We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/polaron pairs and Poisson's equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device is included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system: (i) with focus on the dynamics on the interface and (ii) with the goal of simplifying the bulk dynamics away from the interface. Secondly, we present a two-dimensional hybrid discontinuous Galerkin finite element numerical scheme which is very well suited to resolve: (i) the material changes, (ii) the resulting strong variation over the interface, and (iii) the necessary upwinding in the discretization of drift-diffusion equations. Finally, we compare the numerical results with the approximating asymptotics. © 2013 World Scientific Publishing Company.
|Original language||English (US)|
|Number of pages||34|
|Journal||Mathematical Models and Methods in Applied Sciences|
|State||Published - May 2013|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: The authors acknowledge support from King Abdullah University of Science and Technology (KAUST) Award Number: KUK-I1-007-43. P. A. M. also acknowledges support from the Fondation Sciences Mathematique de Paris, in form of his Excellence Chair 2011, and from the Royal Society through his Wolfson Research Merit Award. M.-T.W. acknowledges financial support from the Austrian Science Foundation (FWF) via the Hertha Firnberg project TU56-N23. K. F. acknowledges the support of NaWi Graz.
ASJC Scopus subject areas
- Modeling and Simulation
- Applied Mathematics