Electron Mean Free Path in a Spherical Shell Geometry

Abstract

Mean free path is calculated for the shell geometry under the assumptions of (i) diffusive, (ii) isotropic, and (iii) billiard, or Lambertian, scattering. Whereas in a homogeneous sphere case the difference between different models of surface scattering is reflected merely by a different slope of the linear dependence of a mean free path Leff on the sphere radius R, qualitatively different nonlinear dependencies on the inner and outer shell radii result for different model cases in the shell geometry. A linear behavior of Leff on the shell thickness (D) can only be established for the billiard model in the thin shell limit, in which case Leff ≈ 2D, whereas, in the same limit, Leff ≈ (D/2)ln(2R/D) in the diffusive case and Leff ≈ 14(2RD)1/2/[3ln(2R/D)] in the isotropic case. The shell geometry turns out a very sensitive setup to distinguish between the different models of electron scattering, which could be performed in future experiments on single and well-controlled dielectric core-metal shell nanoparticles. This would enable one to more precisely assess the contribution of other mechanisms, such as chemical interface damping, to overall plasmon resonance damping. Preliminary experimental results are compatible with the billiard, or Lambertian, scattering model and appear to rule out both the Euler diffusive scattering and the isotropic scattering.