Linking optical and electrical small amplitude perturbation techniques for dynamic performance characterization of dye solar cells

This paper unifies the analytical models used widely but thus far mostly separately for electrical and optical small amplitude perturbation measurements of nanostructured electrochemical dye solar cells (DSC): electrochemical impedance spectroscopy (EIS), intensity-modulated photocurrent spectroscopy (IMPS) and intensity-modulated photovoltage spectroscopy (IMVS). The models are linked by expressing the kinetic boundary condition used for solving the time-dependent continuity equation of electrons in IMPS and IMVS analysis in terms of the series and parallel impedance components found in the complete equivalent circuit impedance model of DSC. As a result, analytical expressions are derived for potentiostatic IMPS and galvanostatic IMVS transfer functions of complete DSCs that are applicable at any operating point along the solar cell current-voltage (IV) curve. In agreement with the theory, impedance spectrum calculated as a ratio of IMVS and IMPS transfer functions measured near the maximum power point matches exactly with the impedance spectrum measured directly with EIS. Consequently, both IMPS-IMVS and EIS yield equal estimates for the electron diffusion length. The role of the chemical capacitance of the nanostructured semiconductor photoelectrode in the interpretation of the so-called RC attenuation of the IMPS response is clarified, as well as the capacitive frequency dispersion in IMPS and IMVS.