Effect Of Band Non-parabolicity Research Articles

Effect of band nonparabolicity on mobility in a δ-doped semiconductor

We calculate the low-temperature mobility of a two-dimensional (2D) electron gas in $\ensuremath{\delta}$-doped GaAs by solving coupled Boltzmann equations in the relaxation-time approximation using one-, two-, or three-subband models depending on the population of the subbands. We assume that the mobility is limited by ionized impurity scattering, including intersubband contribution. Our results suggest that the nonparabolicity of the conduction band plays the important role: it reduces the calculated 2D electron-gas mobility by about 20%, which leads to a better agreement with experimental data.

Influences of conduction band non-parabolicity on intersubband absorption and photon drag in a single quantum well

On the basis of a microscopic nonlocal theory and k· p approach, an analysis of conduction band non-parabolicity effects on the linear absorption and photon drag arising from intersubband transitions in a single quantum well has been carried out. It is shown via detailed numerical simulations that, in comparison with the non-parabolic band model, the parabolic model overestimates intersubband absorption and photon drag current; blueshifts of the absorption peak and zero crossing of photon drag current are also overestimated.

Two-dimensional electron gas and persistent photoconductivity inAlxGa1−xN/GaNheterostructures

We present results of electrical and optical measurements in an ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructure. The presence of a two-dimensional electron gas at the high-quality ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterointerface is confirmed by Shubnikov--de Haas measurement, which shows well-resolved magnetoresistance oscillations starting in fields below 3 T at 1.3 K. From the temperature dependence of the oscillation amplitude, the obtained effective mass $(0.24\ifmmode\pm\else\textpm\fi{}{0.02)m}_{0}$ is in excellent agreement with the value of cyclotron resonance measurements in two-dimensional (2D) systems, but larger than the values of theoretical and experimental results in GaN bulk films. We point out that the effective-mass enhancement in 2D systems is due to the effects of band nonparabolicity and wave-function penetration into the barrier material. The results of photoconductivity measurements reveal that persistent photoconductivity (PPC) does exist in the ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructure, and that the PPC behavior of ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterojunction is quite different from that of the GaN epitaxial thin films. A possible mechanism is presented to interpret the observed PPC effect.

Some effects of conduction band nonparabolicity on electron reflection spectrum of multiquantum barriers

The effect of nonparabolicity of conduction band on the electron reflection spectrum of multiquantum barriers (MQB) has been examined. Drastic reduction in the effective barrier height is expected by adopting the nonparabolic model on the MQB which had been designed using the parabolic model for 1.5 μm semiconductor lasers (LDs). The predicted enhancement in barrier height by the MQB is over 600 meV under parabolic model. However, it decreases to 40 meV under nonparabolic model with the same structure. On the other hand, the experimental enhancement in barrier height by the MQB is estimated to be around 30 meV on 1.5 μm LDs, close to the value calculated by nonparabolic model. Those results suggest that a much higher effective barrier height can be realized by optimizing the MQB design taking the nonparabolicity into account. The conduction band nonparabolicity was incorporated by the k⋅p perturbation method.

Studies of two-subband occupied electron gas in modulation-doped In0.52Al0.48As/In0.53Ga0.47As single quantum well by far-infrared modulated photoluminescence

We report an investigation of electronic and optical properties of two-subband occupied electron gas confined in Al0.48In0.52As/Ga0.47In0.53As quantum well by far-infrared (FIR) modulated photoluminescence (PL) measurements. We show that, in addition to the characterization of the effective mass and Fermi energy, this technique is a useful tool for the understanding of the luminescence processes. Well-resolved Landau-level splittings were observed in the FIR modulated PL spectrum at a fixed magnetic field. It is found that the PL spectrum involves the transitions between localized holes and electrons at all occupied k states. For the FIR modulated spectrum monitored at the peak position as a function of magnetic field, a strong double cyclotron-resonance signal was observed. The double structure of cyclotron resonance is attributed to the cyclotron transitions in the first and second subbands. The obtained effective masses are found to be considerably heavier than the bulk value by 22% and 46% for the first and second subband, respectively. The heavier effective mass of the second subband is opposite to the behavior measured in the triangular quantum well. We point out that, in order to explain the enhanced masses, both the effects of band nonparabolicity and wavefunction penetration into the barrier material have to be taken into account.

Modeling of heterojunction HgCdTe photodiodes using approximate k • p approach

In this paper, we describe a new approach to simulation of HgCdTe devices based on an approximation for the k • p model. We use an approximate expression for the carrier density which includes effects of carrier degeneracy and conduction band nonparabolicity. These effects are essential for accurate modeling of HgCdTe devices. The simplicity of this approximation allows us to use well-established methods of semiconductor device modeling. On the other hand, the new approach demonstrates similar accuracy to more complex models based on numerical evaluation of the nonparabolic Fermi-Dirac integral. The new model is applied to energy band calculation of HgCdTe heterojunctions and dark current calculation of HgCdTe photodiodes.

Radiative interaction and disorder effect in the linear optical response of a multiple-quantum-well structure

Using a nonlocal local-field formalism, we show that, for a multiple-quantum-well (MQW) structure with well-width fluctuations, and in an internal-reflection configuration, the linear optical intersubband absorption spectra including peak positions and line shapes are strongly dependent on the number of quantum wells (QW's) in the structure and of the spatial distribution of the QW's. It is also demonstrated that an inclusion of the barrier-medium--vacuum interface enhances the electromagnetic coupling among QW's, and consequently leads to a significant modification of the optical-absorption spectra. By varying the intersubband relaxation time, we find that the local-field effect may substantially reduce the linewidth broadening arising from the conduction band nonparabolicity effect for a highly doped MQW system. This is in agreement with a previous prediction for a single QW. In addition, the present nonlocal theory is compared with the effective-medium theory (EMT). Our calculations show that the nonlocal effect in the optical response of QW's gives rise to a notable blueshift of the absorption peak compared to the results in the EMT approach. When the QW number is varied, the line shapes predicted from the two theories are also somewhat different.

Observation of double cyclotron resonance in modulation-δ-doped In0.52Al0.48As/In0.53Ga0.47As heterostructure by optical detection

We report an investigation of optical and electronic properties of a two-subband populated electron gas confined at a δ-doped Al0.48In0.52As/Ga0.47In0.53As heterostructure by the technique of far-infrared optically detected cyclotron resonance (ODCR). Oscillatory characteristics are observed in the ODCR spectrum, and interpreted in terms of the crossing between the Landau levels of the two-dimensional electron gas and the Fermi level from which the electron concentration and effective mass of the first and second subbands can be determined. Quite different effective masses associated with these subbands are obtained, reflecting the strong effects of conduction band nonparabolicity as well as polaron coupling in Ga0.47In0.53As quantum well.

Magnetopolaron effect on the donor transition energies in ZnSe.

The donor transition energy in ZnSe is calculated as a function of the magnetic-field strength. Through a variational approach, the wave functions are obtained, which are used in a calculation of the magnetopolaron effect within second-order perturbation theory. Our theoretical analysis finds good agreement with the experimental results for the 1s\ensuremath{\rightarrow}2${\mathit{p}}^{+}$ transition up to the 150-T region if both the effects of magnetopolarons and band nonparabolicity are included.

Effect of band nonparabolicity on the magnetoexciton binding energy in semiconductors.

The effect of conduction- and valence-band nonparabolicity ${\mathrm{\ensuremath{\kappa}}}_{\mathit{e}}$,${\mathrm{\ensuremath{\kappa}}}_{\mathit{h}}$ on the magnetoexciton binding energy is calculated microscopically to the first order in ${\mathrm{\ensuremath{\kappa}}}_{\mathit{e}}$,${\mathrm{\ensuremath{\kappa}}}_{\mathit{h}}$ by converting the Schr\"odinger equation into a five-point difference equation. The band nonparabolicity is shown to affect the field-induced spectral-line shift from magnetoluminescence significantly. For parabolic bands, an important correction to the reduced mass obtained by a conventional method relying on the high-field exciton-energy shift is discussed. The results yield good agreement with the photoluminescence data from InAs and ${\mathrm{InAs}}_{0.93}$${\mathrm{Sb}}_{0.07}$, providing valuable information about band-nonparabolicity parameters.

Green's-function study of the electron tunneling in a double-barrier heterostructure.

The quasi-one-dimensional aspects of the electron tunneling through AlAs/GaAs/AlAs (001) double-barrier structures have been investigated using the tunneling formalism based on the nonequilibrium Green's function developed by Keldysh. In describing the electronic structure of a double-barrier heterostructure, Green's-function formulation of scattering theory incorporated with the multiorbital tight-binding model is used, so as to take into account the effects of indirect band gap, band nonparabolicity, and multiple orbitals in the aperiodic layered structure. The effect of high external bias on the junction is solved exactly within this model. The electron-tunneling situation and the effect of the X-valley originated barrier confined states on the electron tunneling are analyzed with the spectral local density of states of the double-barrier structure in the [001] direction under the external bias. The calculated current density J(${\mathbf{k}}_{\mathrm{\ensuremath{\parallel}}}$=0) versus voltage curve exhibits the structures for the interlayer intervalley electron transfer, which are manifested as the electron propagation through \ensuremath{\Gamma}-valley originated states and through X-valley barrier confined states. The smaller current peak-to-valley ratios are found in the double-barrier structures with thicker barriers, which is consistent with the experimental results. The enhancement of \ensuremath{\Gamma}-X interlayer intervalley electron transfer and reduction of the \ensuremath{\Gamma}-\ensuremath{\Gamma} resonant electron interlayer transfer is found with the increase of the phenomenological imaginary potential term.

Modelling of single barrier heterostructures including band bending and non-parabolicity effects of the band structure

Following the stationary-state approach a modified Thomas-Fermi-approximation (MTFA) is used for the evaluation of the propeties of type-I- and type-II-staggered-single barrier heterostructures. The presented model reflects the real physical situation, but in comparison with the self-consistent technique the numerical efforts are reduced. The non-parabolicity of the band strucutre is also included using simple, but very convenient analytical formulae. Several properties of InGaAs/InAlAs-and InAs/AlGaSb-configurations are investigated. The results of the MTFA, the semi-classical model and the model of Paasch and Übensee [ Physica status solidi (b) 113, 165 (1982)] are mutually compared.

Shallow donor impurities in GaAs/AlxGa1-xAs superlattices in a magnetic field.

A theoretical investigation is presented of the properties of shallow donor impurities in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As superlattice in the presence of a magnetic field directed along the growth axis. The energy levels of several of the lowest donor states have been obtained as functions of (1) the well width, (2) the donor position, and (3) the magnetic-field strength. The calculation is based on a variational approach in which we use a trial wave function with two variational parameters. This wave function shows exponential behavior in sufficiently small magnetic fields and Gaussian behavior in sufficiently large magnetic fields. The magnetopolaron effect on these donor energies is studied within second-order perturbation theory where a formal summation over all electron states is performed. The effect of band nonparabolicity is also included in order to correctly explain magneto-optical experimental results at high magnetic fields. Our results are in very good agreement with the available experimental data in the whole magnetic-field range and for weakly and strongly coupled superlattices.

Erratum: Effects of band nonparabolicity and central-cell corrections on the spectrum of Si donors in GaAs quantum wells

Erratum: Effects of band nonparabolicity and central-cell corrections on the spectrum of Si donors in GaAs quantum wells

Barrier property dependence of band nonparabolicity effects in a quantum well

The barrier material property dependence of band nonparabolicity effects on the discrete energy levels of a GaAs/AlxGa1−xAs quantum-well structure is reported. Results from the modified resonant tunneling method show clear barrier property dependence. The model includes the position-dependent nonparabolicity parameters from which energy-dependent effective mass is calculated. This model can be applied to any shape potential barrier. Both a rectangular quantum well and a parabolic quantum well were analyzed and these results are compared to those from previously reported calculations.

Effects of band nonparabolicity and central-cell corrections on the spectrum of Si donors in GaAs quantum wells.

Data on donor magneto-optical 1s\ensuremath{\rightarrow}2${\mathit{p}}_{+1}$ transitions in four center-doped GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells ranging in width from 10 to 52 nm is presented and analyzed for magnetic fields between 0 and 6 T. It is found that both band nonparabolicity and central-cell corrections must be considered in the narrower wells in order to obtain satisfactory agreement with experiment. A theory of band nonparabolicity is introduced which includes important terms arising from the donor Coulomb potential, terms previously ignored in the analysis of quantum-well donor spectra. In the narrower wells relatively large central-cell corrections are calculated for Si donors from bulk data. A central-cell correction of \ensuremath{\sim}0.75 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ is estimated for bulk Si donors at zero magnetic field from analysis of published data on Si-doped GaAs epitaxial films.

Effect of band nonparabolicity on the hot electron longitudinal conductivity in n-Hg 1− xCd xTe in the extreme quantum limit magnetic fields at low temperatures

High field longitudinal conductivity in narrow band gap semiconductors has been investigated assuming the displaced Maxwellian distribution for carriers, occupying the lowest Landau subbands at low temperatures. The energy relaxation of carriers is due to acoustic phonon scattering via deformation potential dominant at low temperatures while the momentum relaxation is due to ionized impurity and elastic acoustic phonon scatterings. Furthermore, the effect of alloy scattering which is an important scattering mechanism for alloy semiconductors, such as HgCdTe, has been incorporated in the momentum relaxation time. The other complexities such as the magnetic field dependent free carrier screening and non-equipartition of phonons are included in the model. Finally, using the model, the effect of band non-parabolicity on the hot electron longitudinal conductivity of n-HgCdTe has been examined and the theoretical results are compared with the recent experimental results. Inclusion of nonparabolicity in the calculation is found to be important for analysing the experimental results.

Cyclotron emission study of electron masses in GaAs-GaAlAs heterostructures

We study far-infrared cyclotron emission from GaAs-GaAlAs heterostructures, induced by electric pulses in the presence of a magnetic field and hydrostatic pressure. Cyclotron masses are measured as functions of 2D electron density in the strong electron heating regime at the pressures of P=0 and P=7 kbar. The results are described by an effective two-level k.p theory, which takes consistently into account the effect of band non-parabolicity on electric and magnetic quantization. It is shown that the observed emission spectrum is due to several transitions between Landau levels, since the 2D electron gas is non-degenerate. The same theory is used to describe cyclotron absorption data of other authors, obtained at zero and non-zero pressures under the conditions of degenerate electron gas. It is shown that the cyclotron absorption can be measured in two different regimes, which explains a strong dependence of the data on photon energy. A very good theoretical description of various emission and absorption experiments is achieved with the use of bulk GaAs parameters.

D- centers in quantum wells: Spin-singlet and spin-triplet magneto-optical transitions.

We consider the ground and excited states of D - centers, i.e., neutral donors D 0 trapping an extra electron, in the spin-singlet and spin-triplet states in GaAs/Ga 1-x Al x As quantum wells (QW's) in quantifying magnetic fields B>6 T. Taking into account the effects of band nonparabolicity and magnetopolaron corrections, we derive the energies of the dipole-allowed transitions and their line strengths. Very good agreement (e.g., within 1-3 cm -1 below the region ofthe resonant magnetopolaron splittings) with the experimental data of Huant et al. for the singlet transitions is found

Erratum: Donor transition energy in GaAs superlattices in a magnetic field along the growth axis

The transition energies between the ground state (1s-like) and two excited states (2${\mathit{p}}^{\ifmmode\pm\else\textpm\fi{}}$-like) are calculated for shallow donor impurities in GaAs superlattices in the presence of a magnetic field along the growth axis. Results are obtained as a function of the magnetic field and the well width for various widths and heights of the barriers of the superlattices. The dependence of the transition energies on the position of the donors and the effect of band nonparabolicity are also investigated. The calculation is based on a variational approach in which Gaussian-type trial wave functions with two variational parameters are used. Polaron correction to these energies is studied within second-order perturbation theory in which only the three-dimensional-bulk phonon modes of GaAs are included. We found that the polaron effect and band nonparabolicity have to be included in order to correctly describe the experimental transition energies.