Effect Of 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.

Leveraging machine learning to harness non-parabolic effects in semiconductor heterostructures

The engineering of optoelectronic devices is closely related to the dependency of quantum wells properties with structural parameters. Obtaining their properties relies on solving Schrödinger’s equation employing several degrees of approximation as the influence of band non-parabolicity effects. In general, the more sophisticated the approximations the longer the development cycle. To efficiently analyze the response of structures equipped with quantum wells, we propose using an artificial neural network trained with the results from the solution of Schrödinger’s equation. We observe an impressive agreement between the predicted quantum well’s eigenenergies and effective masses, in comparison to the results obtained from the iterative solution of the Schrödinger equation, for an extensive range of structures. The time spent to retrieve the properties of the structures using the artificial neural network was a fraction of the time spent with the solution of Schrödinger’s equation, enabling the neural network to be considered an effective tool in the development and improvement optoelectronic devices.

Investigation of the nonlinear optical rectification coefficient in a multilayered spherical quantum dot

In the framework of the effective mass approximation, we have investigated the effects of hydrostatic pressure, temperature, nonparabolicity of the band, and polaronic mass on nonlinear optical rectification. Furthermore, the optical rectification coefficient's dependency on the inner dot radius and the barrier width is also investigated. The obtained results reveal that geometrical sizes, hydrostatic pressure, and temperature all have a significant impact on the nonlinear optical rectification. Moreover, the combined effects of the conduction band nonparabolicity and polaronic mass produce a redshift of the peak position and a reduction in the resonant peak magnitude.

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.

A nonparabolic conduction band study of circular quantum dot optical properties: modeling of surface roughness by using Koch snowflakes

In this work, we investigate the optical properties of single and multiple quantum dots (QDs) based on AlxGa1-xAs/GaAs with two Koch snowflake-shaped and circular geometries. The idea is to determine the impact of the surface roughness of the circular QDs on the mentioned optical properties. This is an important issue in designing optoelectronic devices (e.g., photodetectors or light-emitting systems) because the position and magnitude of the absorption coefficient play important roles in devising them. We have also studied the effects of the conduction band nonparabolicity, QD size, number of QDs, and composition parameter x on the absorption coefficient. For this purpose, we have used an efficient finite difference method to solve the two-dimensional Schrodinger equation. The computational algorithm of the Koch snowflake-shaped QD production is also described.

Effect of band non-parabolicity on energy sub-band profile for nano-dimensional MOSFET

In this paper, the effect of band non-parabolicity on the sub bands of an nano-dimensional junction less MOSFET have been presented using analytical models. Hence, one- and two-dimensional confinements have been considered. The energy Eigen values and values of effective mass along the direction of propagation and the direction of confinement have also been analyzed separately. The effect of channel width and channel height variations along with the confinements have also been studied. This study would be efficacious for the circuit level implementation of the of nano-dimensional MOSFET using different semiconductor materials.

Influence of conduction-band non-parabolicity on terahertz intersubband Raman gain in GaAs/InGaAs step asymmetric quantum wells

The conduction electron states in step-like strained GaAs/InGaAs quantum wells are theoretically investigated under the effective mass approximation, taking into account the effects of band non-parabolicity. With such information, the intersubband three-level Raman gain is calculated looking to reveal a possible application of the studied systems as sources for THz Raman lasing. A group of high-gain intersubband transitions is identified, and the results are strongly dependent on a suitable geometric design in terms of potential well widths which can lead to values of the Raman gain between 200 and $$400\,\hbox {cm}^{-1}$$, the latter values being close to those previously reported in GaAs-based double asymmetric quantum wells. Secondary radiation frequencies are identified within the range of few tens of THz. It is found that the influence of band non-parabolicity causes a significant reduction of the Raman gain, in comparison with the values obtained neglecting such a phenomenon. Therefore, conduction-band non-parabolicity becomes a crucial element for the accurate quantitative description of the intersubband-related optical response in low-dimensional heterostructures involving small gap materials.

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.

Efficient Modeling of Optical Excitations of Colloidal Core-Shell Semiconductor Quantum Dots by Using Symmetrized Orbitals.

An efficient method for the theoretical investigation of optical properties of semiconductor core-shell quantum dots (CSQDs) is introduced within the multiband k·p approach, which takes the advantage of the symmetry of the system. The heteroepitaxial strain and excitonic effect are included in the calculation of energy levels, envelope wave functions, exciton binding energy, and linear absorption coefficient. The adoption of symmetrized orbitals allows improvement of the computation time significantly. To avoid appearance of spurious solutions caused by imbalance of basis functions adopted, we consider an 8-band k·p model which is block-diagonalized into two conduction bands and six valence bands, that we call the 2 + 6-band model. The band nonparabolicity effect is modeled by an energy-dependent k·p term, such that the density of states obtained can mimic the actual density of states of a full-band model. The simulated absorption spectra of ZnTe/ZnSe CSQD are in good agreement with those observed experimentally, including the high rise of absorption at energies far above the absorption edge.

Effect of Band Nonparabolicity on the Inter Band Tunneling in Semiconductors

A simple yet generalized theory is developed to study inter band tunneling property of narrow band gap III–V compound semiconductors. The band structures of these low band gap semiconductors with sufficiently separated split-off valance band are usually described by the three energy band model of Kane, so this has been adopted here for the analysis of interband tunneling property in the case of InAs, InSb, and In1-xGaxAsyP1-y lattice matched to InP as representative direct band gap semiconductors having varied split-off valence band compared to their bulk state band gap energy. It has been found that the magnitude of tunneling rate from heavy hole decreases with increasing band nonparabolicity and the impact is more significant at high electric field in the three-band model of Kane than those with simple parabolic energy band approximations reflecting the direct influence of energy band parameters on inter band tunneling transitions. With proper consideration of band nonparabolicity, the results of the analysis of tunneling rate of these narrow gap materials show significant deviations from the results when simple parabolic band approximation is considered. The exact physical basis of the sources of deviation in the nonparabolic case from the corresponding parabolic band approximations is discussed in association to band coupling effect, transverse energy dependence, and the interplay between them. Moreover, under certain limiting conditions, our results reduce to the well-known results of parabolic band approximation and thus providing an indirect test to the accuracy of our generalized formulations.

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.