Fast calculation of plasmonic metals nanofilms permittivity in THz–ultraviolet range

Abstract

A theoretical study of the dielectric permittivity tensor for the plasmonic metals (Au, Ag, and Cu) nanofilms of different thicknesses in the THz–ultraviolet frequency range was conducted. Using DFT calculation data, the models for calculating longitudinal and transverse to nanofilm surface components ɛ‖(ω, h) and ɛ⊥(ω, h) for the metal nanofilms of any thickness h are proposed. The model for the ɛ‖(ω, h) calculation uses a sum of the interband contribution of the bulk metal obtained from density functional perturbation theory, the Drude contribution of intraband excitations, and the Lorentz model to account for the film surface influence. The model for the ɛ⊥(ω, h) calculation uses, in addition to the interband term, the contribution of the electron’s motion perpendicular to the film surface, described as its motion in a 1D infinitely deep potential well. This contribution is calculated using transient perturbation theory and Fermi’s golden rule. Based on both of these models, a Python program has been written that allows one to calculate in seconds longitudinal and transverse permittivity components in the THz–ultraviolet range for nanofilms of these metals with surface indices (001), (110), or (111) and any film thickness h. Using Bruggeman’s effective medium theory, the effective permittivities ɛeff(ω, h) of several thin gold films were calculated and shown to be in good agreement with the available experimental data.