1. Design 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. © 2005 Synopsys, Inc. (2) 22 Outline Introduction AAPSM Conflict Detection AAPSM Conflict Correction Conclusions & Future Work

3. © 2005 Synopsys, Inc. (3) 33 Outline

4. © 2005 Synopsys, Inc. (4) 44 Sub-wavelength Lithography Above Wavelength SubWavelength 1980198519901995200020052010 0.1 1.0 10 Silicon Feature Size 3.0  m 2.0  m 1.0  m 0.6  m 0.35  m 45nm 65nm 90nm 0.13  m 0.18  m 0.25  m Lithography Wavelength 436nm 365nm 248nm 193nm 157nm 32nm

5. © 2005 Synopsys, Inc. (5) 55 RET to the rescue.. Design Mask Wafer 250nm 180nm OPC 90nm and Below PSM 0°0° 180° OPC 0°0° 180°

6. © 2005 Synopsys, Inc. (6) 66 AAPSM: Enabling Technology Alternating Aperture Phase Shift Mask (AAPSM): Phase- modulation at the mask level to increase resolution capabilities of optical lithography. Mask 0.11  m Printed using a 0.35 um nominal process Benefits: - Smaller feature sizes. - Improved yield (tighter process control). - Extended useful life of current equipment. 180 o phase-shifter At smaller technology nodes, both gates regions and field poly will need AAPSM.

7. © 2005 Synopsys, Inc. (7) 77 Implications on Design Critical Feature Overlapping Shifters <d 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. Imposes additional constraints on layout design besides traditional design rules. 0180 Shifter

8. © 2005 Synopsys, Inc. (8) 88 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. 0 180 0 0 0 0

9. © 2005 Synopsys, Inc. (9) 99 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 0 0180 Global Conflict 0 180 0 0 0 0

10. © 2005 Synopsys, Inc. (10) 10 Outline

11. © 2005 Synopsys, Inc. (11) 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. © 2005 Synopsys, Inc. (12) 12 AAPSM Conflict Detection Flow Layout L Build Phase Conflict Graph G. D  0; P  0. Build planar graph G P from G by deleting minimal set of crossing edges E. P  E.. E’  Edges deleted by Pl_bipartize to make G P bipartite. D  E’.. For each edge e  P, add e to D if e belongs to an odd cycle in G. D denotes AAPSM conflicts selected for correction. Pl_bipartize: Polynomial- Time Optimal Bipartization Algorithm for planar graphs. 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. © 2005 Synopsys, Inc. (13) 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 nodes of overlapping shifters and subdivide the line by an overlap node. Overlap node Edge shifter node

14. © 2005 Synopsys, Inc. (14) 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. © 2005 Synopsys, Inc. (15) 15 Phase Conflict Graph versus Feature Graph Feature graph 13 edges Conflict graph 9 edges 1. Smaller graph size. 2. More nodes/edges have to be deleted during planar embedding of feature graph.  Edges may intersect.  Nodes may overlap.

16. © 2005 Synopsys, Inc. (16) 16 Results for Conflict Detection

17. © 2005 Synopsys, Inc. (17) 17 Outline

18. © 2005 Synopsys, Inc. (18) 18 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? Overlap node

19. © 2005 Synopsys, Inc. (19) 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 shifters with overlap edge. Overlap edge Feature edge

20. © 2005 Synopsys, Inc. (20) 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. © 2005 Synopsys, Inc. (21) 21 Example Feature graph 13 edges Phase Conflict graph 9 edges Modified Phase Conflict graph 2 edges Modified phase conflict graph+Generalized gadgets: ~7x faster than feature graph+Optimized gadgets.

22. © 2005 Synopsys, Inc. (22) 22 Outline

23. © 2005 Synopsys, Inc. (23) 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. © 2005 Synopsys, Inc. (24) 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. © 2005 Synopsys, Inc. (25) 25 Layout-level AAPSM Conflict Correction I Increase feature width.  Increase width of certain features that need shifters to make them non-critical. No shifters needed for widened feature. Widen Pros: small change in layout. Cons:  Performance degradation.  Spacing restrictions may not allow widening.

26. © 2005 Synopsys, Inc. (26) 26 Layout-level AAPSM Conflict Correction II Increase Spacing  Insert vertical or horizontal gaps between shifters of opposite phases. Spacing Pros: small performance penalty as width of gate features remains unchanged. Cons: may lead to larger area increase.

27. © 2005 Synopsys, Inc. (27) 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. © 2005 Synopsys, Inc. (28) 28 Details of Conflict Correction Layout L, Set D of AAPSM conflicts for correction.. For each AAPSM conflict in D, get intervals where space can be added to correct conflict.. Define a grid in the layout using end-points of the intervals.. Set up weighted set covering problem. Solution of covering problem provides locations and widths of added spaces. 1 2 3 1 2 3 {1, 2} {2} {3}

29. © 2005 Synopsys, Inc. (29) 29 Results for Conflict Correction 2

30. © 2005 Synopsys, Inc. (30) 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. © 2005 Synopsys, Inc. (31) 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. © 2005 Synopsys, Inc. (32) 32 Thank You!