Image charges in spherical quantum dots with an off-centered impurity: algorithm and numerical results

A computational scheme yielding exact (numerical) wave-functions and energies of a spherical nanocrystallite, with a shallow donor impurity located anywhere inside, is presented. Position-dependent effective mass, finite step-like spatial confining potential, coulombic and image potentials originating from the dielectric mismatch at the quantum dot edge are taken into account. Strategies to overcome mathematical divergences, low numerical convergence and computer cut-off errors are discussed. The resulting code is employed to carry out a comprehensive study on the influence of the impurity off-centering on the image charge contribution to the electronic energy. The highly non-additivity of the different contributions to this energy emphasizes the relevance of employing computational schemes like the one presented here, which incorporate all confining potentials in a balanced way.