS language, and circuit simulation is demonstrated using commercial SPICE simulator.

Physics based compact modeling of symmetric double gate MOS transistors with high mobility III-V channel material

In this work, we report a physics-based core model of surface potential, inversion charge, and drain current of a symmetric double-gate MOSFET with high mobility III-V channel material. The model efficiently captures all essential device physics of III-V MOSFETs. The carrier quantization effect inside the quantum well formed between oxide and channel region, is modeled by solving time-independent Schrödinger wave equation. The surface potential and inversion charge are obtained from the explicit solution of the Poisson and Schrödinger equation. A first-order correction has been applied to incorporate the modifications in sub-band energy due to applied gate bias voltages. The conduction band non-parabolicity effect is also included in our proposed model. The drain current has been derived using drift-diffusion transport including the velocity overshoot effect. The core model is free from any empirical parameters. The model predicted results have been validated with self-consistent Schrödinger-Poisson solver and commercial device simulator (TCAD) for different channel thicknesses, effective masses, a wide range of gate and drain bias voltages, and different non-parabolicity factor. The model predicted results are found to be in reasonable agreement with numerical simulation data.

Simultaneous effects of temperature, pressure, polaronic mass, and conduction band non-parabolicity on a single dopant in conical GaAs-Al x Ga1–x As quantum dots

This paper is devoted to the theoretical study of the simultaneous effects of temperature, hydrostatic pressure, conduction band non-parabolicity, and polaronic mass on the electronic states and the photoionization cross-section of a shallow donor impurity confined in a GaAs-Al x GaAs conical quantum dot. The calculations have been made within the effective mass approximation. The shallow donor impurity energy levels have been calculated by employing two methods: the variational approach and the finite element method with finite and infinite confining potential. The obtained results suggest that the effects of conduction band non-parabolicity, temperature, hydrostatic pressure, and variation of the conical quantum dot geometries play a significant role in determining of the electronic states system, as well as in the photoionization cross-section. It is also shown that the donor binding energy is very sensitive to temperature and hydrostatic pressure. Indeed, the temperature decreases the donor binding energy while it is increasing with the applied hydrostatic pressure. Also, the quantum dot effective gap is severely affected by the conduction band non-parabolicity. In the case of polaronic mass effects, the present study suggests that they can be omitted without significantly affecting the study’s main conclusions. In this paper, structures with an apical angle ranging from 10° to 150° are approached, allowing simulating quantum dots with a radius of the base much greater than the height and structures with a height much greater than the radius of the base. In the case of hydrostatic pressure and for quantum dots with finite confinement potential, the Γ-X crossover effect has been considered, which is responsible for significant changes in the carriers’ confinement potential.

LO-Phonons and dielectric polarization effects on the electronic properties of doped GaN/InN spherical core/shell quantum dots in a nonparabolic band model

The electron energy spectrum of a core/shell spherical quantum dot made of zincblende GaN/InN compounds is investigated taking into account the presence of an off-center donor atom and the influence of band nonparabolicity. The interaction of both the charge carrier and the Coulombic core with longitudinal optical phonons is included through Fro hlich and Aldrich-Bajaj theories, respectively. The ground state energy is determined by solving the resulting conduction band effective mass equation via the variational Ritz principle. A detailed analysis of the features of electron and hole spectra as functions of the core and shell sizes is presented, highlighting the possibility of transitioning between type-I and type-II structures. A detailed discussion about the effects of conduction band nonparabolicity, dielectric mismatch and electron-phonon interaction onto the impurity binding energy is provided. It was found that, in general, nonparabolicity of the conduction band leads to larger impurity binding energy, and that LO-phonon and dielectric mismatch effects tend to reduce the value of the latter quantity.

Polaron and conduction band non-parabolicity effects on the binding energy, diamagnetic susceptibility and polarizability of an impurity in quantum rings

By employing a variational approach, we have investigated the effect of conduction band non-parabolicity (NP) on the binding energy ( E b ) and the susceptibility diamagnetic ( χ d i a ) of a donor impurity confined in wurtzite G a N / G a 1 − x A l x N quantum rings (QRs) with finite confinement potential in the presence of an electric field ( F ) applied in the z – direction. The combined effect of conduction band NP and interaction between electron-bulk longitudinal optical (LO) phonon on the E b and the χ d i a are also investigated in the case of infinite confinement potential. It is illustrated that the E b decreases progressively with F , particularly for large height ( H ) or for small radial thickness ( Δ R ) of QR, and the polaronic correction to the E b increases slightly with the increase of the electric field. In the case of infinite potential, the combined effects of NP and polaron leads to a more enhancement on the E b and χ d i a particularly for an on-center donor impurity. In addition, we have examined the dependence of the polarizability ( α p ) on the sizes of QR and the electric field with and without polaron effect. It is shown that the α p increases (decreases) with H (applied the electric field) and it is nearly insensitive to the polaron effect for the strong confinement. Our findings show also that the polaronic effect tends to decrease the α p , especially for thick QR. • The polaron effect enhances the binding energy and the diamagnetic susceptibility. • The binding energy and the diamagnetic susceptibility increases with the non-parabolicity effect. • Polaron effect tends to decrease the polarizability especially for larger quantum rings. • Polarizability decreases with increasing electric field especially for thick quantum rings.

Charge-Based Compact Drain Current Modeling of InAs-OI-Si MOSFET Including Subband Energies and Band Nonparabolicity

In this article, we report a physics-based compact model of drain current for InAs-on-insulator MOSFETs. The quantum confinement effect has been incorporated in the proposed model by solving the 1-D Schrodinger–Poisson equations without using any empirical model parameter. The model accurately captures the variation of surface potential, charge density in the inversion layer, and subband energy levels with gate bias inside the quantum well. The conduction-band nonparabolicity effect on modification in eigenenergy, effective mass, and density of states is derived and incorporated into the proposed model. The velocity overshoot effect that originates from the quasi-ballistic nature of carrier transport is also considered in the model. The proposed drain current model has been implemented in Verilog-A to use in the SPICE environment. The model predicted results are in good agreement with the commercial device simulator results and experimental data.

Wave packet broadening through different semiconducting mediums: A meshless multi-quadric radial base function study

In this paper, we have studied the effect of conduction band nonparabolicity on wave packet broadening in different semiconducting mediums. Here, through a fourth derivative of the wavefunction, we have included the nonparabolicity effect into the one-dimensional Schrödinger equation. We have solved this equation by means of a meshless radial base function approach. We have compared five different semiconducting mediums GaAs, GaN, AlN, InSb and GaSb and showed that the wave packet broadens slower in systems with larger effective masses and smaller nonparabolicity parameters. Thus, we can manage and control the dispersion of a Gaussian wave packet utilizing the nonparabolicity and effective mass parameters.

Effect of Conduction Band Non-Parabolicity on the Nonlinear Optical Properties in GaAs/Ga1-xAlxAs Double Semi-V-shaped Quantum Wells.

In this paper, we investigate the effect of conduction band non-parabolicity (NPBE) on the third harmonic generation(THG), the linear and nonlinear intersub-band optical absorption coefficients (OACs) related with electronic states of double semi-V-shaped GaAs/Ga1−xAlxAs quantum wells(QWs) by using the compact-density-matrix approach. Simultaneously, the work is performed in the position dependent effective mass in order to compute the electronic structure for the system by the finite difference and self-consistent techniques. We also compare the results with and without considering NPBE. It is found that: (1) the NPBE has a significant influence on the sub-band energy levels of double semi-V-shaped QWs, and (2) the amplitude and position of the resonant peaks of the THG and nonlinear OACs in the case of considering NPBE show complicated behavior due to the energy dependent effective mass m*(E) where the energy value was chosen self-consistently.

Conduction-band nonparabolicity effect on refractive index and phase match in asymmetric quantum wells pumped by two infrared beams

An asymmetric quantum well (AQW) system that is pumped by two infrared beams is designed to generate terahertz (THz) waves. The refractive index and phase mismatch associated with the intersubband transition of the AQW structure are calculated and analyzed for both present and absent conduction band nonparabolicity. The calculated results reveal that, for increasing wavelengths, the refractive index of the AQW for the short-wavelength pump beam varies more than 0.83 and undergoes a 0.204 [Formula: see text]m redshift, when the conduction band nonparabolicity is considered. The variation of the refractive index of the AQW with the long-wavelength pump beam, changes from 0.225 to 0.316 after considering the conduction-band nonparabolicity. In addition, no redshift is observed. Whether the refractive index of one pump beam with its specific wavelength increases is determined mainly by the linear terms. However, for increasing the other pump wavelengths, the refractive index of one pump beam mainly depends on the nonlinear terms. Subband energy-levels and dipole transition matrix elements show noticeable changes due to conduction-band nonparabolicity, which change the refractive index. Phase matching can be achieved by adjusting the wavelength of the two pump beams. However, both phase mismatch and coverage increase when the conduction band nonparabolicity is considered.

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.

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.

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 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.