Automated Triple and Quad Coloring for Shape Layouts
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Solution Overview
Problem
The challenge in lithography is the complexity of triple and quad coloring of shape layouts, which is exacerbated by the adoption of multi-patterning solutions in new technology nodes, leading to NP-complete problems in k-coloring graphs, making manual analysis inefficient and inaccurate for large volumes of layouts.
Innovation Solution
A computer-implemented method and system that determines whether a shape layout satisfies specific rules and applies coloring based on defined design rules, utilizing a layout coloring engine to split shapes into columns, assign colors, and ensure no adjacent shapes have the same color, employing polynomial-time algorithms for efficient and accurate triple and quad coloring.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If manual analysis is used for k-coloring graphs in lithography, then flexibility and adaptability are maintained, but efficiency and accuracy deteriorate due to NP-complete complexity for large volumes of layouts
Solution Approach 1:
The patent segments the complex k-coloring problem into two distinct phases: (1) a verification phase that checks whether the shape layout satisfies specific geometric rules (such as column alignment and spacing requirements), and (2) a coloring phase that applies polynomial-time coloring algorithms only to layouts that pass verification. This segmentation transforms the originally NP-complete problem into a tractable two-stage process, dramatically improving productivity while maintaining solution correctness.
2Productivity
If automated coloring algorithms are applied to all shape layouts, then productivity improves, but accuracy deteriorates due to failure to account for specific geometric constraints and design rules
Solution Approach 1:
The patent implements preliminary verification of geometric constraints and design rules before applying automated coloring algorithms. The system first checks whether shapes satisfy required conditions (such as proper column alignment, spacing requirements, and adjacency constraints), and only then proceeds with automated coloring. This preliminary action ensures that automated algorithms operate on valid inputs, guaranteeing both high productivity and coloring accuracy that satisfies manufacturing requirements.
3Adaptability or versatility
If triple and quad coloring is applied to standard cell architectures, then design flexibility improves, but complexity increases due to cell placement and density constraints
Solution Approach 1:
The patent applies local quality principles by implementing specific geometric rules tailored to standard cell architecture requirements. The verification phase checks local properties such as column alignment, spacing between adjacent shapes, and density constraints within specific regions. The coloring algorithm then applies different coloring strategies to different areas based on their local characteristics, enabling design flexibility while managing placement complexity through localized constraint satisfaction rather than global optimization.
Data Source
AI summary
Techniques related to triple and quad coloring of shape layouts are provided. A computer-implemented method comprises coloring, by a system operatively coupled to a processor, a shape layout with a plurality of colors in accordance with a defined design rule based on a determination that a first defined shape within the shape layout satisfies a layout specification and a second defined shape within the shape layout satisfies a defined rule.