Metal-to-non-metal transitions in doped germanium and silicon

Abstract

The metal-to-non-metal (MNM) transitions in shallow donor states of Ge and Si are studied by means of Hubbard's tight-binding model. The donors are assumed to form a regular lattice, and the hopping integral and the intra-donor repulsion integrals are calculated from the wavefunctions of single isolated impurities. The calculated critical densities for the onset of the MNM-transitions compare well with empirical values and with Mott's criterion. The only input parameters to the calculations are the experimentally determined ionization energies, the effective masses in the conduction band, and the background dielectric constants. Estimates are also made for the concentration at which the impurity band merges into the conduction band.