| Issue |
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
|
|
|---|---|---|
| Page(s) | 833 - 856 | |
| DOI | https://doi.org/10.1051/m2an/2024021 | |
| Published online | 24 May 2024 | |
An interface formulation for the poisson equation in the presence of a semiconducting single-layer material
1
Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK, 38000 Grenoble, France
2
Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes” – CNR, Via Ferrata 1, 27100 Pavia, Italy
* Corresponding author: clement.jourdana@univ-grenoble-alpes.fr
Received:
25
January
2023
Accepted:
21
March
2024
In this paper, we consider a semiconducting device with an active zone made of a single-layer material. The associated Poisson equation for the electrostatic potential (to be solved in order to perform self-consistent computations) is characterized by a surface particle density and an out-of-plane dielectric permittivity in the region surrounding the single-layer. To avoid mesh refinements in such a region, we propose an interface problem based on the natural domain decomposition suggested by the physical device. Two different interface continuity conditions are discussed. Then, we write the corresponding variational formulations adapting the so called three-fields formulation for domain decomposition and we approximate them using a proper finite element method. Finally, numerical experiments are performed to illustrate some specific features of this interface approach.
Mathematics Subject Classification: 35J20 / 65N30 / 65N55 / 65Z05
Key words: Poisson equation / interface model / domain decomposition / saddle-point problem / finite element method / single-layer material / graphene field-effect transistor
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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