Rule optimization in lithographic imaging based on correlation of functions representing mask and predefined optical conditions

Abstract

Methods, computer program products and apparatuses for optimizing design rules for producing a mask are disclosed, while keeping the optical conditions (including but not limited to illumination shape, projection optics numerical aperture (NA) etc.) fixed. A cross-correlation function is created by multiplying the diffraction order functions of the mask patterns with the eigenfunctions from singular value decomposition (SVD) of a TCC matrix. The diffraction order functions are calculated for the original design rule set, i.e., using the unperturbed condition. ILS is calculated at an edge of a calculated image of a critical polygon using the cross-correlation results and using translation properties of a Fourier transform. The use of the calculated cross-correlation of the mask and the optical system, and the translation property of the Fourier transform for perturbing the design reduces the computation time needed for determining required changes in the design rules. Once an optimum separation is calculated, it is incorporated into the design rule to optimize the mask layout for improved ILS throughout the mask, including critical and non-critical portions of the mask.