Theory of Donor and Acceptor States in Silicon and Germanium

An exact theory of impurity states in crystals is developed, and an evaluation is given of the applicability of the Wannier equation to the donor states in Si and Ge in view of the multiple energy minima in the conduction band. The theory is extended to include degenerate bands, and it is shown by two different methods that the Wannier equation is to be replaced by a set of coupled wave equations. The theory is applied to acceptor states in Si and Ge. The agreement with experiment is fairly good for both donors and acceptors.