1. l i a b l eh kC o m p u t i n gL a b o r a t o r y Yield Enhancement for 3D-Stacked Memory by Redundancy Sharing across Dies Li Jiang, Rong Ye and Qiang Xu Presenter: Qiang Xu CUhk REliable Computing Laboratory Department of Computer Science & Engineering The Chinese University of Hong Kong

2. Outline Introduction Motivation Redundancy Sharing in 3D-Stacked Memory Die Matching for Yield Enhancement Conclusion

3. Why 3D-stacked Memory? 198019902000Now CPU-Memory Performance Gap Relative Performance Memory Wall Small Die Size Die Size Routing Cost Routing Cost Large Bandwidth Bandwidth Reduced Bus Cap Bus Cap Latency Latency

4. 3D-Stacked DRAM are Already Here … 2002Tezzaron:1Gb,SDRAM NEC:4Gb 2006 4 Gbit density Interposer Peripherals 3 Gbps/pin 8 strata TSV 2009 SamSung:8Gb PCB TSV DRAM I/O Buffer RD/WR IMEC:DRAM+Logic GATech+Tezzaron 2010 Higher Bandwidth Faster Closer to Processor

5. ×× Memory Test: Fault Bitmap Redundancy Analysis Stack Self-Reparable Dies To Guarantee Yield for 3D-Stacked Memory … More self-reparable dies High redundancy cost! More self-reparable dies High redundancy cost!

6. 1R, 2C, Irreparable Redundancy Analysis for Reparability 1R, 2C, Self-Reparable

7. 1R, 2C, Irreparable 0R, 3C, Reparable 2R, 1C, Reparable Redundancy Sharing for Yield Enhancement 1R, 2C, Self-Reparable With the same amount of resources, memory yield can be improved by redundancy sharing!

8. Redundancy Sharing across Dies Programmable Decoder Programmable Decoder Pre-fabricated multiplexor Pre-fabricated multiplexor Full sharing: Num TSV = Num Spare Row + Num Spare Col Full sharing: Num TSV = Num Spare Row + Num Spare Col Repair its own block. Use the rest to repair others What if there are defective TSVs?

9. Programmable Decoder Pre-fabricated multiplexor Partial sharing : Less TSVs Redundancy Sharing across Dies

10. Self-reparable matching: Yield = 25% Self-reparable matching: Yield = 25% Aggressive matching: Yield = 0% Aggressive matching: Yield = 0% Effective matching: Yield = 75% Effective matching: Yield = 75% Conservative matching: Yield = 50% Matching is Critical for the Final Yield

11. How to Conduct Die Matching? Add edges if two dies are reparable with redundancy sharing Add edges if two dies are reparable with redundancy sharing Conduct maximum matching algorithm Conduct maximum matching algorithm Construct an undirected graph with each die as an vertex Construct an undirected graph with each die as an vertex

12. How to Conduct Die Matching? How How do we know whether two dies are reparable after bonding? Run Run final repair algorithm between every pair Best Best yield, but time-consuming We We have to estimate estimate whether two dies matched together can form a reparable stack efficiently

13. Fr: faulty bits suitable for row repair Fc: faulty bits suitable for column repair Fo: orthogonal faulty bits Die Matching a.t. Reparability Condition

14. Optimal Matched Dies Matching a.t. reparability condition is rather conservative

15. Irreparability Condition Given a bipartite graph G = (V;E), the minimum number of vertices that cover all the edges is equal to the number of edges in any maximum bipartite matching of the graph Given two memory blocks with redundancy R/C  The maximum bipartite matching of G a, G b are |M a | and |M b |, the stacked memory is considered to be “reparable” if |M a | +|M b | ≤ R a + C a + R b + C b

16. Die Matching a.t. Irreparability Condition Reparability is NOT guaranteed due to redundancy configuration!

17. Die Matching a.t. Irreparability Condition Optimal Matched Dies Reparable Dies a.t. Irreparability Condition Matched Dies a.t. Irreparability Condition Matching a.t. irreparability condition is rather aggressive

18. Iterative matching a.t. tightened irreparability condition in each run Iterative Die Matching Optimal Matched Dies Reparable Dies a.t. Irreparability Condition Matched Dies a.t. Irreparability Condition + |M a | +|M b | ≤ R a + C a + R b + C b 0

19. Iterative matching a.t. tightened irreparability condition in each run Iterative Die Matching + |M a | +|M b | ≤ R a + C a + R b + C b 1 Rest of Dies Reparable Dies a.t. Irreparability Condition Matched Dies a.t. Irreparability Condition

20. Iterative matching a.t. tightened irreparability condition in each run Iterative Die Matching + |M a | +|M b | ≤ R a + C a + R b + C b 2

21. Iterative matching a.t. tightened irreparability condition in each run Iterative Die Matching + |M a | +|M b | ≤ R a + C a + R b + C b k No more reparable dies found

22. Experiment Setup 1000 1Gb Memory, stacked to 2 Layer chips 4×4 memory blocks, 8k×8k bit-cells Fault Injection Poisson distribution with λ = 2.130 Polya-Eggenberger distribution with λ=2.130 α = 2.382 (more clustered faults) α = 0.6232 (evenly-distributed faults) random TSV faults with faulty rate as 0.1% six kinds of faults FaultSingle CellDouble CellSingle RowSingle ColDouble RowDouble Col case 140%4%20% 8% case 270%4%8% 5%

23. Self-reparable Reparability Matched Irreparability Irreparability Iterative Experimental Results Poisson Distribution

24. Case 1 Case 2 Self Repair Reparability Matched Irreparability Irreparability Iterative Experimental Results

25. Polya-Eggenberger Distribution α = 0.6232 α = 2.38 Self Repair Reparability Matched Irreparability Irreparability Iterative

26. We propose to conduct redundancy sharing across vertical dies in 3D-Stacked Memory We propose to conduct redundancy sharing across vertical dies in 3D-Stacked Memory Significant yield enhancement Significant yield enhancement Minor TSV and routing cost Minor TSV and routing cost We present novel solutions for selective die matching to maximize 3D-stacked memory yield We present novel solutions for selective die matching to maximize 3D-stacked memory yield Summary

27. l i a b l eh kC o m p u t i n gL a b o r a t o r y Thank you for your attention !