WIAS Preprint No. 2958, (2022)

Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells



Authors

  • Abdel, Dilara
  • Chainais-Hillairet, Claire
  • Farrell, Patricio
    ORCID: 0000-0001-9969-6615
  • Herda, Maxime

2020 Mathematics Subject Classification

  • 35Q81 35K57 65M08

Keywords

  • Perovskite solar cells, perovskite, semiconductor devices, drift-diffusion equations, finite volume methods, entropy-dissipation inequality

DOI

10.20347/WIAS.PREPRINT.2958

Abstract

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.

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