Continuum electron wavefunction shifts in semiconductor quantum dot

In this paper, the mathematical model for electron wavefunction shifts in the continuum part of the electronic spectrum of a GaAs-AlxGa1-xAs based semiconductor quantum dot (QD) is presented. The electron states in the continuum are obtained by solving the Schrodinger equation written in the effective-mass approximation. The influence of accumulated charges in the well region of QD on conduction band bending in this model is taken via a self-consistent procedure. Analytical derivation and numerical calculations of the behavior of electron wavefunction shifts, considered as they depend on electron energy in the high energy limit, show their considerable deviation from those expected according to Levinson's theorem, that predicts shifts tending asymptotically to zero. The reason for Levinson's theorem violation in the case of QD is the effective-mass mismatch at the heterointerface of QD constitutive materials.