Daniel Brinkman, Klemens Fellner, Peter A. Markowich, Marie-Therese Wolfram
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 are 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 for the interface. Secondly, we present a
twodimensional 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.
View original:
http://arxiv.org/abs/1202.0817
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