Identifying Pitfalls when using the Miller-Abrahams Rate in Kinetic Monte Carlo Simulations

Abstract

The conventional Miller-Abrahams (MA) rate is a frequently applied rate for modeling hopping transport of charges or excitons in organic semiconductors. However, the expression known as Miller-Abrahams rate is an approximation that has a more limited range of validity than the original, full expression. We study the effect of either rates in Kinetic Monte Carlo simulations on the resulting charge carrier mobility in OFET and OLED structures. We find significant differences for small disorders as well as for high electric fields. While the original, full expression predicts an increase and finally saturation of the mobility with temperature and field, the conventional (approximated) MA rate erronenously yields a decreasing mobility with temperature and field. We demonstrate that this results from the constant rate for energetically downward carrier jumps in the conventional, approximated MA rate in contrast to the full rate where downwards jumps accelerate with increasing energy difference and discuss the physical origin of this. This aspect becomes relevant when downward jumps are rate-limiting, e.g. for small disorders or high fields.