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

Accuracy of the spectroscopic ellipsometry data analysis strongly depends on appropriate modeling of the complex dielectric function epsilon (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 epsilon 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 epsilon(2) of the dielectric function and then provide a certain penalty on the coefficients of adjacent B-splines to tune the smoothness of the epsilon 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.