Layout Small-Angle Rotation and Shift for EUV Defect Mitigation

Hongbo Zhang1, Yuelin Du2, Martin D.F. Wong2, Yunfei Deng3, Pawitter Mangat3

1Synopsys Inc., Hillsboro, OR2Dept. of ECE, University of Illinois at Urbana-Champaign

3GlobalFoundries Inc., Sunnyvale, CA

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Outline

• Introduction of EUV process • Previous works on defect mitigation

– Shift-only approaches analysis.– Motivation to introduce rotation

• Our method and analysis• Experimental results• Conclusions

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Introduction of EUV • Every lithographer has his own EUV dream, since over

15 years ago:– Sweet part: 193nm vs 13.5nm– Nightmare: cost, defect, throughput, process control…

ASML NXE 3100:http://www.mysemicondaily.com/blog/2010/7/6/asmls-pre-production-euv-tool-achieves-first-light.html

http://www.dcsc.tudelft.nl/~mverhaegen/n4ci/pid.htm

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EUV Masks

• EUV mask is a mirror with Multi-layer structure.

• In reality, EUV blanks are defective:– Buried defects– Particles

• EUV defects could cost serious printing problem.

Ideal Mask

Real Mask

C. H. Clifford et. al. SPIE 2010, 76362311/5/2012

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EUV Defect Mitigation Process• In order to mitigate defects, we need…

– Inspection tools– Behavior model– Mitigation method

• Among all defect mitigation approaches, layout relocation is one of most cost-effective ways to mitigate defects.

A B

A B

(b)

(a)

dx

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Validation of Layout Relocation– Fiducial Mark

• Fiducial mark creates coordinates for defect map and layout.

• During mask preparation, the layout could have small angle rotation and shift for coordinate pairing.

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http://ieuvi.org/TWG/Mask/2009/MTG022209/Summary_of_SPIE_FIDUCIAL_MARK_Sematech.pdf

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Previous Work on Pattern Relocation• Industrial Initiations [J. Burns, BACUS 2010]

– Call this “defect avoidance” and demonstrate an initial work– Allow shift in X and Y directions and 90 degree rotation– Very slow.

• 64x146 minute CPU time.– Could only answer yes/no

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Previous Work on Pattern Relocation, cont’

• Improved work [H. Zhang, ASP-DAC’12]– Largely speed up the process (~100x).– Can find the least defective location (non-zero).– Could embed an effective defect model.

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However, Something is Still Missing…• Missing the possibility of small angle rotation of layout.• Low success ratio:

– Highly depends on defect size and #• Need large amount of defect removal process• Need efficient algorithm to the following layout-blank

pairing process

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Importance of Small Angle Rotation • Reticle holder can rotate a tiny small angle for alignment

adjustment.• Small angle rotation helps explore the 3rd exploration dimension.• Previous work becomes a special case when θ=0.• Important to increase success rate of layout-blank pairing.

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LayoutDefect Defect

(a) Without rotation, no defect-free location can be found

(b) With little rotation θ, a defect-free location can be found

θ Blank

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Input/Output of Our Algorithm• Input:

– Layout/Die• Feature location• Boundary sensitivity

– Blank/Mask• Defect info (height, FWHM) and distribution• Freedom (X,Y,θmax)

• Output:– Best Relocation position (∆X, ∆Y, θ) to cover or

avoid the most defects.11/5/2012

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Relocation Bound

• Layout relocation are always bounded– Rotation: ±θmax

– Shift: ±Fmax

• The rotation bound and shift bound are correlated with each other, which can be linearly described as:

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Shift

Rotation

Fmax

θmax

0

𝜃𝑚𝑎𝑥 ∙ h𝑆 𝑖𝑓𝑡+𝐹𝑚𝑎𝑥 ∙𝑅𝑜𝑡𝑎𝑡𝑒=𝜃𝑚𝑎𝑥 ∙𝐹𝑚𝑎𝑥

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Solution Space Analysis• The whole solution space is an octahedron in ∆X-∆Y-θ

space.

• In this octahedron:– The cross-section on the plane ∆X=0 and ∆Y=0 is the θmax-Fmax

triangle (dashed regions).– The cross-section on the plane θ is a square.

• The problem is equal to detecting the best point in the octahedron for layout relocation.

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ΔX

θ

Fmax

Fmax

-Fmax

-Fmax

ΔY

-θmax

θmax

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Definition of Prohibited Rectangle

• Prohibited Rectangle:– The prohibited region of the center of a

defect for one boundary• Target of relocation:

– Avoid any defect center to be shifted into its own Prohibited Rectangles

A defect with radius r

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Definition of Prohibited Relocation Cube

• Prohibited relocation movement (∆X, ∆Y, θ) for each prohibited rectangle

• Small angle approximation

• Prohibited relocation cube (PRC) in ∆X-∆Y-θ space

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Prohibited Rectangle

(Li, Bi)

(Ri, Ti)

θi

(Δ Xi , Δ Yi)

Xd’=Xdcosθi-Ydsinθi

Yd’=Xdsinθi+Ydcosθi

x

y

Defect Center: (Xd, Yd)

(0, 0)

ΔX

θ

ΔY

WidthLen

gth

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Detect the Best Relocation Position• Detect the best relocation Position ↔ Find the

minimum overlapping PRC – Any non-overlapping region works!

• Sweeping line algorithm:

• Early stops when 0 is detected11/5/2012

For each θ: Scan each rectangle overlapping regions:

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Efficiency of the Approach

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• Impact region is very limited– Fmax is usually ±200um– Impact region is much smaller

than a full chip size (4X reduction factor)

• Only prohibited rectangles in the impact region need be considered

Impact region

Layout

rd

Defect

Prohibited Rect.

Feature

Allowable Region

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Efficiency of the Approach, cont’

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• Defect movable region is very limited:– Each defect’s movable region is

much smaller than the overall layout

• Usually a few hundreds micron by a few hundreds micron

• Layout can be chopped based on the defect maps, and only those with movable region need be read in.

Original Layout

Piece Piece Piece Piece …

Defect Mitigation

Useful

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Linearity of the Algorithm

• The default Sweeping Line Algorithm has time complexity O(nlog(n)); n is the rectangle #– O(nlog(n)) is from the sort of the rectangles’ vertices.

• In our problem, the prohibited rectangle # n is comparable to the grid number in a sweeping plane.– Directly use the coordinate grid in the solution space as

the sweeping grid.– The runtime can be reduced to O(F2

maxNθ).– Linear to the solution space.– Much smaller than the brute-force approach: O(n*F2

maxNθ).

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Modification for Alignment Error• We are usually seeing an alignment error or defect

location error (±dx’, ±dy’, ±dθ’) during the fiducial mark alignment process.

• The prohibited relocation cube can be modified to be:

• The prohibited relocation cube overlapping method is still valid.

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Modification for Cover-Only Case • Sometimes, it is required that defects should only be covered by the absorbers.

• Modification on the solution:– Change prohibited rectangle to allowable rectangles.– Change target to find the maximum

overlapping allowable relocation cube

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Experimental Results

• Experiment setup:– One full size test chip (17.25MB in oasis, ~9GB in

GDS)– Randomly generated defect maps with random

size 0~250nm radius– Intel Xeon 2.40GHz CPU– 52GB memory– Fmax=±200um

– Nθ=300

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Experimental Results, cont’

Test Defect #No Rotation Rotation

Runtime (s) Affected Runtime (s) Early Stop Time (s) AffectedMap1 80 318 2 44465 1207 0Map2 80 309 4 43294 711 0Map3 80 283 0 39586 288 0Map4 100 360 0 50390 369 0Map5 100 369 6 51647 2877 0Map6 100 330 2 46169 693 0Map7 120 419 4 58675 3311 0Map8 120 496 8 69423 1636 0Map9 120 345 2 48346 1071 0

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• Rotation can largely benefit the defect relocation approach

• Need support of reticle holder

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Conclusions• This is the first ever paper for the algorithm to relocate layout

for EUV defect mitigation with small angle rotation.• We largely increase the success rate.• The runtime of the algorithm is linear to the size of solution

space.• The algorithm can be expanded for more complex

requirements:– Cover-only requirement– Fiducial mark misalignment.

• The result demonstrates a promising future for EUV defect mitigation with layout relocation approach.

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Thanks

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