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arXiv · 1206.6522

Analytical and Numerical Study of Photocurrent Transients in Organic Polymer Solar Cells

Carlo de Falco·Riccardo Sacco·Maurizio Verri
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Abstract

This article is an attempt to provide a self consistent picture, including existence analysis and numerical solution algorithms, of the mathematical problems arising from modeling photocurrent transients in Organic-polymer Solar Cells (OSCs). The mathematical model for OSCs consists of a system of nonlinear diffusion-reaction partial differential equations (PDEs) with electrostatic convection, coupled to a kinetic ordinary differential equation (ODE). We propose a suitable reformulation of the model that allows us to prove the existence of a solution in both stationary and transient conditions and to better highlight the role of exciton dynamics in determining the device turn-on time. For the numerical treatment of the problem, we carry out a temporal semi-discretization using an implicit adaptive method, and the resulting sequence of differential subproblems is linearized using the Newton-Raphson method with inexact evaluation of the Jacobian. Then, we use exponentially fitted finite elements for the spatial discretization, and we carry out a thorough validation of the computational model by extensively investigating the impact of the model parameters on photocurrent transient times.

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Carlo de Falco, Riccardo Sacco, Maurizio Verri. 2012-06-27. Analytical and Numerical Study of Photocurrent Transients in Organic Polymer Solar Cells. https://doi.org/10.1016/j.cma.2010.01.018

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