Rayleigh-Schrödinger perturbation theory for electron-phonon interaction effects in polar semiconductor quantum dots with parabolic confinement

Abstract

We use the Rayleigh-Schrödinger perturbation theory to obtain a simple closed-form analytical expression for the polaronic correction to the ground state energy of an electron in a polar semiconductor quantum dot in both two and three dimensions. We find that there exists a simple dimensional scaling relation for the ground state polaron energy. We apply our results to GaAs, InSb, CdTe, CdS and CdSe dots and show that the polaronic effects can be quite appreciable if the confinement lengths are smaller than a few nanometers. Furthermore, the polaronic effects are found to be more pronounced in two-dimensional dots than in three-dimensional ones. However, the relative polaronic enhancement in a quantum dot with respect to the corresponding bulk value is independent of both the dimensionality and the electron-phonon coupling constant, but depends on the phonon frequency.