Noise Model for Multiple Segmented Coupled RC Interconnects Andrew B. Kahng, Sudhakar Muddu †, Niranjan A. Pol ‡ and Devendra Vidhani* UCSD CSE and ECE Department, † Sanera Systems, Inc., ‡ Cadence Design Systems, * Sun Microsystems,

KMPV Outline of Talk Signal Integrity Issues Previous Works Our Contributions –Transformed  Model for Segmented Aggressors –Multiple Aggressors Simulation Results Conclusions

KMPV Outline of Talk Signal Integrity Issues Previous Works Our Contributions –Transformed  Model for Segmented Aggressors –Multiple Aggressors Simulation Results Conclusions

KMPV Interconnect Induced Issues –scaled linewidths, increased aspect ratios, larger die sizes greater wire and via RC, electromigration, IR drop, skin effect –more metal layers higher coupling to ground ratio –long wider metal wires magnetic field / inductance Process Induced Issues –low device thresholds, low V DD increased susceptibility to low noise margins Design Induced Issues –high frequency faster slew times, inductive effects, ground bounce Factors Affecting Signal Integrity

KMPV Focus: Crosstalk Issues Cross talk caused by coupling between neighboring signals –Victim Net: Net being affected by coupling –Aggressor Net: Net affecting victim net due to its coupling to victim Coupling capacitance is one of major contributors Functionality Issues –peak noise false switching of noise sensitive nodes in the design Timing Issues –positive/negative delay impact due to crosstalk –issues with timing closure Motivation: find coupling related noise issues ASAP!! –In general, find signal integrity problem earlier in design –provide sufficient conditions for finding problem

KMPV Outline of Talk Signal Integrity Issues Previous Works Our Contributions –Transformed  Model for Segmented Aggressors –Multiple Aggressors Simulation Results Conclusions

KMPV Previous Works on Crosstalk 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; does full chip simulation Kahng et. al., 99:  model; Assume single, full length aggressor

KMPV Previous Works on Crosstalk Circuit models issues –use lumped capacitance models –cannot handle segmented aggressors configurations Noise models issues –estimations very pessimistic –assumptions about R and C –some are simulation based

KMPV Outline of Talk Signal Integrity Issues Previous Works Our Contributions –Transformed  Model for Segmented Aggressors –Multiple Aggressors Simulation Results Conclusions

KMPV Our Work Improved circuit model for peak noise –facilitates segmented aggressors –superposition for multiple aggressors Methodology –for coupled RC interconnects only –takes drivers into account –considers slew times –considers lumped  -Model –considers both local and global line

KMPV 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

KMPV Lumped  - Model C B V s1 V s2 R d2 C c1 D A RaRa RvRv C L1 Aggressor Line Victim Line R d1 C c2 Cg v1 Cg v2 C L2 Cg a1 Cg a2 R d1, R d2 : Driver Resistances Cg v1, Cg v2 : Leg of  model for ground cap for victim Cg a1, Cg a2 : Leg of  model for ground cap for aggressor R a, R v : Wire resistances of used in the model C c1, C c2 : Left and right leg of  model for coupling cap C L1, C L2 : Load caps

KMPV Peak Noise For  Model V peak is given at v c ( t peak ) where

KMPV Segmented Aggressor Nets Simple lumped model deficiencies for general case –general case is when aggressor and victim nets are not overlapped completely –for segmented aggressor overlaps, lumped model gives pessimistic results Extensions to lumped model for general case –improved victim wire and victim driver resistance modeling –improved victim coupling and ground capacitance modeling For multiple segmented aggressor nets coupling to victim net, use superposition to compute noise peak value

KMPV Segmented Aggressor Net Configuration L1 = Left fraction of Victim to the Aggressor Overlap L2 = Fraction of Victim overlapped by Aggressor L3 = Right fraction of Victim to the Aggressor Overlap R dA (R dV ) = Aggressor(Victim) Driver Resistance R wA (Rw V ) = Aggressor(Victim) Wire Resistance C gA (C gV ) = Aggressor(Victim) Capacitance to ground C LA (C LV ) = Aggressor(Victim) Load Capacitance Cc = Coupling Capacitance C LV VAVA Aggressor Net L3 L2 L1 L1+ L2+ L3 = 1 R dA R dV R WA C LA R WV C gV C gA Victim Net C R dA

KMPV Victim wire resistance modeling –Wire resistance to left and right of overlap region not considered part of wire resistance in the  model –Assumed proportional to length of the victim net overlap region with the aggressor, I.e., R v = R wv * L2 Victim driver resistance modeling –Assumed to consist of the actual driver resistance and the resistance of portion of wire to the left of the overlap region, I.e., R d2 = R dv +R wv * L1 Victim Resistance Modeling

KMPV Non Uniform Coupling Capacitance Distribution Coupling capacitance distribution in model and real circuit –In real circuit, coupling capacitance starts L1 distance away from the keeper end of the victim net –In the model, the left leg of the coupling capacitance is at the keeper end of the victim net Discrepancy between model and real circuit –In real circuit, capacitance is shielded by the wire resistance –In the model, the keeper end of the victim net is at zero potential –This causes more discharge from the left leg of coupling cap Solution –Lower the coupling cap on the keeper end of the victim net in the model –Keep it pessimistic (don’t worry about receiver end correction) C c1 = 0.5 * C c * (1-L1) C c2 = 0.5 * C c * (1+L1)

KMPV Non Uniform Victim Ground Cap Distribution Ground capacitance distribution / discrepancy –In real circuit, the ground capacitance is distributed all along the victim wire –In the model, the ground capacitance is visible equally at driver and receiver end of the wire Solution –Make left (right) leg of ground cap account for the ground cap for the portion of the victim wire to the left (right) of the overlap region –Adjust total ground capacitance such that the total ground capacitance is not changed Cg v1 = 0.5* C gv * (1+L1-L3) Cg v2 = 0.5* C gv * (1-L1+L3)

KMPV Outline of Talk Signal Integrity Issues Previous Works Our Contributions –Transformed  Model for Segmented Aggressors –Multiple Aggressors Simulation Results Conclusions

KMPV Multiple Aggressors In real life layouts, need to see contributions of not more than 3 worst aggressors Our model report noise by superposition for individual aggressor’s noise contribution Noise function due to each aggressor is added in time domain to obtain the superimposed peak noise Could potentially be huge number of aggressor configurations Presented results for two and three aggressors

KMPV Outline of Talk Signal Integrity Issues Previous Works Our Contributions –Transformed  Model for Segmented Aggressors –Multiple Aggressors Simulation Results Conclusions

KMPV Criteria –global wires (case 2 and 3) and local wires (case 1 and 4) –different coupling to ground capacitance ratios –The values shown here are corresponding to R int, C int per unit length of the victim wire and coupling cap to the aggressor with L2 assumed equals 1.0 –To compare results for model with spice, we construct multiple  model with 45 nodes in the spice circuit Simulation Configuration

KMPV Segmented Aggressor Net Configuration 1 L1 = Left fraction of Victim to the Aggressor Overlap = 0.2 L2 = Fraction of Victim overlapped by Aggressor = 0.6 L3 = Right fraction of Victim to the Aggressor Overlap = 0.2 R dA (R dV ) = Aggressor(Victim) Driver Resistance R wA (Rw V ) = Aggressor(Victim) Wire Resistance C gA (C gV ) = Aggressor(Victim) Capacitance to ground C LA (C LV ) = Aggressor(Victim) Load Capacitance Cc = Coupling Capacitance C LV VAVA Aggressor Net L3 L2 L1 L1+ L2+ L3 = 1 R dA R dV R WA C LA R WV C gV C gA Victim Net C R dA

KMPV Peak Noise Results for Configuration 1 Peak noise results for configuration 1: L1=0.2, L2=0.6, L3=0.2

KMPV Segmented Aggressor Net Configuration 2 VAVA Aggressor Net L3 L2 R dA R dV R WA R WV C C gv C gA Victim Net C LA L1 = Left fraction of Victim to the Aggressor Overlap = 0.0 L2 = Fraction of Victim overlapped by Aggressor = 0.6 L3 = Right fraction of Victim to the Aggressor Overlap = 0.4 R dA (R dV ) = Aggressor(Victim) Driver Resistance R dA (R dV ) = Aggressor(Victim) Wire Resistance C gA (C gV ) = Aggressor(Victim) Capacitance to ground C gA (C gV ) = Aggressor(Victim) Load Capacitance Cc = Coupling Capacitance L1+ L2+ L3 = L

KMPV Peak Noise Results for Configuration 2 Peak noise results for configuration 1: L1=0, L2=0.6, L3=0.4

KMPV Segmented Aggressor Net Configuration 3 C LV VAVA Aggressor Net L2 L1 R dA R dV R WA R WV C C gv C gA Victim Net C LA L1 = Left fraction of Victim to the Aggressor Overlap = 0.4 L2 = Fraction of Victim overlapped by Aggressor = 0.6 L3 = Right fraction of Victim to the Aggressor Overlap = 0.0 R dA (R dV ) = Aggressor(Victim) Driver Resistance R dA (R dV ) = Aggressor(Victim) Wire Resistance C gA (C gV ) = Aggressor(Victim) Capacitance to ground C gA (C gV ) = Aggressor(Victim) Load Capacitance Cc = Coupling Capacitance L1+ L2+ L3 = L

KMPV Peak Noise Results for Configuration 3 Peak noise results for configuration 1: L1=0.4, L2=0.6, L3=0

KMPV Peak Noise Results for Two Aggressor Peak noise results for two aggressors configurations. Aggressor1: L1=0, L2=0.6, L3=0.4; Aggressor2: L1=0.4, L2=0.6, L3=0

KMPV Peak Noise Results for Three Aggressors Peak noise results for three aggressors configurations. Aggressor1: L1=0, L2=0.6, L3=0.4; Aggressor2: L1=0.2, L2=0.6, L3=0.2; Aggressor3: L1=0.6, L2=0.4, L3=0

KMPV Outline of Talk Signal Integrity Issues Previous Works Our Contributions –Transformed  Model for Segmented Aggressors –Multiple Aggressors Simulation Results Conclusions

KMPV Conclusions Model works for point to point victim net and segmented multiple aggressors Results are accurate for peak noise Pessimism increases with the number of aggressors –One segmented aggressor: 16% max error –Two segmented aggressor: 17% –Three segmented aggressor: 31% Can be used as a quick pruning step in an analytical noise tool

KMPV Future Work More scalable for large system of aggressors Extension to tree like structures (multiple fanouts) Report pulse width / slew degradation and effective switch factor Form a complete analytical system for post layout noise analysis