Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells
- Abdel, Dilara
- Chainais-Hillairet, Claire
- Farrell, Patricio
- Herda, Maxime
2020 Mathematics Subject Classification
- 35Q81 35K57 65M08
- Perovskite solar cells, perovskite, semiconductor devices, drift-diffusion equations, finite volume methods, entropy-dissipation inequality
In this paper, we consider a drift-diffusion charge transport model for perovskite solar cells, where electrons and holes may diffuse linearly (Boltzmann approximation) or nonlinearly (e.g. due to Fermi-Dirac statistics). To incorporate volume exclusion effects, we rely on the Fermi-Dirac integral of order −1 when modeling moving anionic vacancies within the perovskite layer which is sandwiched between electron and hole transport layers. After non-dimensionalization, we first prove a continuous entropy-dissipation inequality for the model. Then, we formulate a corresponding two-point flux finite volume scheme on Voronoi meshes and show an analogous discrete entropy-dissipation inequality. This inequality helps us to show the existence of a discrete solution of the nonlinear discrete system with the help of a corollary of Brouwer's fixed point theorem and the minimization of a convex functional. Finally, we verify our theoretically proven properties numerically, simulate a realistic device setup and show exponential decay in time with respect to the L2 error as well as a physically and analytically meaningful relative entropy.
- IMA J. Numer. Anal., (2023), pp. 1--40, DOI 10.1093/imanum/drad034 .