Analysis of a drift-diffusion model for perovskite solar cells
Authors
- Abdel, Dilara
ORCID: 0000-0003-3477-7881 - Glitzky, Annegret
ORCID: 0000-0003-1995-5491 - Liero, Matthias
ORCID: 0000-0002-0963-2915
2020 Mathematics Subject Classification
- 35K55 35B45 78A35, 35Q81
Keywords
- Drift-diffusion system, perovskite solar cells, charge transport, existence and boundedness of weak solutions, non-Boltzmann statistics
DOI
Abstract
This paper deals with the analysis of an instationary drift-diffusion model for perovskite solar cells including Fermi--Dirac statistics for electrons and holes and Blakemore statistics for the mobile ionic vacancies in the perovskite layer. The free energy functional is related to this choice of the statistical relations. Exemplary simulations varying the mobility of the ionic vacancy demonstrate the necessity to include the migration of ionic vacancies in the model frame. To prove the existence of weak solutions, first a problem with regularized state equations and reaction terms on any arbitrarily chosen finite time interval is considered. Its solvability follows from a time discretization argument and passage to the time-continuous limit. Applying Moser iteration techniques, a priori estimates for densities, chemical potentials and the electrostatic potential of its solutions are derived that are independent of the regularization level, which in turn ensure the existence of solutions to the original problem.
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