1. Multi-Project Reticle Design & Wafer Dicing under Uncertain Demand Andrew B Kahng, UC San Diego Ion Mandoiu, University of Connecticut Xu Xu, UC San Diego Alex Zelikovsky, Georgia State University

2. 2 Images courtesy of EuroPractice and CMP Multi-Project Wafers Mask set cost: >$1M for 90 nm technology Share cost of mask tooling between multiple designs!  Prototyping  Low volume production

3. 3 Design Flow for MPW Die Sizes + Production Volumes Project Partitioning Project Cloning Reticle Floorplaning Shotmap Definition Dicing Plan Definition Reticle, Wafer Shotmap, Wafer Dicing Plans

4. 4 Design Flow for MPW Die Sizes + Production Volumes Project Partitioning Project Cloning Reticle Floorplaning Shotmap Definition Dicing Plan Definition Reticle, Wafer Shotmap, Wafer Dicing Plans

5. 5 Standard wafer dicingMPW dicing Why is Dicing a Problem? Side-to-side dicing! Correctly sliced out dies  Cut lines along all four edges  No cut line partitioning the die

6. 6 Side-to-side Dicing Problem Given:  Production volume for each die  Reticle floorplan  Wafer shot-map Find:  Horizontal and vertical dicing plans for each wafer To Minimize:  #wafers required to meet production volumes

7. 7 1 2 4 3 1 2 4 3 1 2 4 3 Dicing Strategies Wafer Dicing Plan (DP): all horizontal and vertical cut lines used to cut a wafer Row/Column DP: cut lines through row/column of reticle images Single wafer dicing plan (SDP) [ISPD04] [KahngR04]  The same wafer DP used for all wafers  Different DPs used for different rows/cols in a wafer Multiple wafer dicing plans (MDP)  Restricted MDP: the same DP used for all rows/cols of a wafer  Graph coloring based heuristic in [Xu et al. 04]

8. 8 Independent Dies 1 2 4 3 Maximal Independent Sets: {1, 4} {2} {3} Under restricted MDP dicing, all reticle images on wafer yield the same set of dies Independent set: set of dies that that can be simultaneously diced from a reticle image  Only maximal independent sets are of interest!

9. 9 ILP for Restricted MDP

10. 10 CMP Floorplan

11. 11 9 wafers with SDP SDP vs. MDP 5 wafers with MDP

12. 12 4-Part Dicing Partition each wafer into 4 parts then dice each part separately using side-to-side cuts

13. 13 Design Flow for MPW Die sizes + Production Volumes Project Partitioning Project Cloning Reticle Floorplaning Shotmap Definition Dicing Plan Definition Reticle, Wafer Shotmap, Wafer Dicing Plans

14. 14 Shotmap Definition Problem Reticle Floorplan Shotmap #1 Shotmap #2 ? Simple grid-based shotmap definition algorithm yields an average reduction of 13.6% in #wafers

15. 15 Design Flow for MPW Die sizes + Production Volumes Project Partitioning Project Cloning Reticle Floorplaning Shotmap Definition Dicing Plan Definition Reticle, Wafer Shotmap, Wafer Dicing Plans

16. 16 Given:  Die sizes & production volumes  Maximum reticle size Find:  Placement of dies within the reticle To Minimize:  Production cost (reticle cost, #wafers, …) Reticle Floorplaning Problem

17. 17 Reticle Floorplaning Methods Key challenge: cost estimation Previous approaches  Simulated annealing [ISPD04]  Grid-packing [Andersson et al. 04, KahngR04]  Integer programming [WuL05] Our approach: Hierarchical Quadrisection (HQ)

18. 18 Hierarchical Quadrisection Floorplan At most one die assigned to each region at lowest level Region widths/heights easily computed from die assignment HQ mesh more flexible than grid

19. 19 HQ Algorithm Random initial assignment improved using simulated annealing  SA moves: region exchange, die rotation  Max reticle size enforced throughout the algorithm Hierarchical structure enables quick cost estimation

20. 20 Reticle Area = 2.30 (vs. 2.45) HQ Floorplan of CMP Testcase 4 wafers with MDP (vs. 5)

21. 21 Design Flow for MPW Die sizes + Production Volumes Project Partitioning Project Cloning Reticle Floorplaning Shotmap Definition Dicing Plan Definition Reticle, Wafer Shotmap, Wafer Dicing Plans

22. 22 Project Cloning Motivation  Die-to-die inspection [Xu et al.]  Reduced wafer cost when there is large variation in production demands Post-processing approach [WuL05] Insert clones in white space left on reticle Our approach  Before floorplaning: number of clones proportional to square root of production volume; clones arranged in clone arrays  During floorplaning: clone arrays assigned to single cell in HQ; new SA moves: add/delete clone array row/column  After floorplaning: insert additional clone array rows/columns without increasing cell size

23. 23 Design Flow for MPW Die sizes + Production Volumes Project Partitioning Project Cloning Reticle Floorplaning Shotmap Definition Dicing Plan Definition Reticle, Wafer Shotmap, Wafer Dicing Plans

24. 24 Schedule Aware Partition More decision knobs: fabrication schedule I will not pay you after June But, money will be saved if waiting for other orders… ? Project Partitioning Problem  Given: Reticle size, set of projects  Find: Partition of projects into reticles  To minimize: Sum of manufacturing cost and delay cost [BACUS05] Schedule-aware partitioning leads to an average cost reduction of 63.8% vs. schedule-blind partitioning

25. 25 Demand Uncertainty Customer demands (over reticle life period) may not be fully known at design time  Only rough customer demand distribution available (e.g., min/max demand) MPW become even more attractive in this context: sharing of demand misprediction risks Online wafer dicing combined with production of larger wafer lots can bring further economies of scale (see paper)  Feasible when there are no IP protection issues

26. 26 Given:  Die sizes  Maximum reticle size  Distribution of customer orders Find:  Placement of dies within the reticle To Minimize:  Expected #wafers required to meet customer orders over a fixed time horizon Robust Reticle Floorplaning

27. 27 Compared Algorithms HQ with production volume set to the expected customer demand HQ+Cloning with production volume set to the expected customer demand Distribution-driven simulated annealing  Use expected production cost for evaluating SA moves  Monte-Carlo simulation used to estimate expected cost

28. 28 Robustness Results - Normal

29. 29 Robustness Results – Uniform

30. 30 Conclusions & Future Research Improved MPW design flow  Schedule-aware partitioning: 60% average cost reduction  Project cloning: 10% average wafer cost reduction  HQ reticle floorplan: 15% average wafer cost reduction  Wafer shot-map definition: 13% average wafer cost reduction  MDP wafer dicing: 60% average wafer cost reduction Future work  Multi-layer reticle design