Layout Small-Angle Rotation and Shift for EUV Defect Mitigation Hongbo Zhang 1 , Yuelin Du 2 , Martin D.F. Wong 2 , Yunfei Deng 3 , Pawitter Mangat 3 1 Synopsys Inc., Hillsboro, OR 2 Dept. of ECE, University of Illinois at Urbana-Champaign 3 GlobalFoundries Inc., Sunnyvale, CA
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Layout Small-Angle Rotation and Shift for EUV Defect Mitigation
Layout Small-Angle Rotation and Shift for EUV Defect Mitigation. Hongbo Zhang 1 , Yuelin Du 2 , Martin D.F. Wong 2 , Yunfei Deng 3 , Pawitter Mangat 3 1 Synopsys Inc., Hillsboro, OR 2 Dept. of ECE, University of Illinois at Urbana-Champaign 3 GlobalFoundries Inc., Sunnyvale, CA. - PowerPoint PPT Presentation
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Layout Small-Angle Rotation and Shift for EUV Defect Mitigation
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
– 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
ICCAD'12 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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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
• 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.