| Ultra-thin films (with a thickness on the order of one nanometer or less) were studied by Picometrology. Picometrology is an optical approach developed by us to study the film thickness or the complex refractive index with a high sensitivity. It studies a thin film deposited on a substrate with complex reflection coefficient r, and measures the optical properties of the film by monitoring the change of r modified by the thin film. Its excellent performance is rooted in two levels of understandings for thin films: (1) An additional thin film modifies r of a substrate to r', and r' is fully determined by r and the thin film. The information for the coating structure of the substrate is not required. An analytical equation bridging between r' and r was derived. (2) Reflectance and differential phase contrast measurements are simultaneously performed to respectively acquire the amplitude change and the phase change of r caused by the film. Complex change of r is therefore fully recovered and the complex refractive index of the thin film is calculated. The measurements can be performed at a single wavelength, arbitrary incidence angle (including normal incidence) and with a high resolution.;Based on the first level of thin film understanding, we found that r = +/-i/ 3 of the substrates optimizes its response for a lossless thin film and therefore improves the sensitivity. Substrates with such r have been fabricated and applied to the studies of immunoassays on protein arrays and water adsorption on a silica surface. 2 pm detection limit was acquired based on a 4 mm2 detection area. Based on the second level of thin film understanding, we measured the complex refractive index of graphene, the monolayer of graphite. A strong dispersion of graphene was found in the wavelength region of visible light. We also monitored how the effective complex dielectric function epsilon of an ultra-thin gold film evolves as the film thickness increases from 0.2 nm to 10 nm. epsilon was plotted on the complex plane, and rich transition was observed. Especially, epsilon evolves along a circular trajectory at thickness range of 2∼10 nm which is the Drude circle occurring as cluster size becomes smaller than mean free path of free electrons in metal. |
