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Analysis of a hybrid model for the electro-thermal behavior of semiconductor heterostructures
Weierstrass Institute for Applied Analysis and Stochastics, DEU.ORCID iD: 0000-0003-1995-5491
Weierstrass Institute for Applied Analysis and Stochastics, DEU.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Weierstrass Institute for Applied Analysis and Stochastics, DEU.ORCID iD: 0000-0002-4403-6908
2022 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 507, no 2, article id 125815Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2022. Vol. 507, no 2, article id 125815
Keywords [en]
Drift-diffusion, Charge & heat transport, Electro-thermal interaction, Semiconductor heterostructures, Hybrid modeling, Weak solutions
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-88383DOI: 10.1016/j.jmaa.2021.125815ISI: 000775539700015Scopus ID: 2-s2.0-85119611635OAI: oai:DiVA.org:kau-88383DiVA, id: diva2:1635139
Funder
German Research Foundation (DFG)
Note

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.

Available from: 2022-02-04 Created: 2022-02-04 Last updated: 2022-08-10Bibliographically approved

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Nika, Grigor

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