Intensity Dependence of the Back Reaction and Transport of Electrons in Dye-Sensitized Nanocrystalline TiO₂Solar Cells

The lifetime τn and diffusion coefficient Dn of photoinjected electrons have been measured in a dye-sensitized nanocrystalline TiO2 solar cell over 5 orders of magnitude of illumination intensity using intensity-modulated photovoltage and photocurrent spectroscopies. τn was found to be inversely proportional to the square root of the steady-state light intensity, I0, whereas Dn varied with I00.68. The intensity dependence of τn is interpreted as evidence that the back reaction of electrons with I3- may be second order in electron density. The intensity dependence of Dn is attributed to an exponential trap density distribution of the form Nt(E) ∝ exp[−β(E − Ec)/(kBT)] with β ≈ 0.6. Since τn and Dn vary with intensity in opposite senses, the calculated electron diffusion length Ln = (Dnτn)1/2 falls by less than a factor of 5 when the intensity is reduced by 5 orders of magnitude. The incident photon to current efficiency (IPCE) is predicted to decrease by less than 10% over the same range of illumination intensity, and the experimental results confirm this prediction.