Mark J. Kilgard

Haoyu Yang, Zongyi Li, Kumara Sastry et al.

Lithography simulation is a critical step in VLSI design and optimization for manufacturability. Existing solutions for highly accurate lithography simulation with rigorous models are computationally expensive and slow, even when equipped with various approximation techniques. Recently, machine learning has provided alternative solutions for lithography simulation tasks such as coarse-grained edge placement error regression and complete contour prediction. However, the impact of these learning-based methods has been limited due to restrictive usage scenarios or low simulation accuracy. To tackle these concerns, we introduce an dual-band optics-inspired neural network design that considers the optical physics underlying lithography. To the best of our knowledge, our approach yields the first published via/metal layer contour simulation at 1nm^2/pixel resolution with any tile size. Compared to previous machine learning based solutions, we demonstrate that our framework can be trained much faster and offers a significant improvement on efficiency and image quality with 20X smaller model size. We also achieve 85X simulation speedup over traditional lithography simulator with 1% accuracy loss.

Mark J. Kilgard

Stroking and filling are the two basic rendering operations on paths in vector graphics. The theory of filling a path is well-understood in terms of contour integrals and winding numbers, but when path rendering standards specify stroking, they resort to the analogy of painting pixels with a brush that traces the outline of the path. This means important standards such as PDF, SVG, and PostScript lack a rigorous way to say what samples are inside or outside a stroked path. Our work fills this gap with a principled theory of stroking. Guided by our theory, we develop a novel polar stroking method to render stroked paths robustly with an intuitive way to bound the tessellation error without needing recursion. Because polar stroking guarantees small uniform steps in tangent angle, it provides an efficient way to accumulate arc length along a path for texturing or dashing. While this paper focuses on developing the theory of our polar stroking method, we have successfully implemented our methods on modern programmable GPUs.