Single-angle-of-incidence ellipsometry

摘要

We introduce single angle-of-incidence (SAI) ellipsometry [U.S. patent application 20070024850 (14 July 2006)] as a technique to completely identify, i.e., totally characterize, film-substrate systems. We show that only one measurement of the ellipsometric function rho at one angle of incidence and one wavelength is totally sufficient to determine the optical constant of the film N_(1), its thickness d, and the substrate's optical constant N_(2). Obviously, it is also sufficient for characterizing only the film, determining N_(1) and d, and for characterizing only the substrate, determining N_(2) and d, as well as for characterizing only bare substrates. An inverse genetic algorithm (IGA) for complete identification is presented that is based on a physical condition of the transparent-film-absorbing-substrate system. This IGA is used to identify the film-substrate system in four separate cases. We show that removing the film thickness from the fitness function of the genetic algorithm and using the defined optimum population size to characterize the film reduces the computational effort from 20,000 to 69 fitness-function calculations; the number of calculations to characterize an absorbing layer is reduced from 80,000 to 180. This is a very significant reduction and is very welcome in real-time applications. An error analysis is presented that shows that the IGA is resilient to, not affected by, random experimental errors and that it gives very good results in the presence of both random and systematic errors of the ellipsometer system. Experimental results are given that also prove the robustness, stability, and high accuracy of the method. We present data only for the SiO_(2)-Si film-substrate system, but the IGA works for any film-substrate system, physical or not.