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

TLDR

Recent work shows that hopping mobility in semiconducting organic materials depends on charge‑carrier concentration, yet existing models for Gaussian density of states either have not been applied or require major modification. The authors analyzed this effect using six existing semianalytical models applied to a Gaussian density of states. The study finds that mobility is constant below a concentration that decreases with the DOS‑to‑thermal‑energy ratio, rises at higher concentrations, but is capped or reduced at very high concentrations due to final‑state effects; an analytical expression captures this behavior, and the temperature dependence of ln μ suggests a linear relation with 1/T or 1/T², potentially reconciling polaron‑ and disorder‑based hopping models.

Abstract

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 $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{s}$ of the width of the DOS over the thermal energy ${k}_{B}T$, 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, $\ensuremath{\mu}$, in the form of the product of the mobility in the low concentration limit times a concentration $(c)$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{s}$-dependent enhancement factor. Depending on $c$, $\mathrm{ln}(\ensuremath{\mu})$ 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.