GPU-Accelerated Inverse Lithography Towards High Quality Curvy Mask Generation

TL;DR

A GPU-accelerated ILT algorithm that improves not only contour quality and process window but also the precision of curvilinear mask shapes, and demonstrates a significant advantage of the algorithm over leading academic ILT engines.

Abstract

Inverse Lithography Technology (ILT) has emerged as a promising solution for photo mask design and optimization. Relying on multi-beam mask writers, ILT enables the creation of free-form curvilinear mask shapes that enhance printed wafer image quality and process window. However, a major challenge in implementing curvilinear ILT for large-scale production is mask rule checking, an area currently under development by foundries and EDA vendors. Although recent research has incorporated mask complexity into the optimization process, much of it focuses on reducing e-beam shots, which does not align with the goals of curvilinear ILT. In this paper, we introduce a GPU-accelerated ILT algorithm that improves not only contour quality and process window but also the precision of curvilinear mask shapes. Our experiments on open benchmarks demonstrate a significant advantage of our algorithm over leading academic ILT engines.

Figures (5)

• Figure 1: Example disc-shaped structuring element with size 39$\times$39.
• Figure 2: Visualization of morphological operators with eclipse structural element applied on binary images. (a) The original design image with Manhattan shapes; (b) Dilation enlarges the shapes in the original image; (c) Erosion etches the original image that yields smaller shapes; (d) Opening rounds the convex corners of each shape; (e) Closing rounds the concave corners of each shape; (f) CDR rounds both the convex and concave corners of each shape.
• Figure 3: Mask optimization evaluation metrics. EPE violation (EPEV) and PVB are two major measurement in terms of mask lithography quality. We also employ mask shape area violation (MSAV) and mask shape distance violation (MSDV) to represent the curvilinear mask rules.
• Figure 4: Corner pixel mismatch generates over 20% of the gradients during optimization. Design retargeting avoids over optimization on objectives that are unattainable.
• Figure 5: Visualization of the optimization trajectory of our algorithm. From left to right: CDR design, mask, nominal condition image, outermost image, and innermost image.

Theorems & Definitions (4)

• Definition 1: EPEV
• Definition 2: PVB
• Definition 3: MSA
• Definition 4: MSD