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White Paper

A study of ILT-based curvilinear SRAF with a constant width

Sub-resolution assist features (SRAFs) plays a critical role in mask synthesis. They are a fundamental component of masks, both for Manhattan or curvilinear masks, and for either DUV or EUV masks. Inverse lithography technology (ILT) is used to produce high-quality curvilinear, model-based SRAF. With ILT, 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 free-form shapes. Such SRAF is expected to deliver a wafer performance close to the optimum defined by the objective function.

However, the ILT-based curvilinear SRAF is an emerging technology, still on its way to full adoption in production. Therefore, we focus this paper on the ILT SRAF obtained through "constant width SRAF." Constant width SRAF is a more suitable starting point in addressing many practical concerns such as mask rule check (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 free-form SRAF obtained by thresholding the iterated ILT mask, up to their locations and connectivity, and maintaining the edge placement error (EPE) convergence and simulated wafer performance compatible with its free-form counterpart.