Redundant Via Insertion via Conflict Graph Maximal Independent Set
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Solution Overview
Problem
In very deep submicron technologies, via failures in integrated circuits due to process variations lead to yield loss, as partial failures increase contact resistance and parasitic capacitance, while complete failures result in open nets, impacting design functionality and yield. Redundant via insertion is necessary to improve reliability and yield.
Innovation Solution
A method for post-routing redundant via insertion involves constructing a conflict graph, finding a maximal independent set, and replacing single vias with double vias, using R-trees for efficient vertex and edge construction, and heuristic methods to maximize on-track double vias without violating design rules.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If redundant vias are added to improve via yield and reliability, then via failure tolerance improves, but device complexity and layout congestion increase
Solution Approach 1:
The patent applies local quality by selectively adding redundant vias only at specific locations where single via failures would cause critical issues. The conflict graph identifies vertices representing single vias whose failure would create timing problems or open nets, and edges representing spatial conflicts. The maximal independent set selection ensures redundant vias are added only where needed, not uniformly across the entire layout, thus improving via yield locally without unnecessarily increasing overall layout complexity.
Solution Approach 2:
The patent implements partial action by adding redundant vias only for a subset of single vias rather than all vias in the design. The conflict graph and maximal independent set algorithm identify which single vias need redundancy protection, adding double vias only at those critical locations. This partial approach provides sufficient reliability improvement while avoiding the excessive complexity that would result from universal via redundancy.
2Reliability
If redundant vias are added to reduce via resistance and tolerate via failures, then reliability improves, but manufacturing precision requirements increase due to additional alignment constraints
Solution Approach 1:
The patent applies local quality by concentrating redundant via structures only at critical single via locations identified through the conflict graph analysis. Rather than adding double vias uniformly across all via locations, the method selectively places redundancy only where single via failures would cause timing violations or open nets. This localized approach improves via reliability at critical points while minimizing the total number of additional vias requiring alignment, thus reducing the cumulative manufacturing precision burden.
3Reliability
If a comprehensive conflict graph construction method is used to optimize redundant via insertion, then via yield improves, but computational complexity and processing time increase
Solution Approach 1:
The patent applies segmentation by dividing the conflict graph construction into distinct phases: first constructing the vertex set from single vias, then constructing the edge set by identifying conflicts between potential double via locations. The maximal independent set algorithm further segments the problem by iteratively selecting vertices and removing conflicting vertices. This segmented approach to conflict graph construction makes the computational process more manageable and efficient compared to attempting to construct the entire graph simultaneously.
Solution Approach 2:
The patent implements preliminary action by pre-construcing the vertex set of the conflict graph from single vias before adding edges. The R-tree data structure is built in advance to enable efficient spatial queries when determining conflicts. This preliminary construction of vertices and spatial indexes before edge addition optimizes the overall computational process, reducing the complexity of subsequent conflict detection and maximal independent set calculation.
Data Source
AI summary
The objective of the invention is to provide a method for post-routing redundant via insertion. The method is to construct a conflict graph from a post-routing design first, to find a maximal independent set (MIS) of the conflict graph, and to replace a single via with a double via for each vertex in the maximal independent set. Furthermore, since redundant vias can be classified into on-track and off-track ones and since on-track ones have better electrical properties, the invention also presents two methods to increase the amount of on-track redundant vias while a redundant via insertion solution is given.