Unraveling the Role of Multiphonon Excitations and Disorder Concerning the Meyer-Neldel Type Compensation Effect in Organic Semiconductors

The Meyer-Neldel (MN) compensation rule, implying an exponential increase in the prefactor with increasing activation energy in a thermally activated process, is naturally emerging in two-site transition rates as a result of multiphonon excitation processes. However, it has been recently demonstrated [Phys. Rev. B. 90, 245201 (2014)] that the experimentally observed compensation behavior for the temperature-activated charge transport in thin-film organic field-effect transistors (OFETs) is not a genuine phenomenon, but rather it is an apparent extrapolated effect that arises as a consequence of the partial filling of the Gaussian DOS distribution. To resolve the contradiction, we investigate the impact of different jump-rate models on macroscopic hopping-charge transport in a random organic system using an effective medium analytic approach. The principal result of this study is that the averaging over the individual jump rates in a conventional Gaussian disordered system erodes the genuine thermodynamically determined MN compensation effect, and therefore, the macroscopic transport no longer reflects the microscopic rates. The apparent compensation behavior observed for OFET mobilities upon varying the carrier concentrations can be reproduced regardless of the single-phonon or multiphonon character of activated transitions. Another remarkable finding is that the disorder formalism does predict a genuine MN compensation effect using multiphonon rates if a disordered semiconductor contains a significant concentration of deep traps, so that the cumulative DOS features a double-peak Gaussian. Thus, this study bridges the gap between Gaussian disorder and multi-excitation entropy (MEE) models concerning the MN effect, and has important implications for the interpretation of the isokinetic MN temperature in disordered organic semiconductors.