Metal–insulator transition in many valley semiconductors in the spirit of the Hubbard model

The 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 the value of the 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 a∗Nc1/3=0.36ν−1/3 is critically examined in terms of Hubbard model. The effects of Anderson localization, exchange and correlation in the Hubbard model are included in a simple way. 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.