Interpretation of apparent activation energies for electron transport in dye-sensitized nanocrystalline solar cells

Electron transport in dye-sensitized nanocrystalline solar cells appears to be a slow diffusion-controlled process. Values of the apparent electron diffusion coefficient are many orders of magnitude smaller than those reported for bulk anatase. The slow transport of electrons has been attributed to multiple trapping (MT) at energy levels distributed exponentially in the band gap of the nanocrystalline oxide. In the MT model, release of immobile electrons from occupied traps to the conduction band is a thermally activated process, and it might therefore be expected that the apparent electron diffusion coefficient should depend strongly on temperature. In fact, rather small activation energies (0.1-0.25 eV) have been derived from time and frequency resolved measurements of the short circuit photocurrent. It is shown that the MT model can give rise to such anomalously low apparent activation energies as a consequence of the boundary conditions imposed by the short circuit condition and the quasi-static relationship between changes in the densities of free and trapped electrons. This conclusion has been confirmed by exact numerical solutions of the time-dependent generation/collection problem for periodic excitation that provide a good fit to experimental data.