The energy spectrum of charge carriers in a strongly oblate ellipsoidal quantum dot

Abstract

A new method of introducing curvilinear coordinates for an oblate ellipsoid of revolution is developed, which is valid for charge carriers obeying a parabolic isotropic dispersion law. Using this method, simple analytical formulas are derived for the energy spectrum of carriers in an oblate ellipsoidal quantum dot. According to these expressions, there are energy levels of two types. The first type is characterized by a quantum number corresponding to the motion of carriers predominantly along the minor axis of the ellipsoid. The distances between levels of the first type are large: only one such level is found in an InAs quantum well confined between GaAs layers. The second type is characterized by a quantum number corresponding to the motion of carriers along the major axis of the ellipsoid. The distances between levels of the second type are small and many such levels can be sometimes accommodated in a quantum dot, their number rapidly increasing with the degree of oblateness of the ellipsoid.