A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Photovoltaic bilayers: Asymptotic analysis and a 2D hdg finite element scheme

Daniel Brinkman, Klemens J. Fellner, Peter A. Markowich, Marie Therese Wolfram

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)839-872
Number of pages34
JournalMathematical Models and Methods in Applied Sciences
Volume23
Issue number05
DOIs
StatePublished - May 2013

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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