The efficiency of most semiconductor photoelectrodes for water splitting is limited by a slow reaction with electrolyte and a fast recombination. Among the recombination pathways, trap-mediated recombination due to doping and material processing is often the dominant process. Impedance spectroscopy under illumination is a popular and powerful method to investigate time constants of recombination and reaction. Traditionally, an equivalent circuit is involved in the analysis of impedance spectroscopy, nevertheless, it provides limited direct information about the microscopic quantities related to diffusion, reaction, and recombination. In the present study, a theoretical model for diffusion-limited photocurrent under small voltage bias and its application for the simplified evaluation of equivalent circuits for impedance analysis are presented. Full numerical simulations of the semiconductor transport equations are used to validate the theoretical model for typical values of carrier lifetime. This combination of theoretical approximations, equivalent circuit models, and full simulations provides an important background for the analysis of recombination and transport properties of photoelectrode materials.
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