Charge-carrier concentration dependence of the hopping mobility in organic materials with Gaussian disorder

It has recently been demonstrated that the hopping mobility in semiconducting organic materials depends on the charge-carrier concentration. We have analyzed this effect within the framework of six existing semianalytical models, for the case of a Gaussian density of states (DOS). These models were either not applied earlier to the case of a Gaussian DOS, or are shown to require a major modification. The mobility is constant below a certain concentration, which decreases with increasing ratio \^{}s of the width of the DOS over the thermal energy k₁T, and it increases for larger concentrations. At very high concentrations final state effects limit this increase or even give rise to a decrease. An analytical expression is given for the mobility, , in the form of the product of the mobility in the low concentration limit times a concentration (c) and \^{}s-dependent enhancement factor. Depending on c, ln () varies approximately linearly with 1∕T or with 1∕T^2. This finding may lead to a solution for the long-standing controversy between polaron-based and disorder-based hopping models.