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Proceedings Paper

Advanced transformational analysis applied to e-beam proximity effect correction
Author(s): Eytan Barouch; Ronald Raphael Coifman; Jimmy T. Ma; Martin C. Peckerar; Vladimir Rokhlin
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Paper Abstract

In this paper we address the problem of dose correction in the data bases consistent with ultra- large-scale integration. It is shown that recent advances in transformation theory provide a natural platform on which to build these dose correctors. Specifically, transformation approaches making use of compactly supported, smooth basis functions are shown to be particularly suitable. This is a natural result of the evolution of mathematically based correctors currently in use. Previous work in Parikh, MacDonald and others employed global transform method to determine the values of 'corrected' dose. In most cases, the mathematical inversion is essentially ill posed, in other words, the exact pattern desired cannot be obtained using a finite Gaussian sum. In this paper a set of smooth basis elements of compact support are employed. The mathematically smooth form of the basis makes it easy to match doses at boundaries without Gibbs phenomenon. Thus the transform field can be partitioned for optimum speed. Consequently, while most transformation complexities are of order N6 (the inversion of an N2 X N2 matrix) where N2 is the number of grid points characterizing the database, we developed an algorithm of complexity N2 log N. A method of dose field bias is employed to stem the requests for negative dose. The heart of the numerical process is essentially based on an adapted fast non-uniform-grid Fourier Transform combined with proper filtering and geometric localization methods. Several examples are given.

Paper Details

Date Published: 24 June 1993
PDF: 21 pages
Proc. SPIE 1924, Electron-Beam, X-Ray, and Ion-Beam Submicrometer Lithographies for Manufacturing III, (24 June 1993); doi: 10.1117/12.146501
Show Author Affiliations
Eytan Barouch, Princeton Univ. (United States)
Ronald Raphael Coifman, Yale Univ. (United States)
Jimmy T. Ma, Yale Univ. (United States)
Martin C. Peckerar, Naval Research Lab. (United States)
Vladimir Rokhlin, Yale Univ. (United States)


Published in SPIE Proceedings Vol. 1924:
Electron-Beam, X-Ray, and Ion-Beam Submicrometer Lithographies for Manufacturing III
David O. Patterson, Editor(s)

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