Electric field dependence of charge mobility in energetically disordered materials: Polaron aspects

In order to understand the electric-field dependence of charge mobility in molecularly doped organic materials, we consider the one-dimensional migration of carriers between sites with Gaussian energetic disorder. The transition rate of carriers to neighboring sites is assumed to be given by the Marcus rate equation. An exact analytical expression is derived, and is compared to the measured data. A phenomenological Gill's relation occurs in the intermediate region of the S-shaped field dependence of the mobility. The recently observed anomalous field dependence of the mobility, which shows that the mobility increases with field strength at low fields, passes through a maximum, and then decreases with increasing field strength, is reproduced. The increase followed by the decrease of the mobility with increasing field strength is interpreted as a result of energetic disorder and the Marcus inverted region.