Size Evolution of the Surface Plasmon Resonance Damping in Silver Nanoparticles: Confinement and Dielectric Effects

A key parameter for optimizing nanosized optical devices involving small which is intrinsically limited by the confinement-induced broadening (quantum finite size metal particles is the spectral width of their localized surface plasmon resonances (LSPR), effects). I have investigated the size evolution of the LSPR width induced by quantum confinement in silver nanoparticles isolated in vacuum or embedded in transparent matrixes. Calculations have been performed within the time-dependent local density approximation in an extended size range, up to 40000 conduction electrons (diameter D approximate to 11 nm). The slope characterizing the 1/D linear evolution predicted by the simple classical limited mean free path model is found to depend noticeably on the surrounding matrix. The confinement-induced damping of the collective LSPR excitation is shown to be intimately related to the departure of the electron-background interaction from a pure harmonic law. In jellium-type models the damping is governed by the electronic spillout tail, which leads to the decay of the coherent excitation of the electronic center-of-mass coordinate into incoherent intrinsic electronic motions, that is, single particle-hole excitations (Landau damping). The computed linear slope is found roughly two times smaller than the one measured in experiment on single silver particles, indicating that part of the size dependence of the fast plasmon damping results from the contribution of the granular ionic structure, especially the electron-phonon contribution in the large size domain. The strong sensitivity of the LSPR damping to the surface profile of the confining potential, which depends on numerous structural surface parameters, in particular those related to the ionic background modeling, is emphasized. A short analysis of the quantum box model and of the classical approach is also provided.