How To Translate Bit Fail Correlation Data To Die Kill Ratios May2009

Copyright 2009 Stuart L. Riley 1

How to Translate Bit-Fail Correlation Data to Die “Kill Ratios”

Stuart L. RileyValue-Added Software Solutions

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Copyright 2009, Stuart L. Riley

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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


“Kill Ratios” From Bit-Fail Correlation

DieSRAM

SRAM Area = Asram

Die Area = Adie

Area Outsideof SRAM = Adie-sram

r( sram )( sram )

Number of HitsKNumber of Defects

⎡ ⎤′ = ⎢ ⎥

⎣ ⎦

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.

r( sram ) r( sram )K K′ ≠

The prime is used to denote that this kill ratio is calculated based on inspection data only.

K’r(sram) may NOT be the same as the kill ratio based purely on electrical results.

Also, K’r(sram) may NOT be the same as a kill ratio based on CAA.

From now on, all numbers based on inspection data will be denoted by a prime.


“Kill Ratios” From Bit-Fail Correlation

So, we need to find the kill ratio for the die K’r(die) based on K’r(sram).

r( sram ) r( die )K K′ ′≠

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.

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).


Avg Num Fails From Defects in the SRAM

( sram ) r( sram ) ( sram )

( sram ) r( sram ) ( sram )

( sram ) ( sram )( sram )

( sram )

K A DD

K D

Number of Hits DD

Number of Hits

λ

λ

λ

λ

′ ′= × ×

′ ′= ×

⎛ ⎞′ = ×⎜ ⎟⎜ ⎟

⎝ ⎠

′ =

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).


Use Critical Area Ratios to Scale to Die( die ) c( die )A DDλ = ×( sram ) c( sram )A DDλ = ×

( die ) ( sram )

c( die ) c( sram )A Aλ λ

=c( die )

( die ) ( sram )c( sram )

AA

λ λ⎛ ⎞

= ×⎜ ⎟⎜ ⎟⎝ ⎠

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?

c( die )( die )

c( sram )

ANumber of Hits

Aλ

⎛ ⎞′ = ×⎜ ⎟⎜ ⎟

⎝ ⎠

Assume the scaling is the same for inspected defects:

Assume defect densities (DD) are the same:

And

ACs are from CAA.


Die Kill Ratio for Inspected Defects( die )

r( die ) ( die ) r( sram ) ( sram )

Number of HitsK A K A

λ′=

′ ′× ×

r( die ) r( sram ) ( sram )r( die )

( die )

K AK

Number of Hits Aλ′ ′× ×

′ =×

We’ve found K’r(die) -- Now this can be applied to a yield model (another document)

c( die ) ( sram )r( die )

c( sram ) ( die )( sram )

A ANumber of HitsKNumber of Defects A A

⎛ ⎞ ⎛ ⎞⎛ ⎞′ = × ×⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

Substituting terms, K’r(die) reduces to: (see addendum A for more detail)


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)


Addendum A:How to Find the Die Kill Ratio for Inspected Defects


Die Kill Ratio for Inspected Defects( die )

r( die ) ( die ) r( sram ) ( sram )

Number of HitsK A K A

λ′=

′ ′× ×

r( die ) r( sram ) ( sram )r( die )

( die )

r( die ) ( sram )( sram )

r( die )( die )

r( die ) ( sram )r( die )

( die )

r( die )

K AK

Number of Hits A

Number of Hits ANumber of Defects

KNumber of Hits A

AK

Number of Defects A

NumberK

λ

λ

λ

′ ′× ×′ =

×

⎛ ⎞′ × ×⎜ ⎟⎝ ⎠′ =

×

′ ×′ =

×

′ = c( die ) ( sram )

c( sram ) ( die )( sram )

A Aof HitsNumber of Defects A A

⎛ ⎞ ⎛ ⎞⎛ ⎞× ×⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

Result on page 8

Addendum A


Addendum B:Fault Capture Rate


Fault Capture Rate

FaultsCorrelated to DefectsFault Capture RateTotal 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

Addendum B


Die-Based Fault Capture Rate

20 0.5730

Failed DieWith DefectsFault Capture RateFailed Die

= = =

Large circle: All Die (100)

Circle: Failed Die (30)Circle: Die WithDefects (35)

Green area: Good Die WithDefects (15) Yellow area: Failed Die With

Defects (20)

Blue area: Failed DieWithout Defects (10)

This can be applied to bin maps (array not necessary)This could introduce errors - Failed Die With Defects may include nuisance

15 0.4335

Good DieWith DefectsNuisance RateDieWith Defects

= = =

Addendum B


Bit-Fail-Based Fault Capture Rate

2000 0.573000

DefectsWith FailsFault Capture RateAll Fails

= = =

Circle: All Bits(10000)

Circle: All Fails(3000)

Circle: All Defects(3500)

Green area: Defects WithNo Fails(1500)

Yellow area: Defects With Fails(2000)

Blue area: Fails WithoutDefects(1000)

This can only be applied to bit-fail dataFewer chances for errors - Failed Die With Defects may include nuisance

1500 0.433500

DefectsWith No FailsNuisance RateAll Defects

= = =

Addendum B

Technology

How To Translate Bit Fail Correlation Data To Die Kill Ratios May2009