Is Statistical TimingStatistically Significant?

DAC 2004, Panel Discussion, Session 41

Chandu VisweswariahIBM Thomas J. Watson Research Center

Yorktown Heights, NY

Per

form

anc

e

Technology generation

Is this worth a huge

investment?

The march of technology

Corner-based vs. statistical• n = # independent sources of variation (say 9)

= total variability in critical path delay (say 5%)

• Fractional increase in frequency with a 3 sign-off instead of 3n sign-off

• Assumes sources of variation are roughly equally significant

Corner-based vs. statistical

0

10

20

30

40

50

60

70

80

1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

Sigma as fraction of cycle time

% f

req

ue

ncy

dif

fere

nce

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Tooleaky

Simultaneous power/timing sign-off

Tooslow

Pro

babi

lity

Vt

Goodchips

Where will the models come from?

• Clearly, the IDMs have an advantage

• Table-based delay modeling formats are not as conducive to statistical timing as equation-based formats

Can statistical timers handle the size?

• 2.1M gate design timed in 69 minutes with 10.9 GB memory

• 1.1M gate design timed in 110 minutes (dominated by load time) with 4.3 GB memory

BEOL early-mode variability on ASIC part

0.0E+00

5.0E-03

1.0E-02

1.5E-02

2.0E-02

-230 -168 -105 -42

Slack (ps)

Pro

bab

ilit

y

Pessimismreduction

-3

slac

k: -

162

ps

Exh

au

stiv

e c

orn

er a

nal

ysis

: -2

25 p

s

How will it be phased in?

• Phase 1– true 3 timing sign-off with statistical timing

• Phase 2– use statistical timing to guide the physical

synthesis and routing optimization (implicit robustness credit)

• Phase 3– further reduce performance by actively targeting

robustness (explicit robustness credit)

• Phase 4– with the mainstream availability of at-speed test,

enable yield/performance tradeoffs

Propositions/predictions1. Variability is proportionately increasing; therefore,

a new paradigm is required

2. Correlated vs. independent variability matters

3. Statistical timing tools are rising to the challenge

4. Robustness is an important metric

5. Statistical treatment of variability will pervade all aspects of chip design and manufacturing

6. ASICs and processors will both benefit (in that order)

Statistical prediction (ASICs)

• With a probability of ____%, statistical design

analysis will have been used at the _______

technology node by the year ______, to solve the

problem of ___________________________.

The technical foundation of this statistical design

analysis will be __________________________

______________________.

90 nm

2006

performance pessimism

99

(in part) techniques like

those of paper 21.1