Least-Squares Analysis of the Film–Substrate Problem in Ellipsometry

Abstract

We have found that the thickness and refractive indices for the film–substrate problem in ellipsometry can frequently be calculated with a least-squares technique. It is shown that one algorithm can be used with a variety of data to solve problems that were formerly solved with step-by-step searches through parameter space. Moreover, the least-squares technique leads to a statistically meaningful estimate of the variances of the parameters. It is shown that the variances obtained from a correct error analysis can be at least one hundred times as large as those obtained from a naive analysis. It is also shown how the error analysis can provide information that is helpful in deciding if a given experiment is Worthwhile.