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

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 nondimensionalization, 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.

Solution of drift-diffusion models for Organic Light Emitting Diodes (OLEDs)

“…In one of the papers supporting the development of ChargeTransport.jl [22], Abdel et al [8] proved the convergence of their finite volume scheme for non-Boltzmann statistics and demonstrated that their code functions in accordance with their theoretical work. A strength of finite volume methods, such as those developed by Abdel et al [8] is that they are designed to ensure that physical quantities are conserved and that fluxes are estimated accurately. While ChargeTransport.jl was developed with the aim of modelling perovskite solar cells, one possibility for further work would be to explore whether ChargeTransport.jl could be modified to model OLEDs.…”

“…As a result, the literature that deals with modelling and numerical solution of the latter is directly relevant to modelling and simulating OLEDs. Examples of such works include [5,6,7,8,9,10].…”