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.

The random walk numerical simulation (RWNS) method is used to compute diffusion coefficients for hopping transport in a fully disordered medium at finite carrier concentrations. We use Miller-Abrahams jumping rates and an exponential distribution of energies to compute the hopping times in the random walk simulation. The computed diffusion coefficient shows an exponential dependence with respect to Fermi-level and Arrhenius behavior with respect to temperature. This result indicates that there is a well-defined transport level implicit to the system dynamics. To establish the origin of this transport level we construct histograms to monitor the energies of the most visited sites. In addition, we construct ''corrected'' histograms where backward moves are removed. Since these moves do not contribute to transport, these histograms provide a better estimation of the effective transport level energy. The analysis of this concept in connection with the Fermi-level dependence of the diffusion coefficient and the regime of interest for the functioning of dye-sensitised solar cells is thoroughly discussed.

Electron transfer between nanostructured semiconductor oxides and redox active electrolytes is a fundamental step in many processes of technological interest, such as photocatalysis and dye-sensitized solar cells. It has been shown that the transfer kinetics in the dye-sensitized solar cell are determined simultaneously by trap-limited transport and by the relative energetics of donor and acceptor states in the semiconductor and electrolyte. In this work, the transport and recombination mechanisms of photogenerated electrons in dye-sensitized solar cells are modeled by random walk numerical simulations with explicit description of the electron transfer process in terms of the Marcus–Gerischer model. The recombination rate is computed as a function of Fermi level in order to extract the electron lifetime and its influence on the electron diffusion length. The simulation method allows one to relate the recombination reaction order to the trap distribution parameter, the band edge position, and the reorganization energy. The results show that a model involving electron transfer from both shallow and deep traps, coupled with transport via shallow states, adequately reproduces all the experimental phenomena, including the dependence of the electron lifetime and the electron diffusion length on the open-circuit voltage when either the conduction band or the redox potential are displaced. Nonlinear recombination is predicted when the electron diffusion length increases with Fermi level, which is correlated with a reaction order different from one, in an open-circuit voltage decay “experiment”. The results reported here are relevant to the understanding of the effect of using new electrolyte compositions and novel redox shuttles in dye-sensitized solar cells.

The collection efficiency of carriers in solar cells based on nanostructured electrodes is determined for different degrees or morphological one-dimensional order. The transport process is modeled by random walk numerical simulation in a mesoporous electrode that resembles the morphology of nanostructured TiO2 electrodes typically used in dye-sensitized solar cells and related systems. By applying an energy relaxation procedure in the presence of an external potential, a preferential direction is induced in the system. It is found that the partially ordered electrode can almost double the collection efficiency with respect to the disordered electrode. However, this improvement depends strongly on the probability of recombination. For too rapid or too slow recombination, working with partially ordered electrodes will not be beneficial. The computational method utilized here makes it possible to relate the charge collection efficiency with morphology. The collection efficiency is found to reach very rapidly a saturation value, meaning that, in the region of interest, a slight degree of ordering might be sufficient to induce a large improvement in collection efficiency.