1. NanoCAD Lab UCLA Effective Model-Based Mask Fracturing Heuristic Abde Ali Kagalwalla and Puneet Gupta NanoCAD Lab Department of Electrical Engineering, UCLA

2. abdeali@ucla.edu UCLA Outline Mask Fracturing Overview Our Fracturing Method Experimental Results Conclusions

3. abdeali@ucla.edu UCLA Mask Fracturing 101 Variable shaped e-beam (VSB) tool writes mask pattern Fracturing  Get rectangular e-beam shots that VSB tool needs to write given mask pattern Source: Yu et al., ASPDAC 2013 Fractured mask Target mask pattern

4. abdeali@ucla.edu UCLA Mask Write Time Increase Mask write times increasing despite e-beam throughput improvements Aggressive RETs  Curvilinear ILT shapes  Shots One of the key reasons for escalating photomask manufacturing costs 4 Source: M. Chandramouli, et al., SPIE BACUS Photomask 2012 Calibre pxOPC layout

5. abdeali@ucla.edu UCLA Model-Based Mask Fracturing  Overlapping Shots + E-beam Proximity Effect 5 Traditional mask fracturing  3 shots Overlapping shots allowed  2 shots Lower shot count NP-hard Target shape Ebeam shot Source: Bunday et al., MICRO Magazine, 2008 Shot (s) Resist Image Intensity Map I(x, y, s)

6. abdeali@ucla.edu UCLA Mask Fracturing Problem Description 6 000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000 000000000000000000000000222222222222222222200000000000 000000000000000000000002222222222222222222222000000000 000000000000000000000022222222222222222222222200000000 000000000000000000000222222222222222222222222220000000 000000000000000000002222111111111111111111122222000000 000000000000000000022221111111111111111111112222000000 000000000000000000222211111111111111111111111222200000 000000000000000002221111111111111111111111111222200000 000000000000000022221111111111111111111111111122220000 000000000000000222211111111111111111111111111122220000 000000000000002222111111111111111111111111111122220000 000000000000002222111111111111111111111111111122220000 000000000000022221111111111111111111111111111122220000 000000000000022221111111111111111111111111111122220000 000000000000222211111111111111111111111111111122220000 000000000000222211111111111111111111111111111122220000 000000000002222111111111111111111111111111111122220000 000000000002222111111111111111111111111111111122220000 000000000022221111111111111111111111111111111122220000 000000000022221111111111111111111111111111111122220000 000000000222211111111111111111111111111111111122220000 000000000222211111111111111111111111111111111122220000 000000002222111111111111111111111111111111111122220000 000000002222111111111111111111111111111111111122220000 000000022221111111111111111111111111111111111122220000 000000022221111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000002222111111111111111111111111111111111111122220000 000000222211111111111111111111111111111111111122220000 000000222211111111111111111111111111111111111122220000 000000022221111111111111111111111111111111111222200000 000000002222111111111111111111111111111111111222200000 000000002222111111111111111111111111111111111222200000 000000000222211111111111111111111111111111111222200000 000000000022221111111111111111111111111111111222200000 000000000002222111111111111111111111111111112222000000 000000000000222211111111111111111111111111112222000000 000000000000022221111111111111111111111111122220000000 000000000000002222111111111111111111111111122220000000 000000000000000222211111111111111111111111222200000000 000000000000000022222111111111111111111111222200000000 000000000000000002222221111111111111111112222000000000 000000000000000000222222222222222222222222220000000000 000000000000000000022222222222222222222222200000000000 000000000000000000000222222222222222222222000000000000 000000000000000000000002222222222222222220000000000000 000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000 CD tolerance

7. abdeali@ucla.edu UCLA Overview of Our Fracturing Method Approximate Fracturing Get Shot Corner Points Map to Graph Coloring Shot Refinement Adjust shot edges Merge aligned shots Add/remove shots

8. abdeali@ucla.edu UCLA Approximate Fracturing : Covering Curved Shape Boundaries Shot boundary Resist image Orthogonal segment  One shot edge can cover Non-orthogonal segment  Exploit corner rounding Corner rounding of rectangular shot Complex Mask Shape

9. abdeali@ucla.edu UCLA Approximate Fracturing : Find Shot Corner Points Approximate mask boundary using Ramer-Douglas-Peucker method Place shot corner points (location + type{top-right, bottom- left…}) to exploit corner rounding Subset of vertices chosen Approximate boundary Shot corner point Top-right Clustered shot corner points Approximate Boundary Traversal Vertical

10. abdeali@ucla.edu UCLA Approximate Fracturing : Map to Graph Coloring Graph Mapping  Edge between any pair of shot corners that can be combined into one shot Inverse graph  Converts minimum clique cover to graph color Greedy sequential graph coloring  Each color corresponds to one shot Inverse Color Graph mapping

11. abdeali@ucla.edu UCLA Shot Refinement to Fix CD Constraints Cost Reduced in last N iterations ? Yes Greedily move one edge If none found, bias all edges Remove shot Add shot No

12. abdeali@ucla.edu UCLA Merging Shots during Refinement to Reduce Shot Count Evaluate every pair of shots after each refinement iteration If two shots vertically or horizontally aligned, and merged shot lies inside target  merge Shots merged with vertical extension Shots aligned but cannot be merged

13. abdeali@ucla.edu UCLA Experimental Setup

14. abdeali@ucla.edu UCLA Shot Count of Different Heuristics 60nm 105nm 280nm 111nm 55nm 222nm 180nm 125nm 143nm 75nm 95nm 75nm 70nm 132nm 137nm 47nm 190nm 197nm 280nm

15. abdeali@ucla.edu UCLA Shot Count of Different Heuristics Our method has lowest shot count on average For seven shapes, our method is the best among all heuristics

16. abdeali@ucla.edu UCLA Runtime vs Shot Count for 10 Real ILT Mask Shapes GSC MP PROTO-EDA* Our method * Exact running time of PROTO-EDA is not known, but is less than 1 second for each mask shape

17. abdeali@ucla.edu UCLA Conclusions Proposed novel model-based mask fracturing heuristic –Graph coloring based approximate fracturing –Shot refinement to fix CD violations Out-performs known heuristics for ten real ILT mask shapes –23% lower shot count, similar runtime compared to PROTO-EDA –5% lower shot count, 33X faster compared to matching pursuit – 43% lower shot count, similar runtime compared to greedy set cover 1.3X sub-optimality compared to known upper bound on optimal shot count