Advanced transformational analysis applied to e-beam proximity effect correction

Eytan Barouch; Ronald Raphael Coifman; Jimmy T. Ma; Martin C. Peckerar; Vladimir Rokhlin

doi:10.1117/12.146501

24 June 1993 Advanced transformational analysis applied to e-beam proximity effect correction

Eytan Barouch, Ronald Raphael Coifman, Jimmy T. Ma, Martin C. Peckerar, Vladimir Rokhlin

Proceedings Volume 1924, Electron-Beam, X-Ray, and Ion-Beam Submicrometer Lithographies for Manufacturing III; (1993) https://doi.org/10.1117/12.146501
Event: SPIE'S 1993 Symposium on Microlithography, 1993, San Jose, CA, United States

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.

Citation Download Citation

Eytan Barouch, Ronald Raphael Coifman, Jimmy T. Ma, Martin C. Peckerar, and Vladimir Rokhlin "Advanced transformational analysis applied to e-beam proximity effect correction", Proc. SPIE 1924, Electron-Beam, X-Ray, and Ion-Beam Submicrometer Lithographies for Manufacturing III, (24 June 1993); https://doi.org/10.1117/12.146501

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KEYWORDS

Photomasks

Scattering

Algorithm development

Microchannel plates

Data corrections

Photoresist processing

Picosecond phenomena

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