cristian andrades m. andrea rodr´ıguez charles c. chiang signature indexing of design layouts for...
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Cristian Andrades
M. Andrea Rodr´ıguez
Charles C. Chiang
Signature Indexing of Design Layouts for Hotspot Detection
DATE’14
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Outline
Introduction Signature Design Layout Representation and Signature
Extraction Pattern Representation and Signature Extraction Signature-based Searching Experimental Evaluation Conclusion
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Introduction
A process-hotspot is a layout pattern that is sensitive to lithographic process
This work proposes to index the content of design layouts by using a signature as the search criteria
Pre-process layouts in order to extract signatures that characterize windows within the layouts
Signatures can be used as search keys to return only possible layout’s windows
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The key contributions The definition of a signature The extraction of the signature from layouts by windows and from
range patterns The use of the signature with an indexing structure to efficiently
search for candidate windows
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Signature
A signature is a mapping from a geometric configuration composed of non-overlapping rectangles to numbers
Let × 𝑁 𝑀 be a grid representation of a 2D configuration of non-overlapping rectangles. The change-based signature (𝒮+ ) is a tuple of the form ([ℎ0, . . . , ℎ −𝑁 1], [𝑣0, . . . , 𝑣 −𝑀 1])
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𝒮+ is ([1, 1, 2], [1, 0, 1, 0])
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Design Layout Representation and Signature Extraction
A layout is represented by a × 𝑁 𝑀 regular grid 𝐿 denoted by 𝐿 ×𝑁 𝑀
𝐿[ , 𝑖 𝑗] = 1 if there exists a rectangle that overlaps this location; otherwise, 𝐿[ , 𝑖 𝑗] = 0
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A window corresponds to a rectangular sub-portion of the layout and is defined as a ′ × ′ 𝑁 𝑀 sub-grid 𝑊 of 𝐿, denoted by 𝑊 ′× ′𝑁 𝑀
The number of possible windows in the layout is ( − ′ 𝑁 𝑁 + 1) × ( − ′ 𝑀 𝑀 + 1)
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Example simple layout represented with a 8 × 8 regular grid, window size of
6 × 6
𝒮+ for window 0 is ([0, 1, 2, 1], [2, 1, 1]) window 1 is ([0, 2, 0], [1, 1, 1])
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Pattern Representation and Signature Extraction
Patterns are 2D configurations composed of non-overlapping rectangles
There may exists a representative pattern with several similar realizations that vary in the distance between rectangles’ boundaries
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Specification of Range Patterns A range pattern is a configuration of 2D non-overlapping rectangles
with additional specifications about the horizontal or vertical distances between rectangles ’s boundaries
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Specification of Range Patterns
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Since a range pattern may have different realizations, it is not possible to extract 𝒮+ from a range pattern directly
First mapping the range pattern specification to horizontal (HRG) and vertical (VRG) range graphs
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A definite range-graph defines a topological order Above example derive 3 definitive horizontal and 3 definitive
vertical graphs, 9 combinations But the combinations of graphs may produce inconsistent
configuration, that is, configurations where rectangles overlap
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Signature-based Searching
Having patterns and layouts with their 𝒮+ , it is possible to use 𝒮+ for selecting candidate windows of the layout that can contain hotspots
Range patterns 𝒮+
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Layout windows signatures 𝒮+
For efficiency, we can organize the dictionary using a binary search tree
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Experimental Evaluation
Two design layouts 𝐷1 is a layer of 0.88 × 0.88𝑚𝑚2 represented by a 13, 540 × 13,
540 regular grid 𝐷2 is a layer of 0.91 × 0.91𝑚𝑚2 represented by a 14, 000×14, 000
regular grid Extracted 𝒮+ using 10×10 windows
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A realization of each of the 7 different range patterns
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Measures Recall :
Precision :
Results indicate that the recall is always 100% using window-based or area-based measures
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Conclusion
Proposed the use of a signature that can filter out portions of design layouts
How to extract the signature from layouts and also from range patterns