  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 and 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.
