Most photocatalytic and photovoltaic devices operate under broadband, constant illumination. Electron and hole dynamics in these devices, however, are usually measured by using ultrafast pulsed lasers in a narrow wavelength range. In this work, we use excited-state X-ray theory originally developed for transient X-ray experiments to study steady-state photomodulated X-ray spectra. We use this method to attempt to extract electron and hole distributions from spectra collected at a nontime-resolved synchrotron beamline. A set of plasmonic metal core-shell nanoparticles is designed as the control experiment because they can systematically isolate photothermal, hot electron, and thermalized electron-hole pairs in a TiO2 shell. Steady-state changes in the Ti L2,3 edge are measured with and without continuous-wave illumination of the nanoparticle's localized surface plasmon resonance. The results suggest that within error the quasi-equilibrium carrier distribution can be determined even from relatively noisy data with mixed excited-state phenomena. Just as importantly, the theoretical analysis of noisy data is used to provide guidelines for the beamline development of photomodulated steady-state spectroscopy.
Keywords: Bethe-Salpeter equation; X-ray absorption; X-ray spectroscopy; core−shell nanoparticles; hot carriers; photocatalysis; plasmonics.