Detecting Multi-Layer Layout Hotspots withAdaptive Squish Patterns

Haoyu Yang1, Piyush Pathak2, Frank Gennari2,Ya-Chieh Lai2, Bei Yu1

1The Chinese University of Hong Kong2Cadence Design Systems Inc.

1 / 21

Outline

Introduction

The Algorithm

Results

Conclusion

2 / 21

Outline

Introduction

The Algorithm

Results

Conclusion

3 / 21

Moore’s Law to Extreme Scaling

1940 1950 1960 1970 1980 1990 2000 2010 2020

10,000,000,000

110

1001,000

10,000100,000

1,000,00010,000,000

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40048086

286386

486 Pentium

Pentium IIPentium 4

Core 2 Duo Core i7

Doubles every 2.1 yrs

3 / 21

Lithography Proximity Effect

I What you see 6= what you getI Diffraction information loss

I RET: OPC, SRAF, MPLI Worse on designs under 10nm or beyond

4 / 21

Machine Learning based Hotspot Detection

Hotspot&detec*on&model&

Classifica*on&

Extract&layout&features&

I Predict new patternsI Decision-tree, ANN, SVM, Boosting, Deep Neural NetworksI [Drmanac+,DAC’09] [Ding+,TCAD’12] [Yu+,JM3’15] [Matsunawa+,SPIE’15]

[Yu+,TCAD’15][Zhang+,ICCAD’16][Yang+,DAC’17][Yang+,TCAD]

5 / 21

Machine Learning based Hotspot Detection

Non$Hotspot�

Hotspot�

Hotspot&detec*on&model&

Classifica*on&

Extract&layout&features&

Hard,to,trade$off,accuracy,and,false,alarms,

I Predict new patternsI Decision-tree, ANN, SVM, Boosting, Deep Neural NetworksI [Drmanac+,DAC’09] [Ding+,TCAD’12] [Yu+,JM3’15] [Matsunawa+,SPIE’15]

[Yu+,TCAD’15][Zhang+,ICCAD’16][Yang+,DAC’17][Yang+,TCAD]

5 / 21

Multi-Layer Hotspots

(a) (b)

I More complicated patternsI More failure types (e.g. Metal-to-Via failure)

6 / 21

Layout Representations

I Density-based features [Matsunawa+,SPIE’15]

I Concentric circle sampling [Zhang+,ICCAD’16]

I Feature tensor extraction [Yang+,TCAD]

I Squish patterns [Gennari+, US Patent]

7 / 21

Squish Patterns

A simple multilayer pattern example with scan lines.

~T =

1 0 0 00 0 0 01 1 1 11 1 3 11 1 1 1

,~δx =

[0.2 0.072 0.06 0.048

],

~δy =[0.013 0.06 0.017 0.137 0.09

].

I LosslessI Storage-friendlyI Incompatible with most machine learning engines.

Squish representation does not guarantee a fixed tensordimensionality for a given clip size.

8 / 21

Outline

Introduction

The Algorithm

Results

Conclusion

9 / 21

An Alternative of Padding

I Legacy padding induces large fraction ofzeros that are not informative to CNNs.

I Instead of padding, we repeat certainrows or columns of squish topologies.

I ~δs are adjusted accordingly to make thepattern unchanged.

~T =

1 0 0 00 0 0 01 1 1 11 1 3 11 1 1 1

, ~T ′ =

1 1 0 0 00 0 0 0 01 1 1 1 11 1 1 1 11 1 1 3 11 1 1 1 1

.

9 / 21

Which Rows/Columns Are to Be Duplicated/Repeated?

I In machine learning, if some entries of the input are too large/small, there will be biasrelated to those entries.

I Subtract RGB means in conventional image classification tasks.I Duplicate rows/columns with larger deltas.

Adaptive Squish Problem:

min~s||~δ′||∞ (1a)

s.t. δ′i = δi/si,∀i, (1b)si ∈ Z+,∀i, (1c)∑

isi = d. (1d)

10 / 21

Repeat Elements

RepeatElements: ~M′ =RepeatElements(~M,~s, a), which duplicates the columns(a = 0) or rows (a = 1) of a matrix ~M ∈ Ra1×a2 by certain times such that the shape of thenew matrix ~M′ will be increased to a desired value.I a = 0 :

~m′k = ~mj,∀j−1∑i=1

si < k ≤j∑

i=1si. (2)

I a = 1 :

RepeatElements(~M,~s, 1) = RepeatElements(~M>,~s, 0)>. (3)

.

11 / 21

Repeat Elements

For example, if we let~s =[1 1 2 1

]> and a = 0, then the RepeatElementsoperation on the topology matrix ~T will result in

~T =

1 0 0 00 0 0 01 1 1 11 1 3 11 1 1 1

→ ~T ′ =

1 0 0 0 00 0 0 0 01 1 1 1 11 1 3 3 11 1 1 1 1

. (4)

12 / 21

Adaptive Squish: Solution 1

I Extend a 3× 3 squish topology to shape 3× 6.

~T =

1 0 01 0 01 1 1

,~δx =

[28 18 2

], ~δy =

[16 16 16

].

~T ′ =

1 1 1 0 0 01 1 1 0 0 01 1 1 1 1 1

,~δ′x =

[7 7 14 9 9 2

], ~δ′y =

[16 16 16

].

13 / 21

Adaptive Squish: Solution 2

I Extend a 3× 3 squish topology to shape 3× 6.

~T =

1 0 01 0 01 1 1

,~δx =

[28 18 2

], ~δy =

[16 16 16

].

~T ′ =

1 1 1 0 0 01 1 1 0 0 01 1 1 1 1 1

,~δ′x =

[9.33 9.33 9.33 9 9 2

], ~δ′y =

[16 16 16

].

14 / 21

Adaptive Squish: Data Preparation

I The squish topology and ~δs will be stacked together into a 3D tensor [~T ′;~δ′X;~δ′Y ] thatwill be fed into neural networks for training and inference, where,

~T ′ =

1 1 1 0 0 01 1 1 0 0 01 1 1 1 1 1

,~δ′X =

9.33 9.33 9.33 9 9 29.33 9.33 9.33 9 9 29.33 9.33 9.33 9 9 2

,~δ′Y =

16 16 16 16 1616 16 16 16 1616 16 16 16 16

.

15 / 21

ResNet Block

x+f(x)

conv

conv

conv

x

ReLU

ReLU

ReLU

+

f(x)

conv

conv

conv

x

ReLU

ReLU

ReLU

(a) (b)

I Gradient vanishing problem.I Allows gradient to be easily backpropagated to early layers.I Feature reuse.

16 / 21

The Neural Network Architecture

JM3 [Yang+,JM3’17] OursLayer Filter Stride Output Parameter Layer Filter Stride Output Parameter

conv1-1 3×3×4 2 160×160×4 36 conv1-1 5×5×128 2 32×32×128 9600conv1-2 3×3×4 2 80×80×4 144 conv1-2 5×5×128 1 32×32×128 409600conv2-1 3×3×8 1 80×80×8 288 conv1-3 5×5×128 1 32×32×128 409600conv2-2 3×3×8 1 80×80×8 576 conv1-4 5×5×128 1 32×32×128 409600conv2-3 3×3×8 1 80×80×8 576 conv2-1 5×5×256 2 16×16×256 819200pool2 2×2 2 40×40×8 conv2-2 5×5×256 1 16×16×256 1638400

conv3-1 3×3×16 1 40×40×16 1152 conv2-3 5×5×256 1 16×16×256 1638400conv3-2 3×3×16 1 40×40×16 2304 conv2-4 5×5×256 1 16×16×256 1638400conv3-3 3×3×16 1 40×40×16 2304 conv3-1 5×5×512 2 8×8×512 3276800pool3 2×2 2 20×20×16 conv3-2 5×5×512 1 8×8×512 6553600

conv4-1 3×3×32 1 20×20×32 4608 conv3-3 5×5×512 1 8×8×512 6553600conv4-2 3×3×32 1 20×20×32 9216 conv3-4 5×5×512 1 8×8×512 6553600conv4-3 3×3×32 1 20×20×32 9216 conv4-1 5×5×1024 2 4×4×1024 13107200pool4 2×2 2 10×10×32

conv5-1 3×3×32 1 10×10×32 9216conv5-2 3×3×32 1 10×10×32 9216conv5-3 3×3×32 1 10×10×32 9216pool5 2×2 2 5×5×32fc1 2048 1638400 fc1 1024 16777216fc2 512 1048576 fc2 2 2048fc3 2 1024

Summary 2746068 59796864

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Outline

Introduction

The Algorithm

Results

Conclusion

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The Dataset & Configurations

I 14nm metal layer, M3, V3, V4

Train Test Image Squish

Hotspot 3073 6015 320×320 64×64×3Nonhotspot 973197 1457830

I Initial learning rate: 0.001I Decay: 0.7 per 2000 stepsI Weight normalization: 0.001I Xavier, Adam

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Results

I Hit : # of hotspot patterns that are predicted as hotspotsI False Alarm : # of good patterns that are predicted as hotspots

Item JM3 [Yang+,JM3’17] Algorithm 1 Algorithm 2

Accuracy (%) 98.87 97.51 99.24False Alarm Rate (%) 4.81 5.05 4.52

Hit 5947 5865 5969False Alarm 70193 73645 65926Precision (%) 7.81 7.38 8.30

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Receiver Operating Characteristics

I JM3 behaves even better than Algorithm 2 interms of area under curve.

I AUC advantages of JM3 comes from theregion where the decision threshold is above0.9.

I Higher confidence on hotspot patterns thatcan be correctly predicted by classifiers is notnecessary.

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Outline

Introduction

The Algorithm

Results

Conclusion

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Conclusion

I Adaptive Squish Pattern.Attains good properties of squish patterns and compatible with most learningmachines.

I Multilayer Hotspot Detection.First time consider metal-to-via failure.

I ResNet.Allow better convergence and model generality.

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