Combination Law for Drude–Sommerfeld's Electron Damping in Multilayer Thin Metal Films

A combination rule for electron damping in multilayer thin metal films is derived from a mean‐field picture and is applied to optical experimental data. The overall coefficient obeys a parallel law of pure materials damping, , chemical specificity being involved by averaging over densities of low energy states in the free electron model. Geometric and static electromagnetic features of single layers couple via small Fermi's energy fractions (α_i). An application is developed for thin Cu/Au and Au/Ag films, showing an apparently irregular damping trend in the film thickness (d_i = 2.5–7.5 nm). The inferred ⟨γ⟩'s agree in both cases with our data when |α_i| = 10⁻² ÷ 10⁻³ linearly increases with decreasing d_i, suggesting a coupling phenomenology that can bring new insights in the optics and plasmonics of nanostructures.