Donor-polarizability enhancement as the insulator-metal transition is approached from the insulating side

The low-temperature static dielectric constant for n-type semiconductors shows a significant upward deviation from Clausius-Mossotti behavior as the donor concentration N approaches the critical value Nc for the onset of metallic behavior. After reviewing the possible reasons for this upward deviation and the various types of screening applied to the insulator-metal problem, a new continuum-model calculation of the donor-polarizability enhancement αD(N)αD(0) is presented which is based on an electrostatic donor-donor interaction potential and the Clausius-Mossotti relationship for the long-wavelength static dielectric constant ε(N). The Hass\'e variational approach is employed to calculate αD(N). The calculated enhancement contains two contributions: (1) a size effect associated with an enlargement of the donor wave function with N, and (2) an increase in the average effective dielectric constant 〈ε(r,N)〉 with N seen by the localized donor wave function. The results show αD(Nc)αD(0) ranging from about 2 for Si:Sb to about 3 for Si:As. Comparison with the experimental data for Si:As shows the calculated upward deviation from Clausius-Mossotti behavior remains smaller than the data. The values of N_c-calc [based on a polarization catastrophe, a new self-consistent Clausius-Mossotti relationship, and a self-consistent Herzfeld criterion for Nc from ε(N→Nc)→∞] are between 60% and 100% larger than the experimental values for the silicon shallow donors. Possible corrections to this calculation resulting from the donor randomness, charge transfer, and corrections to the Lorentz-Lorenz local field are also discussed.