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Source Mask Optimization (SMO) has played an important role in technology setup and ground rule definition since the 2x nm technology node. While improvements in SMO algorithms have produced higher quality and more consistent results, the accuracy of the overall solution is critically linked to how faithfully the entire patterning system is modeled, from mask down to substrate. Fortunately, modeling technology has continued to advance to provide greater accuracy in modeling 3D mask effects, 3D resist behavior, and resist phenomena. Specifically, the Domain Decomposition Method (DDM) approximates the 3D mask response as a superposition of edge-responses.1 The DDM can be applied to a sectorized illumination source based on Hybrid-Hopkins Abbe approximation,2 which provides an accurate and fast solution for the modeling of 3D mask effects and has been widely used in OPC modeling. The implementation of DDM in the SMO flow, however, is more challenging because the shape and intensity of the source, unlike the case in OPC modeling, is evolving along the optimization path. As a result, it gets more complicated. It is accepted that inadequate pupil sectorization results in reduced accuracy in any application, however in SMO the required uniformity and density of pupil sampling is higher than typical OPC and modeling cases. In this paper, we describe a novel method to implement DDM in the SMO flow. The source sectorization is defined by following the universal pixel sizes used in SMO. Fast algorithms are developed to enable computation of edge signals from each fine pixel of the source. In this case, each pixel has accurate information to describe its contribution to imaging and the overall objective function. A more continuous angular spectrum from 3D mask scattering is thus captured, leading to accurate modeling of 3D mask effects throughout source optimization. This method is applied on a 2x nm middle-of-line layer test case. The impact of the 3D mask model accuracy on the source profile and corresponding lithographic performance is studied in detail. Furthermore, the impact of using a compact resist model in SMO is also investigated by using the same test case.
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