On a drift‐diffusion model for perovskite solar cells

Abstract We introduce a vacancy‐assisted charge transport model for perovskite solar cells. This instationary drift‐diffusion system describes the motion of electrons, holes, and ionic vacancies and takes into account Fermi–Dirac statistics for electrons and holes and the Fermi–Dirac integral of order for the mobile ionic vacancies in the perovskite. The free energy functional we work with corresponds to that choice of the statistical relations. To verify the existence of weak solutions, we consider a problem with regularized state equations and reaction terms on any arbitrarily chosen finite time interval. We motivate its solvability by time discretization and passage to the time‐continuous limit. A priori estimates for the chemical potentials that are independent of the regularization level ensure the existence of solutions to the original problem. These types of estimates rely on Moser iteration techniques and can also be obtained for solutions to the original problem.