Transition from trap-controlled to trap-to-trap hopping transport in disordered organic semiconductors

We advance further the effective-medium theory to describe adequately nondispersive charge transport at arbitrary trap concentrations in a disordered organic material, with special emphasis on trapping phenomena at large trap concentrations when the transport through the trap-state manifold becomes possible. A key point of this model compared to the previous treatment [Phys. Rev. B 66, 205208 (2002)] is that it accounts also for the dependence of the overlap integral upon the trap concentration due to dilution of transport sites by traps. While the previous and present treatments provide similar results for small and moderate trap concentrations, the present theory is superior regarding a quantitative understanding of charge transport at large trap concentrations, notably the transition from trap-controlled to trap-to-trap hopping transport that has been observed experimentally. The theory also provides a more accurate estimate for the effective energetic disorder parameter, ${\sigma }_{\mathit{eff}}$, introduced to account the effect of traps on charge transport in disordered organic solids for arbitrary trap concentrations. The theoretical results have been supported by experiments in the conjugated polymer polyfluorene doped with different concentration of tri-$p$-tolylamine that act as a trap by employing the technique of thermally stimulated luminescence.