Energy levels of an electron with Kaneʹs law of dispersion in a spherical microcrystal

The electronic states in a spherical semiconductor microcrystal are studied theoretically taking into account the nonparabolicity of electron dispersion law. The microcrystal confinement potential is approximated by the three-dimensional spherically symmetric parabolic potential. It is shown that the nonparabolicity leads to the Schroedinger equation with the effective oscillatory potential containing an “anharmonic” term proportional to r4. Within the framework of the stationary theory of perturbation the energy corrections due to the “anharmonicity” are calculated. The problem of partial removal of electronic energy level degeneracy is discussed.