Analysis of a drift–diffusion model for organic semiconductor devices

We discuss drift–diffusion models for charge carrier transport in organic semiconductor devices. The crucial feature in organic materials is the energetic disorder due to random alignment of molecules and the hopping transport of carriers between adjacent energetic sites. The former leads to statistical relations with Gauss–Fermi integrals, which describe the occupation of energy levels by electrons and holes. The latter gives rise to complicated mobility models with a strongly nonlinear dependence on temperature, density of carriers, and electric field strength. We present the state-of-the-art modeling of the transport processes and provide a first existence result for the stationary drift–diffusion model taking all of the peculiarities of organic materials into account. The existence proof is based on Schauder’s fixed-point theorem.