Exact hole-bound states for semiconductor quantum wells with arbitrary potential profiles

An efficient numerical-analytical method for finding confined and continuum states in quantum-well systems with arbitrary potential profiles, described by coupled Schrödinger equations, is presented. The method is based on the analytical properties of the wave functions, in particular, the power series representation of solutions of the corresponding coupled differential equations. Using only the general properties of the coefficients of a system of an arbitrary number of coupled Schrödinger equations, and imposing for definiteness the simplest boundary conditions, we derive exact expressions for the wave functions and present methods for accurate calculations of the energies and wave functions of confined states and of the wave functions of continuum states in quantum wells. The method is applied to the calculation of the dispersion of hole bound states in a single GaAs quantum well with truncated parabolic confining potentials of different strengths. The results are compared with data available from previous calculations.     

Optical phonon modes in graded III-V nitride quantum wells

The dispersion relation for optical phonon modes in graded wurtzite AlN/GaN and AlN/InN quantum wells is calculated taking into account the existence of interfacial transition regions. We make use of a model based on the macroscopic theory developed by Loudon, known as the continuum dielectric model. The optical phonon modes are modelled considering only the electrostatic boundary conditions (neglecting retardation effects), in the absence of charge transfer between ions. We show that the graded interfaces strongly shift the frequencies of the phonon modes of the otherwise abrupt nitrides quantum wells.     

PROPERTIES OF PROPAGATION OF GUIDED ELECTRON WAVES IN COUPLED ASYMMETRIC QUANTUM WELLS

In this article we investigate the properties of the propagation of guided electron waves in the coupled asymmetric quantum wells. By decomposing the eigenfunctions of electron in the coupled double quantum wells in terms of the basis eigenfunctions of the individual wells, the expression of the mode amplitude func-tions for various bare states in wells has been given. By setting up appropriate boundary conditions one can simulate different injecting manners of electron into the system and study how the electron waves trans-fer among various states. The major electron wave transfer happens between the matching bare states in wells. The particular pattern of the transfer depends on the injecting manner and the energy of the inci-dent electron. We also show the influence of the presence of the multimodes on the variatinn of the mode amplitude functions. It leads to producing some oscillations imposed on the original sinusoidal-like func-tions and causing incomplete transfer between a pair of states in channels due to the beating frequency effect or the interference among various modes.     

Quasibound states in semiconductor quantum well structures

We present a study on quasibound states in multiple quantum well structures using a finite element model (FEM). The FEM is implemented for solving the effective mass Schrödinger equation in arbitrary layered semiconductor nanostructures with an arbitrary applied potential. The model also includes nonparabolicity effects by using an energy dependent effective mass, where the resulting nonlinear eigenvalue problem was solved using an iterative approach. We focus on quasibound/continuum states above the barrier potential and show that such states can be determined using cyclic boundary conditions. This new method enables the determination of both bound and quasibound states simultaneously, making it more efficient than other methods where different boundary conditions have to be used in extracting the relevant states. Furthermore, the new method lifted the problem of quasibound state divergence commonly seen with many other methods of calculation. Hence enabling accurate determination of dipole matrix elements involving both bound and quasibound states. Such calculations are vital in the design of intersubband optoelectronic devices and reveal the interesting properties of quasibound states above the potential barriers.     

Donor states in tunnel-coupled quantum wells

We study the energy spectrum of the impurity states in tunnel-coupled double quantum wells for Coulomb and short-range donor potentials. We calculate the impurity contribution and the density of states and detect the transformation of a localized donor state into a resonant state when the binding energy of the donor in an isolated quantum well is less than the separation of the energy levels of the double quantum wells. In the opposite case, where the binding energy is greater than the level separation, there is tunneling repulsion between adjacent impurity levels, with the degree of degeneracy of the levels changing when there is tunneling mixing of the ground and excited impurity states from different wells. Resonant states emerge in an asymmetric double quantum well, while in a symmetric double quantum well the impurity level at the barrier’s center proves to be localized even against the background of the continuum. The calculations are based on a general expression for the impurity contribution to the density of states in terms of a 2-by-2 matrix Green’s function, i.e., only a pair of tunnel-coupled levels of the double quantum wells is taken into account. For an impurity with a short-range potential, we derive a matrix generalization of the Koster-Slater solution, while the impurity with a Coulomb potential is analyzed by using the approximation of a narrow resonance and close arrangement of the repulsive levels. Zh. éksp. Teor. Fiz. 115, 1337–1352 (April 1999)     

Electron energy states and miniband parameters in a class of non-uniform quantum well and superlattice structures

A simple method to compute the carrier energy states, miniband parameters and dispersion characteristics for single and multiple quantum well and superlattice structures is presented. The method utilizes the continuity of the envelope function across the heterojunctions according to the boundary conditions that both the wavefunction ψ and the particle current density $\text{ψ′}\text{m}{}^{\mathrm{★}}$ be continuous at each interface. The nonuniform potential distribution encountered in doped or compositionally graded materials is approximated by piecewise constant potential functions. In addition to being conceptually simple, the method is readily adopted to fairly complex structures where other more sophisticated methods such as LCAO, reduced Hamiltonian and tight binding theories may become unfeasible or unmanageable. It is shown that for an arbitrary stepped potential variation, the eigenvalues (or the energy states) of quantum wells or a finite number of coupled quantum wells can be found by utilizing a transverse resonance method which is readily implemented on a digital computer for the computation of these eigenvalues. For the case of periodic superlattices, the miniband parameters and the dispersion characteristics are computed from a suitably defined transmission matrix associated with a unit cell of the superlattice which may itself consist of multiple layers. Typical results for the computed parameters for several wells and simple, biperiodic, binary and polytype superlattices consisting of various Al_xGa_1?xAs and In_xGa_1?xAs alloys are presented.     

Energy sublevels in an Al0.5Ga0.5As/GaAs/Al0.5Ga0.5As quantum wire

We report the successful fabrication of a V-grooveAl_0.5Ga_0.5As/GaAs/Al_0.5Ga_0.5As quantum wire system and the temperature-dependent photoluminescence (PL) measurement. The PL spectra are dominated by four features at 681, 642, 635 and 621 nm attributed to the luminescences from quantum wire, top, vertical and side-wall well regions by micro-PL measurements. By the calculations of the energy structure, discrete states (localized sublevels) in the quantum wire region and continuum states (extended along the side-wall and vertical quantum wells) in side-wall and vertical quantum wells have been obtained in both the conduction and valence bands. The calculated excitation energies explain very well the peak positions and their temperature dependence in the photoluminescence measurements.     

Numerical study of localization in quantum spin hall state of HgTe/CdTe system

HgTe/CdTe quantum well has served as a new material in realizing the quantum spin Hall state. We investigate the localization and scaling behavior of electronic states in HgTe/CdTe quantum wells through the scaling analysis. A phase diagram where the boundary separating the localized and extended states is plotted in the parameter space which is spanned with disorder strength and Fermi energy. We also discuss the implications of these results on the behavior of topological insulator.     

DYNAMICS OF CARRIER CAPTURE IN AlGaAs/GaAs MULTIPLE QUANTUM WELLS

Dynamics of carrier relaxation and capture in AlGaAs/GaAs multiple quantum wells (MQW) at 80 K is studied using picosecond luminescence and femtosecond absorption saturation measurements. Carriers generated in the wells and in the barriers scatter initially out of the excited states to a quasi-equilibrium state in 35 and 400 femtoseconds, respectively, before they are captured into the bound states of the quantum wells. Carrier capture occurs during carrier cooling and recombination. A carrier capture time of 25 ps has been deduced from time-resolved luminescence.     

Charge and energy transfer in double asymmetric quantum wells with quantum dots

The luminescence and luminescence excitation spectra of CdSe/ZnSe quantum dots are studied in a set of double quantum wells with the ZnSe barrier of width 14 nm, the same amount of a deposited CdSe layer forming a deep well and shallow wells with different depths. It is found that for a certain relation between the depths of shallow and deep wells in this set, conditions are realized under which the exciton channel in the luminescence excitation spectrum of a shallow well dominates in the region of kinetic exciton energies exceeding 10 longitudinal optical phonons above the bottom of the exciton band of the ZnSe barrier. A model is developed for the transfer of electrons, holes, and excitons between the electronic states of shallow and deep quantum wells separated by wide enough barriers. It is shown that the most probable process of electronic energy transfer between the states of shallow and deep quantum wells is indirect tunneling with the simultaneous excitation of a longitudinal optical phonon in the lattice. Because the probability of this process for single charge carriers considerably exceeds the exciton tunneling probability, a system of double quantum wells can be prepared in which, in the case of weak enough excitation, the states of quantum dots in shallow quantum wells will be mainly populated by excitons, which explains experimental results obtained.     

Structural control of Fano resonances in semiconductor heterostructures

Structural control of quantum interference in the optical intrasubband absorption spectrum of GaAs/AlGaAs multi-quantum wells is investigated theoretically. Our study shows that pronounced Fano resonances are in general difficult to obtain in quantum well heterostructures, with a presence of distinct Fano resonance features being the exception rather than the rule. Guided by an analogy to Young’s double-slit experiment, we design increasingly improved structures to display Fano resonances. Best results are achieved in structures where there is strong overlap between the ground-state wavefunction and scattering states associated with the uncoupled continuum. Alternatively one may use ionization via two or more resonances. In this case, resonances should not be separated by more than 25 meV to give significant effects. Moreover, we show that resonance features may also be induced without potential barriers to a continuum merely via orthogonality between bound and excited states.     

Nonlinear properties in InxGa1 − xAs/GaAs multiple quantum well laser structures

In this paper we investigated nonlinear properties and lasing in In_xGa_1 − xAs/GaAs multiple quantum wells grown by metal-organic chemical vapour deposition. A systematic study, performed by high excitation photoluminescence measurements as a function of excitation intensity, allowed us to identify the minimum well width for observing stimulated emission from well states. We also determined the threshold for stimulated emission for well and barrier lasing. Radiative recombination energies are identified by using theoretical data obtained in the effective mass approximation, including boundary conditions and strain.     

Model calculations of diffusion limited trapping dynamics in quantum well laser structures

We present a phenomenological theoretical model to treat the trapping of carriers into quantum wells of semiconductor laser structures. We consider explicitely the transport within the barrier layers by solving the continuity equation with the appropriate boundary conditions taking into account surface recombination, radiative and nonradiative recombination in the barrier layers and trapping of carriers into the quantum wells. The experimental findings for the trapping dynamics in GaAs/AlGaAs quantum well structures can be consistently interpreted by the model calculations.     

Self-consistent electronic structure of quantum wells by invariant embedding method

A new approach based on the invariant embedding method for the self-consistent calculation of electronic structure of quantum wells is presented and is applied to both neutral quantum well and parabolic quantum well. Numerical results obtained for these structures agree very well with those of previous theoretical and experiment studies. The present approach is expected to lead to a more efficient and stable scheme for the calculation of electronic band structure of quantum structures. Realistic boundary conditions are naturally taken into account in the present calculation which provides a convenient way for studying boundary effects. Received 21 September     

Intersubband relaxation of hot carriers in quantum well systems

We use an ensemble Monte Carlo simulation of coupled electrons, holes and nonequilibrium polar optical phonons in multiple quantum well systems to model the intersubband relaxation of hot carriers measured in ultra-fast optical experiments. We have investigated the effect of various models of confined photon modes on the energy relaxation and intersubband transition rate in single quantum well and coupled well systems. In particular, the symmetry of the atomic displacement with respect to the quantum well has a marked effect on the relative intersubband versus intrasubband scattering rates, depending on whether one considers electrostatic boundary conditions(slab modes) or mechanical boundary conditions(guided modes). In single quantum wells systems, the overall intersubband relaxation time is not found to be strongly dependent on the confined mode model used due to competing effects of hot phonons and the relative intrasubband scattering rates. For coupled well systems, the relaxation rate is much more dependent on the exact nature of the phonon amplitude. Large effects are found associated with localized AlAs interface modes which dominate the intersubband relaxation time.     

Some mathematical aspects of Anderson localization: boundary effect,multimodality, and bifurcation

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach, and further investigate some mathematical aspects of Anderson localization that are rarely discussed before. First, we observe that under the Neumann boundary condition, the low energy quantum states are localized on the boundary of the domain with high probability. We provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional case. Second, we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary conditions. Finally, we examine a bifurcation phenomenon of the localization subregion as the strength of disorder varies. The critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.     

Bound states in continuum of complex potentials generated by supersymmetric quantum mechanics

It is shown that bound states in continuum can be generated by applying supersymmetric quantum mechanics to real potentials in such a way that the transformed potential becomes complex. Three cases of the initial potential are considered in more detail: flat potential, step potential and rectangular quantum well. The conditions are found for the existence of bound state in continuum in these cases, as well as the expressions for the wavefunction of this state and the corresponding complex potential in analytic form.     

Off-resonant two-photon-assisted electron transfer between quantum dots

Electron transfer between bound states of remote quantum dots driven by an off-resonant electromagnetic pulse is analyzed. In the case of nearly equal energies of the states, a two-photon transfer mechanism related to the high-frequency off-resonant Stark effect is proposed. An equivalent transformation is used to derive an effective Hamiltonian that provides a basis for correct treatment of continuum (conduction-band) states. It is shown that optimal conditions for electron transfer correspond to quasi-resonant excitation of states near the lower edge of the continuum. The characteristics of the process are evaluated.     

Finite Space Complete Basis Method: Precision Computation of High-Resolution Spectrum near Ionization Threshold

A new method is proposed to describe quantum dynamical processes in finite space by using of a set of discretized complete bases. In this method, the finite space complete basis is obtained by solving the self-consistent field equation with reflecting boundary conditions. Hence, both negative and positive orbital energies can be obtained. Such method can be used in systems which involve dynamics only in the reaction zone, i.e., in a finite space. To illustrate the validity of the method, we present two examples: theoretical calculation of the high excited states spectra including the continuum of sodium and barium.     

GaAs体材料及其量子阱的光学极化退相特性

采用飞秒时间分辨瞬态简并四波混频技术，在室温下测量了GaAs体材料及其量子阱材料GaAs/Al_0.3Ga_0.7As的光学极化超快退相时间，当激光中心波长为785nm，受激载流子浓度为10¹¹cm^-2时，它们的退相时间分别为28fs和46fs.量子阱材料的退相时间比体材料的长，这是由于量子阱中的载流子在垂直于GaAs/AlGaAs界面的运动受到限制，运动呈现二维特性，大大减小了载流子的散射概率.实验中观察到瞬态简并四波混 关键词： 时间分辨简并四波混频 飞秒激光脉冲 退相 密度矩阵