Hierarchical Dummy Fill for Process Uniformity

1. Supported by Cadence Design Systems, Inc. NSF, and the Packard Foundation Hierarchical Dummy Fill for Process Uniformity Y. Chen, A. B. Kahng, G. Robins, A. Zelikovsky (UCLA, UCSD, UVA and GSU) http://vlsicad.cs.ucla.edu

2. Outline • Chemical Mechanical Processing & Filling Problem • Previous Works • Linear programming approaches • Monte-Carlo (MC) approaches • Our Contributions: • Hierarchical filling problem • Hierarchical filling algorithm • Hybrid hierarchical / flat filling approach • Computational Experience • Summary and Future Research

3. Chemical-Mechanical Polishing (CMP) = wafer surface planarization Uneven features cause polishing pad to deform Features ILD thickness Dummy features ILD thickness CMP and Interlevel Dielectric Thickness • Interlevel-dielectric (ILD) thickness  feature density • Insert dummy features to decrease variation

4. CMP in STI Process • Shallow Trench Isolation (STI) technique for isolation on the active layer in all deep submicron CMOS productions (figure) • deposit nitride layer on silicon • Etch shallow trenches through nitride silicon • deposit oxide to fill trenches and cove nitride • remove excess oxide and partially nitride by CMP • Uniformity requirement on CMP in STI • not enough polish (figure) • over polish (figure)

5. Objectives of Density Control • Objective for Manufacture = Min-Var minimizewindow density variation subject to upper bound on window density • Objective for Design = Min-Fill minimize total amount of filling subject to fixed density variation

6. Filling Problem • Given • rule-correct layout in n  nregion • window size = w  w • window density upper bound U • Fill layout with Min-Var or Min-Fill objective such that nofill is added • within buffer distance B of any layout feature • into any overfilled window that has density  U

7. w w/r tile Overlapping windows n Fixed-Dissection Regime • Monitor only fixed set of w  w windows • “offset” = w/r (example shown: w = 4, r = 4) • Partition n x n layout intonr/w nr/w fixed dissections • Each w w window is partitioned into r2tiles

8. tile Slack Area Feature Area Layout Density Models • Spatial Density Model window density  sum of tiles feature area • Effective Density Model (more accurate) window density weighted sum of tiles' feature area • weights decrease from window center to boundaries

9. Requirements on Dummy Filling • Estimation of RC parasitics, gate/interconnect delays and device reliability in PD & verification • Compatibility of master cells and macros • Consistent with design hierarchy

10. Outline • Chemical-Mechanical Polishing & Filling Problem • Previous Works • Linear programming approaches • Monte-Carlo (MC) approaches • Our Contributions: • Hierarchical filling problem • Hierarchical filling algorithm • Hybrid hierarchical / flat filling approach • Computational Experience • Summary and Future Research

11. Min-Var Objective (Kahng et al.) Maximize: M Subject to: for any tile 0  p[T]  slack[T] for any window  TW (p[T]+area[T])  U M   TW (p[T] + area[T]) p[T] = fill area of tile spatial density model Linear Programming Approaches • Min-Fill Objective (Wong et al.) • Minimize: fill amount • Subject to: for any tile 0  p[T]  slack[T] LowerB  0(T)  UpperB MAX 0(T) - MIN 0(T)   0(T)= the effective density of tile T • effective density model

12. Monte-Carlo Approach • Min-Var objective • pick the tile for next filling geometry randomly • higher priority of a tile  higher probability to be filled • lock tile if any containing window is overfilled • update window priorities • Min-Fill objective • Fill-Deletion problem • delete as much fill as possible while maintaining min window density  L. • Min-Fill Monte-Carlo algorithm • if (min covering-window density < L) lock the tile • randomly select unlocked tile by its priority • delete a filling geometry from tile • update priorities of tiles

13. Min-Var No Improvement Min-Fill Iterated Monte-Carlo Approach • Repeat forever • run Min-Var Monte-Carlo with max window density U • exit if no change in minimum window density • run Min-Fill Monte-Carlo with min window density M

14. LP vs. Monte-Carlo for Flat Filling • LP • impractical runtime for large layouts • r-dissection solution may be suboptimal for 2r dissections • essential rounding error for small tiles • Monte-Carlo • very efficient: O((nr/w)log(nr/w)) time • scalability: handle large values of r • accuracy: reasonably high comparing with LP

15. Outline • Chemical-Mechanical Polishing & Filling Problem • Previous Works • Linear programming approaches • Monte-Carlo (MC) approaches • Our Contributions: • Hierarchical filling problem • Hierarchical filling algorithm • Hybrid hierarchical / flat filling approach • Computational Experience • Summary and Future Research

16. Two instances of a master cell features Flat fill solution Hierarchical fill solution Original layout Hierarchical Filling Problem • Dummy fill are added only to master cells • Each cell of the filled layout is a filled version of the corresponding original master cell

17. Why Hierarchical Filling? • Hierarchical characteristics of design flows • Enables and faster verification of the filled layout • Decreases data volume for standard cell designs

18. Difficulties in Hierarchical Filling • Density constraints for all instances of the master • Interactions / interferences at master cell boundaries • Always worse than flat solutions

19. Outline • Chemical-Mechanical Polishing & Filling Problem • Previous Works • Linear programming approaches • Monte-Carlo (MC) approaches • Our Contributions: • Hierarchical filling problem • Hierarchical filling algorithm • Hybrid hierarchical / flat filling approach • Computational Experience • Summary and Future Research

20. Why Not LP? • Complexity caused by constraints • need a huge number of variables and constraints for each window, cell instance, and feasible fill position • Transformations • hard to represent the transformations of master cell instances • Overlaps between cell instances • ownership of overlapping regions • unavailable regions for fill

21. 1 1 1 1 1 1 1 1 density analysis 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Original layout 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Monte-Carlo Hierarchical Filling

22. Overlaps between  2 instances of the same master • Overlaps between master and features • Overlaps between  2 instances of different masters Exclude the overlapping regions buffer slack slack Computing Slack Hierarchically Master cell

23. Cause high layout density variation features ! ! ! ! three instances of a master cell Drawbacks of Hierarchical Filling • Sparse or unfilled region in the solution • the overlaps • bloat regions

24. Outline • Chemical-Mechanical Polishing & Filling Problem • Previous Works • Linear programming approaches • Monte-Carlo (MC) approaches • Our Contributions: • Hierarchical filling problem • Hierarchical filling algorithm • Hybrid hierarchical / flat filling approach • Computational Experience • Summary and Future Research

25. Create k copies of master cell Ci • Link contained master cells C` with the new copies C1 C2 Ci,2 Ci,1 C2 C2 C2 C1 C1 C1 C1` C1` C2` C2` Ci C1` C1` C1` C2` C2` C2` C1` C2` Ci Ci,2 Ci,1 k-way Master Cell Splitting • Randomly replace Ci in master cells with new copies • k  : hierarchical layout  flat layout

26. features Flat fill `cleanup` phase three instances of a master cell Hybrid Hierarchical / Flat Filling Purely hierarchical fill phase Split-hierarchical phase

27. Outline • Chemical-Mechanical Polishing & Filling Problem • Previous Works • Linear programming approaches • Monte-Carlo (MC) approaches • Our Contributions: • Hierarchical filling problem • Hierarchical filling algorithm • Hybrid hierarchical / flat filling approach • Computational Experience • Summary and Future Research

28. Test cases Part of a metal layer from industry custom-block layout Computational Experience • Implementation features • grid slack computation • doughnut area computation • wraparound density analysis and synthesis • different pattern types • Testbed • GDSII input • hierarchical polygon database • C++ under Solaris

29. Computational Experience Comparison among hierarchical, flat and hybrid filling approaches

30. Outline • Chemical-Mechanical Polishing & Filling Problem • Previous Works • Linear programming approaches • Monte-Carlo (MC) approaches • Our Contributions: • Hierarchical filling problem • Hierarchical filling algorithm • Hybrid hierarchical / flat filling approach • Computational Experience • Summary and Future Research

31. Summary and Future Research • Hierarchical filling problem for CMP uniformity • Practical pure hierarchical filling algorithm • Practical hybrid hierarchical filling approach • trade off runtime, solution quality and data volume • Ongoing research • Alternate pure hierarchical filling heuristics • Tradeoffs between solution quality & data volume • Reusable solutions • Dual-material polish model