MOS OSAIC: : Mas ask k Opt ptimiz imizing ing Solut olution - - PowerPoint PPT Presentation

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MOS OSAIC: : Mas ask k Opt ptimiz imizing ing Solut

• lution

ion Wit With h Proces

• cess Window

Window Awar are e Inv nver erse e Cor

• rrect

ection ion

Jhih-Rong Gao, Xiaoqing Xu, Bei Yu, and David Z. Pan

• Dept. of Electrical and Computer Engineering

The University of Texas at Austin Supported in part by NSF, SRC, NSFC, and Oracle

Outline

t Mask Optimization: Why & How? t Proposed Approach: MOSAIC t Experimental Results t Conclusions

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Sub-wavelength Lithography

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Target

Image distortion due to light scattering

OPC Mask

Image distortion is compensated

Mask Printed Image

Optical Proximity Correction (OPC)

t Resolution enhancement technique t Required for advanced technology nodes to ensure printability

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Ruled-based

[A. K. Wong, SPIE Press’01]

Model-based (Edge)

[N. B. Cobb+, SPIE’03] [P. Yu+, ICCAD’07]

Inverse Lithography Technique (ILT)

t Further scaling demands more aggressive OPC t Pixel-based OPC

› Higher contour fidelity than conventional OPC methods

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[Y. Granik, JM3’06] [A. Poonawala+, TCAD’07] [J. Zhang, ICCAD’08] [Y. Shen+, OpEx’09] [N. Jia+, J. Opt.’10] [J. Zhang, ASPDAC’10] [X. Zhao+, VLSID’12]

ILT-based OPC

Our Contributions

t Limitations of previous works

› Design target optimization

» Distortion Area à however, not all distortion matters » What really matters is edge placement error (EPE) beyond threshold » No study for direct EPE minimization

› Process variations » Optical conditions: defocus, dose, … » One ILT study, [Jia+ J. Opt.’10], considered defocus only

t Our contributions

› Provide exact optimization for EPE › Optimize both Design Target and Process Variation › Outperform the 1st place winner at 2013 ICCAD contest » 11% improvement for the overall score

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Outline

t Mask Optimization: Why & How? t Proposed Approach: MOSAIC t Experimental Results t Conclusions

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Forward/Inverse Lithography

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Mask Optical Projection Photoresist Printed Pattern

thI t Forward lithography t Inverse Lithography

Z = f(M).

Mopt = f −1(Zt) (

Difficulty

• Ill-posed problem (not
• ne-to-one mapping)
• No closed form solution

Gradient Descent Based Approach

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F ß obj(M) to minimize repeat M ß M – stepSize x F until F converges Δ

Initial Solution Iteration 2 Iteration 3 Convergence M F(M)

Still difficult

• How to define F such

that it ü Integrates Design Target & Process Variation ü Is Differentiable

Design Target Optimization (Fast)

t Total distortion minimization

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I(x, y) ⇡

Nh

X

k=1

wk|M(x, y) ⌦ hk(x, y)|2.

Z(x, y) = ⇢ if I(x, y) 6 thr 1 if I(x, y) > thr

Optical Photoresist Mask (M) Pattern (Z) Intensity (I) Target Nominal ) = sig(I(x, y)) =

1 1+e−θZ (I(x,y)−thr)

Ftd =

N

X

i=1 N

X

j=1

(Znom(i, j) Zt(i, j))γ

Design Target Optimization (Exact)

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t Edge Placement Error (EPE) violation minimization

› Common measurement for yield impact (EPE > thepe)

EPE Violation = ⇢ if EPE < thepe 1 if EPE > thepe

Image contour may be inside

• r outside of the desired

boundary è èCalculating boundary-to- boundary EPE is not a continues function (Non-differentiable)

Image EPE EPE Target contour

EPE Violation = ⇢ if EPE < thepe 1 if EPE > thepe

Design Target Optimization (Exact) (cont’)

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• Dsum

Outer Inner

EPE Violation = ⇢ if Dsum < thepe 1 if Dsum > thepe

t EPE violation minimization

› Formulated as a continuous function (Differentiable!)

Observation: distortion is continuous

Fepe = X

(i,j)∈HS

sig(Dsumi,j) + X

(i,j)∈V S

sig(Dsumi,j) (

Image EPE EPE Target contour VS HS

(Continuous/Differentiable) thepe Vio EPE 1 sigmoid

Process Window Optimization

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PV Band

Fpvb =

Np

X

k=1

(Zk Zt)2

t Process variability band (PV band)

› Area between the outermost and the innermost edges among all process conditions Np: #Process conditions

Outline

t Mask Optimization: Why & How? t Proposed Approach: MOSAIC t Experimental Results t Conclusions

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Experiment Setup

t MOSAIC_fast (Total Distortion + PV band) t MOSAIC_exact (EPE Violation + PV band) t Benchmark

t 10 layout clips from 32nm M1 layer released by IBM

t Lithography parameters

› 193nm wavelength › Process variations: ±25nm defocus, ±2% dose

t Evaluation (ICCAD Contest 2013)

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Fexact = αFepe + βFpvb

: Score = Runtime + 4 × PV B + 5000 × #EPE

Ffast = αFtd + βFpvb

Score Comparison

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Both approaches outperform ICCAD’13 contest winners 7% Imp. 11% Imp.

Runtime Comparison

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Conclusion

t ILT-based OPC that simultaneously optimizes

Design Target and Process Variation

› More accurate EPE formulation into the ILT engine › Continuous and differentiable › 11% overall improvement than the 1st place winner

t Future directions

› Our framework can be extended to handle mask complexity › Multiple patterning, 3D effects › New emerging lithography such as DSA › Co-optimizations with design rules, hotspots, etc…

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Thank you!

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Gradient Descent Convergence

t All benchmarks converges within 20 iterations

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Jump out of local optimum

Regularization: Needed or Not?

t An example of E-beam mask writing [Zable+, SPIE’2010]

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Curved lines may be well handled with advanced techniques Target OPC Fractured Mask Image Wafer Image

Runtime/EPE/PVB Comparison

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OPC Results

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Target OPC Mask Final pattern PV Band