Hot electron relaxation in a metal nanoparticle: Electron surface-phonon interaction

Abstract

The relaxation of hot electrons is considered in a metal nanoparticle. When the particle size is of the order of electron mean free path, the main channel of hot electron energy loss is through surface-phonon generation, rather than bulk phonon generation. A calculation for the hot electron relaxation by the generation of surface-phonons is given, assuming that electrons and surface-phonons are described by their equilibrium Fermi and Bose distribution functions. The assumption is valid because the time required to establish equilibrium in the electron gas is much less than the time for achieving equilibrium between the electrons and the surface-phonons. The expressions obtained for low-temperature and high-temperature regimes are inversely proportional to the radius of the particle. This shows that size dependency of electron surface-phonon energy exchange arises from the geometric effect.