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The detailed understanding of the physical parameters that determineLocalized Surface Plasmon Resonances (LSPRs) is essential to develop newapplications for plasmonics. A relatively new area of research has been openedby the identification of LSPRs in low carrier density systems obtained bydoping semiconductor quantum dots. We investigate theoretically how diffusesurface scattering of electrons in combination with the effect of quantizationdue to size (QSE) impact the evolution of the LSPRs with the size of thesenanosystems. Two key parameters are the length $R_0$ giving the strength of theQSE and the velocity $\beta_T$ of the electronic excitations entering in thelength scale for diffuse surface scattering. While the QSE itself only producesa blueshift in energy of the LSPRs, the diffuse surface scattering mechanismgives to both energy and linewidth an oscillatory-damped behavior as a functionof size, with characteristic lengths that depend on material parameters. Thus,the evolution of the LSPRs with size at the nanometer scale is very dependenton the relation of size to these lengths, which we illustrate with severalexamples. The variety of behaviors we find could be useful for designingplasmonic devices based on doped semiconductor nano structures having desiredproperties.

Diffuse Surface Scattering and Quantum Size Effects in the Surface Plasmon Resonances of Low Carrier Density Nanocrystals