Temperature scaling of effective polaron mobility in energetically disordered media

TL;DR

This paper derives an analytical expression for effective polaron mobility in disordered media, confirming the coefficient for 2D and 3D systems, and validates it with simulations and experimental data analysis.

Contribution

It provides the first theoretical estimate of the coefficient C_d for 2D systems and validates the mobility model through simulations and experimental data.

Findings

C_d=1/2 for both 2D and 3D systems.

The mobility model accurately describes data under certain conditions.

Validated theoretical predictions with kinetic Monte-Carlo simulations.

Abstract

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 $\mu_{\rm eff}\propto\exp\left[-\lambda/\left(4 k_{\rm B} T\right)- C_d\sigma^2/\left(k_{\rm B} T\right)^2 \right]/\left[\sqrt{\lambda} (k_{\rm B} T)^{3/2}\right]$, where $\lambda$ is the reorganization energy, $\sigma$ 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 $\lambda$. We also give examples of analysis of experimental data for 2D and 3D systems based on our theoretical results.