Breakdown of the resistor-network model for steady-state hopping conduction

Master equations are used to study steady-state hopping in a disordered solid. We express each site's occupancy in terms of its quasi-electrochemical potential (QECP); currents flow between sites whose QECP's differ. Coupled nonlinear circuit equations result from the steady-state condition and a boundary condition. When site-to-site QECP differences are much smaller than the thermal energyk _B T, the effect of current flow on occupancies is ignorable, and the equations reduce to those of a resistance network. But this resistor-network model fails: a) at low temperatures, b) with increasing disorder, and c) with increasing emf. We therefore study hopping conduction beyond this approximation. Exactly soluble examples show the importance of current-induced charge redistribution in non-ohmic steady-state flow.