Temperature dependent normal and anomalous electron diffusion in porous TiO2 studied by transient surface photovoltage

A model system of nanoporous TiO2 sensitized with dye molecules at the outer surface is investigated by time resolved surface photovoltage SPV at temperatures between −120 °C and 270 °C to get information about electron diffusion over more than 10 orders of magnitude in time. The SPV transients increase in time due to independent electron diffusion and reach a maximum at a certain peak time due to reaching the screening length. The increasing parts of the SPV transients are characterized by a power law while the SPV power coefficient amounts to half of the dispersion parameter of anomalous diffusion. Anomalous diffusion is observed for times down to the duration time of the laser pulse 150 ps . With increasing temperature, the SPV power coefficient increases to its saturation value of 0.5 corresponding to normal diffusion. At lower temperatures, the SPV power coefficients decrease with increasing intensity of the exciting laser pulses. The decay of the SPV transients is determined by thermally activated normal diffusion. The minimal charge transfer time of an electron back to the positively charged dye molecule amounts to 2 ps which is obtained from thermally activated logarithmic decays.