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.

Date Published: 17 October 2014
PDF: 7 pages
Proc. SPIE 9231, 30th European Mask and Lithography Conference, 92310J (17 October 2014); doi: 10.1117/12.2065812

Published in SPIE Proceedings Vol. 9231:
30th European Mask and Lithography Conference
Uwe F. W. Behringer, Editor(s)