BOUNDSTATES OF TWO‐ELECTRON SYSTEMS IN QUANTUM CONFINED GEOMETRIES

Abstract

With the advent of sophisticated growth techniques such as Molecular Beam Epitaxy and Metal Organic Chemical Vapor Deposition, the calculation of the energy boundstates and electron wave‐functions of the one‐electron Schrödinger equation has received a lot of attention over the last decade. With the more recent fabrication of quantum wires and dots, it seems now imperative to extend the boundstates calculation to systems containing only a few electrons. Hereafter, we investigate the effect of electron exchange and Coulomb interactions on the boundstates of a two‐electron system in a square quantum well. The technique is based on a general Alternating Direction Implicit algorithm ( T. Singh and M. Cahay, SPIE Vol. 1675, Quantum Wells and Superlattice Physics IV (1992), p.11) combined with a Fourier spectrum analysis of the two‐particle wavefunction correlation , <ψ(χ1,χ2;0)/ψ(χ1,χ2;τ)> , where χ1, χ2 are the coordinates of the two electrons. The precise location of the energy eigenvalues requires the appropriate use of window functions before calculating the Fourier transform of the correlation function. We also compare our results for the boundstate energies with those obtained using a first order time‐independent perturbation theory.