Resonant phonon scattering 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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