Self-consistent calculation of discrete and continuous states in spherical semiconductor quantum dots

Abstract

A self-consistent procedure for calculating the energy structure, wave functions, and charge distribution in spherically symmetric semiconductor quantum dots is presented that takes account of both bound and free-electron states. The Schr\"odinger and Poisson equations are solved iteratively while using the Morse-type parametrized potential to keep the charge neutrality in each iterative step. Numerical calculations performed for a GaAs-${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As based quantum dot indicate that under realistic doping conditions bound states account for most of the charge accumulated in the dot. However, the self-consistent potential very significantly modifies the free-state wave functions and hence the bound-free transition matrix elements.