Bright-Field AAPSM Conflict Detection and Correction

1. Bright-Field AAPSM Conflict Detection and Correction C. Chiang, Synopsys A. Kahng, UC San Diego S. Sinha, Synopsys X. Xu, UC San Diego A. Zelikovsky, GSU

2. Outline • Introduction • AAPSM Conflict Detection • AAPSM Conflict Correction • Conclusions & Future Work

3. Outline • Introduction • AAPSM Conflict Detection • AAPSM Conflict Correction • Conclusions & Future Work

4. Above Wavelength SubWavelength Sub-wavelength Lithography 10 3.0mm 2.0mm 1.0mm 1.0 0.6mm 436nm 365nm 248nm 193nm 0.35mm 157nm 0.25mm 0.18mm 0.1 0.13mm 90nm Silicon Feature Size 65nm 45nm Lithography Wavelength 32nm 1980 1985 1990 1995 2000 2005 2010

5. 180nm 90nm and Below 250nm PSM OPC 0° 180° 0° OPC 180° RET to the rescue .. Design Mask Wafer

6. 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 Printed using a 0.35 um nominal process AAPSM: Enabling Technology Mask • Benefits: • - Smaller feature sizes. • - Improved yield (tighter process control). • - Extended useful life of current equipment. At smaller technology nodes, both gates regions and field poly will need AAPSM.

7. 0 180 Shifter <d Overlapping Shifters Implications on Design Imposes additional constraints on layout design besides traditional design rules. Critical Feature • Condition 1: Shifters on two sides of critical features must have opposite phases. • Critical Feature: Feature that is smaller than pre-specified threshold. Condition 2: Shifters that are separated by less than a certain spacing should be merged and assigned the same phase.

8. 0 0 0 0 180 180 180 0 Phase-Assignable Layouts • Layout that satisfies conditions 1 and 2 is called a phase-assignable layout. • Layouts that obey all design rules may not always satisfy these conditions: AAPSM Conflict: Adjacent Shifter pair that belongs to a cyclic sequence of phase dependencies that cannot be properly mapped.

9. 0 0 0 0 0 180 180 180 0 180 0 Global Conflict Local AAPSM Conflicts versus Global AAPSM Conflicts • Local Conflicts • T-shapes and line-end conflicts. • Can be detected using DRC rules : Prior work in industry. • Global Conflicts • Hard to detect and correct. • Our Focus. Local Conflict

10. Outline • Introduction • AAPSM Conflict Detection • Bipartite Formulation • Non-bipartite Formulation • AAPSM Conflict Correction • Conclusions & Future Work

11. Conflict Detection: Bipartite Formulation • Build graph from layout such that, • Layout is phase-assignable  Graph is bipartite. • Our graph: Phase Conflict Graph. • Conflict Detection  Minimum-weight bipartization problem on constructed graph. • Minimum-weight Bipartization: Find minimum weight set E’ such that the modified graph G’=(V,E-E’) is bipartite. • NP-hard: general graphs, polynomial time: planar graphs. • Edges deleted during bipartization  AAPSM Conflicts for Correction.

12. Build Phase Conflict Graph G. D0; P 0. Build planar graph GP from G by deleting minimal set of crossing edges E. P  E. . E’ Edges deleted by Pl_bipartize to make GP bipartite. D  E’.. For each edge e e P, add e to D if e belongs to an odd cycle in G. D denotes AAPSM conflicts selected for correction. AAPSM Conflict Detection Flow Layout L Pl_bipartize: Polynomial-Time Optimal Bipartization Algorithm for planar graphs. Key idea: Solve a large part of the bipartization problem using optimal polynomial-time algorithm.

13. Phase Conflict Graph • Each shifter is represented by an edge shifter node. • Rule 1: Connect the shifter nodes with an edge. • Rule 2: Connect edge shifter nodesof overlapping shiftersand subdivide the line by an overlap node. Edge shifter node Overlap node

14. Previous Work in Conflict Detection • Greedy Bipartization Schemes: • Spanning Tree-Based Algorithm most successful. • Build maximum spanning tree from the given graph. • Edges not included in the tree are the chosen AAPSM errors. • Optimal Solution for layouts that obey certain restrictions. • Use a different graph construction from the layout called the feature graph. • Uses Pl_Bipartize for bipartization.

15. Phase Conflict Graph versus Feature Graph 1. Smaller graph size. 2. More nodes/edges have to be deleted during planar embedding of feature graph. • Edges may intersect. • Nodes may overlap. Conflict graph 9 edges Feature graph 13 edges

16. Results for Conflict Detection

17. Outline • Introduction • AAPSM Conflict Detection • Bipartite Formulation • Non-bipartite Formulation • AAPSM Conflict Correction • Conclusions & Future Work

18. Overlap node Runtime Optimization • Pl_Bipartize : Bipartization in phase conflict graph  T-join problem on dual graph Perfect matching on gadget graph. # nodes in gadget graph ~ # edges in dual graph ~ # edges in the conflict graph • Improved reduction from T-join to perfect matching: • generalized gadgets reduces node count of gadget graph  20% runtime reduction. • Can we also reduce # edges in phase conflict graph? • Overlap nodes are added to make the graph bipartite : bipartite formulation really necessary?

19. Modified Phase Conflict Graph • Use edge shifter node to represent each shifter (same as before). • Connect two shifter nodes of the same feature with feature edge. • Connect overlapping shifterswithoverlap edge. Overlap edge Feature edge

20. Conflict Detection: Non-bipartite formulation • New coloring problem: • Two nodes connected by overlap edge have the same color. • Two nodes connected by feature edge have different colors. • Conflict cycle = cycle with odd # feature edge. • Conflict Detection Remove all conflict cycles in the modified phase conflict graph. • T-join formulation needs to be modified for this new problem. • Undeletable edges can be removed from the dual graph.

21. Example Feature graph 13 edges Modified Phase Conflict graph 2 edges Phase Conflict graph 9 edges Modified phase conflict graph+Generalized gadgets: ~7x faster than feature graph+Optimized gadgets.

22. Outline • Introduction • AAPSM Conflict Detection • AAPSM Conflict Correction • Conclusions & Future Work

23. Basic Idea of Conflict Correction • Two types of AAPSM conflicts chosen for correction: • Shifters on opposite sides of critical feature are of the same phase. • Shifters of opposite phase are overlapping. • Modify layout and/or mask to remove these conflicts. • Conflicts chosen for correction should depend on correction strategy being used.

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

25. Widen No shifters needed for widened feature. Layout-level AAPSM Conflict Correction I • Increase feature width. • Increase width of certain features that need shifters to make them non-critical. • Pros: small change in layout. • Cons: • Performance degradation. • Spacing restrictions may not allow widening.

26. Spacing Layout-level AAPSM Conflict Correction II • Increase Spacing • Insert vertical or horizontal gaps between shifters of opposite phases. • Pros: small performance penalty as width of gate features remains unchanged. • Cons: may lead to larger area increase.

27. Our Approach Correct AAPSM Conflict  Add space between shifter pair corresponding to the conflict. • End to end cuts are inserted to avoid introducing DRC errors. • Problem Statement: • Given the set of AAPSM conflicts for correction, determine minimum number and widths of end-to-end horizontal and/or vertical spaces that need to be added.

28. Layout L, Set D of AAPSM conflicts for correction. 2 2 1 1 {1, 2} . For each AAPSM conflict in D, get intervals where space can be added to correct conflict. {2} 3 3 . Define a grid in the layout using end-points of the intervals. {3} . Set up weighted set covering problem. Solution of covering problem provides locations and widths of added spaces. Details of Conflict Correction

29. Results for Conflict Correction 2

30. Summary • AAPSM Conflict Detection: • Selected smaller number of conflicts for correction compared with previous methods. • Maximum reduction: 49.5%, Minimum reduction:16.1%. • Smaller is better as this implies smaller amount of modification, either to mask or layout. • Non-bipartite formulation produces ~7x runtime improvement. • AAPSM Conflict Correction: • Simple yet efficient layout modification scheme. • Small area increase on the average (4.0%). • Tried standard cells and large macro blocks. • Presented scheme quite flexible: • Can be modified to solve the maximum number of AAPSM conflicts for a given area increase. • Can be combined with mask modification schemes.

31. Future Work • Layout modification is shown to be a feasible approach for AAPSM conflict correction. • Combine several end-to-end cuts to minimize area increase. • Incorporate feature widening as an option to handle all sorts of AAPSM conflicts. • Combine with current mask modification solutions.

32. Thank You!