Evaluation of the Charge-Collection Efficiency of Dye-Sensitized Nanocrystalline TiO2 Solar Cells

Intensity modulated photovoltage spectroscopy (IMVS) and intensity modulated photocurrent spectroscopy (IMPS) are used to evaluate the charge-collection efficiency of dye-sensitized nanocrystalline TiO₂ solar cells. The charge-collection efficiency of the photoinjected electrons from dye sensitization is estimated from the respective time constants for charge recombination at open circuit τ_oc and the combined processes of charge collection and charge recombination at short circuit rsc obtained by IMVS and IMPS measurements. Three models are developed for relating the charge-collection efficiency to τ_oc/τ_sc. The first model determines the charge-collection efficiency from τ_oc/τ_sc without considering the underlying physical processes measured by IMVS and IMPS. The second model obtains τ_oc/τ_sc by simulating the frequency response of IMVS and IMPS from the time-dependent continuity equation for simplified conditions. The third model determines the time constants for IMVS and IMPS from electron-concentration profiles calculated for constant light intensity and more realistic conditions. To obtain a realistic steady-state electron concentration profile, a nonlinear dependence of the rate of recombination on the electron concentration in the TiO₂ film is considered. Furthermore, the continuity equation is modified to account for charge trapping and detrapping. For the first time, expressions are derived for calculating the time constants from the steady-state electron concentration profile. The validity of this method is demonstrated for the second model from which the exact IMPS and IMVS responses are calculated. The three models are compared with each other. A simple expression is derived for calculating the charge-collection efficiency from the measured values of τ_oc/τ_sc and the light intensity dependence of τ_oc.