A coarse-grained electrothermal model for organic semiconductor devices
- Glitzky, Annegret
- Liero, Matthias
- Nika, Grigor
2020 Mathematics Subject Classification
- 35J57 35K05 78A35
- Drift-diffusion, charge & heat transport, electrothermal interaction, organic semiconductor, coarse-grained model, weak solutions
We derive a coarse-grained model for the electrothermal interaction of organic semiconductors. The model combines stationary drift-diffusion based electrothermal models with thermistor type models on subregions of the device and suitable transmission conditions. Moreover, we prove existence of a solution using a regularization argument and Schauder's fixed point theorem. In doing so, we extend recent work by taking into account the statistical relation given by the Gauss--Fermi integral and mobility functions depending on the temperature, charge-carrier density, and field strength, which is required for a proper description of organic devices.
- Math. Methods Appl. Sci., 45 (2022), pp. 4809--4833 (published on 26.01.2022), DOI 10.1002/mma.8072 .