No abstract

We propose a simple method for calculating the on-and off-axis neutral and negatively charged donors in axially symmetrical quantum dots whose thickness is much smaller than the base diameter. The adiabatic approximation is used to separate the slow in-plane motion from the rapid transversal displacements. We show that the low-lying free electron levels can be found by solving a two-dimensional central force problem with effective potential whose shape strongly depends on the quantum dot profile in radial direction. The energies of the off-axis neutral and negatively charged donors are calculated by using fractal dimension method. Novel curves and contour plots for the energies of donors confined in quantum disks, lens, pyramids and rings as functions of the base radius and the distance from the axis are presented.

A problem of two electrons spatially separated in vertically coupled one-dimensional rings is solved exactly by using the numerical trigonometric sweep method. The change of the level-ordering and the crossover of the curves of the energy levels as a functions of the rings radii, the separation between rings and the magnetic field, applied along the axis, are found and discussed. As the distance between rings tends to zero our results are in an excellent agreement with those obtained previously for the single two-electron one-dimensional ring.

The ground state of the two-electron donor-impurity complexes and confined in a quantum well is analysed by using a variational procedure. A model approximation that can be used in the two-electron problem in order to separate the variables is proposed, and it is shown that, for the negative ion and the complex, the electron-electron interaction may be eliminated, in this approximation, by introducing an additional effective charge at a centre of symmetry. The binding energy is calculated as a function of the quantum-well width for different magnetic field strength values, whereas the and dissociation energies are calculated as functions of the spacing between the impurities in the complexes, and for different well widths. The results for the first and the second ionization binding energies as functions of the well width are presented for different separations between impurities. Finally, the scheme that we propose is extremely simple and provides a realistic description of few-particle ground-state electronic structures confined in a quantum well.