Analysis of a hybrid model for the electrothermal behavior of semiconductor heterostructures
- Glitzky, Annegret
- Liero, Matthias
- Nika, Grigor
2010 Mathematics Subject Classification
- 35J57 35K05 35R05 78A35
- Drift-diffusion, charge & heat transport, electro-thermal interaction, semiconductor heterostructures, hybrid modeling, weak solutions
We prove existence of a weak solution for a hybrid model for the electro-thermal behavior of semiconductor heterostructures. This hybrid model combines an electro-thermal model based on drift-diffusion with thermistor type models in different subregions of the semiconductor heterostructure. The proof uses a regularization method and Schauder's fixed point theorem. For boundary data compatible with thermodynamic equilibrium we verify, additionally, uniqueness. Moreover, we derive bounds and higher integrability properties for the electrostatic potential and the quasi Fermi potentials as well as the temperature.