In double patterning technology (DPT), two adjacent features must be assigned opposite colors, corresponding to different exposures if their pitch is less than a predefined minimum coloring pitch. However, certain design orientations for which pattern features separated by more than the minimum coloring pitch cannot be imaged with either of the two exposures. In such cases, there are no aerial images formed because in these directions there are no constructive interferences between diffractive orders in the pupil plane. The 22nm and 16nm nodes require the use of pixelized sources that will be generated using SMO (source mask co-optimization). Such pixelized sources while helpful in improving the contrast for selected configurations can lead to degraded contrast for configurations which have not been set during the SMO process. Therefore, we analyze the diffractive orders interactions in the pupil plane in order to detect limited orientations in the design and thus propose a decomposition to overcome the problem.

SRAF plays a critical role in mask synthesis. It is a fundamental component of masks, for Manhattan or curvilinear masks, and for DUV or EUV masks. ILT is one of the technologies that can produce high-quality curvilinear, modelbased SRAF. With this technology, the actual shapes of curvilinear assist features are naturally obtained by thresholding an optimized ILT mask that is represented as an image grid, ending up with freeform shapes. In this case, the ILT mask is formed through iterations of an optimization process. The shapes and widths of the freeform SRAF vary from location to location. Such SRAF is expected to deliver a wafer performance close to the optimum defined by the objective function. Nevertheless, the ILT-based curvilinear SRAF is an emerging technology, still on its way to full adoption in production. Therefore, this report focuses on the ILT SRAF obtained differently - constant width SRAF. Constant width SRAF is a more suitable starting point in addressing many practical concerns such as MRC compliance, SRAF printing avoidance, tile boundary stitching friendliness, run-time robustness, and data volume control. The SRAF in this study is characterized by skeletons, each of which is in turn given by the coordinates of ordered “critical” points. These critical points mainly consist of local minima of the gradient map of the objective function. Here the gradient map, roughly speaking, is the partial derivative of the ILT objective function with respect to the transmission values of a grid-represented mask. We will show that the shapes of such constant width SRAF closely match that of the freeform SRAF obtained by thresholding the iterated ILT mask, up to their locations and connectivity, and maintaining the EPE convergence and simulated wafer performance compatible with its freeform counterpart.

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