Two-electron singlet states in semiconductor quantum dots with Gaussian confinement: asingle-parameter variational calculation

Abstract

The problem of two electrons in a three-dimensional quantum dot with Gaussianconfinement is investigated for the singlet pairing by a variational method with a verysimple wavefunction containing only a single parameter and a Jastrow-like factor, which isshown to yield fairly good results for deep confining potentials. The calculation is alsoperformed for a few realistic semiconductor quantum dots and the phase diagrams for thetwo-electron singlet states are obtained for these materials. The pair density function iscalculated for several parameter values and its peak positions are obtained as a function ofthe confinement length and the depth of the potential to study the behaviour ofthe electron-pair size. The size of the bound pair of electrons is also obtainedby directly calculating the average distance between the two electrons in threedifferent ways and compared with the pair correlation results. It is furthermoreshown that, other properties remaining the same, the two-electron energy and theelectron-pair size depend crucially on the effective electronic mass and the dielectricconstant of the material. Finally, the ways of improving the wavefunction are alsoindicated.