2022/09/16 by Dilara Abdel, Abdel, Dilara, Claire Chainais-Hillairet +5 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Material Dynamics and Properties #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2209.07934
openalex publication_date 2022/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.