In this study, we have investigated the confined donor impurity in a hollow cylindrical-shell quantum dot. The charges are assumed to be completely confined to the interior of the shell with rigid walls. Within the framework of the effective-mass approximation and by using a simple variational approach, we have computed the donor binding energy as a function of the shell sizes in order to study the behavior of the electron-impurity attraction for a very small thickness. Our results show that the binding energy of a donor impurity placed at the center of cylindrical core/shell dots depends strongly on the shell size. The binding energy increases when the shell-wideness becomes smaller and shows the same behavior as in a simple cylindrical quantum dot. A special case has been studied, which corresponds to the ratio between the inner and outer radii near to one (a/b → 1) for which our model gives a non-significant behavior of the impurity binding energy. This fact implies the existence of a critical value (a/b) for which the binding energy of the donor impurity tends to the limit value of 4 effective Rydbergs as in a 2D quantum well. We also analyse the photoionization cross section considering only the in-plane incident radiation polarization. We determine its behavior as a function of photon energy, shell size, and donor position. The measurement of photoionization in such systems would be of great interest to understand the optical properties of carriers in quantum dots.

This paper reports a recent study on the polarizability and the photoionization cross section (PCS) of a hydrogenic impurity confined in a spherical $AlAs/GaAs$ core/shell quantum dot under external electric field and hydrostatic pressure. In the framework of effective mass theory, a variational approach is used to determine the polarizability, binding energy, and the PCS of a single donor in a spherical core/shell quantum dot. Our numerical calculations reveal that all these fundamental parameters are deeply dependent on the core and shell radii. The study of the localization of the impurity inside the core/shell indicates that the Stark shift is more important when the impurity is positioned at the center of the core/shell and becomes less important when the donor moves toward the boundaries of the shell layer. In addition, a rapid decrease of the intensity of electric polarizability under hydrostatic pressure is observed. In order to understand the optical responses during the photoionization of the donor dopant, we investigated the PCS under hydrostatic pressure, electric field, ionized donor position, and core/shell sizes.