1. Noise and Delay Uncertainty Studies for Coupled RC Interconnects Andrew B. Kahng, Sudhakar Muddu † and Devendra Vidhani ‡ UCLA Computer Science Department, abk@cs.ucla.edu † Silicon Graphics Inc., muddu@mti.sgi.com ‡ Sun Microsystems, dv@eng.sun.com

2. KMV - ASIC992 Outline of Talk  Signal Integrity issues  Previous works  Our Contributions –Circuits Models –Delay and Noise Equations  Simulation results  Conclusions

3. KMV - ASIC993  Interconnect induced issues –scaled linewidths greater wire and via RC –increased aspect ratios greater wire and via RC –larger die sizes greater wire and via RC –more metal layers higher coupling to ground ratio  Process Induced Issues –low device thresholds increased susceptibility to low noise margins –low V DD increased susceptibility to low noise margins –high frequency faster slew times Factors Affecting Signal Integrity

4. KMV - ASIC994 Focus: Crosstalk Issues  Functionality Issues –peak noise  false switching of noise sensitive nodes in the design  Timing Issues –delay uncertainty  maximum difference between maximum and minimum victim line delay over all possible cases of switching activity on neighboring aggressor line(s)  Motivation: find noise issues ASAP!! –find signal integrity problem earlier in deisgn –provide sufficient conditions for finding problem

5. KMV - ASIC995 Outline of Talk  Signal Integrity issues  Previous works  Our Contributions –Circuits Models –Delay and Noise Equations  Simulation results  Conclusions

6. KMV - ASIC996 Previous Work on Signal Integrity  Vittal et. Al., 97: L model; step input; ignore R int, C int  Kawaguchi et. Al., 98: diffusion equations; step input; same peak noise expressions as Vittal  Nakagawa et. Al., 98: L model; assumptions about peak noise time  Shepard et. Al., 97: L model; ignores R and C of aggressors; uses ramp with heuristics

7. KMV - ASIC997 Previous Work on Signal Integrity Issues  Circuit models issues –use lumped capacitance models –use charge sharing models  Noise models issues –estimations very pessimistic –assumptions about R and C –assume zero slew rate –some are simulation based

8. KMV - ASIC998 Outline of Talk  Signal Integrity issues  Previous works  Our Contributions –Circuits Models –Delay and Noise Equations  Simulation results  Conclusions

9. KMV - ASIC999 Our Work  Improved peak noise and delay and noise models –better peak noise estimates –analytical equations for delay uncertainty  Methodology –for coupled RC interconnects only –takes drivers into account –considers slew times –considers both lumped L-Model and  -Model –considers both local and global lines

10. KMV - ASIC9910 Our Work  Circuit model  L model   model  Noise analysis and peak noise expressions  Delay analysis and delay uncertainty

11. KMV - ASIC9911 Circuit Model  Two parallel coupled lines  Aggressor - Green; Victim - Red  Coupling capacitance - C c  Supply voltages - V s1, V s2 Aggressor Line Victim Line V s1 V s2 Driver 1 Driver 2 Load 1 Load 2 CcCc

12. KMV - ASIC9912  No resistance  Lumped capacitance - C 1, C 2  Load capacitance - C L1, C L2  Node C has noise voltage Charge Sharing Model C B V s1 V s2 C L1 Aggressor Line Victim Line C c1 C’1C’1 C1C1 C L2

13. KMV - ASIC9913 Noise Analysis For Charge Sharing Model  Basic noise analysis model –Victim line quiet –Aggressor line switching  Peak noise defined by ratio of coupling capacitance to total capacitance of wire

14. KMV - ASIC9914  All resistances considered  Lumped capacitances  Different slew times considered Lumped L Model B C V s1 V s2 R d2 R1R1 R’1R’1 C L1 Aggressor Line Victim Line R d1 C c1 C’1C’1 C1C1 C L2  Solve using nodal equations at B and C

15. KMV - ASIC9915  M 1, M 2, a 1, and a 2, are given as Solving L Model  Transfer functions for nodes B and C are

16. KMV - ASIC9916 Noise Analysis For L Model  L model voltage function for ramp input at victim node C (T S is slew time)  L model peak noise expression for step input reduces to Vittal et. Al. peak noise expression

17. KMV - ASIC9917 Peak Noise For L Model  Differentiate v c (t) to get t peak  L Model peak noise at t peak

18. KMV - ASIC9918 Lumped  - Model C B V s1 V s2 R d2 C1C1 C c1 D A R1R1 R’1R’1 C L1 Aggressor Line Victim Line R d1 C c2 C’1C’1 C’2C’2 C2C2 C L2

19. KMV - ASIC9919 Peak Noise For  Model  V peak is given at v c ( t peak ) where

20. KMV - ASIC9920 Delay Uncertainty  Maximum difference between maximum and minimum delay  Caused by crosstalk between victim and aggressor switching simultaneously  Maximum delay by worst case –Aggressor and victim switching in opposite directions  Minimum delay by best case –Aggressor and victim switching in same direction

21. KMV - ASIC9921 Time  General Case –both victim ramp (T S2 ) and aggressor ramp (T S2 ) and four regimes of operation Simultaneous Switching of Victim & Aggressor  Our Case: first region is empty 0 V0V0 0 V0V0 T s1 V s2 T s2 V s1

22. KMV - ASIC9922 Delay Uncertainty  Our delay uncertainty study based on  Model  Corresponding voltage function at node C

23. KMV - ASIC9923 Delay Function  Delay Function at node C

24. KMV - ASIC9924 Outline of Talk  Signal Integrity issues  Previous works  Our Contributions –Circuits Models –Delay and Noise Equations  Simulation results  Conclusions

25. KMV - ASIC9925 Simulation Results  Simulation configuration –0.25 micron technology –analyzing different metal layer wires –analyze different factors like slew, coupling cap, etc.  Peak noise results w.r.t. slew  Best and worst delay result  Delay uncertainty w.r.t. aggressor slew and coupling

26. KMV - ASIC9926 Simulation Configuration  Criteria –global wires (case 2 and 3) and local wires (case 1 and 4) –different coupling to ground capacitance ratios

27. KMV - ASIC9927 Peak Noise Results  Peak noise for different models  Comparison with previous work ( Vittal et. Al. and Kawaguchi et. Al. )  Our results considered different slew times at aggressor

28. KMV - ASIC9928 Peak Noise Results  Peak noise for different models  Comparison with previous work ( VittalM97 and Kawaguchi-Sakurai )  Our results considered different slew times at aggressor

29. KMV - ASIC9929 Peak Noise Variation For Local Wires  Peak noise variation with respect to slew of aggressor for local wire case 1

30. KMV - ASIC9930 Peak Noise Variation For Global Wires  Peak noise variation with respect to slew of aggressor for global wire case 3

31. KMV - ASIC9931 Victim Delay Results (Best/Worst Case)  Worst case delay values using 50% threshold delay  Aggressor and victim switching in opposite directions  Same slew time on victim and aggressor  Case 1 and 4 - local  Case 2 and 3 - global

32. KMV - ASIC9932 Victim Delay Uncertainty With Slew Times  Delay uncertainty constant with same slew time on victim and aggressor  accuracy within 15% of spice

33. KMV - ASIC9933 Victim Delay Variation W.R.T. Coupling  Best and worst case delays variation with coupling capacitance variation  Same slew time on victim and aggressor  Case 1 is local interconnect and case 2 is global interconnect

34. KMV - ASIC9934 Victim Delay Variation With Aggressor Slew  Impact of aggressor slew on delay  Victim slew constant at 400 ps  15% accuracy w.r.t. spice  Local interconnect (case1) delay highly sensitive to slew time

35. KMV - ASIC9935 Victim Delay Variation With Aggressor Slew  Impact of aggressor slew on delay  Victim slew constant at 400 ps  15% accuracy w.r.t. spice  Local interconnect (case1) delay highly sensitive to slew time

36. KMV - ASIC9936 Conclusions  Provide simple, fast and accurate analytical expressions for peak noise and delay estimates  Consider all R and C and all slew times  Provide noise awareness methodology possibility earlier in design phase  Easy extensions –multiple aggressor lines –slew offsets