Monte-Carlo Methods for Chemical-Mechanical Planarization on Multiple-Layer and Dual-Material Models

1. Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and State of Georgia’s Yamacraw Initiative Monte-Carlo Methods for Chemical-Mechanical Planarization on Multiple-Layer and Dual-Material Models Y. Chen,A. B. Kahng, G. Robins, A. Zelikovsky (UCLA, UCSD, UVA and GSU) http://vlsicad.ucsd.edu

2. Outline • Layout Density Control for CMP • Our Contributions • STI Dual-Material Dummy Fill • Multiple-layer Oxide CMP Dummy Fill • Summary and Future Research

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

4. Layout Density Model • Effective Density Model window density weighted sum of tiles' feature area • weights decrease from center tile to neighboring tiles

5. Filling Problem • Given • rule-correct layout in n  nregion • upper bound U on tile density • Fill layout subject to the given constraints • Min-Var objective • minimize density variation subject to upper bound • Min-Fill objective • minimize total amount of filling subject to fixed density variation

6. LP and Monte-Carlo Methods • Single-layer fill problem  linear programming problem • impractical runtime for large layouts • essential rounding error for small tiles • Monte-Carlo method (accurate and efficient) • calculate priority of each tile according to its effective density • higher priority of a tile  higher probability to be filled • pick the tile for next filling randomly • if the tile is overfilled, lock all neighboring tiles • update priorities of all neighboring tiles

7. Outline • Layout Density Control for CMP • Our Contributions • new Monte-Carlo methods for STI Min-Var and Min-Fill objectives • LP formulations for a new multiple-layer fill objective • new Monte-Carlo methods for multiple-layer fill problem • STI Dual-Material Dummy Fill • Multiple-layer Oxide CMP Dummy Fill • Summary and Future Research

8. Our Contributions • Fill problem in STI dual-material CMP • new Monte-Carlo methods for STI Min-Var objective • new Monte-Carlo/Greedy methods with removal phase for STI Min-Fill objective • Fill problem in Multiple-layer oxide CMP • a LP formulation for a new multiple-layer fill objective • new Monte-Carlo methods

9. Outline • Layout Density Control for CMP • STI Dual-Material Dummy Fill • new Monte-Carlo methods for Min-Varr and Min-Fill objectives • Multiple-layer Oxide CMP Dummy Fill • Summary and Future Research

10. Nitride Silicon etch shallow trenches through nitride silicon nitride deposition on silicon remove excess oxide and partially nitride by CMP height difference H nitride stripping Shallow Trench Isolation Process Oxide oxide deposition • Uniformity requirement on CMP in STI • under polish • over polish

11. STI CMP Model • STI post-CMP variation can be controlled by changing the feature density distribution using dummy features insertion • Compressible pad model • polishing occurs on both up and down areas after some step height • Dual-Material polish model • two different materials are for top and bottom surfaces

12. STI Fill Problem • Non-linear programming problem • Min-Var objective: minimize max height variation • Previous method (Motorola) • dummy feature is added at the location having the smallest effective density • terminates when there is no feasible fill position left • Min-Fill objective: minimize total number of inserted fill, while keeping the given lower bound • Previous method (Motorola) • adds dummy features greedily • concludes once the given bound for ΔΗis satisfied • Drawbacks of previous work • can not guarantee to find a global minimum since it is deterministic • for Min-Fill, simple termination when the bound is first met is not sufficient to yield optimal/sub-optimal solutions.

13. Monte-Carlo Methods for STI Min-Var • Monte-Carlo method • calculate priority of tile(i,j) as H - H (i, j, i’, j’) • pick the tile for next filling randomly • if the tile is overfilled, lock all neighboring tiles • update tile priority • Iterated Monte-Carlo method • repeat forever • run Min-Var Monte-Carlo with max height difference H • exit if no change in minimum height difference • delete as much as possible pre-inserted dummy features while keeping min height difference M

14. MC/Greedy methods for STI Min-Fill • Find a solution with Min-Var objective to satisfy the given lower bound • Modify the solution with respect to Min-Fill objective • Algorithm • Run Min-Var Monte-Carlo / Greedy algorithm • Compute removal priority of each tile • WHILE there exist an unlocked tile DO • Choose unlock tile Tij randomly according to priority • Delete a dummy feature from Tij • Update the tile’s priority

15. STI Fill Results Methods (Greedy, MC, IGreedy ad IMC) for STI Fill under Min-Var objective Methods(GreedyI, MCI, GreedyII and MCII) for STI Fill under Min-Fill objective

16. Outline • Layout Density Control for CMP • Our Contributions • STI Dual-Material Dummy Fill • Multiple-layer Oxide CMP Dummy Fill • LP formulations for a new multiple-layer fill objective • new Monte-Carlo methods • Summary and Future Research

17. Layer 1 Layer 0 Multiple-Layer Oxide CMP • Each layer except the bottom one can’t assume a perfect flat starting surface • Multiple-layer density model : step height : local density for layer k ^ : fast Fourier transform operator :effective local density

18. LP formulation Min M Subject to: Multiple-Layer Oxide Fill Objectives • (Min-Var objective) minimize • sum of density variations on all layers • can not guarantee the Min-Var objective on each layer • A bad polishing result on intermediate layer may cause problems on upper layers • maximum density variation across all layers

19. tiles on each layer tile stack layer 3 layer 2 layer 1 Multiple-Layer Monte-Carlo Approach • Tile stack • column of tiles having the same positions on all layers • Effective density of tile stack • sum of effective densities of all tiles in tile stack

20. Multiple-Layer Monte-Carlo Approach • Compute slack area and cumulative effective density for each tile stack • Calculate priority of each tile stack according to its cumulative effective density • WHILE ( sum of priorities > 0 ) DO • randomly select a tile stack according to its priority • from its bottom layer to top layer, check whether it is feasible to insert a dummy feature in • update slack area and priority of the tile stack • if no slack area left, lock the tile stack

21. Multiple-Layer Fill Results Performance of LP0, LP1, Greedy, MC, IGreedy and IMC for Min-Var-Sum

22. Outline • Layout Density Control for CMP • Multiple-layer Oxide CMP Dummy Fill • STI Dual-Material Dummy Fill • Summary and Future Research

23. Summary and Future Research • STI fill problem • Monte-Carlo methods for STI Min-Var • Monte-Carlo / Greedy methods for STI Min-Fill • Multiple-layer fill problem • LP formulation for a new Min-Var objective • efficient multiple-layer Monte-Carlo approaches • Ongoing research • further study of multiple-layer fill objectives • more powerful Monte-Carlo methods for multiple-layer fill problem • CMP simulation tool

24. Thank you!