Binding Energy of Impurity States in Spherical GaAs–Ga1xAlxAs Quantum Dots

Abstract

The binding energy of a shallow hydrogenic impurity in spherical GaAs–Ga1–xAlxAs quantum dots is calculated following a variational and a perturbation method. A finite confining potential well with depth determined by the discontinuity of the band gap in the quantum dot and the embedding material is used. We also calculate the binding energy for a dot with infinite confining potential. The calculated energies are computed as functions of both the radius of the dot and the location of the impurity within the dot. The results show that as the dot radius decreases, the impurity binding energy increases for the infinite potential well. On the other hand, for the finite potential well, it reaches a peak value and then diminishes to a limiting value corresponding to the radius for which there are no bound states in the well. The results obtained by the perturbation method are almost similar in nature but differ to some degree from those obtained by the variational method.