Conflict Diagram Node Degree Filtering for Semiconductor Layout Colorability
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Solution Overview
Problem
Current multiple patterning techniques in semiconductor manufacturing face inefficiencies in identifying potential coloring solutions for conflict graphs, particularly due to high processing times associated with heuristic approaches and the potential elimination of viable solutions in rule-based methods.
Innovation Solution
A method is introduced that generates a conflict diagram, sets anchor nodes to a degree equal to the number of masks, excludes nodes with lower degrees, and checks the coloring status to determine colorability, thereby reducing processing time and avoiding the elimination of potential solutions by focusing on the remaining nodes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If heuristic approaches are used to identify multiple coloring solutions, then the solution space exploration is improved, but the processing time increases
Solution Approach 1:
The conflict graph is segmented by identifying and excluding removable nodes (nodes with degree less than n) from the graph. This segmentation allows the algorithm to focus computational effort only on the essential subgraph that contains all viable coloring solutions, thereby maintaining solution space exploration while reducing processing time.
Solution Approach 2:
The method extracts and removes removable nodes from the conflict graph before performing coloring operations. By taking out these nodes that cannot contribute to valid coloring solutions (as their degree is insufficient to require multiple colors), the algorithm reduces the problem size and processing time while preserving all meaningful solutions.
2Loss of time
If rule-based approaches are used to identify coloring solutions, then the processing time is reduced, but viable coloring solutions may be eliminated
Solution Approach 1:
The method performs preliminary action by excluding removable nodes from the conflict graph before applying coloring rules. This preliminary filtering ensures that subsequent rule-based coloring operations are applied only to nodes that can actually participate in valid coloring solutions, preventing the elimination of viable solutions while maintaining efficiency.
Solution Approach 2:
The conflict graph modification (removal of removable nodes) acts as an intermediary step between the raw conflict graph and the coloring operation. This intermediary transformation preserves the essential coloring relationships while eliminating redundant elements, allowing rule-based approaches to work efficiently without losing viable solutions.
3Adaptability or versatility
If the number of masks is increased to accommodate more features, then the manufacturing flexibility is improved, but the complexity of the conflict graph increases
Solution Approach 1:
The method extracts and removes removable nodes from the conflict graph, reducing graph complexity. By eliminating nodes with degree less than n (where n is the number of masks), the algorithm reduces the number of nodes and edges that need to be processed, thereby managing conflict graph complexity even as the number of masks increases.
Solution Approach 2:
The method changes the parameter of node degree by excluding nodes with degree less than n. This parameter-based filtering reduces the effective size of the conflict graph in proportion to the number of masks, allowing the system to handle increased manufacturing flexibility without proportionally increasing computational complexity.
Data Source
AI summary
A method of determining colorability of a layout includes generating a conflict diagram based on circuit information. The conflict diagram includes a plurality of nodes, each node of the plurality of nodes is connected to at least another node of the plurality of nodes by a link, and each node of the plurality of nodes has a degree equal to a number of links connected to the node. The method includes setting a degree of each anchor node within the conflict diagram to a value of n, where n is equal to a number of mask usable to manufacture the layout. The method further includes excluding, using a processor, nodes having a degree less than n from the conflict diagram. The method further includes performing a color status check on the conflict diagram after the excluding; and determining whether the layout is colorable based on the performed color status check.