1. Hongbo Zhang, Yuelin Du, Martin D.F. Wong, Yunfei Deng, Pawitter Mangat Synopsys Inc., USA Dept. of ECE, Univ. of Illinois at Urbana-Champaign GlobalFoundries Inc., USA Layout Small-Angle Rotation and Shift for EUV Defect Mitigation ICCAD 2012

2. Outline Introduction Background Problem Formulation Problem Solutions Experimental Results Conclusion

3. Introduction EUV lithography has become a major solution to the next generation lithography process with finer resolution and reasonable throughput. Challenges Exotic light source setup Resist tuning for line edge roughness and sensitivity defect-free mask manufacturing

4. Introduction At present, to make a defect-free EUV mask blank is still too costly and impractical. The buried defects in the multilayer (ML) reflective structure are the main source of blank defect. Defects could have significant impact when they are adjacent to the feature boundary, and severe printability issues, such as bridging or breaking of the printed lines

5. Introduction Mitigating the defect Remove the defect from the blank by using Ion-beam and electron beam The defect location detection with 10–30nm inaccuracy Throughput is still far from the requirement Damage on the ML structure OPC-like defect modeling and pattern modification method Requires extremely precise defect location, height, width and process variation control

6. Introduction As the phase change is insignificant on the feature boundary, defects will have little impact on the printed wafer.

7. Background EUV Mask Preparation Because of the 13.5 nm wavelength, a multilayer (ML) structure is needed for the reflective optics. EUV mask is prepared through two steps ML structure is coated and blank defects will also be randomly generated Mask absorbers with designed patterns are placed on top of the mask blank with 4X reduction factor As the layout to print is smaller than the blank, there is certain freedom to find the best layout location on the blank.

8. Rotation helps defect mitigation.

9. Mask preparation and fiducial generation flow

10. Problem Formulation Definition of Solution Space Depending on the limits of the mask alignment tool and EUV scanner, the reticle may have a certain freedom in its small angle rotation and shift maximum shift upper bound F max maximum rotation upper bound θ max This small angle rotation does not contradict the possible 90 ◦, 180 ◦ or 270 ◦ rotation, which can happen simultaneously.

11. Problem Formulation Definition of Solution Space The shift amount in X-Y directions as ( Δ X, Δ Y ) rotation amount as θ the whole solution space is an Bounding Octahedron (BO)

12. Problem Formulation Prohibited Relocation Cube During the layout relocation process, a defect might potentially impact different boundaries according to certain shift and rotation amount Prohibited rectangle (PR) represent the defect relocation positions that a defect center should avoid.

13. Problem Formulation Prohibited Relocation Cube If we notate such prohibited relocation movement as ( Δ X i, Δ Y i, θ i ), the prohibited movement should satisfy the following equations:

14. Problem Formulation Prohibited Relocation Cube When θ i is small, a small angle approximation sin θ i ≒ θ i and cos θ i ≒ 1 becomes valid. To guarantee the validation of eq. 3 and eq. 4, the total error must be within the accuracy requirement E max Therefore, the maximum allowable rotation for linearity is less than a rotation bound θ linear, depending on the relocation accuracy and (X d, Y d ).

15. Problem Formulation Prohibited Relocation Cube For the scenario that, we can always slice the rotation range into small pieces For each new piece, we only need to regenerate the new defect map (Xd,Yd) by calling rotation function once

16. Problem Formulation Mitigation for Relocation Inaccuracy The real Δ Xi, Δ Yi and i could have offset.

17. Problem Formulation Minimum Cube Overlapping Problem each pair of defect and feature boundary will generate a PRC through previous steps If we draw all the PRCs together in the BO, all the PRCs might overlap with each other The overlapping PRC number on one point represents the number of damaged boundaries once that relocation is adopted.

18. Problem Solutions Problem Reduction The outside defects have much larger movable regions than the inside ones. Only the prohibited rectangles covered by the cropped region need to be considered. The size of prohibited rectangle is exaggerated for better illustration.

19. Problem Solutions Solutions for Min-CO Problem the sweeping line algorithm is an efficient algorithm to solve the rectangle overlapping problem extend this sweeping line algorithm to solve the overlapping problem in 3D space, which is to sweep the ( Δ X, Δ Y ) plane along the θ axis and then find the minimum overlapping region in each cross-section.

20. The overall flow

21. Experimental Results

22. Conclusions a novel algorithm to mitigate defects by layout shift and rotation on blanks. transform the pattern relocation problem into a minimum cube relocation problem