Ohm’s Law for a Bipolar Semiconductor: The Role of Carrier Concentration and Energy Nonequilibria

The effective linear electrical conductivity of a nondegenerate bipolar semiconductor, sandwiched between two metals, is investigated taking into account both its nonequilibrium charge carriers (both electrons and holes) and nonequilibrium temperature. We stress that even in the linear perturbative approximation both carrier concentration and energy nonequilbria arise automatically when an electrical current flows. The expression for the effective electrical conductivity is obtained and shown to depend on the electron and hole electrical conductivity, the thermal conductivity, the bandgap, charge carriers lifetimes, and both bulk and surface recombination rates. The effective electrical conductivity is equal to the classical result, i.e., the sum of the electron and hole electrical conductivities, only if the surface recombination rate at the interface is sufficiently strong or the charge carrier lifetime is sufficiently small. In this article, partial cases are considered, specifically, semiconductors with small and large thermal conductivities, semiconductors with monopolar electron and monopolar holes, strong and weak surface recombination rates, and small and large charge carrier lifetimes. Expressions for the effective electrical conductivity are obtained in all partial cases.