Intensity dependence of the back reaction and transport of electrons in dye-sensitized nanacrystalline TiO2 solar cells

The lifetime tau(n) and diffusion coefficient D-n 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, tau(n) was found to be inversely proportional to the square root of the steady-state light intensity, I-0, whereas D-n varied with I-0(0.68). The intensity dependence of tau(n) is interpreted as evidence that the back reaction of electrons with I-3(-) may be second order in electron density. The intensity dependence of D-n is attributed to an exponential trap density distribution of the form N-t(E) proportional to exp[-beta(E - E-c)/(k(B)T)] with beta approximate to 0.6. Since tau(n) and D-n vary with intensity in opposite senses, the calculated electron diffusion length L-n = (D(n)tau(n))(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.