A step-by-step description on how to translate defect-to-bit-fail maps to the rest of the die area.

1. How to Translate Bit-Fail Correlation Data to
Die “Kill Ratios”
Stuart L. Riley
Value-Added Software Solutions
slriley@valaddsoft.com
Copyright 2009 Stuart L. Riley 1

2. Copyright Statement
Copyright 2009, Stuart L. Riley
Rights reserved.
This document may be downloaded for personal use; users are forbidden to
reproduce, republish, redistribute, or resell any materials from this
document in either machine-readable form or any other form without
permission from Stuart L. Riley or payment of the appropriate royalty for
reuse.
Email: slriley@valaddsoft.com
Copyright 2009 Stuart L. Riley 2

3. Terms
• Anomaly
– Anything detected by in-line inspection
– Includes defects, and nuisance (cosmetic or inspection noise) anomalies
– It is assumed the inspection operator will optimize recipes to minimize noise
• Defect
– An anomaly that has been identified through classification as a possible cause of faults
– Has a specific probability of failure – sometimes called “kill ratio”
• Kill Ratio / Hits (% of Hits)
– Probability that a specific defect, or defect group can cause an electrical fault
– Fraction of all defects in a group that may cause faults
– Not the same as fault capture rate
– May be different per defect group, depending on the region the group falls in
– May be different for each technology with different die layouts
• Fail / Fault
– Electrical fail/fault as determined at test
– May or may not be associated with detected defects
– Can be caused by issues undetected by inspection
• Fault Capture Rate
– Fraction of all faults that are associated with detected defects
– Not the same as kill ratio
Copyright 2009 Stuart L. Riley 3

4. “Kill Ratios” From Bit-Fail Correlation
Use bit-fail correlation to determine the “% of hits” for defects falling in the tested area (SRAM).
The “% of hits” is the ratio of defects that correlate to failing bits (faults) to the number of
defects in the test area. This number is equivalent to a “kill ratio” for defects in the SRAM.
Correlation does not guarantee causality, but let’s assume it’s close enough for our purposes.
⎡ Number of Hits ⎤
′
K r( sram ) = ⎢ ⎥
⎣ Number of Defects ⎦( sram )
SRAM Area = Asram
The prime is used to denote that this kill ratio is
Die Area = Adie calculated based on inspection data only.
SRAM Die
K’r(sram) may NOT be the same as the kill ratio
based purely on electrical results.
Area Outside Also, K’r(sram) may NOT be the same as a kill ratio
of SRAM = Adie-sram
based on CAA.
′
K r( sram ) ≠ K r( sram )
From now on, all numbers based on inspection data will be denoted by a prime.
Copyright 2009 Stuart L. Riley 4

5. “Kill Ratios” From Bit-Fail Correlation
K’r(sram) may work for the area inside the SRAM, but it may not be applicable to the entire
die area, due to the differences in critical areas.
′ ′
K r( sram ) ≠ K r( die )
The defect inspection engineer needs to find K’r(die) so it can be applied to all defects
detected within the die area (assuming a full-die scan is used).
So, we need to find the kill ratio for the die K’r(die) based on K’r(sram).
Copyright 2009 Stuart L. Riley 5

6. Avg Num Fails From Defects in the SRAM
λ(′sram ) = K r( sram ) × A( sram ) × DD
′
λ(′sram ) = K r( sram ) × D( sram )
′
⎛ Number of Hits ⎞
λ(′sram ) =⎜
⎜ ⎟ × D( sram )
⎟
⎝ D( sram ) ⎠
λ(′sram ) = Number of Hits
As with the kill ratio, the prime is used to denote that average number of fails per die is
based on inspection data only.
λ’(sram) may NOT be the same as the λ based purely on electrical results.
Also, λ’(sram) may NOT be the same as a λ based on Critical Area Analysis (CAA).
Copyright 2009 Stuart L. Riley 6

7. Use Critical Area Ratios to Scale to Die
λ( sram ) = Ac( sram ) × DD And λ( die ) = Ac( die ) × DD
Assume defect densities (DD) are the same:
λ( die ) λ( sram ) ⎛ Ac( die ) ⎞ ACs are
λ( die ) = λ( sram ) × ⎜
⎜ Ac( sram ) ⎟
from CAA.
= ⎟
Ac( die ) Ac( sram ) ⎝ ⎠
Assume the scaling is the same for inspected defects:
⎛ Ac( die ) ⎞
λ(′die ) = Number of Hits × ⎜
⎜ Ac( sram ) ⎟
⎟
⎝ ⎠
Must be able to account for Ac at ANY layer that can be affected by defects. The
defects causing fails then need to be associated with the proper layer of fail origin.
Example: Can defects from different layers be interpreted as being associated with
the same group fail mechanisms? For a particular fail mechanism, how many
correlate to defects causing poly shorts vs. the number causing M1 shorts?
Copyright 2009 Stuart L. Riley 7

8. Die Kill Ratio for Inspected Defects
λ(′die ) Number of Hits
=
′
K r( die ) × A( die ) ′
K r( sram ) × A( sram )
′ ′
λr( die ) × K r( sram ) × A( sram )
′
K r( die ) =
Number of Hits × A( die )
Substituting terms, K’r(die) reduces to: (see addendum A for more detail)
⎛ Number of Hits ⎞ ⎛ Ac( die ) ⎞ ⎛ A( sram ) ⎞
′
K r( die ) =⎜ ⎟ ×⎜ ⎟×⎜ ⎟
⎝ Number of Defects ⎠( sram ) ⎜ Ac( sram ) ⎟ ⎜ A( die ) ⎟
⎝ ⎠ ⎝ ⎠
We’ve found K’r(die) -- Now this can be applied to a yield model (another document)
Copyright 2009 Stuart L. Riley 8

9. Assumptions
• Fail mechanisms are the same between SRAM and die
• Causal relationship between defects and fails is strong
• Nuisance anomalies are not significantly creating many false-positives
• Fault Capture Rate is significant (see addendum B)
• Defect types do not change much over time
• Able to find Kr(sram) and Kr(die) for ALL technologies in the fab
• No inspection sensitivity issues between regions
– Some defect types may be found easier in or out of SRAM area
• Defect grouping is accurate and consistent
• Grouping can include single or groups of def types
– As you resolve to a single type, the accuracy may get worse
• Critical Area Analysis (CAA)
– Has been run on all layers
– Ac can be correctly applied to the proper layer based on physical cause analysis (FA)
Copyright 2009 Stuart L. Riley 9

10. Addendum A:
How to Find the Die Kill Ratio for Inspected Defects
Copyright 2009 Stuart L. Riley 10

11. Die Kill Ratio for Inspected Defects
Addendum A λ(′die ) Number of Hits
=
′
K r( die ) × A( die ) ′
K r( sram ) × A( sram )
λr( die ) × K r( sram ) × A( sram )
′ ′
′
K r( die ) =
Number of Hits × A( die )
⎛ Number of Hits ⎞
λr( die ) × ⎜
′ ⎟ × A( sram )
⎝ Number of Defects ⎠( sram )
′
K r( die ) =
Number of Hits × A( die )
λr( die ) × A( sram )
′
′
K r( die ) =
Number of Defects × A( die )
⎛ Number of Hits ⎞ ⎛ Ac( die ) ⎞ ⎛ A( sram ) ⎞
′
K r( die ) =⎜ ⎟ ×⎜ ⎟×⎜ ⎟
⎝ Number of Defects ⎠( sram ) ⎜ Ac( sram ) ⎟ ⎜ A( die ) ⎟
⎝ ⎠ ⎝ ⎠
Result on page 8
Copyright 2009 Stuart L. Riley 11

12. Addendum B:
Fault Capture Rate
Copyright 2009 Stuart L. Riley 12

13. Addendum B Fault Capture Rate
Faults Correlated to Defects
Fault Capture Rate =
Total Faults
• Applications of Fault Capture Rate
– Determine the % of fault mechanisms that can be captured from in-line inspection
– Identify gaps from in-line monitoring for important yield-limiting causes
– Indicate where adjustments should be made - if any - to in-line monitoring
– Inspection sensitivity
– Inspection areas
– Visible and invisible defects
Copyright 2009 Stuart L. Riley 13

14. Die-Based Fault Capture Rate All Die (100)
Large circle:
Addendum B
Circle: Die With Circle: Failed Die (30)
Defects (35)
Blue area: Failed Die
Without Defects (10)
Green area: Good Die With
Yellow area: Failed Die With
Defects (15)
Defects (20)
Failed DieWith Defects 20 Good DieWith Defects 15
Fault Capture Rate = = = 0.57 Nuisance Rate = = = 0.43
Failed Die 30 DieWith Defects 35
This can be applied to bin maps (array not necessary)
This could introduce errors - Failed Die With Defects may include nuisance
Copyright 2009 Stuart L. Riley 14

15. Bit-Fail-Based Fault Capture All Bits
Circle: Rate
Addendum B (10000)
Circle: All Defects
(3500) Circle: All Fails
(3000)
Blue area: Fails Without
Defects
(1000)
Green area: Defects With
No Fails Yellow area: Defects With Fails
(1500) (2000)
DefectsWith Fails 2000 DefectsWith No Fails 1500
Fault Capture Rate = = = 0.57 Nuisance Rate = = = 0.43
All Fails 3000 All Defects 3500
This can only be applied to bit-fail data
Fewer chances for errors - Failed Die With Defects may include nuisance
Copyright 2009 Stuart L. Riley 15