Nonparabolicity Of Conduction Band Research Articles

Electron effective mass in GaN revisited: New insights from terahertz and mid-infrared optical Hall effect

Electron effective mass is a fundamental material parameter defining the free charge carrier transport properties, but it is very challenging to be experimentally determined at high temperatures relevant to device operation. In this work, we obtain the electron effective mass parameters in a Si-doped GaN bulk substrate and epitaxial layers from terahertz (THz) and mid-infrared (MIR) optical Hall effect (OHE) measurements in the temperature range of 38–340 K. The OHE data are analyzed using the well-accepted Drude model to account for the free charge carrier contributions. A strong temperature dependence of the electron effective mass parameter in both bulk and epitaxial GaN with values ranging from (0.18 ± 0.02) m0 to (0.34 ± 0.01) m0 at a low temperature (38 K) and room temperature, respectively, is obtained from the THz OHE analysis. The observed effective mass enhancement with temperature is evaluated and discussed in view of conduction band nonparabolicity, polaron effect, strain, and deviations from the classical Drude behavior. On the other hand, the electron effective mass parameter determined by MIR OHE is found to be temperature independent with a value of (0.200 ± 0.002) m0. A possible explanation for the different findings from THz OHE and MIR OHE is proposed.

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.

Theoretical study of the non-parabolicity and size effects on the diamagnetic susceptibility of donor impurity in Si, HgS and GaAs cylindrical quantum dot and quantum disk: applied magnetic field influence is considered

ABSTRACT Through this work, we have investigated the influence of the conduction band non-parabolicity (NP) and magnetic field on the diamagnetic susceptibility for a confined shallow donor impurity in a homogeneous cylindrical quantum dot (CQD) and quantum disk (QDisk); the size effect has been considered. Our calculations have been performed using the variational method which consists of the choice of a trial wave function. The Schrodinger equation has been solved within the effective-mass approximation considering the infinite height potential barrier. The numerical calculations are performed taking into account different semiconductor materials (i.e. Si, HgS and GaAs). Our results reveal that both the size and conduction band NP have a significant impact on the behaviour of the diamagnetic susceptibility for both studied systems (i.e. CQD and QDisk). It has been also noticed that, for both CQD and QDisk, the NP increases the diamagnetic susceptibility (). Furthermore, this effect is remarkable for low band gap semiconductors, especially in large QD (weak radial confinement). However, it is much more important in HgS due to its narrow band gap compared to Si and GaAs materials.

Effects of applied magnetic field and pressure on the diamagnetic susceptibility and binding energy of donor impurity in GaAs quantum dot considering the non-parabolicity model’s influence

ABSTRACT In this article, we investigate the influence of the hydrostatic pressure, magnetic field, and conduction band non-parabolicity on both the diamagnetic susceptibility and the binding energy of shallow donor impurity in a quantum disk made out of GaAs. The Hamiltonian of the investigated problem has been solved within the framework of the effective-mass approximation. The energy minimisation has been performed using a variational approach. Our results reveal that both the diamagnetic susceptibility and binding energy have been reduced with increasing the disk size. Moreover, the diamagnetic susceptibility increases as the impurity moves from the extremity to the centre of the disk. However, both the diamagnetic susceptibility and binding energy have been improved under applied magnetic field, hydrostatic pressure, and by considering the conduction band non-parabolicity model as well. We hope that the reported results will be a modest contribution to further theoretical research in the field of nanostructures.

Study of photoionization cross section and binding energy of shallow donor impurity in multilayered spherical quantum dot

In the framework of the effective mass approximation and by using the finite element method , we have studied the simultaneous effects of position dependent effective mass (PDEM) and dielectric function on the shallow donor impurity binding energy and photoionization cross section in a multilayered spherical quantum dot . We have also investigated the influence of conduction band nonparabolicity and polaronic mass on the both binding energy and photoionization cross section (PCS). The obtained results have shown that the nonparabolicity and polaronic mass effects enhance the binding energy and photoionization cross section. Furthermore, it can be concluded from this research that the binding energy and the PCS are strongly dependent on the geometrical parameters, and PDEM. Changes in binding energy and photoionization cross section have physical reasons, which are discussed in details. • The photoionization cross section (PCS) and the binding energy are strongly dependent on the width of the structure layers. • The conduction band nonparabolicity and the polaronic mass effects enhance the binding energy and reduce the PCS peak magnitude. • The dependence of the dielectric function ε ( r ) on the electron coordinates makes the amplitude peak of the PCS take high values.

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.

Effect of the nonparabolicity on the resonant lifetimes and resonant energies of symmetric GaAs/AlxGa1-xAs double barrier nanostructures

We investigate the effect of nonparabolicity of the GaAs conduction band on the resonant lifetime and the associated lowest resonant energy for electrons tunneling through undoped symmetric GaAs/AlxGa1-xAs double barrier nanostructures. The effective mass theory is considered by employing the spatial and energy dependence of the effective masses for both well and barrier materials of the structure. It is found that, both resonant lifetime and the corresponding resonant energy are mainly affected by nonparabolicity, mass mismatch, and the aluminum content that controls the barrier height. The results of the present work showed a strong dependence of the resonant lifetime and the resonant energy on the barrier thickness and well width. Pronounced discrepancies are obtained between the results of the present work and other works which neglected the effects of the nonparabolicity and the mass mismatch. A good agreement is obtained in comparing the results of the present work with the experiment data.

Time-frequency analysis of nonlinear terahertz signals due to hot electrons in the nonparabolic conduction bands of n -doped In0.57Ga0.43As films

In this Research Letter, we study the transient carrier dynamics and the nonlinear terahertz effects induced by an intense multicycle terahertz pulse in the $n$-doped semiconductor ${\mathrm{In}}_{0.57}{\mathrm{Ga}}_{0.43}\mathrm{As}$. For incident terahertz pulses with relatively high frequency $\ensuremath{\ge}1$ THz, we reveal the generation of low- and high-frequency components in the transmitted intensity spectra. We study the time emission of these components at different frequencies using the G\'abor transform, showing that the low- and high-frequency components are due to the nonparabolicity of the conduction band. Our results demonstrate that for a multicycle terahertz pulse, we generate a distorted biphasic truncated exponential current with the driving terahertz fields, leading to discrete high-order harmonic generation in the transmitted intensity spectra.

Factors influencing mobility in ITO thin films and the consequent effects on optical and NIR surface plasmon resonance properties

Metal oxide-based plasmonics is an emergent field for which indium tin oxide (ITO) is a promising material. Improving the performance of ITO-based surface plasmon resonance (SPR) sensors requires a deeper knowledge of their optical and electrical properties. The effects of microstructural parameters and defects on mobility, which strongly influences SPR in the near-IR regime was explored. The proposed model incorporates different scattering mechanisms and non-parabolic conduction bands to obtain realistic values of mobility. The results show that larger grain sizes and higher carrier concentrations in ITO thin films improve SPR performance at near-IR wavelengths as low as 1300 nm

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.

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.

Impact of conduction band non-parabolicity and dielectric mismatch on photoionization cross section of donor bound polaron in spherical GaN/InN core-shell nanoparticle

Understanding the behavior of single dopant in semiconductors is a challenge to attain a high control on optoelectronic devices. Based on the fact that the external perturbations have an important impact on properties of doped nanocrystals, we have studied the simultaneous effects of phonons and conduction band non-parabolicity combined to dielectric mismatch and donor position on the photoionization cross section of an off-center donor in spherical GaN/InN core-shell quantum dots. The calculations were carried out within the framework of the effective-mass approximation and the eigenvalues equation has been solved using the Ritz variational method. The examination of the photoionization cross section, corresponding to the first donor energy level and the non-parabolic conduction band optical transition, shows clearly that the existence of non-parabolicity band or dielectric environment causes a blue shift of resonance peaks while the existence of phonon red shift them with a non-neglected variations in their intensity. The donor position has also an important effect on peaks position and amplitude.

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.

Copper(I)-Based Flexible Organic-Inorganic Coordination Polymer and Analogues: High-Power Factor Thermoelectrics.

We investigated the transport properties of the single layer and bulk copper(I) 4-hydroxythiophenolate (Cu(SC6H4OH)) coordination polymers and their analogues Cu(SeC6H4OH) and Cu(TeC6H4OH) on the basis of density functional calculations. We found that the bulk phases show superior power factors when compared with single-layer phases. This performance is comparable to the reported best organic thermoelectric candidates p-type poly(3.4-ethylenedioxythiophene) (PEDOT) and n-type poly[Kx(Ni-ett)] (ett = ethylenetetrathiolate). The non-parabolic conduction band minimum of Cu(SeC6H4OH) along the x direction can decouple the transport quantities, Seebeck coefficient, and electrical conductivity to achieve the highest power factor among all the candidates.

High Field Carrier Transport Properties of Al0.45Ga0.55N

This work presented Monte Carlo (MC) simulation of Al 0.45 Ga 0.55 N to investigate the carrier transport properties in the high electric field region including impact ionization. The simulation investigates both electron and hole considering two non-parabolic conduction band and valence band respectively. The carriers’ drift velocity, energy and occupancy are simulated with respect to electric field at room temperature. The electron drift velocity peak at 2.70 × 10 7 cm/s with the electric field of 240 kV/cm. The electron starts to excite to higher valley at 170 kV/cm and has a spike in energy at 700 kV/cm due to the occurrence of impact ionization. The impact ionization rates are computed using modified Keldysh equation and it is shown that hole impact ionization rate is higher than that of electron for Al 0.45 Ga 0.55 N. This work also presents the impact ionization coefficient with hole dominating the impact ionization process above the electric field of 2.6 MV/cm.

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.

Lattice strain influence on conduction band nonparabolicity in GaAs and InAs: Application to intraband optical absorption in InGaAs-GaAs asymmetric step quantum wells

We use empirical sps*d5 tight-binding calculations to determine the effects of compressive biaxial lattice strain, perpendicular to the [001] crystal direction, in zinc blende GaAs and InAs. Under that approach, we have been able to compute the behavior of quantities such as the average valence band energy, the energy band gap, the conduction band effective mass, and the spin-orbit split-off energy, as functions of the biaxial strain, within a range from 0 to −7%. Expressions governing these dependencies are reported for both materials. With such information at hand it is possible to calculate the variation of the coefficient of conduction band nonparabolicity due to the presence of strain. Also, the outcome for such quantities allows to evaluate the valence band offset in GaAs/InGaAs heterointerfaces as a consequence of the strain appearing from the difference between the lattice constants of the involved materials. Taking advantage of the above mentioned results, we have performed the calculation of confined conduction band states in step-like asymmetric quantum wells of the GaAs/Inx1Ga1-x1As/Inx2Ga1-x2As/GaAs prototype, using a k→⋅p→ formalism that solves the effective mass equation arising from a bi-cuadratic (nonparabolic) dispersion law. We report the calculation of the optical absorption coefficient related with intraband transitions that involve the ground and first excited energy levels. For that purpose, the study takes into account the variation of the layer widths and compositions.