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Automated Layout and Phase Assignment for Dark Field PSM

Automated Layout and Phase Assignment for Dark Field PSM. Andrew B. Kahng, Huijuan Wang, Alex Zelikovsky UCLA Computer Science Department http://vlsicad.cs.ucla.edu Supported by a grant from Cadence Design Systems, Inc. Outline. Phase assignment for dark field Alt PSM

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Automated Layout and Phase Assignment for Dark Field PSM

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  1. Automated Layout and Phase Assignment for Dark Field PSM Andrew B. Kahng, Huijuan Wang, Alex Zelikovsky UCLA Computer Science Department http://vlsicad.cs.ucla.edu Supported by a grant from Cadence Design Systems, Inc.

  2. Outline • Phase assignment for dark field Alt PSM • Removing odd cycles from conflict graph • previous work • proposed methods • Algorithms for odd cycle elimination • Implementation experience • Conclusions

  3. Outline • Phase assignment for dark field Alt PSM • Removing odd cycles from conflict graph • previous work • proposed methods • Algorithms for odd cycle elimination • Implementation experience • Conclusions

  4. Alternating PSM conventional mask phase shifting mask glass Chrome Phase shifter 0 E at mask 0 0 E at wafer 0 0 I at wafer 0

  5. Features Conflict areas (<B) < B > B 0 180 0 Phase Assignment Problem Assign phases 0, 180 to all features s.t. pairs with separation < B have opposite phases  b b  minimum separation B  minimum separation between same-phase features

  6. Conflict Graph Vertices: features Edges: conflicts (feature pairs with separation< B ) < B

  7. Odd Cycles in Conflict Graph No valid phase assignment exists, because of odd cycle (triangle) in conflict graph Valid assignment  2-colorable  bipartite  no odd cycles

  8. Breaking an Odd Cycle  B

  9. Outline • Phase assignment for dark field Alt PSM • Removing odd cycles from conflict graph • previous work • proposed methods • Algorithms for odd cycle elimination • Implementation experience • Conclusions

  10. Previous Work • Interactive methods (Ooi et al., Moniwa et al.) • detect odd cycles • manually widen spacing for chosen pairs • Compaction method (Ooi et al.) • symbolic layout from mask layout • phase assignment in symbolic layout • PSM design rules • compaction of symbolic layout

  11. Proposed Methods • Iterative coloring and compaction • One-shot phase assignment • Conflict edge weight • Splitting of features • Vertical/horizontal spacing • Layer assignment

  12. Iterative Phase Assignment and Compaction Iterate until conflict graph becomes bipartite: • Compact the layout and find conflict graph • Find minimum set of edges to be deleted from conflict graph for 2-colorability • Add new separation constraints: one per deleted edge

  13. Iterative Phase Assignment and Compaction conflict graph find minimum # edges to be deleted for 2-colorobility already 2-colorable yes phase assignment no PSM constraints compaction

  14. One-Shot Phase Assignment • Find conflict graph • Find minimum set of edges to be deleted from conflict graph for 2-colorability • Assign phases such that only chosen conflict edges connect features of the same phase • Compact layout with PSM design rules: • B-separation if features have the same phase • b-separation if features have different phase

  15. One-Shot Phase Assignment conflict graph find minimum # edges to be deleted for 2-colorobility phase assignment compaction

  16. Conflict Edge Weight • Compaction moves all features left • Constraint graph contains arcs between edges • Critical path between leftmost, rightmost features • Conflict edges not on critical path: break for free critical path

  17. Feature Splitting • Splitting features may eliminate odd cycle • Green areas: phase shift between 0, 180 degrees

  18. Vertical / Horizontal Spacing • Introducing a vertical or horizontal gap eliminates all conflict edges that cross gap • Optimal algorithm to find min # gaps

  19. Layer Assignment

  20. Outline • Phase assignment for dark field Alt PSM • Removing odd cycles from conflict graph • previous work • proposed methods • Algorithms for odd cycle elimination • Implementation experience • Conclusions

  21. Optimal Odd Cycle Elimination • Construct conflict graph G • Construct dual graph D • Find odd-degree vertices ODD in D • Find minimum weighted perfect matching of ODD (weights = the length of path) • Delete all edges of G which correspond to paths of the minimum matching of ODD

  22. Optimal Odd Cycle Elimination blue features/red conflicts conflict graph matching of odd degree nodes dual graph

  23. Optimal Odd Cycle Elimination blue features/red conflicts delete green conflicts matching of odd degree nodes conflict graph

  24. 3 Fast Algorithm • For each odd degree vertex V in dual graph • Voronoi regioneven degree vertices which are closer to V than to any other odd degree vertex • Connect two vertices if there is an edge between their Voronoi regions • edge weight  path cost in dual graph • Find matching between odd degree nodes in Voronoi graph

  25. Outline • Phase assignment for dark field alt PSM • Removing odd cycles from conflict graph • previous work • proposed methods • Algorithms algorithm for odd cycle elimination • Implementation experience • Conclusions

  26. Compaction • Shape constraints • Connectivity constraints • Spacing constraints (PSM design rules) • Bellman-Ford solution for constraint graph for one-dimensional constraint graph in x-direction • Flip design and solve in y-direction

  27. Data Flow • GDSII  CIF • CIF  internal layout representation • New layer with phase shift  CIF

  28. Results

  29. Outline • Phase assignment for dark field alt PSM • Removing odd cycles from conflict graph • previous work • proposed methods • Algorithms algorithm for odd cycle elimination • Implementation experience • Conclusions

  30. Conclusions

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