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A method of calculating the energies of bound states associated with imperfections described by short-range potentials in semiconductors is presented and applied. The method is based on solid-state scattering theory and involves expansion of physical quantities in terms of the Wannier functions for a many-band system. The properties of Bloch functions and Wannier functions are investigated to enable the numerical computation of matrix elements. Application is made to the neutral vacancy in silicon. A pseudopotential is employed to represent the change in the crystal potential produced by the vacancy. It is found that the vacancy produces a localized state in which low-lying energy bands and interband couplings are important, in contrast to the shallow donor and acceptor states which have been studied in the past.
Callaway et al. (Sat,) studied this question.