Effective Mass Schrodinger Equation Research Articles

Tunneling and time-dependent magnetic phase transitions in a bilayer electron system

In this work, we have numerically integrated in space and time the effective-mass nonlinear Schrodinger equation for an electron wave packet in a bilayer electron system. Considering a time-dependent magnetic phase transition from the usual unpolarized ground state to spin-polarized one, we have calculated the tunneling dynamics between the two quantum wells when an external bias is applied. Due to the nonlinear effective-mass equation, it is found that the charge dynamically trapped in both wells produces a reaction field that modifies the system resonant condition. In this way, we have shown the possibility of having another kind of tunneling oscillations between both quantum wells after an optical excitation of the sample.

Tunneling escape process from a spin-polarized two-dimensional electron system

In this work, we have numerically integrated in space and time the effective-mass nonlinear Schrodinger equation for an electron wave packet in a double barrier heterostructure. Considering both polarized and unpolarized magnetic phases, we have studied the tunneling escape process from the two-dimensional electron gas. Due to the nonlinear effective-mass equation, it is found that the charge trapped dynamically in the quantum well produces a reaction field, which modifies the tunneling escape process in the quantum well. At different electronic sheet densities, we have shown the possibility of having magnetic phase-dependent tunneling rates.

Improved Multi-band Transfer Matrix for Calculating Eigenvalues and Eigenfunctions of Quantum Well and Superlattice Structure

We present an improved transfer matrix algorithm which can be used in solving general n-band effective-mass Schrodinger equation for quantum well structures with arbitrary shaped potential profiles (where n specifies the number of bands explicitly included in the effective-mass equation). In the proposed algorithm, specific formulas are presented for the three-band (the conduction band and the two heavy- and light-hole bands) and two-band (the heavy- and light-hole bands) effective-mass eigensystems. Advantages of the present method can be taken in its simple and unified treatment for general n × n matrix envelope-function equations, which requires relatively smaller computation efforts as compared with existing methods of similar kind. As an illustration of application of the method, numerical computations are performed for a single GaAs/AlGaAs quantum well using both the two-band and three-band formulas. The results are compared with those obtained by the conventional variational procedure to assess the validity of the method.

Influence of magneto-coupling between the longitudinal motion component and transverse Landau orbits of an electron on transmission features in single quantum barriers

In this paper we study the influence of the magneto-coupling effect between the longitudinal motion component and the transverse Landau orbits of an electron on transmission features in single barrier structures. Within the parabolic conduction-band approach, a modified one-dimensional effective-mass Schrodinger equation, including the magneto-coupling effect generated from the position-dependent effective mass of the electron, is strictly derived. Numerical calculations for single barrier structures show that the magneto-coupling effect brings about a series of the important changes for the transmission probability, the above-barrier quasi-bound states, and the tunneling time. Through examining the variation of the above-barrier resonant-transmission spectrum with the barrier width and observing the well-defined Lorentzian line-shape of the above-barrier resonant peaks, we convincingly show that the above-barrier resonant transmission in single barrier structures is delivered by the above-barrier quasibound states in the barrier region, just as the below-barrier resonant tunneling in double barrier structures is mediated by the below-barrier quasi-bound states in the well. Furthermore, we come to the conclusion that the magneto-coupling effect brings about not only the splitting of the above-barrier quasi-bound levels but also the striking reduction of the level-width of the quasi-bound states, correspondingly, the substantial increase of the density of the quasi-bound states. We suggest that magneto-coupling effects may be observed by the measurements of the optical absorption spectrum associated with the above-barrier quasi-bound states in the single barrier structures.

Nonlinear dynamics of excitons in asymmetric coupled quantum wells

In this work, we have numerically integrated in space and time the effective-mass Schrödinger equation for an excitonic wave packet in a coupled quantum well system. Considering an electronic many-body interaction and an external electric field, we have obtained a nonlinear dynamical evolution for the excitonic wave function. At large electronic sheet densities, it is found that the charge dynamically trapped in both wells produces a reaction field which modifies the system resonant condition.

Piezoelectric effect on optical properties of pseudomorphically strained wurtzite GaN quantum wells

The presence of internal strain in wurtzite quantum-well (QW) structures may lead to the generation of large polarization fields. These piezoelectric fields cause a spatial separation of the electrons and holes inside the QW to screen the internal fields. A self-consistent calculation of optical gain and the corresponding differential gain is presented in pseudomorphically strained GaN quantum wells as a function of carrier density. Based on the local exchange-correlation potential, electron and hole band structures are obtained by coupling Poisson's equation with an effective-mass Schrodinger equation in the conduction band and an envelope-function (or k/spl middot/p) Hamiltonian in the valence band. Our calculations show that self-consistent calculations including the piezoelectric effects are essential for accurate description of strained wurtzite QW structures.

Quasi-bound states determination using a perturbed wavenumbers method in a large quantum box

A perturbed wavenumbers method (PWM) is presented that is capable of determining the quasi-bound-state eigenenergies and their lifetimes for quantum heterostructures having arbitrary potential profiles. The numerical method presented solves the single-band effective-mass Schrodinger equation without using complex energies. It is applicable to quantum structures that are symmetric, asymmetric, unbiased, or biased. For multiple quantum heterostructures, extensive comparisons of this numerical method with other currently used techniques are included. In addition, a modified density of states formulation is presented and applied to these example cases.

Electron-phonon interaction and tunneling escape process in GaAs/AlAs quantum wells

In this work, we have numerically integrated in space and time the effective mass Schrödinger equation for an electron in a GaAs/AlAs quantum well. Considering the electron–phonon interaction and an external electric field, we have studied the electronic tunneling escape process from semiconductor quantum wells. In this way, electronic lifetimes have been obtained at different well widths and applied electric fields.

MODFET versus MESFET: the capacitance argument

In this paper a detailed charge control analysis is presented for a MESFET and a MODFET to show how the various capacitances associated with the region under the gate contact influence device performance. Where necessary, an exact description of electron confinement is included in the solution scheme by solving the effective mass Schrodinger equation for a single band and within a self-consistent framework. In the case of the MESFET, the analysis shows that the filling of donor impurity states, which are coincident in real space with the conducting channel, gives rise to a large parasitic capacitance which severely degrades both the intrinsic transconductance and cutoff frequency performance. In the case of the MODFET, the separation of the donor impurity level in real space from the conducting channel, and in energy from the Fermi-level, results in a low parasitic capacitance over the whole operating region of the device. Thus it is shown that the MODFET appears to be more suited to millimeter-wave applications, regardless of any electron transport effects.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Electronic structure of single ultrasmall electron devices and device arrays

Several questions must be addressed to develop the theory of the electronic structure of single ultrasmall (submicrometer) electron devices and the band structures of device arrays. The effects of intradevice Coulomb interactions and correlations on the electronic structure of individual devices have been studied by use of the multi-electron effective-mass Schrodinger equation for interacting few-electron systems confined in a single ultrasmall device. The band structures for noninteracting electrons in device arrays have been studied by performing augmented plane wave calculations for two-dimensional arrays of two-dimensional circular quantum wells and quantum barriers. Results are presented and the impact on the understanding of the electronic structure of devices and arrays is discussed.

Anisotropy of Effective Electron Mass in Gallium Phosphide

Approximate solutions of the effective mass Schrodinger equation for donor states in gallium phosphide are calculated by a variational method with a parameter γ= m ⊥ / m // . Comparison of the calculated energies of p -like states of donor with the experimental energy separations between several excited states from the “ two-electron ” recombination radiation of excitons bound to neutral donors by Dean et al. , determines the transverse mass m ⊥ =(0.21±0.01) m 0 and the longitudinal mass m // =(1.15±0.05) m 0 at the bottom of the conduction band in gallium phosphide.