1. 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, OR
2Dept. of ECE, University of Illinois at Urbana-Champaign
3GlobalFoundries Inc., Sunnyvale, CA

2. 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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3. 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:
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4. EUV Masks EUV mask is a mirror with Multi-layer structure.
Ideal Mask
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.
Real Mask
EUV is a potential lithography technique for the future sub-20nm technolology node. Absorber is deposited on top of the multilayer structure. The buried defect will impact the feature when the feature boundary is too close to the defect. To mitigate the defects, one simple way would be let the feature cover the defects or push the feature far away from the defects.
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C. H. Clifford et. al. SPIE 2010,

5. 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.
EUV is a potential lithography technique for the future sub-20nm technolology node. Absorber is deposited on top of the multilayer structure. The buried defect will impact the feature when the feature boundary is too close to the defect. To mitigate the defects, one simple way would be let the feature cover the defects or push the feature far away from the defects.
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6. 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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7. 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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8. 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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9. 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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10. 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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11. Input/Output of Our Algorithm
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.
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12. 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:
𝜃 𝑚𝑎𝑥 ∙𝑆ℎ𝑖𝑓𝑡+ 𝐹 𝑚𝑎𝑥 ∙𝑅𝑜𝑡𝑎𝑡𝑒= 𝜃 𝑚𝑎𝑥 ∙ 𝐹 𝑚𝑎𝑥
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13. 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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14. Definition of 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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15. 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
𝐿≤ 𝑋 ′ =𝑋𝑐𝑜𝑠𝜃−𝑌𝑠𝑖𝑛𝜃+∆𝑋≤𝑅
𝐵≤ 𝑌 ′ =𝑋𝑠𝑖𝑛𝜃+𝑌𝑐𝑜𝑠𝜃+∆𝑌≤𝑇
𝐿≤ 𝑋 ′ =𝑋−𝑌∙𝜃+∆𝑋≤𝑅
𝐵≤ 𝑌 ′ =𝑋∙𝜃+𝑌+∆𝑌≤𝑇
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16. 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 detected
For each θ:
Scan each rectangle overlapping regions:
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17. Efficiency of the Approach
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
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18. Efficiency of the Approach, cont’
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 …
Defect Mitigation
Useful
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19. 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(F2maxNθ).
Linear to the solution space.
Much smaller than the brute-force approach: O(n*F2maxNθ).
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20. 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.
𝐿≤ 𝑋 ′ =𝑋−𝑌∙𝜃+∆𝑋±𝑑𝑥′±𝑌∙𝑑𝜃′≤𝑅
𝐵≤ 𝑌 ′ =𝑋∙𝜃+𝑌+∆𝑌±𝑑𝑦′±𝑋∙𝑑𝜃′≤𝑇
𝐿−𝑑 𝑥 ′ −𝑌∙𝑑 𝜃 ′ ≤𝑋−𝑌∙𝜃+∆𝑋≤𝑅+𝑑 𝑥 ′ +𝑌∙𝑑𝜃′
𝐵−𝑑 𝑦 ′ −𝑋∙𝑑𝜃′≤𝑋∙𝜃+𝑌+∆𝑌≤𝑇 +𝑑 𝑦 ′ +𝑋∙𝑑𝜃′
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21. 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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22. 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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23. Experimental Results, cont’
Test
Defect #
No Rotation
Rotation
Runtime (s)
Affected
Early Stop Time (s)
Map1 80
318 2
44465
1207
Map2
309 4
43294
711
Map3
283
39586
288
Map4
100
360
50390
369
Map5 6
51647
2877
Map6
330
46169
693
Map7
120
419
58675
3311
Map8
496 8
69423
1636
Map9
345
48346
1071
Rotation can largely benefit the defect relocation approach
Need support of reticle holder
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24. 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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25. Thanks
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