1. Yield Optimization: Divide and Conquer Method
Christopher Wottawa
June 10, 2010
EE201C

2. Outline Yield Estimation: Probability Weighting
Yield Optimization: Divide and Conquer
Results
Discussion
Ideas for Improvement

3. Yield Estimation: Baseline algorithm
1) Generate N random parameter sets
2) Simulate
3) Count the number of successes
if circuit passes
if circuit fails

4. Another way to look at Yield Rate:
“Randomly” select one parameter set.
(using Gaussian distribution for each parameter)
The probability that this parameter set gives a successful circuit should equal the yield rate.

5. Yield Estimation: Probability Weighting
Goal
Have more samples in failure region (Importance Sampling)
Algorithm:
Use uniform distribution to select parameter sets
Assign a weight to each parameter set
Calculate yield:
Suppose one parameter…
wi equals the probability of this parameter set coming up “normally.”

6. Yield Estimation: Results
Normal
Probability Weighting
Test Procedure:
Do 5 Monte Carlo simulations using each method
Used initial design values for parameter set
Used 3000 MC samples per run
Read Yield
Write Yield
Total Yield
53.33
86.00
47.20
53.10
84.50
44.67
52.73
85.06
44.37
55.53
85.10
47.60
52.93
85.56
45.20
48.85
86.24
42.26
52.65
81.72
43.13
53.20
85.41
44.49
44.20
86.77
36.55
50.14
85.87
42.09

7. Yield Optimization: Baseline
Try every single possible combination of parameter values
6 values for Vth2, Vth5
7 values for Leff2, Leff5
1764 possible parameter sets
~60 hours to simulate

8. Yield Optimization: Divide and Conquer
Assumptions:
Yield rates change gradually, continuously over the parameter space
“Better” parameter sets lie near “Good” parameter sets
Algorithm:
Parameter space
Parameter space
74%
90%
50%
82%
88%
70%
89%
65%
Parameter set
80%
15%
50%
70%
Parameter space

9. Implementation Details
Used recursion, storing results in a global array
Set configuration parameters:
Number of depth levels
Number of “best regions” to choose per level
Number of MC samples in yield estimation
Number of parameter sets per parameter space
Some time saving measures:
Check Area and Power before doing Yield Simulation
A “fuzzy” constraint tightens at each depth level
If either constraint fails, skip simulations and set yield to zero.
If read yield is too low, skip write yield.
Use Perl for text parsing.

10. Results Simulations Characteristics: Configuration: “Optimal” Results:
336 parameter sets (w/ 500 MC runs per)
84 best results
10.25 hours
Configuration:
# values per parameter = 2
( 16 sets per parameter space)
# levels = 3;
# parameters = 4;
# best regions = 4
# MC samples = 500
Read yield skip % = 70
“Optimal” Results:
1) Assuming that the failure region lies nearer the edges
Leff2
Leff5
Vth2
Vth5
Area
Power
R Yield
W Yield
T Yield
0.0980
0.0975
0.3238
0.2762
1.1274
97.74%
90.86%
88.75%
0.0950
0.35
0.21 -
99.6%
99.9%
0.1
0.2607
1.1291
48.084
54.6%
85.2%
46.4%
Divide & Conquer
TA’s baseline
Initial design

11. Yield Optimization: Discussion
Positive outcomes
Significant run time gains, fewer MC simulations
Higher resolution than standard baseline algorithm
(can hit those “in-between” spots)
Issues
Algorithm has difficulty reaching the edges of the parameter space
TA Optimal Leff is at the edge (0.095)
Optimal solution may lie in “unchosen” regions
1) Assuming that the failure region lies nearer the edges

12. Ideas for Improvement Yield Estimation: Yield Optimization:
Use a shifted Gaussian rather than uniform distribution, but this requires a different weight calculation.
Yield Optimization:
Change way parameter space is divided, so that edge is more reachable.
Choose different number of best regions at each depth level
(50% at first level, 25% at second level, etc)
Choose best regions based on merit, rather than number
(i.e. all regions that pass 50% yield in level 1, 70% in level 2)
Try changing the “fuzzy” constraint parameters
(i.e. allow all area/power violations for just first level)
Processing:
Use a faster language (C++? Perl? Java? Linux shell?)

13. Thank you!