Electron energy spectrum in a spherical quantum dot with smooth confinement

Abstract

The electron energy spectrum in a quantum dot (QD) with smooth dependences of the quasiparticle potential energy and the effective mass at the interface between semiconductor media is calculated in the effective mass approximation. It is shown that the electron energy corrections due to the tailing of the interface are nonmonotonous functions of the QD radius, the increasing of which brings to the rapid increasing of shifts, reaching their maxima, and slowly decreasing for the QDs of big sizes. The calculations prove that the relative corrections for the different electron energy levels in a spherical QD are placed closer to each other with increase in the radius. The growth of the parameter of interface tailing leads to the proportional increase in the corrections to electron energy spectra. Numerical calculations are performed for HgS/CdS and GaAs/AlxGa₁₋xAs QDs, all dependences being qualitatively similar.