Nonthermalized electron transport in dye-sensitized nanocrystalline TiO2 films: Transient photocurrent and random-walk modeling studies

A random-walk approach is developed to model the electron-transport dynamic s in dye-sensitized TiO2 Solar cells within a multiple-trapping framework, and the predicted results are compared with those measured by transient pho tocurrent. The illumination geometry and the wavelength of the probe light are used to create certain initial spatial distributions of photoinjected e lectrons in the TiO2 films. Both have a dramatic effect on the shape of the measured photocurrent transient. Cells are probed with light incident from either the collecting (substrate) electrode side or the counter-electrode side. Excellent correspondence between simulated and measured current trans ients is observed. When electrons are injected far from the collecting elec trode, their diffusion is found to be classical, corresponding to thermaliz ed (nondispersive) transport. Nonthermalized (dispersive) electron transpor t is shown to be important when electrons are injected near the collecting electrode, which corresponds to the illumination condition under which the cell normally operates. For strongly absorbed light incident from the colle cting electrode side, it is estimated that about 80% of injected electrons are collected before they are within 95% of complete thermalization. Failur e to account for the presence of nonthermalized electrons is shown to be a major limitation of previous theories of electron transport. The total dens ity of trap states is estimated to be relatively small, on the order of I t rap per particle. The average detrapping time is on the order of 10 ns. Whe n electrons are generated far from the collecting electrode, they undergo a n average of about 10(6) trapping events before being collected. Analytical expressions are derived that relate the experimentally measured collection time to other parameters affecting transport (e.g., trap density, light in tensity, film thickness, and free-electron mobility). Experimental evidence is presented for ambipolar diffusion.