Electron pair in a Gaussian confining potential

Abstract

Two electrons confined in quantum dots (QD's) are studied under an assumption of a Gaussian confining potential and its parabolic approximation. We have calculated the energy levels of singlet and triplet states as functions of the range and depth of the confining potential in the two-dimensional (circular) and three-dimensional (spherical) QD's, and determined the critical values of these parameters, for which the electrons form bound states. The present results allow us to explain why the commonly used parabolic approximation fails in a description of transport-spectroscopy data for QD's. The applicability of the Gaussian potential to the QD's has been discussed.