We have examined the combined effects of grain morphology and electron trapping on the transient response of photoelectrons moving through the TiO2 grains in a dye-sensitized nanocrystalline solar cell using a multitime-scale random walk Monte Carlo model. Our use of a multi-time-scale approach enables us to simulate transport for electrons moving through spherical connected grains in a three-dimensional (3D) voided network and look at the effect of the size of interparticle boundaries on carrier dynamics. We can also address similar times to those over which measurements are taken, namely, 0.1 ins. These times are long because of deep traps in the TiO2 grains. The grains have 2-fold connectivity in one dimension (linear chains) or 4-fold or 6-fold connectivity in three dimensions and traps with an exponential distribution of energies. Photoelectrons are generated by a light pulse of short duration. The spatial distribution of the photogenerated electron density from this pulse either has a uniform profile or is peaked on the electrolyte side. We show that the constrictions at the grain necks slow the electrons, making trapping more likely and hence further delaying their passage to the extracting electrode. By comparing our results for 4-fold and 6-fold coordinated particles on a cubic lattice with 2-fold coordinated particles on linear chains, we show that transport is slowed in the former case due to the additional paths available to the electrons in the 3D network. We also find that the charge and current transients cannot be fit to an analytical solution of the continuum equations with an effective diffusion coefficient even at long times. Therefore, caution must be exercised when attempting to fit experimental transient data with an effective diffusion coefficient.
Cass, M. J., Walker, A. B., Martinez, D., & Peter, L. M. (2005). Grain morphology and trapping effects on electron transport in dye-sensitized nanocrystalline solar cells. Journal of Physical Chemistry B, 109(11), 5100-5107. https://doi.org/10.1021/jp047073f