Non-equilibrium transport of charge carriers in disordered organic materials

An analytic theory of non-equilibrium hopping charge transport in disordered organic materials is developed. It rests on the concept of effective transport energy and includes quasi-equilibrium (normal) and extremely non-equilibrium (dispersive) regimes of hopping transport as limiting cases at long and short times, respectively. Special attention is paid to the regime of moderately weak non-equilibrium transport. In this regime the quasi-equilibrium value of the mobility is nearly established, whereas the coefficient of field-assisted diffusion continues to increase at long times. Analytic expressions for relaxation times in the context of field-assisted diffusion and carrier drift have been obtained. The results of the theory are in agreement both with the data of time-of-flight experiments for molecularly doped polymers and the results of numerical simulations of the Gaussian disorder model. The impact of non-equilibrium effects on the transit time of charge carriers in thin organic films with a thickness of the order of 100 nm, which is typical for organic light-emitting diodes, is outlined.