Field dependence of hopping mobility: Lattice models against spatial disorder

The theoretical description of the effect of the electric field F on the hopping mobility mu belongs to the not-yet-resolved problems related to charge transport in disordered materials. An often proposed solution is to simulate hopping transport via sites placed on regular grids and to fit the results by phenomenological equations. This approach currently dominates the theoretical research of hopping transport in organic disordered semiconductors. We show that the dependence mu(F) in the case of regular grids can drastically differ from that in systems with spatial disorder. While mu increases with F on lattices, it can decrease in random systems with the same material parameters. Moreover, the material parameters responsible for the dependence mu(F) on lattices differ from those responsible for mu(F) in spatially disordered systems, which makes lattice models inappropriate for studying the field dependence of the hopping mobility.