Spectroscopic ellipsometry data analysis using penalized splines representation for the dielectric function

Abstract

Accuracy of the spectroscopic ellipsometry data analysis strongly depends on appropriate modeling of the complex dielectric function ε (or the complex index of refraction N) over required spectral range. In this paper, we outline penalized B-spline (P-spline) formulation for an arbitrary dielectric function ε modeling in spectroscopic ellipsometry data analysis. The main idea is to first use a generous number of equally-spaced knots (up to the number of spectral points) to describe even highly complicated structure in the imaginary part ε2 of the dielectric function and then provide a certain penalty on the coefficients of adjacent B-splines to tune the smoothness of the ε curve. Two real-data applications have been provided to evaluate the practical performance and effectiveness of the proposed penalized formulation for dielectric function representation. A comparison of obtained results with the findings of our previous studies without penalization demonstrates a good agreement between the proposed method and ordinary B-spline representation in an equally-spaced fashion with optimal number of knots.