Influence of the Network Geometry on Electron Transport in Nanoparticle Networks

Computer simulations are applied to understand the influence of network geometry on the electron transport dynamics in random nanoparticle networks, and the predicted results are compared with those measured in one class of random nanoparticle networks: dye-sensitized nanocrystalline TiO₂ solar cells. The model is applicable to all classes of random nanoparticle networks, such as highly disordered quantum dot arrays. The random nanoparticle networks are simulated by the step-wise condensation of a diffusion-limited aggregate. 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 of TiO₂ nanoparticle films. Electron transport on the computer-generated networks is simulated by random walk. The experimental measurements and random-walk simulations are found to be in quantitative agreement. For both a power-law dependence of the electron diffusion coefficient D on the film porosity P is found as described by the relation: D ∝ | P-P_c |^μ. This power-law relation can also be derived from percolation theory, although only qualitatively. The critical porosity P_c (percolation threshold) and the conductivity exponent μ are found to be 0.76 ± 0.01 and 0.82 ± 0.05, respectively. It is estimated that during their respective transit through 50 and 75% porous 10-μm thick films as employed in the dye-cell, the average number of particles visited by electrons increases by 10-fold, from 10⁶ to 10⁷.