Steiner Tree Polygon Fracturing for Mask Data Preparation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current polygon partitioning methods for mask data preparation in integrated circuit manufacturing face challenges such as increased complexity, longer run times, and quality issues due to the growing number of geometries and geometrical constraints, particularly with 193 nm lithography, leading to difficulties in minimizing small unprintable geometries (slivers) and avoiding critical dimension slicing cut lines.
Innovation Solution
A tree-based approach is introduced, utilizing a variant Steiner minimal tree to partition polygons into sub-polygons by considering all candidate cut lines as tree edges, allowing for optimal partitioning without being affected by processing order or iteration depth, and enabling easy changes in optimization objectives, such as switching from minimizing total cut line length to maximizing minimal cut line length.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If cut line based heuristics are used for polygon partitioning, then the partitioning can be performed, but the run time increases and quality deteriorates due to iterations of local cut line evaluation and correction
Solution Approach 1:
The patent replaces the iterative mechanical heuristic process of cut line evaluation and correction with a mathematical optimization approach using convex hulls and Delaunay triangulation. This substitution eliminates the need for repeated local evaluations and corrections, directly computing the optimal partitioning solution in a more efficient manner.
Solution Approach 2:
The invention changes the fundamental parameters of the partitioning approach by shifting from local cut line adjustments to global geometric properties. By using convex hulls and Delaunay triangulation, the method transforms the problem into one of optimizing geometric parameters rather than iteratively adjusting cut line positions, thereby improving both speed and quality.
2Manufacturing precision
If cut line based heuristics with deep iteration are applied to improve partition quality, then slivers can be reduced, but the complexity and run time increase significantly
Solution Approach 1:
The patent substitutes the complex iterative heuristic system with a more elegant mathematical system based on convex hulls and Delaunay triangulation. This replacement reduces algorithmic complexity by using well-established geometric algorithms rather than custom iterative heuristics, while effectively minimizing slivers through optimal geometric partitioning.
Solution Approach 2:
The invention employs universal geometric concepts (convex hulls and Delaunay triangulation) that can handle various partitioning scenarios without requiring problem-specific adjustments. These universal mathematical tools provide a single framework that addresses sliver minimization, run time optimization, and quality improvement simultaneously, reducing overall algorithmic complexity.
3Manufacturing precision
If multiple cut line based heuristics are tailored for different optimization objectives, then specific objectives can be optimized, but the flexibility and portability of the algorithm decrease
Solution Approach 1:
The patent creates a universal algorithmic framework based on convex hulls and Delaunay triangulation that can address multiple optimization objectives through a single unified approach. By parameterizing the optimization criteria within this universal framework, the system maintains high flexibility and portability while achieving various optimization goals without requiring separate tailored heuristics.
Data Source
AI summary
Roughly described, a method for mask data preparation is described, for use with a preliminary mask layout that includes a starting polygon, the vertices of the starting polygon including I-points (vertices of the starting polygon having an interior angle greater than 90 degrees), including steps of developing a rectilinear partition tree on at least the I-points of the starting polygon, and using the edges of the partition tree to define the partition of the starting polygon into sub-polygons for mask writing.