Organic solar cell physics analyzed by Shockley diode equation

The standard drift–diffusion model (DDM) was used for calculation of organic solar cells’ (OSCs) J–V characteristics under different assumption sets. One analytical (DDMA) and two numerical (DDMN1, DDMN2) solutions were obtained. In the DDMA, a Beer–Lambert absorption profile, a constant electric field and a monomolecular charge carrier recombination were used. Interference effects as well as space charge effects were included in numerical models. The monomolecular recombination mechanism was applied in the DDMN1, while the Langevin bimolecular recombination was assumed in the DDMN2. Simulated and measured J–V curves are compared for ITO/PEDOT:PSS/P3HT:PCBM/Al solar cells in the dark regime and under illumination. Experimentally obtained dark J–V curves are best reproduced by the DDMA, while the DDMN2 gives the best prediction for J–V characteristics under illumination. Additionally, it was shown that the recombination of holes and electrons can be neglected in the dark mode and a simple Shockley-like J(V) expression was derived from the DDMA. From our analysis, it can be concluded that in the dark regime the electric field in OSCs is homogeneous and electrons and holes recombine monomolecularly, although to a negligible extent. When the OSC is illuminated, the space charge effects become significant in the active layer, as well as the charge carrier recombination, which gains the bimolecular Langevine character.