Localized surface plasmon resonances (LSPRs) have recently been identified in extremely diluted electron systems obtained by doping semiconductor quantum dots. Here we investigate the role that different surface effects, namely electronic spill-out a
nd diffuse surface scattering, play in the optical properties of these ultra-low electron density nanosystems. Diffuse scattering originates from imperfections or roughness at a microscopic scale on the surface. Using an electromagnetic theory that describes this mechanism in conjunction with a dielectric function including the quantum size effect, we find that the LSPRs show an oscillatory behavior both in position and width for large particles and a strong blueshift in energy and an increased width for smaller radii, consistent with recent experimental results for photodoped ZnO nanocrystals. We thus show that the commonly ignored process of diffuse surface scattering is a more important mechanism affecting the plasmonic properties of ultra-low electron density nanoparticles than the spill-out effect.
Nanometer-sized metal particles exhibit broadening of the localized surface plasmon resonance (LSPR) in comparison to its value predicted by the classical Mie theory. Using our model for the LSPR dependence on non-local surface screening and size qua
ntization, we quantitatively relate the observed plasmon width to the nanoparticle radius $R$ and the permittivity of the surrounding medium $epsilon_m$. For Ag nanospheres larger than 8 nm only the non-local dynamical effects occurring at the surface are important and, up to a diameter of 25 nm, dominate over the bulk scattering mechanism. Qualitatively, the LSPR width is inversely proportional to the particle size and has a nonmonotonic dependence on the permittivity of the host medium, exhibiting for Ag a maximum at $epsilon_mapprox2.5$. Our calculated LSPR width is compared with recent experimental data.
