Drift-diffusion modeling, analysis and simulation of organic semiconductor devices
- Doan, Duy Hai
- Glitzky, Annegret
- Liero, Matthias
2010 Mathematics Subject Classification
- 35J55 78A35 82A57 82A70 65N08
- Drift-diffusion system, organic semiconductor, charge transport, existence of weak solutions, Gauss-Fermi statistics
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 so-called Gauss-Fermi statistics, 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. Finally, we discuss the numerical discretization of the model using finite-volume methods and a generalized Scharfetter-Gummel scheme for the Gauss-Fermi statistics.