Analytical and numerical study of photocurrent transients in organic polymer solar cells |
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| Authors: | Carlo de Falco Riccardo Sacco Maurizio Verri |
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| Affiliation: | 1. School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, PR China;2. State Key Laboratory of Robotics and System (HIT), Harbin 150001, PR China;1. Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA;2. Department of Civil and Environmental Engineering, Duke University, Durham, NC 27708, USA;3. Department of Electrical Engineering, Pennsylvania State University, University Park, PA 16802, USA;4. Institute of Electromagnetics and Acoustics, Xiamen University, Xiamen, Fujian, 361005, China;1. Oden Institute for Computational Engineering & Sciences, University of Texas at Austin, Austin, TX 78712, USA;2. Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA;3. Institute of Electromagnetics and Acoustics, Xiamen University, Xiamen, Fujian 361005, China;1. Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano, Italy;2. IUPUI Department of Mathematical Sciences, 402 N. Blackford St., LD 270 E Indianapolis, IN 46202-3267, United States;3. ABB Switzerland Ltd., Corporate Research, Segelhofstrasse 1K 5405, Baden-Dättwil, Switzerland;4. MOX Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano, Italy;5. CEN Centro Europeo di Nanomedicina, Piazza L. da Vinci 32, 20133 Milano, Italy |
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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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