Model selection in spectroscopic ellipsometry data analysis: Combining an information criteria approach with screening sensitivity analysis

Abstract

In the field of optical metrology, the selection of the best model to fit experimental data is absolutely nontrivial problem. In practice, this is a very subjective and formidable task which highly depends on metrology expert opinion. In this paper, we propose a systematic approach to model selection in ellipsometric data analysis. We apply two well-established statistical methods for model selection, namely, the Akaike (AIC) and Bayesian (BIC) Information Criteria, to compare different dispersion models with various complexities and objectively determine the “best” one from a set of candidate models. The information criteria suggest the most optimal way to quantify the balance between goodness of fit and model complexity. In combination with screening-type parametric sensitivity analysis based on so-called “elementary effects” (the Morris method) this approach allows to compare and rate various models, identify key model parameters and significantly enhance process of ellipsometric measurements evaluation.