TEMPO: Fast Mask Topography Effect Modeling with Deep Learning Wei - - PowerPoint PPT Presentation

Wei Ye1, Mohamed Baker Alawieh1, Yuki Watanabe2, Shigeki Nojima2, Yibo Lin3, David Z. Pan1

1ECE Department, University of Texas at Austin 2Kioxia Corporation

3CS Department, Peking University

TEMPO: Fast Mask Topography Effect Modeling with Deep Learning

⧫ Moore’s law brings increasing manufacturing cost and challenges ⧫ Need to make sure design is manufacturable with high yield

Bottleneck in IC Manufacturing: Lithography

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Light source Lens Photomask Projection lens Wafer

What you see (at design) ≠ what you get (at fab)

Wafer Design target

Mask Topography Effects in Advanced Lithography

Near-field Aerial image Near-field Aerial image Source Condenser Mask Lens Pupils Resist Substrate

Thin mask approximation (Kirchhoff) Thick mask approximation

Pupils

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Aerial Image Generation

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Resist Pattern Mask Layout Aerial Image Slicing Threshold

Optical model Resist model Post processing

h = 0 nm h = 10 nm h = 60 nm h = 70 nm . . . h = 110 nm h = 120 nm . . .

x y Intensity

Optical model (thin/thick mask)

2D aerial image at certain resist height

Image-to-Image Translation Problems

Computer Vision & Machine Learning Computer Graphics & Computational Photography

Semantic labeling [Long et al. 15’] Boundary detection [Xie and Tu. 15’] Image colorization [Zhang et al. 16’] Super-resolution [Johnson et al. 16’]

[“On Image-to-Image Translation”, Jun-Yan Zhu]

Image-to-Image Translation In Lithography

These applications are all single-domain transfer

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ILT Engine Generator

GAN-OPC [Yang+, DAC’18]

Mask pattern Aerial image Threshold Resist pattern Optical model Resist model Contour processing LithoGAN

Encoder Decoder Generator Discriminator Real Input Fake Diff Fake/Real

GAN-SRAF [Alawieh+, DAC’19] LithoGAN [Ye+, DAC’19]

Cast as Multi-Domain Image-to-Image Translation

⧫ Facial image translation (facial attributes/expressions)

› Bidirectional translation: original domain ⇔ target domain

⧫ Single mask pattern to multiple resist heights

› Unidirectional translation: original domain ⇒ target domain

Input . . . h = 0 nm h = 10 nm h = 20 nm h = 90 nm h = 100 nm h = 110 nm h = 120 nm

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Multi-Domain Image-to-Image Translation

T1

T1

T2

T2

Tm

Tm

Ti

Ti

Source domain Target domain 1 Target domain 2 Target domain i Target domain m Encoders Decoders Source domain Target domain 1 Target domain 2 Target domain i Target domain m i Target domain label Encoder Decoder

⧫ #Models scales up with #domains ⧫ Models are independent ⧫ Exploit the high correlation between

different domains Simple model Ideal model

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Multi-Domain Image Translation

⧫ ComboGAN [Anoosheh+, arXiv’17]

T1

S

S

T1

T2

T2

Tm

Tm

Cycle loss GAN loss

Generators Discriminators

Ti

S

S

Ti

S

Ti

Inference Joint training for the m different 2- domain transfer models, i ∈ {1,2,...,m}

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Multi-Domain Image Translation

⧫ StarGAN [Choi+, CVPR’18]

1 1

Reconstructed image Fake image Input image Target domain Fake image Source domain Fake image Real / Fake Domain classification

Original-to-target domain Target-to-original domain Fooling the discriminator

Concat Concat 10

Special Properties about Aerial Image Generation

⧫ Target-to-source domain transfer is difficult

› Mask shape has sharp edges › Model is not guaranteed to generate polygon shapes › Sharp edges can complicate gradient propagation

Source domain Target domain

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Special Properties about Aerial Image Generation

⧫ Similarity between target domains

› Intensity values at same (x, y) location change smoothly across target domains › Latent space carries the most critical information

A B

X (um) Z (um)

A B

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Generator Design

Encoder Decoder Latent space Target domain i 1 Target domain

i

Concat

Source domain Encoder Decoder Latent space Target domain i

Label

+

i

Source domain Concat

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G1 G2

Discriminator Design

Real/Fake? Discriminator Concat 1

i

Label i

Real/Fake? Discriminator Concat

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Ordinal encoding: single channel to denote all the domains The !-th domain: "#$%&"#'(

)

* ! + ,-./ D1 D2

TEMPO

Encoder Decoder Label Real/Fake? Label Latent space Source domain Discriminator +

Target domain i

i

Concat Concat 15

⧫ Combination of G2 and

D2

⧫ Compact ⧫ Information sharing ⧫ Lower risk of overfitting

Can We Further Improve Accuracy?

⧫ Thin mask simulation can provide

guidance

⧫ Thin mask simulation is relatively

fast

500 1000 1500 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Intensity Thin Thick Encoder Decoder Latent space Target domain i (thick mask) Label i

Real/Fake? Discriminator Concat Aerial image (thin mask)

Label

+

i

Source domain Concat Concat

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TEMPO Overall Flow

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Mask pattern Thin mask model ∼Hours Aerial image (thin mask) CGAN ∼Minutes Aerial image (thick mask) Mask pattern CGAN ∼Minutes Aerial image (thick mask) Mask pattern Rigorous thick mask model ∼Days Aerial image (thick mask)

Scheme 2 Scheme 1 Rigorous Simulation

TEMPO

Runtime for 1000 mask clips

Experimental Setup

⧫ Python 2.7 + Tensorflow 1.4.1 ⧫ GPU: Nvidia TITAN Xp ⧫ SRAF, OPC: Mentor Graphics Calibre ⧫ Aerial image by rigorous simulation: Synopsys S-Litho ⧫ 966 mask clips at 10nm node

› Different types of contact arrays [Lin+, TCAD’18] › 75% for training, 25% for test

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Experimental Results

⧫ Across-height information sharing benefits performance ⧫ Latent space encoding in generator gives better accuracy ⧫ Ordinal encoding in discriminator further improves accuracy

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10 20 30 40 50 60 70 80 90 100 110 120 Height (nm) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 NRMSE (10−2) Individual G1+D1 G2+D1 G1+D2 G2+D2 (TEMPO) 20 40 60 80 100 120 140 160 180 200 220 240 Height (nm) 2 4 6 8 10 12 14 RMSE (10−4) Individual G1+D1 G2+D1 G1+D2 G2+D2 (TEMPO) 10 20 30 40 50 60 70 80 90 100 110 120 Height (nm) 2 4 6 8 10 12 14 RMSE (10−4) Individual G1+D1 G2+D1 G1+D2 G2+D2 (TEMPO) Different generators Different discriminators

Apply different models in Scheme 2

Experimental Results

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Bottom Middle Top Golden Scheme 1 Diff Scheme 2 Diff Input

Experimental Results

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Bottom Middle Top Golden Scheme 1 Diff Scheme 2 Diff Input

CD Error and Runtime Comparison

22 1 2 3 4 CD error in the X direction (nm) 50 100 Count Baseline (Scheme 1) TEMPO (Scheme 1) Baseline (Scheme 2) TEMPO (Scheme 2) 1 2 3 4 CD error in the Y direction (nm) 50 100 Count

900 1000 1100 1200 Sim. ML Rigorous Scheme 1 Scheme 2 50 Minutes

1X 44X 1170X

Baseline: the individual model approach

Conclusion

⧫ TEMPO: framework for 3D aerial image generation considering

mask topography effects

⧫ One-fits-all CGAN model

› Novel target domain encoding › Compact › Superior accuracy: leveraging across-domain information sharing

⧫ Two schemes provide trade-offs between accuracy and efficiency

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Thank you!