# Fundamental characteristic length scale for the field dependence of hopping charge transport in disordered organic semiconductors

## TL;DR

This study reveals that the field dependence of hopping charge mobility in disordered organic semiconductors is governed by the localization length, not site concentration, challenging previous assumptions and providing new insights into charge transport mechanisms.

## Contribution

It demonstrates that the localization length determines the electric field dependence of mobility, contrasting with the traditional focus on site concentration in the literature.

## Key findings

- Mobility dependence on electric field is governed by localization length a.
- Site concentration N^{-1/3} does not influence the field dependence of mobility.
- Effective temperature combines electric field and temperature through eFa.

## Abstract

Using analytical arguments and computer simulations we show that the dependence of the hopping carrier mobility on the electric field $\mu(F)/\mu(0)$ in a system of random sites is determined by the localization length $a$, and not by the concentration of sites $N$. This result is in drastic contrast to what is usually assumed in the literature for a theoretical description of experimental data and for device modeling, where $N^{-1/3}$ is considered as the decisive length scale for $\mu(F)$. We show that although the limiting value $\mu(F \rightarrow 0)$ is determined by the ratio $N^{-1/3}/a$, the dependence $\mu(F)/\mu(0)$ is sensitive to the magnitude of $a$, and not to $N^{-1/3}$. Furthermore, our numerical and analytical results prove that the effective temperature responsible for the combined effect of the electric field $F$ and the real temperature $T$ on the hopping transport via spatially random sites can contain the electric field only in the combination $eFa$.