Charge-carrier and polaron hopping mobility in disordered organic solids: Carrier-concentration and electric-field effects

The effective-medium approximation (EMA) analytical theory is advanced further to describe charge transport at arbitrary charge-carrier concentration in a disordered organic material with superimposed polaron effects. A key point of this model compared to the previous treatment [Phys. Rev. B 76 (2007) 045210] is that it is formulated for arbitrary electric fields and is able to describe consistently both the carrier-concentration and field dependences of charge mobility. The mobilities of both bare charge carriers and polarons were calculated using the Miller-Abrahams and polaron jump rate models, respectively. An excellent quantitative agreement was obtained between the theoretical calculations and the recent numerical simulations of the field- and carrier-density dependences of the mobility for bare charge carriers using the same parameters. The polaronic carrier density effect was also calculated using the complete Marcus jump rate equation and straightforward EMA configurational averaging, and the results compared to that obtained with the use of the symmetrical jump rate model and the effective transport energy concept. This study confirms that a strong dependence of carrier mobility upon increasing carrier density and electric field, which has conventionally been observed in experiment for numerous organic semiconducting materials, is incompatible with the notion of large polaron binding energy in these materials, implying that the energetic disorder plays a dominant role.