Shallow and deep impurity levels in multivalley semiconductors: A Green-function study of a cubic model by the recursion method

Abstract

We study by the recursion method impurity levels in a cubic model semiconductor with parameters corresponding to silicon. Nearest- and second-nearest-neighbor interactions can be varied to produce in the Brillouin zone either a single minimum at point \ensuremath{\Gamma} or a set of three equivalent minima at point X, all with the same effective mass. This way we can study the dramatic effect that intervalley scattering has, when combined with a relatively strong central-cell potential, in producing a shallow-deep instability in the impurity binding energies. We find that this instability has the characteristics previously found by an intervalley effective-mass-equation (IVEME) approach, although the two methods are completely independent and none of the approximations made in the IVEME are made here. We also find that contributions to deep levels from the Coulombic tail of the impurity potential are substantially larger than the corresponding effective-mass-equation (EME) binding energies and cannot be treated perturbatively, at least for Z\ensuremath{\ge}2. This Green-function approach based on the recursion method accurately reproduces both central-cell-potential-only and EME limits and allows one to study, on an equal footing, all cases in between, i.e., deep, intermediate, and shallow impurity levels.