Self-capacitance of a quantum dot: Dependence on the shape of the confining potential

Semiconductor quantum dots (QDs) came to be identified as “artificial atoms” on account of sophisticated and careful experiments on single-electron and Coulomb blockade effects in the last decade. Earlier works on quantum confinement and excitonic effects modeled QDs by a square-well potential with a finite or infinite barrier. On the other hand, Coulomb blockade calculations are generally performed using parabolic confinement. However, there is a growing realization that these shapes of the potential may not represent the correct picture. In this paper we study the many electron effects in QDs within the local-density approximation and the Harbola-Sahni scheme. The latter incorporates the exchange effects essentially exactly. Further, we investigate the effect of the shape of the potential on these systems. The shapes considered are quasitriangular, quasiharmonic, and varying degrees of quasisquare. We examine the level spacing, level degeneracy, and the scaling of the electron-electron interaction with size. We find that the scaling laws have a complex dependence on the size and shape of the potential. Finally, we compare our calculations with experiments on a CdSe quantum dot.