On the rate-equation formulations of hopping conductivity in amorphous semiconductors: quantum transport approach

The present controversy regarding the validity of the AC and DC rate-equation formulations of hopping conductivity is examined within the exact resolvent theoretic framework of quantum transport theory. It has been argued that terms representing field-induced charges in the local value of the chemical potential which appear in rate-equation theory should not be present: this would destroy the percolation theoretic interpretations of the DC conductivity. The present theory, based on the Kubo formalism, demonstrates the validity of the rate equations in the weak-coupling, low-frequency and DC limits. The controversy is resolved by the observation that the anti-rate-equation theories have neglected an infinite sequence of terms appearing in perturbation theory which restore the disputed chemical potential terms to the rate-equation formulation.