Area Fill Generation With Inherent Data Volume Reduction

1. Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and State of Georgia’s Yamacraw Initiative Area Fill Generation With Inherent Data Volume Reduction Yu Chen, Andrew B. Kahng, Gabriel Robins, Alexander Zelikovsky and Yuhong Zheng (UCLA, UCSD, UVA, GSU) http://vlsicad.ucsd.edu/

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

3. Filled layout with area features in 9 AREFs Fill Compression Problem • Compressible Fill Generation Problem (CFGP) Given a design rule-correct layout, create the minimum number of GDSII AREFs to represent area fill features such that the window density variation is within the given bounds (L,U) Filled layout with 82 area features Original layout

4. Tile with original features Grid the tile with feature size Satisfy fixed fill requirement (e.g., 56 fill features) with minimum number of AREFs (e.g., 4 AREFs) Grid the tile with feature size Satisfy ranged fill requirement (e.g., 50 ~ 60 fill features) with minimum number of AREFs (e.g., 3 AREFs) windows Original layout in fixed-dissection regime Tile with original features tile • Ranged CFGP in Fixed-Dissection Regime • Given a design rule-correct layout consisting of tiles, the site arrays for each tile, and fill requirement range for each tile, create the minimum number of AREFs to represent area fill features such that each tile contains a number of area fill features in the range Fill Compression in Fixed-Dissection Regime • Fixed CFGP in Fixed-Dissection Regime • Given a design rule-correct layout consisting of tiles, the site arrays for each tile, and fill requirement for each tile, create the minimum number of AREFs to represent area fill features such that each tile contains exactly area fill features

5. Minimize: # covered slack sites = given # fill features all sites covered by AREF are filled only the sites covered by AREF can be filled if is occupied by original features Linear Programming Based Methods • Main idea: • Find minimum #AREFs in free sites for given fill requirements • Single-Tile Integer LP Formulations site in position (p,q) in tile (i,j) feasible AREF in layout is covered by AREF AREF is chosen otherwise otherwise

6. for tiles Compressible Fill Generation with AREF • Multiple-Tile Integer LP Formulations • Ideally consider fill compression on entire layout at one time • Multiple-tile compression as a tradeoff • Ranged Fill Compression • Exploit allowed range of fill features for each tile • Single-Tile • Multiple-Tile for tiles

7. Greedy Speedup Approaches • Motivation of Speedup • Strict greedy heuristic • O(n4) time complexity • Provide good solutions but is impractical • Greedy speedup schemes • Trade-off between time complexity and compression performance • Pick acceptableAREFs instead of maximalAREFs • Greedy Speedup Approach 1 (GS-1) • Find the largest AREFs originating from each free site • Pick the AREF that fills the maximum number of free sites but does not overfill the tiles if such an AREF exists • Otherwise, select the maximum AREF from the largest AREFs, and take one of its sub-AREFs which do not overfill the tiles • Time complexity of the algorithm is reduced to O(n3)

8. Greedy Speedup Approaches (cont’d) • Greedy Speedup Approach 2 (GS-2) • Pick the acceptable AREFs originating from each free site • Criteria of an acceptable AREF: • Size is smaller than K  L • Fill maximum free sites but does not overfill the tiles • Time complexity of the algorithm is reduced to O(KLn2) • GS-1 vs. GS-2 • Compared to GS-1, GS-2 achieves better tradeoff between compression results and time complexity. While K·L << n,GS-2 results are just ~4% worse but ~39× faster than GS-1 based on our experiments. • GS-1 cannot guarantee better behavior with multiple-tile option than with single-tile option because the sets of the largest AREFs are different for the single-tile option and the multiple-tile option • GS-2 does guarantee better behavior with multiple-tile option

9. Experiments: Greedy Speedup Approaches • Greedy approach can achieves very large compression ratios, especially when the fill features are small • GS-1 gets better results for single-tile than for multiple-tile • GS-2 results are always better for multiple-tile than for single-tile

10. Experiments: Greedy Speedup Approaches • GS-2 achieves better tradeoff between performance and runtime • GS-2 is much faster than GS-1, with only small quality degradation

11. GS-1 is more efficient in run time than ILP method Comparison of fill compression methods • Performance of GS-1 is very close to optimal ILP method

12. Contributions: New compressed fill strategies with AREF to reduce data volume Linear programming based methods Greedy based optimization methods Conclusions & Future Works • Future Works • Improve compression ratios and scalability • Exploit new standard layout format • Open Artwork System Interchange Standard (OASIS) • Compressible fill generation problem with underlying layout hierarchy

13. Thank You!