Regensburg 2025 – wissenschaftliches Programm
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DS: Fachverband Dünne Schichten
DS 9: Optical Analysis of Thin Films II
DS 9.1: Hauptvortrag
Donnerstag, 20. März 2025, 09:30–10:00, H3
Inverse Problems and Uncertainty Quantification for the analysis of thin films and nanostructured surfaces — •Sebastian Heidenreich1, Nando Hegemann1, Victor Soltwisch2, and Markus Bär1 — 1Mathematical Modelling and Data Analysis, PTB, Abbestr. 2-12, 10587 Berlin — 2Radiometry with Synchrotron Radiation, PTB, Abbestr. 2-12, 10587 Berlin
For the analysis of thin films and nanostructured surfaces, indirect optical measurement techniques are often used to determine the optical and geometrical properties by solving an inverse problem. Due to measurement errors and model errors, the results are subjected to uncertainties. In the talk we give an overview about statistical inverse problems with applications in the metrology of thin films and nanostructured surfaces. We start with a discussion of the advantages and disadvantages of frequently used Least-Squares, then consider the Maximum-Likelihood method and introduce the Bayesian approach as a statistical method [1]. We apply the Bayesian approach to thin film examples as well as to line grating structures and show how to deal with measurement uncertainties and model errors. Furthermore, we discuss some drawbacks of the Bayesian method and present recent developments like polynomial chaos, transport maps or neural networks to tackle these drawbacks [2]. --[1] Soltwisch, Fernandez Herrero, Pflüger, Haase, Probst, Laubis, Krumrey, Scholze, J. Appl. Cryst. 50, 2017; Heidenreich, Gross, Bär, Metrologia 55(6), 2018. [2] Hegemann, Heidenreich, J. Open Software 8 (89), 2023; Hagemann, Hertrich, Casfor, Heidenreich, Steidl, Mach. Learn:Sci. Technol. 5, 2024.
Keywords: Scatterometry; Reflectometry; Inverse Problems; Bayesian inversion; Uncertainty