  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 L^2 error as well as a physically and analytically meaningful
relative entropy.
