A computation of partially coherent imaging illuminated by a polarized source via the stack pupil shift matrix approach

Yu Chen; Yong Liu

doi:10.1117/12.916260

13 March 2012 A computation of partially coherent imaging illuminated by a polarized source via the stack pupil shift matrix approach

Yu Chen, Yong Liu

Author Affiliations +

Proceedings Volume 8326, Optical Microlithography XXV; 832628 (2012) https://doi.org/10.1117/12.916260
Event: SPIE Advanced Lithography, 2012, San Jose, California, United States

Abstract

×We report a computation of the partially coherent imaging with a polarized illumination using an improved SVD algorithm applied to the stack pupil shift matrix computation method. The case of a polarized source is taken into account by directly stacking the x-, y- and z-direction stack pupil shift operator. The polarization of the source is described with a 22 coherency matrix which is decomposed into two independent polarization modes with certain weights determined by the polarization. For each of the polarization, we compute the stack pupil shift function in each of the x-, y- and z-direction. For a fast computation the aerial image, the SVD algorithm is applied to each of the polarized directional kernel. In this way, the total complexity of the SVD computation is reduced. To compute the full mask image, we compute the sum of convolution of the eigenvectors of each of the kernels and a 2D mask. For a fast decaying spectrum of the stack pupil shift matrix, we make the truncation of the sum with an estimate of the global precision. In a test with an annular source, we design a mask pattern. The result in the zero polarization case of our computation agrees with that of a computation with the Prolith® simulator.

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Yu Chen and Yong Liu "A computation of partially coherent imaging illuminated by a polarized source via the stack pupil shift matrix approach", Proc. SPIE 8326, Optical Microlithography XXV, 832628 (13 March 2012); https://doi.org/10.1117/12.916260

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KEYWORDS

Polarization

Coherence imaging

Computer simulations

Optical proximity correction

Photomasks

Matrices

System on a chip

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