1. Is Statistical Timing Statistically Significant?
DAC 2004, Panel Discussion, Session 41
Chandu Visweswariah
IBM Thomas J. Watson Research Center
Yorktown Heights, NY

2. The march of technology
Performance
Is this worth a huge investment?
Technology generation

3. 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 3n sign-off
Assumes sources of variation are roughly equally significant

4. Corner-based vs. statistical

5. Simultaneous power/timing sign-off
Probability
Good
chips
Too
slow
Too
leaky Vt

6. 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

7. 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

8. BEOL early-mode variability on ASIC part
Exhaustive corner analysis: -225 ps
Pessimism
reduction
-3 slack: -162 ps

9. 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

10. Propositions/predictions
Variability is proportionately increasing; therefore, a new paradigm is required
Correlated vs. independent variability matters
Statistical timing tools are rising to the challenge
Robustness is an important metric
Statistical treatment of variability will pervade all aspects of chip design and manufacturing
ASICs and processors will both benefit (in that order)

11. 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 __________________________ ______________________. 99
90 nm
2006
performance pessimism
(in part) techniques like
those of paper 21.1