Numerical ellipsometry: Examination of growing nickel and rhenium thin films using n-k plane analysis and effective numerical substrates

Useful thin film information may be obtained using ellipsometry data recorded during film growth. In cases in which the growing film overlies a substrate already coated with other films, it is possible to use a model which includes prior knowledge of the optical properties and layer thicknesses of all underlying films and the substrate. However, accuracy of the analysis is limited by imprecision in knowledge of the underlying structure and is not possible if the underlying material structure is unknown. These problems may be addressed by substituting a four-variable “numerical substrate” in place of the underlying materials. The “numerical substrate” exactly mathematically replaces a model of the physical substrate. It is represented by two effective optical indices which are independent of the growing film and dependent only upon light incidence angle and wavelength. The method may be implemented with a set of five measurements at a single wavelength and incidence angle or a set of three measurements at each of two incidence angles. Measurements may be made in-situ during film growth or ex-situ using “step deposited” films of different thicknesses. The work presented here is to demonstrate the method for nickel and rhenium films deposited on a BK7 substrate by Yamamoto using ion sputtering.