Optimization of the dielectric-function modeling by B-splines in spectroscopic ellipsometry analysis: A hybrid approach

Abstract

Currently, a Kramers–Kronig consistent B(asis)-spline representation of the dielectric function is an efficient and widely used method for accurate modeling of the material optical functions in ellipsometric data analysis. However, the B-spline approach to the dielectric function modeling should include an appropriate and user-independent way of a knot vector generation, i.e., the proper selection of the number and locations of knots. In this paper, we advocate for a systematic approach which combines a specific knot allocation method, based on so-called “Integral Span”, a slope-weighting factor, with a selection of optimal number of knots using the Akaike and Bayesian Information Criteria, two statistical estimators, thereby replacing an intuitive and time-consuming “trial-and-error” strategy. The proposed hybrid approach is used to optimize the B-spline models for an epitaxial cobalt disilicide (CoSi2) thin film and a crystalline silicon substrate (c-Si).