Role of the reorganization energy for charge transport in disordered organic semiconductors

While it is commonly accepted that the activation energy of the thermally activated polaron hopping transport in disordered organic semiconductors can be decoupled into a disorder and a polaron contribution, their relative weight is still controversial. This feature is quantified in terms of the so-called $C$ factor in the expression for the effective polaron mobility: ${\ensuremath{\mu}}_{e}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}{E}_{a}/{k}_{B}T\ensuremath{-}C{(\ensuremath{\sigma}/{k}_{B}T)}^{2}]$, where ${E}_{a}$ and $\ensuremath{\sigma}$ are the polaron activation energy and the energy width of a Gaussian density of states (DOS), respectively. A key issue is whether the universal scaling relation (implying a constant $C$ factor) regarding the polaron formation energy is really obeyed, as recently claimed in the literature [Seki and Wojcik, J. Chem. Phys. 145, 034106 (2016)]. In the present work, we reinvestigate this issue on the basis of the Marcus transition rate model using extensive kinetic Monte Carlo simulations as a benchmark tool. We compare the polaron-transport simulation data with results of analytical calculations by the effective medium approximation and multiple trapping and release approaches. The key result of this study is that the $C$ factor for Marcus polaron hopping depends on first the degree of carrier localization, i.e., the coupling between the sites, further whether quasiequilibrium has indeed been reached, and finally the $\ensuremath{\sigma}/{E}_{a}$ ratio. This implies that there is no universal scaling with respect to the relative contribution of polaron and disorder effect. Finally, we demonstrate that virtually the same values of the disorder parameter $\ensuremath{\sigma}$ are determined from available experimental data using the $C$ factors obtained here irrespective of whether the data are interpreted in terms of Marcus or Miller-Abrahams rates. This implies that molecular reorganization contributes only weakly to charge transport, and it justifies the use of the zero-order Miller-Abrahams rate model for evaluating the DOS width from temperature-dependent charge transport measurements regardless of whether or not polaron effects are accounted for.