Conditions for diffusion-limited and reaction-limited recombination in nanostructured solar cells

The performance of Dye-sensitized solar cells (DSC) and related devices made of nanostructured semiconductors relies on a good charge separation, which in turn is achieved by favoring charge transport against recombination. Although both processes occur at very different time scales, hence ensuring good charge separation, in certain cases the kinetics of transport and recombination can be connected, either in a direct or an indirect way. In this work, the connection between electron transport and recombination in nanostructured solar cells is studied both theoretically and by Monte Carlo simulation. Calculations using the Multiple-Trapping model and a realistic trap distribution for nanostructured TiO₂ show that for attempt-to-jump frequencies higher than 10¹¹–10¹³ Hz, the system adopts a reaction limited (RL) regime, with a lifetime which is effectively independent from the speed of the electrons in the transport level. For frequencies lower than those, and depending on the concentration of recombination centers in the material, the system enters a diffusion-limited regime (DL), where the lifetime increases if the speed of free electrons decreases. In general, the conditions for RL or DL recombination depend critically on the time scale difference between recombination kinetics and free-electron transport. Hence, if the former is too rapid with respect to the latter, the system is in the DL regime and total thermalization of carriers is not possible. In the opposite situation, a RL regime arises. Numerical data available in the literature, and the behavior of the lifetime with respect to (1) density of recombination centers and (2) probability of recombination at a given center, suggest that a typical DSC in operation stays in the RL regime with complete thermalization, although a transition to the DL regime may occur for electrolytes or hole conductors where recombination is especially rapid or where there is a larger dispersion of energies of electron acceptors.