Shape effects on the one- and two-electron ground state in ellipsoidal quantum dots

The ground state of two conduction-band electrons confined in ellipsoidally shaped quantum dots has been calculated within the effective-mass approximation, using both a perturbative scheme and a variational approach. The problem is studied using prolate spheroidal coordinates, which allows us to exactly solve the single-particle problem and therefore to make a suitable ansatz for the two-electron variational wave function. The different contributions arising from the Coulomb repulsion and dielectric effects are calculated and discussed. The dot anisotropy is shown to strongly influence the electron-electron correlation.