Unified treatment of dielectric enhancement and conduction-electron screening in the Mott transition in semiconductors

The possibility is discussed that in a heavily doped $n$-type semiconductor a small but significant fraction of electrons may be released from the donor levels even at 0°K. The theory is based on the model of both the free-electron screening and the donor-electron screening of the potential. The latter screening arises from the neutral-donor polarizability which enhances the dielectric constant via the dipole-dipole interaction. The partial release of electrons into the conduction band starts at such a donor concentration that the bound state would disappear if only the donor electron screening is assumed. The fraction of the released electrons and the binding energy of the donor are calculated for $n$-type Si and Ge on the basis of a schematic model. Support for the present theory is provided by the magnetic data which are sensitive to the concentration of the conduction-band electrons.