Finite-Size Effects in Surface-Enhanced Raman Scattering from Molecules Adsorbed on Noble-Metal Nanoparticles

We study the role of strong electron confinement in surface-enhanced Raman scattering from molecules adsorbed on small noble-metal particles. We describe a new source of Raman signal enhancement which originates from different behavior of sp-band and d-band electron densities near the particle boundary. In small particles, a spillover of sp-electron wave-functions beyond the classical radius gives rise to a thin layer with diminished population of d-electrons. In this surface layer, the screening of sp-electrons by d-band electron background is reduced. We demonstrate that the interplay between finite-size and underscreening effects results in an increase of the surface plasmon local field acting on a molecule located in a close proximity to the particle boundary. Our calculations, based on two-region model, show that the additional enhancement of Raman signal gets stronger for smaller nanoparticles due to a larger volume fraction of underscreened region.