Statistical Performance Modeling and Optimization (Foundations and Trends in Electronic Design Automation)

162 Pages·2007·1.548 MB·English

by  Xin Li, Jiayong Le, Lawrence, T Pileggi

EDAv1n4.qxd 7/17/2007 5:04 PM Page 1
F
n
T
E
D Foundations and Trends® in
A
1 Electronic Design Automation
Statistical Performance Modeling :4
S 1:4 (2006)
and Optimization ta
tis
tic
Xin Li, Jiayong Le, and Lawrence T. Pileggi a
l P
e
r
Statistical Performance Modeling and Optimization reviews various statistical methodologies for
m
that have been recently developed to model, analyze and optimize performance variations at an Statistical Performance
both transistor level and system level in integrated circuit (IC) design. The following topics are c
e
discussed in detail: sources of process variations, variation characterization and modeling, M
o Modeling and Optimization
Monte Carlo analysis, response surface modeling, statistical timing and leakage analysis, d
e
probability distribution extraction, parametric yield estimation and robust IC optimization. lin
g
These techniques provide the necessary CAD infrastructure that facilitates the bold move from a
n
deterministic, corner-based IC design toward statistical and probabilistic design. d Xin Li, Jiayong Le, and Lawrence T. Pileggi
O
p
Statistical Performance Modeling and Optimization reviews and compares different statistical tim
iz
IC analysis and optimization techniques, and analyzes their trade-offs for practical industrial a
applications. It serves as a valuable reference for researchers, students and CAD practitioners. tio
n
X
in
L
i,
J
ia
y
o
n
g
L
e
,
a
n
d
L
a
w
r
e
n
c
e
T
.
P
ile
g
g
i
This book is originally published as
Foundations and Trends®in Electronic Design Automation,
Volume 1 Issue 4 (2006), ISSN: 1551-3939.
n now
o
w
the essence of knowledge
Statistical Performance
Modeling and
Optimization

Statistical Performance
Modeling and
Optimization
Xin Li
Carnegie Mellon University
Pittsburgh, PA 15213, USA
[email protected]
Jiayong Le
Extreme DA
Palo Alto, CA 94301, USA
[email protected]
Lawrence T. Pileggi
Carnegie Mellon University
Pittsburgh, PA 15213, USA
[email protected]
Boston – Delft
Foundations and Trends(cid:13)R in
Electronic Design Automation
Published, sold and distributed by:
now Publishers Inc.
PO Box 1024
Hanover, MA 02339
USA
Tel. [phone]
www.nowpublishers.com
[email protected]
Outside North America:
now Publishers Inc.
PO Box 179
2600 AD Delft
The Netherlands
Tel. [phone]
ThepreferredcitationforthispublicationisX.Li,J.LeandL.T.Pileggi,Statistical
Performance Modeling and Optimization, Foundations and Trends(cid:13)R in Electronic
Design Automation, vol 1, no 4, pp 331–480, 2006
ISBN: 978-1-60198-056-4
(cid:13)c 2007 X. Li, J. Le and L. T. Pileggi
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system,ortransmittedinanyformorbyanymeans,mechanical,photocopying,recording
orotherwise,withoutpriorwrittenpermissionofthepublishers.
Photocopying. In the USA: This journal is registered at the Copyright Clearance Cen-
ter, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for
internal or personal use, or the internal or personal use of specific clients, is granted by
now Publishers Inc for users registered with the Copyright Clearance Center (CCC). The
‘services’foruserscanbefoundontheinternetat:www.copyright.com
For those organizations that have been granted a photocopy license, a separate system
of payment has been arranged. Authorization does not extend to other kinds of copy-
ing, such as that for general distribution, for advertising or promotional purposes, for
creating new collective works, or for resale. In the rest of the world: Permission to pho-
tocopy must be obtained from the copyright owner. Please apply to now Publishers Inc.,
PO Box 1024, Hanover, MA 02339, USA; Tel. [phone]; www.nowpublishers.com;
[email protected]
nowPublishersInc.hasanexclusivelicensetopublishthismaterialworldwide.Permission
tousethiscontentmustbeobtainedfromthecopyrightlicenseholder.Pleaseapplytonow
Publishers,POBox179,2600ADDelft,TheNetherlands,www.nowpublishers.com;e-mail:
[email protected]
Foundations and Trends(cid:13)R in
Electronic Design Automation
Volume 1 Issue 4, 2006
Editorial Board
Editor-in-Chief:
Sharad Malik
Department of Electrical Engineering
Princeton University
Princeton, NJ 08544
Editors
Robert K. Brayton (UC Berkeley)
Raul Camposano (Synopsys)
K.T. Tim Cheng (UC Santa Barbara)
Jason Cong (UCLA)
Masahiro Fujita (University of Tokyo)
Georges Gielen (KU Leuven)
Tom Henzinger (EPFL)
Andrew Kahng (UC San Diego)
Andreas Kuehlmann (Cadence Berkeley Labs)
Ralph Otten (TU Eindhoven)
Joel Phillips (Cadence Berkeley Labs)
Jonathan Rose (University of Toronto)
Rob Rutenbar (CMU)
Alberto Sangiovanni-Vincentelli (UC Berkeley)
Leon Stok (IBM Research)
Editorial Scope
Foundations and Trends(cid:13)R in Electronic Design Automation
will publish survey and tutorial articles in the following topics:
• System Level Design • Physical Design
• Behavioral Synthesis • Circuit Level Design
• Logic Design • Reconfigurable Systems
• Verification • Analog Design
• Test
Information for Librarians
Foundations and Trends(cid:13)R in Electronic Design Automation, 2006, Volume 1,
4 issues. ISSN paper version 1551-3939. ISSN online version 1551-3947. Also
available as a combined paper and online subscription.
FoundationsandTrends(cid:13)R in
ElectronicDesignAutomation
Vol.1,No.4(2006)331–480
(cid:13)c 2007X.Li,J.LeandL.T.Pileggi
DOI:10.1561/1000000008
Statistical Performance Modeling
and Optimization
Xin Li1, Jiayong Le2 and Lawrence T. Pileggi3
1 Department of ECE, Carnegie Mellon University, Pittsburgh, PA 15213,
USA, [email protected]
2 Extreme DA, 165 University Avenue, Palo Alto, CA 94301, USA,
[email protected]
3 Department of ECE, Carnegie Mellon University, Pittsburgh, PA 15213,
USA, [email protected]
Abstract
As IC technologies scale to finer feature sizes, it becomes increasingly
difficult to control the relative process variations. The increasing fluc-
tuations in manufacturing processes have introduced unavoidable and
significantuncertaintyincircuitperformance;henceensuringmanufac-
turability has been identified as one of the top priorities of today’s IC
designproblems.Inthispaper,wereviewvariousstatisticalmethodolo-
gies that have been recently developed to model, analyze, and optimize
performance variations at both transistor level and system level. The
following topics will be discussed in detail: sources of process varia-
tions, variation characterization and modeling, Monte Carlo analysis,
responsesurfacemodeling,statisticaltimingandleakageanalysis,prob-
ability distribution extraction, parametric yield estimation and robust
IC optimization. These techniques provide the necessary CAD infras-
tructurethatfacilitatestheboldmovefromdeterministic,corner-based
IC design toward statistical and probabilistic design.

Contents
1 Introduction 1
2 Process Variations 5
2.1 Front-End of Line (FEOL) Variations 5
2.2 Back-End of Line (BEOL) Variations 9
2.3 Variation Characterization 11
2.4 Variation Modeling 14
2.5 Manufacturing Yield 25
3 Transistor-Level Statistical Methodologies 27
3.1 Monte Carlo Analysis 28
3.2 Statistical Performance Modeling 37
3.3 Statistical Performance Analysis 53
3.4 Statistical Transistor-Level Optimization 78
4 System-Level Statistical Methodologies 95
4.1 Statistical Timing Analysis 96
4.2 Statistical Timing Sensitivity Analysis 111
4.3 Statistical Timing Criticality 123
4.4 Statistical Leakage Analysis 125
ix