Timing Analysis with Waveform Propagation

1. Timing Analysis with Waveform Propagation Moon-Su Kim, SunikHeo, DalHee Lee, DaeJoon Hyun, Byung Su Kim, Bonghyun Lee, Chul Rim, Hyosig Won, Keesup Kim Samsung Electronics Co., Ltd. System LSI Division

2. ACKNOWLEDGEMENT • Dr. Cho Moon • Dr. Peter Kim • PrimeTime Group(Amrita, JW Jang) • SiliconSmart Group(Moninder, JH Song)

3. Contents • Introduction • Background • Library Characterization Waveform • Waveform Propagation Using Library Noise Model • Experimental Results • Runtime Impact • Conclusion

4. Introduction • Impact of Scaling • Wire resistance is linearly increased according to process nodes • Long tail due to wire resistance • No significant change in wire capacitance • Device pin cap has relatively larger impact on delay • Accurate analysis of Miller effect between input and output pin is more important <Wire Cap Trend> <Wire Resistance Trend>

5. Motivation • Conventional timing analysis with non-linear delay model (NLDM) • NLDM cannot consider Miller effect and long tail effect • Timing analysis results can be more optimistic than SPICE results • Composite current source (CCS) model results are similar to NLDM results Drive Strength Strong miller effect Long tail effect

6. Background • Long tail effect • Slew degradation by wire resistance  long tail • Same input transition(30% ~ 70%)  different propagation delay : long tail effect waveform at driver output Waveform @ next A(real) waveform at end of wire Waveform @Y(real) Waveform @ next A(driver model) Waveform @Y(driver model) Delay difference due to tail of waveform Input output < Slew Degradation due to Wire > < Long Tail Effect>

7. Background • Miller effect • Impact on current stage delay • Large receivers that are lightly loaded can inject a bump back to the interconnect through the Miller cap (similar to crosstalk) • Receiver acts as an aggressor driver even though there is no external crosstalk source. • Impact on output waveform • Waveform is too distorted to be modeled by any pre-driver accurately • Distortion is instance specific and cannot be modeled by characterization • Representing this complex waveform with delay and slew is not accurate

8. Library Characterization Waveform • Goal is to drive library cells with waveforms that approximate real waveforms • Need to consider both fast input slew with no RC network effect and slow input slew with significant RC network effect • Can control waveform shape by varying weights of linear ramp vs. exponential component • V_pre-driver = V_linear * ratio + V_exponential *(1-ratio) • Can consider slew degradation at wire by using the lower ratio (more exponential component) • Pre-driver ratio (PDR) of 0.3 means 30% linear and 70% exponential <Pre-driver model>

9. Vi Miller Cap Timing Model Waveform Propagation • Library noise model is required • Library was characterized using a pre-driver waveform generated from a mixture of linear ramp and exponential waveform • Waveform propagation method • Enable propagation of waveforms for both clock and data networks • CCS-Noise  gate level simulation  accurate waveform propagation & accuracy improvement on the delay and slew Accurate Waveform Propagation + Improved Path Delay & Slew Accuracy = Noise Model +

10. Waveform Propagation • How well STA consider waveform distortion SPICE Waveform Results Static Timing Analysis Waveform Results

11. 14 nm Experimental Results • Samsung structural test cases • 415 test cases with 14nm technology • Inverter / Buffer chains with various fanouts, parasitic loading, and driving strengths • Static timing analysis results using library noise model • Waveform propagation analysis is enabled for graph-based analysis (GBA) and path-based analysis (PBA) • Path delay comparison with SPICE Accuracy significantly improved with waveform propagation

12. Runtime Impact of Waveform Propagation • Comparison was made between two models: • Old but very fast model (NLDM) • New and most accurate model (waveform propagation) • On a real 60 M instance design, waveform propagation was 14% slower than NLDM • Waveform propagation was enabled for both clock and data networks • Runtime increase is tolerable for improved accuracy

13. Conclusion • Studied waveform distortion due to long tail and miller effect • Libraries were characterized using SiliconSmart • Timing analysis was performed using PrimeTime • SPICE results were obtained using HSPICE • For accurate static timing analysis • Pre-driver waveform with ratio 0.3 (30% linear ramp and 70% exponential) provided the best accuracy for a slow corner library • Accuracy significantly improved with waveform propagation • Runtime degradation by waveform propagation is acceptable(14%)