Comparing three numerical methods for current–voltage characteristics simulations of organic solar cells considering surface recombination effects

In this paper, three different numerical approaches were used for solving the steady-state drift–diffusion model (DDM) of organic solar cells. In order to simplify the standard DDM, the electron and hole continuity equations were decoupled by assuming a recombination rate for each type of carriers proportional to its concentration squared and a constant electric field throughout a device. The surface recombination and thermionic emission of electrons and holes on both electrode contacts were considered through Robin-type boundary conditions. The most often used numerical solution based on the finite difference method with Schaffeter-Gummel discretization (FDMSG) showed significant instabilities when certain surface recombination velocities (SRVs) were reduced. Trying to avoid instabilities, a Discontinuous Galerkin method with Lax-Friedricks numerical flux (DGLF) was proposed. The DGLF calculations turned out to be even more unstable than the FDMSG ones. To improve the developed Discontinuous Galerkin scheme, the Schaffeter-Gummel numerical flux was implemented (DGSG). A significant progress in the calculation stability has been achieved for a wide range of SRVs. Using each of the considered numerical models, the intervals of SRVs for which the electrode contacts act as (1) ideally blocking, (2) neither blocking nor conductive, or (3) ideally conductive, were defined for holes and electrons. The SRV ranges in which the calculation instabilities occur were determined for each numerical approach. The current density–voltage ( J – V ) characteristics simulated by the DDM and solved with the DGSG method were compared to a measured ITO/PEDOT:PSS/P3HT:PCBM/Al solar cells J – V curve for model validation.