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

Abstract

In this article, we deal with the mathematical modeling and numerical simulation of photocurrent transients in nanoscale mono-layer Organic polymer Solar Cells (OSCs). The mathematical model consists of a system of non-linear 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 which makes it similar to the classical drift-diffusion system for inorganic semiconductor devices. This allows us, on the one hand, to prove the existence of a solution for the problem in both stationary and transient conditions and, on the other hand, 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