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We have studied the electronic properties in presence of an off-center hydrogenic shallow donor impurity confined in GaAs semiconductor quantum dot with toroidal geometry by considering the infinite confinement potential. This study has been performed within the parabolic band and the effective mass approximations in the presence of an off-center donor impurity. Three-dimensional Schrödinger equations are discretized using the finite difference method on a mesh containing Nr*Nθ*Nφ nodes. The numerical results of the analytical calculations demonstrate that the variation of the geometrical and torus radii (Rg and Rc) has a remarkable effect on the donor energy and the average electron-impurity distance, which is quite remarkable in small hemi-Toroidal quantum dot. On the other hand, we've demonstrated that the donor atom's position has a considerable impact on their energy. Furthermore, our numerical results show that the geometrical radius and donor atom's position significantly affect the electron impurity binding energy.

The unbound exciton properties in multilayered cylindrical quantum dot (CQD) (core/shell/shell) have been studied theoretically, within the effective mass approximation and two-band model. The uncorrelated energy of an exciton confined in GaAs/Ga1-x1Alx1As/Ga1-x2Alx2As CQD as a function of the core and first shell radius is presented. The numerical results show that the quantum dot size and the confinement potentials depth significantly adjust the ground state uncorrelated energy of exciton. However, the exciton wave function parameters are dependent on the core and first shell radius (R1 and R2), as well as the concentration of the barrier’s materials.

Within the effective mass approximation and the infinite confinement potential, this work focused on studying the electronic properties of spherical quantum dot (SQD) nanostructure through the finite difference method. The effects of shallow donor impurity position, temperature (T), and hydrostatic pressure (P) on the binding energy, the electron spatial extension e> and the average electron-impurity distance D-e> in a SQD have been evaluated. Our findings show that the binding energy increases as a function of hydrostatic pressure and decreases with the temperature effect. However, the binding energy presents very clear maximum around the spherical nanostructure center depending on the impurity position. For higher SQD, the impact of externals perturbations (P and T) on the electron spatial extension are more significant. The distance e> decreases with the augmentation of hydrostatic pressure when the impurity is near the center, which is conversely when the impurity is near the edge. In addition, applying the hydrostatic pressure and temperature leads to decreasing and increasing the average distance D-e>, respectively.