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 generalise 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 sp-band state or from an sp-band state to another sp-band state. We apply this formalism to spherical silver nanoparticles with radii up to 20~nm and also study the dependence of hot carrier rates on the energy of the d-bands. We find that for nanoparticles with a radius less than 2.5~nm sp-band state to sp-band state transitions dominate hot carrier production while d-band state to sp-band state transitions give the largest contribution for larger nanoparticles.