Effect of Nonuniform Generation and Inefficient Collection of Electrons on the Dynamic Photocurrent and Photovoltage Response of Nanostructured Photoelectrodes

This paper investigates how nonuniform generation and inefficient collection of electrons influence the dynamic photocurrent and photovoltage response of nanostructured photoelectrodes. The standard diffusion model theory of small amplitude light intensity modulated photocurrent (IMPS) and photovoltage (IMVS) spectroscopy is refined and generalized to an arbitrary electron generation profile, allowing straightforward coupling to any optical model. Expressions are derived for the local electron concentration and IMPS and IMVS transfer functions, for localized, uniform, and exponential generation profiles. Both limited collection and nonuniform generation of electrons modify the photoelectrode thickness (d) dependence of the characteristic IMPS and IMVS time constants and complicate their interpretation. This can lead to significant overestimation of the electron diffusion coefficient, diffusion length, and collection efficiency when using common approximate relations. With near contact electron generation, the IMPS response exhibits two time constants, only the slower one of which corresponds to electron transport across the film and scales with d. In the presence of this effect it is possible that in case of two equally thick samples, the one with smaller electron diffusion coefficient displays apparently faster electron transport. These errors demonstrated by experimental IMPS data of pressed TiO2 photoelectrodes can be minimized by using modulated light incident from the counter electrode side and avoided when analyzing the ratio of IMPS at opposite directions of illumination.