Fast calculation of the permittivities of gold thin films in the frequency range of 0–6 eV

Abstract

The permittivity tensor of gold nanofilms of different orientations and thicknesses in the frequency range of 0–6 eV is theoretically studied, revealing significant differences from the bulk gold permittivity. Two models are proposed to calculate the longitudinal ɛ‖(h, ω) and transverse ɛ⊥(h, ω) parts of the permittivity tensor in the specified frequency range for gold nanofilms of different thicknesses and surface orientations (001), (110), and (111). These models explain intense peaks in the real and imaginary parts of permittivity at 0–2 eV. The model for calculating the transverse permittivity does not use the Drude model but uses the interband contribution of the bulk material determined through DFT calculations and the contribution of electron motion perpendicular to the nanoslab surface. This contribution takes into account the electron motion inside an infinitely deep one-dimensional potential well with a set of discrete electron levels and makes it possible to calculate the imaginary part of the permittivity using Fermi’s golden rule. The model for calculating the longitudinal permittivity employs an interpolation scheme using the tabulated permittivity of bulk gold and that of several plates with different thicknesses. The difference between experimental permittivity values and those calculated using DFT and the proposed models is discussed. The proposed algorithms enabled a Python program for fast calculation of ɛ⊥(h, ω) and ɛ‖(h, ω) of gold nanofilms of any thickness and above-mentioned orientations in the 0–6 eV range without computationally expensive DFT calculations. This program is included in the supplementary material. The proposed approaches can be easily applied to nanofilms made of other metals.