Dielectric function trajectory of ultrathin gold films

There have been attempts to study the complex refractive index $\tilde {n}_g $ of gold films by ellipsometry, but the measurements become unreliable when the average film thickness is below several nanometers, presumably because of optical anisotropy of the thin film. Here, we apply interferometric picometrology to measure $\tilde {n}_g $ by analyzing the Fourier-domain anisotropic diffraction of a normal-incidence scanning Gaussian laser beam reflected by a stripe-patterned gold film. The $\tilde {n}_g $ and dielectric constant $\varepsilon _g $ of the gold film were measured for thicknesses ranging continuously from 0.1 nm to 10 nm at a wavelength of 488 nm. Three distinct regimes of the $\varepsilon _g $ trajectory on the complex plane were observed as the gold thickness increased. The first regime (gold thickness: 0.1 nm $\sim $ 0.7 nm) reveals an evolution from sparse clusters to dense clusters. The real part of $\varepsilon _g $ changes from 2.3 to 7.0 and the imaginary part changes from 0 to 0.7. The Maxwell-Garnett equation is applied for this regime by treating the film as an effective medium consisting of air and gold clusters. The second regime (0.7 nm$\sim $ 2 nm) is a linear curve of $\varepsilon _g $ suggesting a transition from isolated clusters into a continuous thin film. The third regime (2 nm $\sim $ 10 nm) shows a circular trajectory of $\varepsilon _g $ moving towards the bulk value, which can be interpreted by the Drude equation.