Relaxation of Plasmon-Induced Hot Carriers

Plasmon-induced hot carrier generation has attracted much recent attention due to its promising potential in photocatalysis and other light harvesting applications. Here we develop a theoretical model fore hot carrier relaxation in metallic nanoparticles using a fully quantum mechanical jellium model. Following pulsed illumination, nonradiative plasmon decay results in a highly nonthermal distribution of hot electrons and holes. Using coupled master equations, we calculate the time dependent evolution of this carrier distribution in the presence of electron-electron, electron-photon, and electron-phonon scattering. Electron-electron relaxation is shown to be the dominant scattering mechanism and results in efficient carrier multiplication where the energy of the initial hot electron-hole pair is transferred to other multiple electron-hole pair excitations of lower energies. During this relaxation, a small but finite fraction of electrons scatter into luminescent states where they can recombine radiatively with holes by emission of photons. The energy of the emitted photons is found to follow the energies of the electrons and thus redshifts monotonically during the relaxation process. When the energies of the electrons approach the Fermi level, electron-phonon interaction becomes dominant and results in heating of the nanoparticle. We generalize the model to continuous-wave excitation and show how nonlinear effects become important when the illumination intensity increases. When the temporal spacing between incident photons is shorter than the relaxation time of the hot carriers, we predict that the photoluminescence will blueshift with increasing illumination power. Finally, we discuss the effect of the photonic density of states (Purcell factor) on the luminescence spectra.