Analytical view of metal–insulator transition in many valley semiconductors

Metal–insulator transition using different dielectric functions is investigated for a many valley semiconductor system within the effective mass approximation. The critical concentration as well as the value of Mott constant is enhanced when the Hartree–Fock dielectric function is used with the inclusion of exchange and correlation effects. In the absence of localization, the obtained value of Mott constant View the MathML source is critically examined in terms of the Hubbard model. The effects of Anderson localization with the inclusion of two different relevant distribution functions, exchange and correlation in the Hubbard model, are brought out analytically in a simple way. The better approximation is elicited nicely. The relationship between the present model and the Mott criterion in terms of Hubbard model is also brought out. The critical concentration is enhanced when a random distribution of impurities is considered. The value of α is fixed demanding the vanishing of the donor binding energy with the donor concentration for several donors in Si and Ge. Results are compared with the existing data available and discussed in the light of existing literature.