Calculations of impurity states in semiconductors: I

A new method of calculating the energies of bound states associated with shallow and/or deep impurities in semiconductors is presented and applied to substitutional acceptors in silicon. A screened local pseudopotential is used to represent the impurity potential. The impurity wavefunction is expressed as a linear combination of the pseudofunctions associated with the valence bands of the host crystal. The integration over the Brillouin zone is reduced to a sum over a set of sampling points, and the band energies and pseudofunctions at these points are generated from the empirical pseudopotential of Cohen and Bergstresser (1966). The calculation of the impurity energy is performed without invoking the knowledge of the Wannier functions. The only approximations involved are those implicit in the pseudopotential theory and the finite size of the sample which is used in the numerical integration over the Brillouin zone.