Determination of the Electron Diffusion Length in Dye-Sensitized Solar Cells by Random Walk Simulation: Compensation Effects and Voltage Dependence

The diffusion length is a crucial parameter controlling the electron collection efficiency in dye-sensitized solar cells (DSCs). In this work, we carry out a direct computation of this parameter for a DSC with a short diffusion length by running a random walk numerical simulation with an exponential distribution of trap states and explicit incorporation of recombination. The diffusion length and the lifetime are estimated from the average distance traveled and the average survival time of the electrons between recombination events. The results demonstrate the well-known compensation effect between diffusion and recombination that keeps the diffusion length approximately constant on a wide range of illumination intensities or applied biases. The assumptions considered in the present model indicate that the two alternative views described in the literature to rationalize this effect (either "dynamic" or "static") are equivalent. As a further development of the model, we introduce a recombination probability that depends exponentially on the Fermi level. This leads to a nonconstant diffusion length, as shown in recent experiments.