Self-consistent calculation of the enhanced donor polarizability below the insulator-metal transition

A continuum model potential taking into account a spatially varying dielectric constant is employed to make a fully self-consistent calculation of the enhancement of the donor polarizability as a function of donor concentration N D as N D approaches N c, the critical concentration for metallic behavior. The results yield a new self-consistent Clausius-Mossotti criterion for the polarization catastrophe at N c. Using the dilute concentration value of the donor polarizability N c is uniquely determined. The results are compared with earlier experimental results for N-type silicon and with other theoretical calculations.