Theory of Photoinjection of Hot Plasmonic Carriers from Metal Nanostructures into Semiconductors and Surface Molecules

We investigate theoretically the effects of generation and injection of plasmonic carriers from an optically excited metal nanocrystal to a semiconductor contact or to surface molecules. The energy distributions of optically excited hot carriers are dramatically different in metal nanocrystals with large and small sizes. In large nanocrystals, the majority of hot carriers has very small excitation energies, and the excited-carrier distribution resembles the case of a plasmon wave in bulk. For nanocrystal sizes smaller than 20 nm, the carrier distribution extends to larger energies and occupies the whole region EF < ε < EF + ℏω. The physical reason for the above behaviors is nonconservation of momentum in a nanocrystal. Because of the above properties, nanocrystals of small sizes are most suitable for designing opto-electronic and photosynthetic devices based on injection of plasmonic electrons and holes. For gold nanocrystals, the optimal sizes for efficient generation of hot carriers with overbarrier energies are in the range of 10–20 nm. Another important factor is the polarization of the exciting light. For efficient excitation of carriers with high energies, the electric-field polarization vector should be perpendicular to a prism-like nanoantenna (slab or platelet). We also show the relation between our theory for injection from plasmonic nanocrystals and the Fowler theory of injection from a bulk metal. Along with a prism geometry (or platelet geometry), we consider cubes. The results can be applied to design both purely solid-state opto-electronic devices and systems for photocatalysis and solar-energy conversion.