Fast and Area-Efficient Phase Conflict Detection and Correction in Standard-Cell Layouts

1. Fast and Area-Efficient Phase Conflict Detection and Correction in Standard-Cell Layouts Charles Chiang, Synopsys Andrew B. Kahng, UC San Diego Subarna Sinha, Synopsys Xu Xu, UC San Diego

2. Outline • Introduction of AAPSM • AAPSM Conflict Detection • AAPSM Conflict Correction • Conclusions

3. Alternating Aperture Phase Shift Mask (AAPSM): Phase-modulation at the mask level to increase resolution capabilities of optical lithography. AAPSM: Enabling Technology Mask Wafer

4. Alternating Aperture Phase Shift Mask (AAPSM): Phase-modulation at the mask level to increase resolution capabilities of optical lithography 180 o phase-shifter AAPSM: Enabling Technology Mask Wafer

5. Alternating Aperture Phase Shift Mask (AAPSM): Phase-modulation at the mask level to increase resolution capabilities of optical lithography. 180 o phase-shifter 0.11mm AAPSM: Enabling Technology Mask Wafer Shifters 180 Mask 0 Wafer Printed using a 0.35 um nominal process Feature

6. AAPSM: Enabling Technology Alternating Aperture Phase Shift Mask (AAPSM): Phase-modulation at the mask level to increase resolution capabilities of optical lithography. • Benefits: • - Smaller feature sizes. • Better optical resolution • - Extend equipment life

7. Outline • Introduction • AAPSM Conflict Detection • AAPSM Conflict Correction • Conclusions

8. Feature 0 180 Shifters Additional Layout Rules • Feature Rule:Shifters of the same feature must have different phases • Overlapping Rule:Overlapping shifters must have the same phase Overlapping Shifters • Conflict:A pair of shifters violate the rules after phase assignment • Legal Layout:No conflicts

9. Conflict Detection Problem Formulation • Conflict correction lead to increased area • Given:A layout (a set of shifters) • Conflict weights = area increase for correcting the conflict • Assign:phases to shifters • To minimizethe total area increase of all conflicts Conflict Area increase after correction

10. AAPSM Conflict Detection Flow Layout Conflict Cycle Graph Construction

11. AAPSM Conflict Detection Flow Layout Conflict Cycle Graph Construction Graph Planarization

12. AAPSM Conflict Detection Flow Layout Conflict Cycle Graph Construction Graph Planarization Graph Legalization / Phase Assignment

13. AAPSM Conflict Detection Flow Layout Conflict Cycle Graph Construction Graph Planarization Graph Legalization / Phase Assignment Check Removed Edge During Planarization

14. AAPSM Conflict Detection Flow Layout Conflict Cycle Graph Construction Graph Planarization Graph Legalization / Phase Assignment Check Removed Edge During Planarization Set of AAPSM conflicts for correction

15. Review of Work in Conflict Detection • Conflict Graph Construction • Feature Graph (Kahng et al. ASPDAC 2003) • Phase Conflict Graph (Chiang et al. DATE 2005) • Conflict Cycle Graph (Non-bipartite Formulation) • Graph Legalization • Iterative Voronoi Graph (Kahng et al. BACUS 98) • T-join based bipartization for planar graph (Berman et al. TCAD 2000) • Spanning Tree-Based Algorithm (Kahng et al. ASPDAC 2003) • Modified T-join algorithm for non-bipartite graph

16. Conflict Cycle Graph • Node represents a shifter • Feature edge connects two nodes of the same feature • Nodes of the feature edge have different phases • Overlap edge connects overlapping nodes • Nodes of the overlap edge have the same phase • Edge weight = conflict weight • Remove one edge = correct the corresponding conflict Overlap edge Feature edge

17. Conflict Cycle and Conflict Face • Conflict cycle = cycle with odd # feature edges • Legal cycle = cycle with even # feature edges Conflict Fact: • Legal Layout No conflict cycles

18. Comparison with Previous Graph After removing uncorrectable edges 2 edges Phase Conflict Graph (DATE 2005) 9 edges Conflict Cycle Graph (Proposed) 5 edges Uncorrectable edges can be removed with non-bipartite formulation

19. Min-Weight Edge-Deletion Fact: • A planar graph has no conflict cycle if • Remove even number of edges for legal faces • Remove odd number of edges for conflict faces Conflict Face Legal Face

20. Min-Weight Edge-Deletion Problem Formulation • Given:A planar conflict cycle graph G(V,E) • Find:a set of edges E’to be deleted such that • For each legal face, the number of edges in E’ is even • For each conflict face, the number of edges in E’ is odd • To minimizethe total weight of edges in E’ Flow to optimally solve the problem • Conflict cycle graph  Dual graph (T-join problem) • Dual graph  Gadget graph (Perfect matching problem) • From optimal matching solution  edges to be deleted

21. Conflict Cycle Graph  Dual Graph 5 4 face 6 node • Conflict face  Conflict node • Legal face  Legal node 2 3 1 Conflict Graph 4 edge dual edge 3 2 1 5 6 Dual Graph

22. T-join Problem Formulation • Given:A graph GD(V, E, T) (T is the set of all conflict nodes) • Find:a set of edges E’to be deleted such that • For each node v, the edge number in E’ is odd iff • To minimizethe total weight of edges in E’ 4 face node 4 5 3 2 6 2 1 3 5 6 1 edge dual edge Conflict Graph Dual Graph

23. Dual Graph  Gadget Graph • T-join problem  min-weight perfect matching 4 4 6 node gadget 3 2 3 2 1 5 6 1 true node edge 5 Dual Graph Gadget Graph

24. Perfect Matching 4 6 4 6 3 3 Perfect Matching 2 2 1 1 5 5 5 4 4 5 6 Delete edges 1 and 2 + Phase assignment 6 2 2 3 3 1 1

25. Experiments Setup • Implement proposed algorithms in C • Use 4X400M Ultra-Sparc II with 4G RAM • Ten large industry testcases • 90 nm designs • # features from 10,274 to 159,070

26. Conflict Detection Results Speedup 5.9x Faster Ten Test Cases

27. Conflict Detection Results # Conflicts 3.88% Reduction Ten Test Cases

28. Outline • Introduction • AAPSM Conflict Detection • AAPSM Conflict Correction • Conclusions

29. Mask-level Conflict Correction • Modify shifters on mask. • Split shifter region whenever two shifters of opposite phase overlap. Split • Pros: no design modification • Cons: • Increases mask complexity, correction not always possible • Can negatively affect process latitude

30. Widen Feature • Increase width of certain features to make them non-critical Widen No shifters needed for widened feature • Pros: small change in layout • Cons: performance degradation

31. Add Spacing • Insert vertical or horizontal gaps between overlapping shifters of different phases. Spacing • Pros: small performance penalty as width of gate features remains unchanged • Cons: larger area increase •  Our focus

32. Insert gap across the whole layout Large area increase Local versus Global Spacing Insert gap locally Introduce new conflict

33. PSM Conflict Correction Original Layout Divide layout into rows Divide each row into cells

34. PSM Conflict Correction Original Layout Divide layout into rows Divide each row into cells Insert gap across the cell to remove conflicts

35. PSM Conflict Correction Original Layout Adjust row distance Divide layout into rows Adjust cell distance to avoid new conflicts Divide each row into cells Insert gap across the cell to remove conflicts

36. PSM Conflict Correction Original Layout Modified Layout Adjust row distance Divide layout into rows Adjust cell distance to avoid new conflicts Divide each row into cells Insert gap across the cell to remove conflicts

37. 1 2 3 5 4 6 Generalized Correction Scheme H • Solve conflicts within each region • From the bottom of the tree • Insert spacing along the slicing line to avoid the conflicts between features of different regions V V V H H H H H 1 2 3 4 5 6

38. Conflict Correction Results

39. Outline • Introduction • AAPSM Conflict Detection • AAPSM Conflict Correction • Conclusions

40. Conclusion • AAPSM Conflict Detection: • First non-bipartite graph based approach • 5.9x runtime improvement • 3.88% conflict reduction • AAPSM Conflict Correction: • Hierarchical layout modification • Small area increase on the average ( 6.1%) for large testcases • Future Work: • Incorporate feature widening as an option • Timing-driven PSM conflict correction

41. Thank You!