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.
