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With the advent of curvilinear mask enabled by multi-beam mask writing and curvilinear ILT, full reticle curvilinear mask processing is emerging as one of the new challenges in electronic design automation and specially in the mask data preparation (MDP) domain. Whether for 193i or for EUV, curvilinear masks provide superior wafer results from larger process windows. Although the curvilinear photomask designs can provide an excellent opportunity to improve mask process window compared to traditional Manhattan designs, they put a strain on the MDP data path due to the increasing complexity of data representation. The mask industry is tackling this issue using a Bezier and B-spline based “Multigon” format to replace the traditional piecewise linear polygon-based formats. Pixel-based computing and consequently a representation of curves that is aware of the mask writer pixel size can further assuage the problems of data path and computational overhead in using curvilinear photomasks. This paper demonstrates the inherent advantages of pixel-based computing for curvilinear photomasks, when using a GPU-based platform, through comprehensive analysis and empirical evidence. GPU acceleration has played a very important role in making the full chip curvilinear mask correction for shapes represented using piecewise linear polygons. Since CPU-based algorithms perform better with piecewise linear polygons, this approach to GPU acceleration is necessary and important to the industry. By taking a different approach that assumes the presence of GPUs in a compute node, however, pixel-based computations are enabled, taking advantage of the Single Instruction Multiple Data (SIMD) nature of GPUs. This paper studies the advantages of using GPU acceleration for pixel-based computing in various mask processing and verification steps. The paper highlights the natural runtime predictability of pixel-based computing, which is in the order of number of pixels, or O(p), irrespective of the complexity of the mask shapes. The paper also emphasizes that pixel dose equivalence and information theory provide a mathematical basis for the practical accuracy of pixel-based approach towards MDP. Pixel-based computing has been the backbone of various fields in computer science and computer-aided design (CAD) tools. However, it is still a relatively unexplored computational paradigm for the photomask industry, especially in the mask verification and processing steps. GPU performance scales by bit-width rather than by clock speed. The continued scaling of GPU processing speed has enabled the shift in perspective towards GPU-based computing. This paper concludes that the O(p) approach for GPU acceleration enables accurate and practical data processing for curvy masks governed by information theory, as we leap into an increasingly complex curvy world.
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