Timing Analysis with Waveform Propagation MoonSu Kim Sunik

Timing Analysis with Waveform Propagation Moon-Su Kim, Sunik Heo, Dal. Hee Lee, Dae. Joon Hyun, Byung Su Kim, Bonghyun Lee, Chul Rim, Hyosig Won, Keesup Kim Samsung Electronics Co. , Ltd. System LSI Division

ACKNOWLEDGEMENT • Dr. Cho Moon • Dr. Peter Kim • Prime. Time Group(Amrita, JW Jang) • Silicon. Smart Group(Moninder, JH Song) 1

Contents • Introduction • Background • Library Characterization Waveform • Waveform Propagation Using Library Noise Model • Experimental Results • Runtime Impact • Conclusion 2

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> 3

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 4

Background • Long tail effect • Slew degradation by wire resistance long tail • Same input transition(30% ~ 70%) different propagation delay : long tail effect waveform at. Waveform driver@Y(real) Waveform @Y(driver model) output Waveform @ next A(real) Waveform @ next A(driver model) waveform at end of wire Delay difference due to tail of waveform Input < Slew Degradation due to Wire > output < Long Tail Effect> 5

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. - 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 • Impact on output waveform 6

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> 7

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

Waveform Propagation • How well STA consider waveform distortion SPICE Waveform Results Static Timing Analysis Waveform Results 9

14 nm Experimental Results • Samsung structural test cases • 415 test cases with 14 nm 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 NLDM waveform propagation PDR 0. 5 PDR 0. 3 GBA PBA average -6. 0% -1. 8% -4. 8% -2. 2% -2. 1% -1. 6% stdev 7. 5% 6. 4% 4. 5% 1. 5% 4. 3% 1. 5% Accuracy significantly improved with waveform propagation 10

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 NLDM Waveform Propagation (min) read_db update_timing 104. 9 157. 3 113. 9 175. 0 PBA (max 10000 paths) 68. 0 89. 0 Total TAT 330. 2 377. 9 Ratio 1. 00 1. 14 11

Conclusion • Studied waveform distortion due to long tail and miller effect • Libraries were characterized using Silicon. Smart • Timing analysis was performed using Prime. Time • 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