Excitonic and electronic states in ellipsoidal and semiellipsoidal quantum dots

A simple model is assumed to obtain analytical solutions of the Schrödinger equation in prolate spheroidal coordinates for the electron-hole pair confined to an ellipsoidal quantum dot (EQD) or to a semiellipsoidal quantum dot (SEQD). Numerical calculations are carried out to find the excitonic states as well as the electronic states decoupled from holes in such geometries. Their dependence on the inverse of the eccentricity of the ellipsoidal surfaces for different interfocal distances is investigated. The binding energy and the recombination radiation energy are calculated for GaAs and InAs QDs; the same dependences are also investigated. Comparison with previous calculations and experiments shows a good order-of-magnitude agreement. It is demonstrated that some of the available states in an EQD are forbidden in the SEQD and, consequently, some of the photoluminescence lines observed in the former case are suppressed in the latter geometry.