Post on 01-Mar-2021
transcript
Rapid Layout Pattern Classification
Jen-Yi Wuu, Fedor G. Pikus, Andres Torres, Malgorzata Marek-
Sadowska
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Outline
IntroductionSupervised Machine LearningTwo-Level Hotspot Pattern ClassificationAccuracy and Runtime EnhancementExperimental Results and Analysis
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Illumination
IC Fabrication and Optical Lithography
Fundamental of IC fabrication: Optical LithographyLithography
Accounts for about 30% of manufacturing cost.Tends to be the technical limiter for advance in feature size reduction.
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Reference: Chris Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication, John Wiley & Sons, 2007.
Sub-wavelength Lithography
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Courtesy of Raghunath Murali (http://www.mirc.gatech.edu/raghu/?p=185&cpage=1)
Resolution Enhancement Techniques
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Optical Proximity Correction (OPC)
Sub-Resolution Assist Feature
(SRAF)
Illumination
Mask
Off-Axis Illumination (OAI)
Intensity
Wafer
180o Phase0o Phase
Phase Shift Mask (PSM)
Mask
Lithographic Hotspots
Lithographic hotspots cannot be completely eliminated.Studies have shown that hotspots are largely pattern dependent.Radius of influence becomes larger. Peripheral patterns can no longer be ignored.
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Pinching Bridging
Central Pattern
Peripheral Pattern
Physical Verification Tools
Design Rule CheckingOne-dimensional geometrical rules are too simple and cannot describe two-dimensional patterns wellChecks become overly conservative or result in escaped hotspots
Model-Based Lithography SimulationGenerates accurate printed images and enables robust checkingExtremely computationally expensiveRequires well-calibrated process models
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Early Lithographic Hotspot Detection
Pattern Matching-Based MethodsCollect known bad patterns into database, and scan design for occurrencesFast and efficient, but weak in recognizing previously unseen bad patternsReferences: V. Dai, et al. (SPIE, 2007), H. Yao, et al. (IET-CDS, 2008), J. Ghan, et al. (SPIE, 2009).
Dual Graph-Based MethodDerive graphs from layout geometry to model cumulative effects from patterns in close proximityReference: A.B. Kahng, et al. (TCAD, 2008).
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Early Lithographic Hotspot Detection
Machine Learning-Based Methods Construct classification models from known good and bad patternsCapable of making prediction on unseen patterns References: J.-Y. Wuu, et al. (SPIE, 2009), D. Ding, et al. (ICICDT, 2009), D. G. Drmanac, et al. (DAC, 2009).
We present a rapid two-level hotspot pattern classification flow, utilizing both central and peripheral pattern information.
Detailed analysis of classification results is presented.
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Supervised Machine Learning
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Training Set
Feature Encoding
Classifier Training
Machine Learning Classifier
Training
Testing Set Feature Encoding Prediction
Predicted Class Labels
Testing
SVM maps the training data into a higher dimensional space where samples of different classes are separated by a hyperplane.
Support Vector Machine (SVM)
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Margin
Hyperplane
Support Vectors
Support Vectors
Decision Value:
Density-Based Feature Encoding
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Candidate
Clip Size
Pixel Size
d1
d2
d3
d4
d5
d6
d7
d8
d9
d10
d11
d12
d13
d14
d15
d16
Feature Vector = (d1, d2, …, d16)
Two-Level Lithographic Hotspot Pattern Classification Flow
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Test Samples
Level-1 Classifier
Level-2 Classifier
Prediction Output
Fast filteringusing central patterns
False alarm reductionusing central & peripheral patterns
Two-Level Lithographic Hotspot Pattern Classification Flow
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HotspotHotspot Non-HotspotNon-Hotspot
Feature EncodingFeature Encoding
Level-1 ClassifierLevel-1 Classifier
Feature EncodingFeature Encoding
Level-2 ClassifierLevel-2 Classifier
Training DesignTraining Design
ClassificationClassification
Sampling
Predicted: HS
Training FlowTraining Flow Testing FlowTesting Flow
Feature EncodingFeature Encoding
Feature EncodingFeature Encoding
Level-2 ClassificationLevel-2 Classification
Non-HotspotNon-Hotspot HotspotHotspot
Test DesignTest Design
Test SamplesTest Samples
Level-1 ClassificationLevel-1 ClassificationNHS HS
NHS HS
Global Density Pre-Computation
Align pixel grids and save density computation time.
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Global GridGlobal Grid
Output Density Vectors
Output Density Vectors
DesignDesign Grid SizeGrid Size
Candidate LocationsCandidate Locations
Global Density Database
Global Density Database Snapped LocationsSnapped Locations
Pattern Morphing
Symmetrical variants of a pattern may be equivalent in terms of printability.Equivalent variants are created for each training sample.
Performed on feature vectors.No modification on original design layout.
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Experimental Setup
Test Cases (Layer: Metal-1)
Hotspot locations verified using Mentor Graphics Calibre with real process models and RET recipesLIBSVM used for classifier construction and pattern classification.
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Experimental Results
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Level-1 vs. (Level-1 + Level-2) Classification
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Distribution of Classification Results
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Level-1 Classification
Level-1 + Level-2 Classification
Pattern Examples
Two layout patternsUndistinguishable for Level-1 ClassifierSeparated by Level-2 Classifier
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Hotspot Non-Hotspot
Effect of Global DensityPre-Computation
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Effect of Pattern Morphing
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Runtime Information
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SampleLocation
Extraction
GlobalDensity
Database
Density Vector
SynthesisPrediction Total
L2Global 0.1 0.4 0.9 0.4 1.9[1] 0.1 N/A 147.2 0.4 147.7
LithographySimulation N/A 251.1
[1] Jen-Yi Wuu, Fedor G. Pikus, Andres Torres, and Malgorzata Marek-Sadowska, “Detecting Context Sensitive Hotspots in Standard Cell Libraries,” Proc. SPIE, Vol. 7275, 727515, 2009.
False Positive Analysis
Analysis shows that most false positives are very close to hotspots.
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Conclusions
We presented a two-level lithographic hotspot pattern classification method, based on machine learning techniques.
We utilize density-based feature encoding.Accuracy and runtime enhanced by global density pre-computation and pattern morphing.Fast and effective, suitable for early design stages.
Our method is verified on several 45nm and 32nmreal designs.Analysis on classification results shows the false positives are very close to hotspots.
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