Publications Details
Breakdown of the resistor-network model for steady-state hopping conduction
General master equations are used to study steady-state hopping transport in a disordered solid. We express a site`s occupancy in terms of its quasi-electrochemical potential (QECP); currents flow between sites whose QECP`s differ. Coupled nonlinear circuit equations for the QECP`s result from the steady-state condition and the boundary condition that the total QECP drop is the applied emf. When the site-to-site QECP differences are much smaller than the thermal energy, K{sub B}t, the effect of current flow on site occupancies is ignorable. These equations then reduce to those of a resistance network. However, the 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. Exact examples show the importance of current-induced charge redistribution in non-ohmic steady-state flow.