Fast Marching Level Set Methods for Three-Dimensional Photolithography Development

J.A. Sethian

Proceedings, SPIE 1996 International Symposium on Microlithography, Santa Clara, California, March, 1996.


The Fast Marching Method, , introduced by Sethian in 1996, is a numerical technique for solving the Eikonal equation, and results from combining upwind schemes for viscosity solutions of Hamilton-Jacobi equations, narrow band level set methods, and a fast $min$-heap algorithm. On a rectangular grid of N total points, the fast marching level set method computes the solution to the Eikonal equation from given initial data in O(N log N) steps. In a series of papers, we have applied this technique to a wide collection of problems, including construction of geodesics on surfaces, computer vision, shape-from-shading, and computation of earthquake travel times. In this paper, we analyze the application of the fast marching method to photolithography development. Our results show that application of this scheme results in three-dimensional photolithography development times of under one minute on a Sparc 10 for rate functions defined on 100x100x100 grids. We provide studies of timings, accuracy, and examples of realistic applications to fully three-dimensional development.

Explanation of Fast Marching Method

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