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

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.