Temperature scaling of effective polaron mobility in energetically disordered media

We study effective mobility in 2 dimensional (2D) and 3 dimensional (3D) systems, where hopping transitions of carriers are described by the Marcus equation under a Gaussian density of states in the dilute limit. Using an effective medium approximation (EMA), we determined the coefficient $C_d$ for the effective mobility expressed by $μ_{\rm eff}\propto\exp\left[-λ/\left(4 k_{\rm B} T\right)- C_dσ^2/\left(k_{\rm B} T\right)^2 \right]/\left[\sqrtλ (k_{\rm B} T)^{3/2}\right]$, where $λ$ is the reorganization energy, $σ$ is the standard deviation of the Gaussian density of states, and $k_{\rm B} T$ takes its usual meaning. We found $C_d=1/2$ for both 2D and 3D. While various estimates of the coefficient $C_d$ for 3D systems are available in the literature, we provide for the first time the expected $C_d$ value for a 2D system. By means of kinetic Monte-Carlo simulations, we show that the effective mobility is well described by the equation shown above under certain conditions on $λ$. We also give examples of analysis of experimental data for 2D and 3D systems based on our theoretical results.

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