An explicit FDM calculation of nonparabolicity effects in energy states of quantum wells

An explicit finite difference method (FDM) to solve the nonparabolic effective mass approximation of Schrodinger wave equation (SWE) for arbitrary quantum wells (QWs) is presented. The explicit nature of the presented method and its sparse matrices allow fast computation for energy states in QWs. The nonparabolicity effects are considered explicitly without iteration. This in turn results in faster and more stable calculations. The method is used to study the nonparabolicity effects in energy states and states overlapping in asymmetric AlGaAs/GaAs QWs.     

Donor binding energies and spin-orbit coupling in a spherical quantum dot

The ground state and a few excited state energies of a hydrogenic donor in a spherical quantum dot (GaAs in a GaAlAs matrix) are computed. While the 1s and the 2s-state energies behave normally for dots of all radii, the 2p₀ and 2p_± states are unbound for most of the radii of interest. It is predicted that a semiconductor quantum dot with a hydrogenic donor will exhibit photoconductivity for a low threshold wavelength ∼12 μm. The spin-orbit coupling gives a contribution of the order of 10⁻⁵ meV for both 2p₀ and 2p_± states.     

Stress effects on the photoluminescence energies and binding energies of excitons in ultra-thin ZnTe/CdTe/ZnTe quantum wells

Using the variational method and the effective mass and parabolic band approximations, electron and heavy-hole ground-state energies and exciton and photoluminescence energies are calculated in ultra-thin quantum wells of CdTe/ZnTe heterostructures. The results indicate dependencies on the well width, the barrier height, and stress-related effects and occur because the wave functions of both free carriers and those bound in exciton form determine the system energy and are shaped by the geometry of the well. Critical system thicknesses were estimated for the point at which stress effects become negligible: a value of five monolayers was obtained based on the exciton binding energy, and a value of seven monolayers was obtained based on the free-carrier ground-state energy.     

Effect of strain and nonparabolicity on interband transition energies of InAs/GaAs coupled double quantum dots

Strained potential profiles and electronic subband energies of InAs/GaAs coupled double quantum dots (DQDs) were calculated by using a three-dimensional finite-difference method (FDM) taking into account shape-based strain and nonparabolic effects. The interband transition energies from the ground electronic subband to the ground heavy-hole band (E₁-HH₁) in the InAs/GaAs DQDs, as determined from the FDM calculations taking into account strain and nonparabolic effects, were in reasonable agreement with the experimental peaks corresponding to the (E₁-HH₁) interband transition energies at several temperatures, as determined from the temperature-dependent photoluminescence spectra.     

Influence of nonparabolicity on boundary conditions in semiconductor quantum wells

In this Letter we present precise derivation of the second boundary condition for the wavefunctions (the first boundary condition is the continuity of the wavefunctions) at the interface of two III-V compound semiconductors, starting from an accurate expression for the bulk conduction-band structure expanded up to fourth order in wavevector. The obtained boundary condition is valid for all states (both bound and continuous) of the quantum well, and follows directly from constantness of the probability current along the quantum well and does not conflict with the double integrating of the Schrödinger equation around the interface.     

Excitons in GaAs quantum wells

This paper attempts to summarize some of the salient properties of excitons in GaAs quantum wells and in doing so it will emphasize work at AT&T Bell Labs with which the authors have been associated. Although the text relies heavily on published material, an effort has been made to stress new material, and where feasible, unpublished aspects, e.g., figures, related to earlier work. Topics discussed on the quasi-2D excitons in GaAs quantum well include: their inherent tendency for intrinsic free-exciton emission, exciton binding energies, bound and localized excitons including biexcitons and excitons bound to neutral impurities, effects of n- and p-type modulation and antimodulation doping, and the developments leading to a proposed set of quantum well parameters that results in acceptable fits to the observed exciton transitions for GaAs quantum wells with both square and parabolic potential profiles.     

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)     

The effects of indium segregation on the valence band structure and optical gain of GaInAs/GaAs quantum wells

The effects of indium segregation on the valence band structures and the optical gain in GaInAs/GaAs quantum wells are theoretically investigated using 4×4 Luttinger–Kohn Hamiltonian matrix. The method for the band structure calculation is based on the finite difference method, then the optical gain is calculated using the density matrix approach. For segregation coefficient R less than 0.7, indium segregation has little influence on optical gain, but for segregation coefficient R more than 0.7, it has a significant influence on optical gain, the gain spectra can be blue-shifted with the increase of segregation coefficient R, and the peak gains are decreased as segregation coefficient R increases, which is mainly due to the reduction of the carrier population inversion.     

Exciton binding energy in GaAs quantum wells deduced from magneto-optical absorption measurement

Magneto-optical absorption spectra due to exciton states and Landau-levels were measured in GaAs/AlAs multi-quantum-wells. By extrapolating the photon energies of the absorption peaks to zero magnetic field, the lowest state (1S) heavy hole exciton binding energy, E^B_$\text{h}$(1S), was obtained as a function of well size L_z in the range $\text{58}\text{A}\text{?}\text{?}\text{L}{}_{\mathrm{z}}\text{?252}\text{A}\text{?}$. The L_z dependence of E^B_h showed the change of the exciton character from three-dimensional to two-dimensional with decreasing L_z. The diamagnetic shift observed for the heavy hole exciton peak was larger than that for the light hole exciton peak, showing the anisotropic nature of the Luttinger-Kohn Hamiltonian. The diamagnetic shift of the heavy hole exciton peak became smaller as L_z was decreased, suggesting the enhancement of the two-dimensional exciton character.