Static dielectric constant of heavily doped semiconductors

One of the major effects of heavy doping in semiconductors is that the dielectric constant κ changes with impurity density and thus with position. The change is significant for impurity densities N greater than 10¹⁷ cm^?3. The low temperature classical relation of Castellan and Seitz is modified by including the contribution to the local field at the atomic site by the polarization of the host atoms due to an electric field. This correction makes an appreciable difference in κ(N). A new model for the polarizability of the impurity atoms is also developed. It is found that there is good agreement between the values of the dielectric constant of Si doped with As, P and Sb predicted by this theory and those found experimentally by Bethin et al. The critical impurity concentration for the metal-nonmetal transition found from this theory is however higher than that given by Castner et al. Reasons for this discrepancy are given.