The symmetry of donor-bound electron wavefunctions in quantum wells

In order to investigate the symmetry (i .e. sphericity) of donor-bound electron wavefunctions in quantum wells, we have invoked a two-parameter trial wavefunction. One parameter is the Bohr radius λ, whilst the other is the eccentricity parameter ζ. The latter incorporates the effect of the quantum well (QW) on the carrier motion in the growth (i.e. the z) direction. Working with in the envel opefunction approximation it is shown that the donor wavefunction has the form of a prolate spheroid. However, calculations of the ratio λ/ζ shows that it is the value of λ which determines the essential symmetry of the wavefunction.