Dye-sensitized solar cells (DSC) are based on a porous, nanostructured metal oxide film sensitized by a dye with a large absorption coefficient in the visible. The transport properties of the solar cell are complicated as both the electron diffusion coefficient in the metal oxide film and the lifetimes are generally found to be dependent on electron density. Electron transport is usually assumed to be limited by trapping and de-trapping of electrons in states in the band gap. Recombination corresponds to the process of transfer of photogenerated electrons to acceptors in the solution or to oxidized dye molecules, leading to a decrease in the efficiency of the cell. The continuity equation describing these processes consists of a second order, non-linear differential equation which cannot be solved analytically.
In this work, we have extended a previous numerical model [J. Phys. Chem. B, 2006, 110, 5372], suitable to obtain current-voltage characteristics under these premises. We pay especial attention to the recombination mechanism and study two alternative models: electron transport limited and electron transfer limited recombination. We obtain mathematical expressions to reproduce experimental open-circuit voltage decays and discuss their relationship to the “quasi-static” approximation of Walker et al. [J. Phys. Chem. B 2006, 110, 25504]. The model is also used to make theoretical predictions on the thickness dependence of the short-circuit current [Ito et al. Adv. Mater. 2006, 18, 1202].