On the Transition to Metallic Conduction in Semiconductors

A discussion is given of the conductivity to be expected from a crystalline array of atoms when the interatomic distance a is varied. It is shown that both for monovalent atoms and divalent atoms the conductivity is zero at T = 0 when a is large, the wave function of the system being real so that no current is possible. In both types of atom a discontinuous transition to a state showing metallic conductivity is predicted at a definite value of a. For divalent atoms calculations using Bloch orbitals and localized Wannier functions give essentially the same result; for monovalent metals they do not, and correspond to physically different states of the system. Applications are made to impurity-band conduction in semiconductors, the impurity centers being treated by the usual model as expanded atoms in a uniform dielectric. It is shown that the concentrations at which "metallic" conductivity sets in are not unexpected, but that it is difficult to understand impurity band conduction at lower concentrations unless the semiconductors are "compensated", either chemically or through the presence of dislocations.