Description of Absorption and Scattering Properties

For spherical, metal particles having a diameter much smaller than the incident wavelength, the electric field intensity is uniformly distributed across the particle surface, such that all conduction band electrons are equally excited. In this case, electron movement can be well approximated by the Drude free-electron model, 

In its basic expression, the Drude model does not predict that the absorption bandwidth is affected by particle size. Experimentally, colloidal systems having a weak cluster-matrix interaction show a well-established inverse correlation with respect to the plasmon bandwidth with particle size. In order to describe the bandwidth dependency on particle size. Hovel et al. [47] proposed a classical view of free-electron metals here, the scattering of electrons with other electrons, phonons, lattice defects and impurities leads to a damping of the Mie resonance. Briefly, in realistic metals, the dielectric function is composed of contributions from both interband transitions and the free-electron portion [48]. The free-electron dielectric function can be modified by the Dmde model to account for this dependency, giving [47-50] 

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