  A tight-binding parametrization for silicon, optimized to correctly reproduce
effective masses as well as the reciprocal space positions of the
conduction-band minima, is presented. The reliability of the proposed
parametrization is assessed by performing systematic comparisons between the
descriptions of donor impurities in Si using this parametrization and
previously reported ones. The spectral decomposition of the donor wavefunction
demonstrates the importance of incorporating full band effects for a reliable
representation, and that an incomplete real space description results from a
truncated reciprocal space expansion as proposed within the effective mass
theory.
