Effects of the quantum size and an off-center donor atom on energy levels in a quantum dot

Abstract

Gorecki and Brown [J. Phys. B 22, 2659 (1989)] proposed a variational theory for the ground state. They assumed the trial wave function in confined systems as f phi, where f acted as a variable contour function to minimize the energy. In practical calculations, it is only possible to calculate electronic energy levels at some shapes of f to decide which f gives the minimal energy. Due to this constraint in the variational calculation of f, their method gives unsatisfactory results in asymmetrical quantum problems, and therefore is rarely used. We generalize their method by assuming the trial wave function as f psi, where psi is a linear combination of basis functions. In our improvement, the use of the linear combination of basis functions acts not only to simulate efficiently the asymmetrical state but also to the give energy levels of the excited state. For the same reason, our method can be applied in open systems and in the problem where a new potential exists. Therefore, the goal of our improvement is to propose a general variational method. As applications, the changes of binding energies and donor states in spherical and ellipsoidal semiconductor quantum dots are studied when the position of the donor is shifted and when the size of the dot is changed.