Influence of the Percolation Network Geometry on Electron Transport in Dye-Sensitized Titanium Dioxide Solar Cells

Percolation theory is applied to understand the influence of network geometry on the electron transport dynamics in dye-sensitized nanocrystalline TiO2 solar cells, and the predicted results are compared with those measured by transient photocurrent. The porosity of the films was varied experimentally from 52 to 71%. Electron transport was modeled using simulated mesoporous TiO2 films, consisting of a random nanoparticle network, and the random-walk approach. The electron transport pathway through the network was correlated with the film porosity and the coordination numbers of the particles in the film. The experimental measurements and random-walk simulations were in quantitative agreement with percolation theory, which predicts a power-law dependence of the electron diffusion coefficient D on the film porosity as described by the relation: D ∝ |P − Pc|μ. The critical porosity Pc (percolation threshold) and the conductivity exponent μ were found to be 0.76 ± 0.01 and 0.82 ± 0.05, respectively. The fractal dimension of the nanoparticle films was estimated from the simulations to be 2.28, which is in quantitative agreement with gas-sorption measurements. It is shown that as the porosity increases, the distribution of the coordination numbers of the particles shifts from an emphasis on high coordination numbers to low ones, causing the electron transport pathway to become more tortuous and electron transport to slow. Another consequence of increasing the porosity is that the fraction of terminating particles (dead ends) in the TiO2 film increases markedly, from less than 1% for a 50% porous film to 31% for a 75% porous film. It is estimated that during their respective transit through 50 and 75% porous 10-μm thick films, the average number of particles visited by electrons increases by 10-fold, from 106 to 107. This study provides the first clear evidence that network topology has a strong influence on the electron transport dynamics in mesoporous TiO2 films.