The Meyer–Neldel rule and hopping conduction

A Meyer–Neldel rule (MNR)-type relationship is found to exist between the slope (activation energy) and the intercept (prefactor), in the T − 1 / 4 plot of hopping conductivity. This new relation (hopping MNR) is obeyed by a large number of systems, including those obeying the conventional MNR. Further, all the materials lie on a single straight line on the hopping MNR plot. Hopping in the exponentially rising density of localized states can give such a relationship in amorphous semiconductors. This may be used to roughly estimate a parameter, e.g., the density of states at the Fermi level or its slope, if either is known from some other experiment. However, like conventional MNR, a general explanation is missing for hopping MNR also.