Interpretation of Apparent Activation Energies for Electron Transport in Dye-sensitized Nanocrystalline Solar Cells

Electron transport in dye-sensitized nanocryst. solar cells appears to be a slow diffusion-controlled process. Values of the apparent electron diffusion coeff. are many orders of magnitude smaller than those reported for bulk anatase. The slow transport of electrons was attributed to multiple trapping (MT) at energy levels distributed exponentially in the band gap of the nanocryst. oxide. In the MT model, release of immobile electrons from occupied traps to the conduction band is a thermally-activated process, and it can be expected that the apparent electron diffusion coeff. should depend on temp. In fact, rather small activation energies (0.1-0.25 eV) were derived from time- and frequency-resolved measurements of the short-circuit photocurrent. 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 relation between changes in the densities of free and trapped electrons. This conclusion is confirmed by exact numerical solns. of the time-dependent generation/collection problem for periodic excitation that provide a good fit to exptl. data.