Binding Energy of Donor States in a Quantum Dot with Parabolic Confinement

The donor binding energies associated with the ground state and a few excited states are computed as a function of the dot size and the impurity position within two- and three-dimensional GaAs quantum dots. The calculation has been done using the Potential Morphing Method, a recently developed numerical method for the solution of the time-independent Schrodinger equation with any arbitrary interaction potential. The agreement with both perturbation and variational methods is excellent regarding the dependence of the binding energies on the location of the impurity within the quantum dot. Furthermore, we have shown that this method works well in all confinement limits-from weak to strong confinement-in contrast to the usual perturbation method, which works only in the strong confinement limit.