A robust numerical method for self-polarization energy of spherical quantum dots with finite confinement barriers

By utilizing a novel three-layer dielectric model for the interface between a spherical quantum dot and the surrounding matrix, a robust numerical method for calculating the self-polarization energy of a spherical quantum dot with a finite confinement barrier is presented in this paper. The proposed numerical method can not only overcome the inherent mathematical divergence in the self-polarization energy which arises for the simplest and most widely used step-like model of the dielectric interface, but also completely eliminate the potential numerical divergence which may occur in the Bolcatto–Proetto's formula [P.G. Bolcatto, C.R. Proetto, Partially confined excitons in semiconductor nanocrystals with a finite size dielectric interface, J. Phys. Condens. Matter 13 (2001) 319–334], an approximation method commonly employed for more realistic three-layer dielectric models such as the linear and the cosine-like models frequently mentioned in the literature. Numerical experiments have demonstrated the convergence of the proposed numerical method as the number of the steps used to discretize the translation layer in a three-layer model goes to infinity, an important property that the Bolcatto–Proetto's formula appears not necessarily to possess.