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.
Abstract
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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