Excitonic binding energy in prolate and oblate spheroidal quantum dots

Excitonic energy is theoretically investigated in a spheroidal quantum dot as a function of an ellipticity parameter χ defined as the semi-axes ratio. The total energy is determined through the variational method using a trial wave function build from exact electron and hole spheroidal functions. For a fixed volume of the dot, it is shown that the total energy varies considerably against the parameter χ in contrast with the binding energy which is weakly dependent on the ellipticity.