Noise and Delay Uncertainty Studies for Coupled RC Interconnects Andrew B. Kahng, Sudhakar Muddu † and Devendra Vidhani ‡ UCLA Computer Science Department, † Silicon Graphics Inc., ‡ Sun Microsystems,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

KMV - ASIC9923 Delay Function  Delay Function at node C

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

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

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

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

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

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

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

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

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

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

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

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

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