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

TL;DR

This paper develops a comprehensive mathematical and numerical framework to analyze photocurrent transients in organic polymer solar cells, emphasizing exciton dynamics and device turn-on times.

Contribution

It introduces a reformulated model with existence proofs and implements a robust numerical scheme combining semi-discretization, Newton-Raphson linearization, and finite elements.

Findings

Validated the computational model through extensive parameter analysis.

Highlighted the role of exciton dynamics in device turn-on time.

Provided a self-consistent approach for modeling photocurrent transients.

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.