Methods for Determining and Modelling Indices of Refraction Versus Thickness of Silver, ITO, and Chromium

摘要

Optical thin film design has typically used the simplifying assumption that real films are homogeneous throughout their thickness, although this has been known to be only an approximation. It has also been known that there is a nucleation stage wherein the coating starts as islands on the substrate somewhat like the first drops of rain on a dry pavement which eventually build to percolate and finally cover the whole surface. With recent discussions of the design and control benefits of thin films, such as Fencepost designs, the increased application of thin layers is anticipated. Metallic and conductive layers have often been used which are much thinner than QWOTs in the visible spectrum. This paper and its predecessor present a few approaches to using a spectrophotometer to measure and model the indices of refraction of layers of silver (Ag), Indium-Tin-Oxide (ITO), and chromium (Cr) as a function of thickness from as thin as 1.5 nm up to thicknesses of more than 400 nm. The techniques can also be applied to strictly dielectric films whose indices vary with thickness. A mathematical model of the indices versus thickness and wavelength for Ag and other materials is discussed.