Modeling carrier transport and electric field evolution in Gaussian disordered organic field-effect transistors

Stimulated by the time resolved microscopic optical second-harmonic generation (TRM-SHG) experiment, we model the carriers transport and electric field evolution in the channel of three-dimensional Gaussian disordered organic field-effect transistors (OFETs) by the coupled time-dependent master equation and Poisson equation. We show that this model with the Miller-Abrahams rate can satisfactorily account for the experimental observations that include different profiles of the electric field in the channel and the diffusionlike migration of the field peaks with respect to time. Particularly, we find that the dynamic mobility proposed by us earlier is distinct from the standard one in the presence of a typical disorder, which is attributed to the uncompleted energy relaxation of the carriers in the transport process.