Aerial image simulation for partial coherent system with programming development  in MATLAB

Md. Nazmul Hasan; Md. Momtazur Rahman; Ariful Banna Udoy

doi:10.1117/12.2065812

17 October 2014 Aerial image simulation for partial coherent system with programming development in MATLAB

Md. Nazmul Hasan, Md. Momtazur Rahman, Ariful Banna Udoy

Proceedings Volume 9231, 30th European Mask and Lithography Conference; 92310J (2014) https://doi.org/10.1117/12.2065812
Event: 30th European Mask and Lithography Conference, 2014, Dresden, Germany

Abstract

Aerial image can be calculated by either Abbe’s method or sum of coherent system decomposition (SOCS) method for partial coherent system. This paper introduces a programming with Matlab code that changes the analytical representation of Abbe’s method to the matrix form, which has advantages for both Abbe’s method and SOCS since matrix calculation is easier than double integration over object plane or pupil plane. First a singular matrix P is derived from a pupil function and effective light source in the spatial frequency domain. By applying Singular Value Decomposition (SVD) to the matrix P, eigenvalues and eigenfunctions are obtained. The aerial image can then be computed by the eigenvalues and eigenfunctions without calculation of Transmission Cross Coefficient (TCC). The aerial final image is almost identical as an original cross mask and the intensity distribution on image plane shows that it is almost uniform across the linewidth of the mask.

Citation Download Citation

Md. Nazmul Hasan, Md. Momtazur Rahman, and Ariful Banna Udoy "Aerial image simulation for partial coherent system with programming development in MATLAB", Proc. SPIE 9231, 30th European Mask and Lithography Conference, 92310J (17 October 2014); https://doi.org/10.1117/12.2065812

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KEYWORDS

MATLAB

Diffraction

Fourier transforms

Light sources

System on a chip

Photomasks

Computer programming

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