Christoph Kirsch, University of North Carolina at Chapel Hill


Charge carrier transport in organic photovoltaic cells

Abstract: We present our current state of research in the development of a mathematical model for polymer solar cell devices with a three-dimensional, periodic nanostructure. These photonic crystal films enhance the absorption of light and are expected to increase solar cell efficiency. Our mathematical model for the charge carrier transport in the solar cell device combines a classical physics driven semiconductor device model (van Roosbroeck, 1950) with the Onsager-Braun theory of electric field assisted exciton dissociation; it is thus both an extension to 3D space and a generalization to multiple materials of a 1D model developed by Koster et al. in 2005. A system of nonlinear partial differential equations (drift-diffusion-Poisson equations) in three space dimensions needs to be solved for the numerical simulation. We use a Gauss-Seidel type iterative method to obtain a sequence of linear PDEs; these are solved numerically with an exponential upwinding scheme, to handle both the exponential variation and the jump discontinuities in the PDE coefficients. Solar cell efficiency factors are computed from the current-voltage characteristic obtained by numerical simulation. This work is carried out in an interdisciplinary project on the design, fabrication and optimization of photonic crystal solar cells, which involves scientists from applied mathematics, chemistry and physics.

Mentor: Sorin Mitran (University of North Carolina at Chapel Hill)