Timing Analysis with Waveform Propaga-tion

Moon-Su Kim, Sunik Heo, DalHee Lee, DaeJoon Hyun, Byung Su Kim, Bonghyun Lee, Chul Rim,

Hyosig Won, Keesup KimSamsung Electronics Co., Ltd.

System LSI Division

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ACKNOWLEDGEMENT

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

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Contents

• Introduction

• Background

• Library Characterization Waveform

• Waveform Propagation Using Library Noise Model

• Experimental Results

• Runtime Impact

• Conclusion

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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>

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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

Strong miller effect

Long tail ef -fect

Drive Strengt

h

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Background

• Long tail effect• Slew degradation by wire resistance long tail• Same input transition(30% ~ 70%) different propagation delay : long tail ef -

fect

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

Input output

< Slew Degradation due to Wire >

< Long Tail Effect>

Delay differ-ence due to tail of wave-

form

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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

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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>

Waveform Propagation

• Library noise model is required• Library was characterized using a pre-driver waveform generated from a mix-

ture 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 & accu-

racy improvement on the delay and slew

Noise Model

+-

+- Vi

Miller Cap

Timing ModelReceiver Model

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

C1,C2

Driver Model +Accurate Waveform

Propagation +

Improved Path Delay & Slew Accuracy

=

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Waveform Propagation

• How well STA consider waveform distortion

SPICE Waveform Results Static Timing Analysis Waveform Results

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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 im-proved with waveform prop-

agation

NLDM waveform propagation PDR 0.5 PDR 0.3 PDR 0.5 PDR 0.3

GBA PBA GBA PBAaverage -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%

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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

(min)

WaveformPropagation(min)

read_db 104.9 113.9update_timing 157.3 175.0

PBA (max 10000 paths) 68.0 89.0

Total TAT 330.2 377.9Ratio 1.00 1.14

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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%)