1. Moon-Su Kim, Sunik Heo, DalHee Lee, DaeJoon Hyun, Byung Su Kim, Bonghyun Lee, Chul Rim, Hyosig Won, Keesup Kim Samsung Electronics Co., Ltd. System LSI Division

2. Dr. Cho Moon Dr. Peter Kim PrimeTime Group(Amrita, JW Jang) SiliconSmart Group(Moninder, JH Song) 1

3. Introduction Background Library Characterization Waveform Waveform Propagation Using Library Noise Model Experimental Results Runtime Impact Conclusion 2

4. 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 3

5. 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 4 Strong miller effect Long tail effect Drive Strength

6. Long tail effect Slew degradation by wire resistance  long tail Same input transition(30% ~ 70%)  different propagation delay : long tail effect 5 Waveform @Y(real) Waveform @Y(driver model) Waveform @ next A(real) Waveform @ next A(driver model) waveform at end of wire waveform at driver output Inputoutput Delay difference due to tail of waveform

7. 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 6

8. 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 7

9. 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 Noise Model Vi Miller Cap Timing Model + Accurate Waveform Propagation + Improved Path Delay & Slew Accuracy Accurate Waveform Propagation + Improved Path Delay & Slew Accuracy =

10. How well STA consider waveform distortion 9 SPICE Waveform ResultsStatic Timing Analysis Waveform Results

11. 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 10 Accuracy significantly improved with waveform propagation NLDMwaveform propagation PDR 0.5PDR 0.3 PDR 0.5PDR 0.3 GBAPBAGBAPBA average-6.0%-1.8%-4.8%-2.2%-2.1%-1.6% stdev7.5%6.4%4.5%1.5%4.3%1.5%

12. 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 11 NLDM (min) Waveform Propagation (min) read_db104.9113.9 update_timing157.3175.0 PBA (max 10000 paths)68.089.0 Total TAT330.2377.9 Ratio1.001.14

13. 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%) 12