Semiconductors involved in photocatalysis and water splitting often exhibit a bandgap in the UV, which represents only a few percents of the solar spectrum. This drastically limits photogeneration by direct interband absorption inside a semiconductor for solar driven photocatalysis.
In this frame, photogeneration of hot electrons in a metallic structure and their injection into an adjacent semiconductor is a crucial mechanism since it allows generating electrons in the conduction band of the semiconductor with incident photon energies larger than the energy barrier between the two media, however, in general much smaller than the bandgap of the semiconductor. This leads to an increase of the spectral range of photon energies participating to photocatalysis, e.g., a substantial part of the solar spectrum can be used.
The theoretical efficiency of the hot electron injection process can be described by Fowler’s law  that quantifies the percentage of hot electrons that carry kinetic energy from their velocity component normal to the surface larger than the energy barrier at the metal-semiconductor interface. This assumes a homogeneous distribution of initial energy of hot electrons and isotropic initial propagation directions. Using this model, the injection efficiency as a function of the incident photon energy is a square law and doesn’t exceed a few percents for a gold-titania system.
Some studies reported injection efficiencies that follow Fowler’s law  , but other studies also reported values up to 50%, and independent of the incident photon energy   . In this work, we quantify the limits of the hot electron injection efficiency by analyzing the ballistic transport of hot electrons in metallic nanostructures, and we compare these limits with the values reported in the studies mentioned previously. For a gold-titania system, we show that the size and shape of the gold nanostructure can increase the injection efficiency beyond what is possible when the planar interface between two half spaces of metal and semiconductor is considered. Additional effects that modify the propagation direction of the electrons can also increase the efficiency, such as electron-phonon scattering events and diffuse reflections at the interface. This is due to the fact that modifications of the propagation direction increase the probability that the propagation direction matches with the escape cone at the interface.
Nevertheless, the maximum efficiencies calculated are still far from those reported in   , which suggest that additional effects, such as surface effects  , are predominant.
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