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Mathematical Modelling and Data Analysis

Department 8.4

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Title: Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures
Author(s): H. Groß and A. Rathsfeld
Journal: Waves in Random and Complex Media
Year: 2008
Volume: 18
Issue: 1
Pages: 129--149
Taylor & Francis Group
DOI: 10.1080/17455030701481823
ISSN: 1745-5030
Web URL: http://www.tandfonline.com/doi/abs/10.1080/17455030701481823
Keywords: 8.41,Scatter-Inv,Scatterometrie
Tags: 8.41,Scatter-Inv
Abstract: We discuss numerical algorithms for the determination of periodic surface structures from light diffraction patterns. With decreasing details of lithography masks, increasing demands on metrology techniques arise. Scatterometry as a non-imaging indirect optical method is applied to simple periodic line structures in order to determine parameters like side-wall angles, heights, top and bottom widths and to evaluate the quality of the manufacturing process. The numerical simulation of diffraction is based on the finite element solution of the Helmholtz equation. The inverse problem seeks to reconstruct the grating geometry from measured diffraction patterns. Restricting the class of gratings and the set of measurements, this inverse problem can be reformulated as a non-linear operator equation in Euclidean spaces. The operator maps the grating parameters to special efficiencies of diffracted plane-wave modes. We employ a Gauß â€“Newton type iterative method to solve this operator equation. The reconstruction ...

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