Screening of donor ions in silicon

It is pointed out that group-theoretical ideas similar to those used to study bound states of a neutral donor in a many-valley semiconductor can be extended to the problem of screening of a donor ion by delocalized electrons. A transformation from the set of conduction-band Bloch states in Si to a new set of states which transform according to the irreducible representations of the tetrahedral group $T_d$ is used. This new set of states approximately block diagonalizes tetrahedrally symmetric potentials and simplifies the problem of including both intervalley and umklapp parts. We use the new representation to find the long-wavelength correction due to intervalley and umklapp scattering to the induced potential near a donor ion in an electron gas in Si the RPA. The strength of this correction is estimated by comparison with the experimentally known properties of the P-neutral-donor ground state, using a model potential to represent the effects of intervalley and umklapp scattering on that state.