Generation of plasmonic hot carriers from d-bands in metallic nanoparticles

We present an approach to master the well-known challenge of calculating the contribution of d-bands to plasmon-induced hot carrier rates in metallic nanoparticles. We generalize the widely used spherical well model for the nanoparticle wavefunctions to flat d-bands using the envelope function technique. Using Fermi's golden rule, we calculate the generation rates of hot carriers after the decay of the plasmon due to transitions from either a d-band state to an s-band state or from an s-band state to another s-band state. We apply this formalism to spherical silver nanoparticles of a wide range of sizes (from 5~nm to 65~nm) and find that d-to-s and s-to-s transitions have contributions of the same order of magnitude near the plasmon energy. For small nanoparticles with radii less than 65 nanometers s-band state to s-band state transitions are larger while for larger nanoparticles, d-band state to s-band state transitions give the greater contribution.