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.
Absorber material with high and stable p-type doping that does not impede free carrier lifetime is the key component enabling efficiency and stability improvements in thin-film CdTe technology. To better understand the compensation mechanism and the metastable effects related to Cu acceptors, the most common p-type dopant in CdTe, i.e., a detailed kinetic model describing the behavior of intrinsic and Cu-related defects in this material, has been developed and applied for the first time. Migration and reactions of these point defects in single crystal CdTe have been investigated by solving diffusion-reaction equations in the time-space domain self-consistently with free carrier transport. The simulation results supported by reasonable match to experimental data have shed light on the nature of limited Cu incorporation (also known as the Cu solubility limits) and Cu self-compensation during the annealing and cooling processes.
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