Quantifying and Elucidating Thermally Enhanced Minority Carrier Diffusion Length Using Radius-Controlled Rutile Nanowires

The minority carrier diffusion length (L_D) is a crucial property that determines the performance of light absorbers in photoelectrochemical (PEC) cells. Many transition-metal oxides are stable photoanodes for solar water splitting but exhibit a small to moderate L_D, ranging from a few nanometers (such as α-Fe₂O₃ and TiO₂) to a few tens of nanometers (such as BiVO₄). Under operating conditions, the temperature of PEC cells can deviate substantially from ambient, yet the temperature dependence of L_D has not been quantified. In this work, we show that measuring the photocurrent as a function of both temperature and absorber dimensions provides a quantitative method for evaluating the temperature-dependent minority carrier transport. By measuring photocurrents of nonstoichiometric rutile TiO_2-x nanowires as a function of wire radius (19-75 nm) and temperature (10-70 °C), we extract the minority carrier diffusion length along with its activation energy. The minority carrier diffusion length in TiO_2-x increases from 5 nm at 25 °C to 10 nm at 70 °C, implying that enhanced carrier mobility outweighs the increase in the recombination rate with temperature. Additionally, by comparing the temperature-dependent photocurrent in BiVO₄, TiO₂, and α-Fe₂O₃, we conclude that the ratio of the minority carrier diffusion length to the depletion layer width determines the extent of temperature enhancement, and reconcile the widespread temperature coefficients, which ranged from 0.6 to 1.7% K^-1. This insight provides a general design rule to select light absorbers for large thermally activated photocurrents and to predict PEC cell characteristics at a range of temperatures encountered during realistic device operation.