The Einstein relation in systems with trap-controlled transport

The applicability of the Einstein relation considering diffusivity and mobility of charge carriers with respect to disordered systems has been a matter of serious discussion in recent years. Here the validity of the Einstein relation, using the generalized form, is checked for two specific density-of-states functions within a multiple trapping model and the mobility edge concept. It is shown that the classical Einstein relation is valid for almost all charge-carrier densities relevant for experimental purposes. It is demonstrated that this result is dependent on the charge-carrier mobility definition.