B-spline and Bézier curvilinear representations: a comparative discussion

Benjamin Venitucci; Jean-Franҫois Bougron; Nivea Schuch; Frederic Robert; Thiago Figueiro

doi:10.1117/12.3010979

9 April 2024 B-spline and Bézier curvilinear representations: a comparative discussion

Benjamin Venitucci, Jean-Franҫois Bougron, Nivea Schuch, Frederic Robert, Thiago Figueiro

Proceedings Volume 12956, Novel Patterning Technologies 2024; 129560X (2024) https://doi.org/10.1117/12.3010979
Event: SPIE Advanced Lithography + Patterning, 2024, San Jose, California, United States

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Abstract

Curvilinear shapes are created by ILT (Inverse Lithography Technology) from design layouts, to compensate lithography process errors. Such shapes are better stored as combination of polygons and curves than merely polygons for efficiency reasons as modeling runtime, mask-writing time, and data volume. This is why a curvilinear format has been proposed by mask-writer suppliers, while its OASIS counterpart has been developed by a curvilinear work group created in 2019. As for their curve parts, these curvilinear formats support: Explicit Bézier, B-Spline, and Implicit Bézier curves. The last two are of particular interest, since they both offer more compaction properties than Explicit Bézier curves, from which they are derived. This paper introduces the different curves as mathematical objects in order to derive their properties, advantages, and disadvantages in terms of compaction and conversion capabilities.

Citation Download Citation

Benjamin Venitucci, Jean-Franҫois Bougron, Nivea Schuch, Frederic Robert, and Thiago Figueiro "B-spline and Bézier curvilinear representations: a comparative discussion", Proc. SPIE 12956, Novel Patterning Technologies 2024, 129560X (9 April 2024); https://doi.org/10.1117/12.3010979

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