Computing exact Fourier series coefficients of IC rectilinear polygons from low-resolution fast Fourier coefficients

Robin Scheibler; Paul Hurley

doi:10.1117/12.916360

13 March 2012 Computing exact Fourier series coefficients of IC rectilinear polygons from low-resolution fast Fourier coefficients

Robin Scheibler, Paul Hurley

Author Affiliations +

Proceedings Volume 8326, Optical Microlithography XXV; 83262V (2012) https://doi.org/10.1117/12.916360
Event: SPIE Advanced Lithography, 2012, San Jose, California, United States

Abstract

We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.

Citation Download Citation

Robin Scheibler and Paul Hurley "Computing exact Fourier series coefficients of IC rectilinear polygons from low-resolution fast Fourier coefficients", Proc. SPIE 8326, Optical Microlithography XXV, 83262V (13 March 2012); https://doi.org/10.1117/12.916360

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KEYWORDS

Fourier transforms

Photomasks

Optical lithography

Image transmission

Calculus

Fourier optics

Image analysis

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