Magnetoconductance of a stadium-shaped quantum dot: A finite-element-method approach

Shallow Donor Impurity States with Excitonic Contribution in GaAs/AlGaAs and CdTe/CdSe Truncated Conical Quantum Dots under Applied Magnetic Field

Using the effective mass approximation in a parabolic two-band model, we studied the effects of the geometrical parameters, on the electron and hole states, in two truncated conical quantum dots: (i) GaAs-(Ga,Al)As in the presence of a shallow donor impurity and under an applied magnetic field and (ii) CdSe-CdTe core-shell type-II quantum dot. For the first system, the impurity position and the applied magnetic field direction were chosen to preserve the system's azimuthal symmetry. The finite element method obtains the solution of the Schrödinger equations for electron or hole with or without impurity with an adaptive discretization of a triangular mesh. The interaction of the electron and hole states is calculated in a first-order perturbative approximation. This study shows that the magnetic field and donor impurities are relevant factors in the optoelectronic properties of conical quantum dots. Additionally, for the CdSe-CdTe quantum dot, where, again, the axial symmetry is preserved, a switch between direct and indirect exciton is possible to be controlled through geometry.

Donor impurity energy and optical absorption in spherical sector quantum dots

The properties of the conduction band energy states of an electron interacting with a donor impurity center in spherical sector-shaped GaAs-Al_0.3Ga_0.7As quantum dots are theoretically investigated. The study is performed within the framework of the effective mass approximation through the numerical solution of the 3D Schrödinger equation for the envelope function via the finite element method. The modifications undergone by the spectrum due to the changes in the conical structure geometry (radius and apical angle) as well as in the position of the donor atom are discussed. With the information regarding electron states the linear optical absorption coefficient associated with transition between confined energy levels is evaluated and its features are discussed. The comparison of results obtained within the considered model with available experimental data in GaAs truncated-whisker-like quantum dots shows very good agreement. Besides, our simulation leads to identify the lowest energy photoluminescence peak as donor-related, instead of being associated to acceptor atoms, as claimed after experimental measurement (Hiruma et al. (1995) [14]). Also, a checking of our numerical approach is performed by comparing with analytical solutions to the problem of a spherical cone-shaped GaN with infinite confinement and donor impurity located at the cone apex. Coincidence is found to be remarkable.

Local-gauge finite-element method for electron waves in magnetic fields

The finite-element method (FEM) has already been extended to analyze transport properties of electron waves of two-dimensional electron systems in magnetic fields. Although many researchers have created new formulations or improvements to this method, few have analyzed how this method is applied to realistic systems. The present paper suggests that conventional formulations of the FEM do not give accurate results for large systems or for strong magnetic fields; in addition, it suggests that the selected gauge significantly influences the numerical results. Furthermore, this paper proposes a conceptually different formulation of the FEM that solves the poor convergence problem. This formulation is simple: matrix elements are multiplied by the Peierls phase in the absence of a magnetic field. To show the advantages of this formulation, numerical examples are presented.