Certain topics in ellipsometric data modeling with splines: A review of recent developments

Abstract

Dielectric function representation by a variety of polynomial spline functions provides a consistent and efficient method for accurate modeling of the material optical properties in the context of spectroscopic ellipsometry data interpretation. Splines as an elegant and purely mathematical way for such modeling task were introduced about three decades ago. In the following years the use of splines in the area of ellipsometric data analysis became widely utilized. The goal of this review is to provide a self-contained presentation on the current status of the dielectric function modeling by splines for advanced industrial ellipsometry users but, hopefully, it can be useful for some scholarly users as well. It is also intended to promote more extended recognition of the spline-based modeling among optical metrology professionals. Here, a brief description of different ways, - ordinary polynomials, piecewise polynomials (splines), and B(asis)-spline functions, - is presented to parameterize an arbitrary function which can be used as an analytic representation of the dielectric-function curves. A number of particular polynomial-based models for the optical functions of materials and how they may be used in applications are also discussed. Particular attention is paid to different concepts of the efficient and optimal spline construction.