A Drift-Diffusion-Reaction Model for Excitonic Photovoltaic Bilayers: Asymptotic Analysis and A 2-D HDG Finite-Element Scheme

TL;DR

This paper develops a comprehensive mathematical model for organic photovoltaic bilayers, combining drift-diffusion, reaction, and electrostatic equations, and introduces a 2D hybrid finite element scheme with asymptotic analysis for improved simulation accuracy.

Contribution

It presents a coupled drift-diffusion-reaction model for bilayer organic photovoltaics and a novel 2D hybrid discontinuous Galerkin finite element scheme with asymptotic analysis.

Findings

Asymptotic analysis simplifies bulk dynamics away from the interface.

The 2D HDG finite element scheme effectively resolves material interfaces.

Numerical results align well with asymptotic approximations.

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 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.