The random free-energy barrier model for ac conduction in disordered solids

A brief review of the history of ac ionic and electronic conduction in disordered solids is given, followed by a detailed discussion of the simplest possible realistic model: the random free-energy barrier model. This model assumes conduction takes place by hopping, where the hopping charge carriers are subject to spatially randomly varying energy barriers. The model is solved in the continuous time random walk and in the effective medium approximation, and it is shown that the two solutions are almost indistinguishable. In the random free-energy barrier model, the frequency-dependent conductivity is completely determined by the dc conductivity and the dielectric loss strength. The model correctly predicts all qualitative features of ac conduction in disordered solids, and a comparison to experiment on a large number of solids shows that the model is also quantitatively satisfactory.