How To Set Kill Ratios For Defects

February 1, 2010 Copyright Stuart L. Riley 1

How to Set Kill Ratios for Defects

Stuart L. [email protected]

Member American Society for Quality


Copyright Statement

Original work by Stuart L. Riley: Copyright 2009

Rights reserved.

This document may be downloaded for personal use.

Users are forbidden to reproduce, republish, redistribute, or resell any materials from this document as their original work.

All references to this document, any quotation, or figures should be made to the author.

Questions or comments can be addressed to Stuart L. Riley, at [email protected] or [email protected]


Introduction

• Defect inspection is a necessary part of monitoring the fab• Applied correctly, defect inspection can be used to estimate yield impact • The problem: How to estimate the yield impact of defects as seen in the fab• Kill ratios are needed to

– Set priorities to define which defect types to work on– Understand the yield impact of defects on product

• Numerous papers have been devoted to various methods for determining the kill ratios of defects

– Virtually all papers assume direct defect-to-fail correlation is needed – not so– None of the papers adequately deal with ways to associate defect types across circuit

types and products– These techniques are not practical in the real world

• We will review different methods of estimating kill ratios, and how well each can work in practice


Defect ClassificationExamples of defects as seen during classification.Some obviously impact the product, others aren’t as obvious.Different defects have different probabilities (kill ratio) of affecting the die circuits.So each type will have its own kill ratio assignment.How well this assignment works, depends on how defects are groped.How would you group these different types?


Example of Defect Groupings

Embedded ParticleIn Pattern – Not affecting

Embedded Particle Extension

Embedded ParticleBridge Blocked Etch

Bridge

Blocked EtchExtension

Blocked EtchNot Affecting

Embedded ParticleNot affecting

ParticleOff Pattern

ParticleOn Pattern

Small Contact

ExtraContact

Polysilicon Lines and Contacts

How you group defects depends on the abilities of the classifier and the level of acceptable complexity. The more you can separate types, the better. But, you run the risk of loosing classification accuracy.


Classification Example

Array A Array B

In this example, we have 2 different line/pitch layouts with exactly the same defect distributions. Array B is about 2x as dense as array A. So array B should be more sensitive to defects than array A. If these defects are classified with the right level of detail, we can capture these differences.

ShortExtension On line

Between line


How to Combine Defect Classification Data

( )1

M

i ii

p nK

N=

×=∑

After classification, we can apply the probability of fail for each type, pi (same as the defect’s “kill ratio”), to each defect type, ni, to find the overall weighted kill ratio for the group of defects, K. This is equivalent to the overall weighted averaged probability a group of defects can cause a fail.

1

All M

ii

N n=

= ∑

Where “M” is the number of defect groups, and “N” is the total number classified:

The numerator is the sum of the “killer” defects.


Classification Results of Arrays

Classification Groupings Array A Array B

Type Affect EstimatedKill Ratio Count

Correctionfor KillRatio

CountCorrection

for KillRatio

Shorts 1 0 0 11 11

Extensions 0.5 18 9 9 4.5

On Line 0 0 0 0 0

BetweenLines 0 2 0 0 0

Circles

TotalCircularGroup

-- 20 9 20 15.5

Shorts 1 0 0 8 8

Extensions 0.5 16 8 12 6

On Line 0 1 0 0 0Between

Lines 0 3 0 0 0Squares

TotalSquareGroup

-- 20 8 20 14

Summary of the classifications from arrays A and B from our example.

( )1

M

i ii

p n=

×∑

Sum of the “killer” defects (circled).

Note: The estimated kill ratio assignments are educated approximations. We’ll discuss how kill ratios can be determined later.


Classification and Critical Area Information

• The relative sensitivity to defects of the area of array B to array A is: Kb / Ka = 0.738/0.425 = 1.74– This is equivalent to the critical area analysis of the 2 arrays– This ratio estimates the difference in defect sensitivity between the 2 arrays: Array B is about 2x array A– We get this level of detail because of our level of detail in the classification groupings.

• Kill ratios depend on– How codes are grouped (by affect on product)– The product being inspected (different critical areas by product type)– Where defects fall within the die (different critical areas by region)

( )1

M

i ii

p nK

N=

×=∑

Total weighted kill ratios (circled).

Summary of the kill ratios from arrays A and B from our example.


Summary for Classifications

• Kill ratios depend on how we group defect classifications• The better we can define the effect of the defects on the circuit,

the better we can assign kill ratios• Due to resource constraints, we cannot always classify to this

level of detail• But if we cannot classify to the right level of detail, then we run

the risk of creating groups that are vague• If the groups are vague, then our kill ratio assignments become

vague• This is the most important limitation to accurate kill ratio

assignments


Set Kill Ratios Based on Defect Size?

KLA Size = 0.36umPixel Size = 0.25umx = 0.70umy = 5.05umArea = 0.13um



1 um 5 um 5 um

Here are 3 examples of large defects that have been assigned small sizes.

Defect sizing by the inspection tools is not reliable enough to be considered an accurate means to set kill ratios.


Summary for Defect Size

• There have been many papers published that claim defect sizes can be used to set kill ratios

• But defect sizing is not always that reliable• Even if the sizing was reliable, the impact of defects of different

sizes change depending where they fall on the die• So kill ratio assignment by defect size is not as “accurate” as

typically claimed• Once again, we are faced with vague definitions of kill ratios


Match Defects to Fails

• This approach is probably the most popular among the published papers

• The general assumption is that this somehow makes kill ratio assignments more accurate

• There are 2 methods that have been described– Direct matching of bit-fails to defects: coord-to-coord matching– Associative matching of defects to failing die: match defects in a broad region

• We’ll look at each method separately


Bit-Fail Matching

• Bit fail matching must be done on addressable arrays where fails can be located at a specific point in the array

• This can only be done on memory arrays or SRAMs which are sub-sets of the total die area

• The “kill ratios” will then be defined as the number of defects matching fails, divided by the number of defects

• Unless we review each match, we won’t know if a failing bit is caused by a real defect, or some spurious noise

• Assuming we are running full-die inspections, we must somehow translate the array kill ratios to the overall die area

DieSRAM

SRAM Area = Asram

Die Area = Adie

Area Outsideof SRAM = Adie-sram


“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

⎡ ⎤′ = ⎢ ⎥

⎣ ⎦

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 )

f ' K A DD

f ' K D

Number of Hitsf ' DD

f ' 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.

f’(sram) may NOT be the same as the f based purely on electrical results.

Also, f’(sram) may NOT be the same as a f based on Critical Area Analysis (CAA).


Use Critical Area Ratios to Scale to Die( die ) c( die )f A DD= ×

( sram ) c( sram )f A DD= ×

( die ) ( sram )

c( die ) c( sram )

f fA A

=c( die )

( die ) ( sram )c( sram )

Af f

A⎛ ⎞

= ×⎜ ⎟⎜ ⎟⎝ ⎠

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 )

Af ' Number of Hits

A⎛ ⎞

= ×⎜ ⎟⎜ ⎟⎝ ⎠

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 )

f ' Number of HitsK A K A

=′ ′× ×

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

( die )

f ' K AK

Number of Hits A′× ×

′ =×

So in order to apply the kill ratios as defined in the SRAM region to the entire die, we must know something about the differences in the critical areas of the regions inside and outside the SRAM region.

Note: The reader may have noticed that if we classified to the level of detail shown earlier, it may be possible to capture the differences in critical area between the different regions. If it were possible to classify to that level of detail, overlay analysis would be irrelevant.

c( die ) ( sram )r( die )

c( sram ) ( die )( sram )

A ANumber of HitsKNumber of Defects A A

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

Substituting terms, K’r(die) reduces to:


Summary for Bit-Fail Correlations

• Fail correlation rates (kill ratios) inside the array areas do not correspond to the kill ratios for the entire die

• In order to “scale up” the kill ratios for the entire die, we must know the critical area for other regions of the die

• This approach becomes too complicated for any real accuracy– You need to know all the critical areas for all layers– This gets complicated when trying to apply this to multiple products (if applicable)– You still have the same issues with defect classifications as discussed earlier– You need to review each defect matched to a fail to ensure it is real

• Any claims that this is an accurate method of finding defect kill ratios is suspect, due to the limitations discussed here

• But this can be a good way to – Qualitatively validate assumptions about impact of specific defects on yield– Get a feel for how well possible yield issues are detected at inspection


Match Defects to Failing Die

Source: http://blogs.mentor.com/david_abercrombie/blog/2009/08/

Example of defect map overlaid with an electrical bin map.Defects are matched to die failing for specific bins.


Match Defects to Failing Die: 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)

15 0.4335

Good DieWith DefectsNuisance RateDieWith Defects

= = =

Example of defect / bin overlay analysis.

There really isn’t much information we can extract from this analysis about kill ratios.

However, the fault capture rate may indicate the effectiveness of inspection to catch yield issues. But you must be sure to exclude noisy layers.


Bit and Bin Fail Overlay Review

• Kill ratio extraction from bit-fail or bin overlays is no more accurate than simple engineering judgment

• Classification groupings are the biggest driver of kill ratio accuracy

• Bit-fail overlay data may work ok for arrays, but scaling to the entire die area will severely reduce any apparent accuracy

• Bin-fail overlay data doesn’t align with any specific fails. It is a vague indicator of inspection data efficiency at best.

• Regardless of any method – you MUST be able to apply kill ratios to multiple products (for fabs running multiple products)

• There is NO reliable way to guarantee accuracy when defining kill ratios


Use Engineering Judgment to Define Kill Ratios

• If accuracy cannot be guaranteed using the complicated bit-fail or bin-fail methods, the easiest solution is to just use engineering judgment

• Assume kill ratios are only a way to rank defect types on their level of importance: least (0) to most (1)

• Apply the “wisdom of the crowds” (Vox Populi)* approach to get collective agreement on the kill ratios– Get the input of a cross-section of key personnel by reviewing sample images

of defect groupings and define kill ratios– Try to keep the number of people manageable: 10-30– Be sure to involve key engineers in the decision-making process– If applicable, you can apply different kill ratio sets for each product type

* Watch this video: http://www.pbs.org/wgbh/nova/sciencenow/0301/04.htmlAnd be sure to view this: http://www.pbs.org/wgbh/nova/sciencenow/0301/04-video-extr.html


Summary• Kill ratios are important to know so priorities can be set on

which defects to focus on• Bin and bit fail extraction of kill ratios

– Is an expensive, time-consuming distraction from action on real issues– MAY work some times, but this method has NEVER been proven to be

applicable to the typical broad spectrum of product types run in most fabs– Numerous papers written on how to do this in specific cases, but no paper has

demonstrated a workable solution for general purpose• Simple estimates of kill ratios based on the collective input of

the fab experts are no worse than expensive, complicated bin and bit fail extractions

• Once kill ratios are defined, you may apply them to estimate theimpact of defects on the product** http://www.valaddsoft.com/Documents/Semiconductor-Defect-Management---Separating-the-Vital-Few-From-the-Trival-Many.pdf


ReferencesPatterson, O. and Hansen, M., “The Impact of Tolerance on Kill Ratio Estimation for Memory”, IEEE Transactions On Semiconductor Manufacturing, Vol. 15, No. 4, November 2002, pp 404-410.

Schraub, D., et. Al., “Using bitmap analysis to help identify yield-critical issues in the fab”, Micro Magazine, October 1999.

Lee, Fourmun, “Yield Management: Present and Future”, Semiconductor International, March 2000, pp 85-94.

Menon, Venu B., "Chapter 27: Yield Management", "Handbook of Semiconductor Manufacturing Technology", Marcel Dekker Inc., 2000, pp. 869-887.

Nurani, R.K., "Effective Defect Management Strategies For Emerging Fab Needs", Statistical Methodology, IEEE International Workshop, 2001, pp. 33-37.

Riley, Stuart, "A Simplified Approach to Die-Based Yield Analysis", Semiconductor International, Vol. 30, No. 8, August 2007, pp. 47-51.

Riley, Stuart L., "Limitations to Estimating Yield Based on In-Line Defect Measurements," dft, pp.46, 1999 International Symposium on Defect and Fault Tolerance in VLSI Systems, 1999

Riley, Stuart L., "Estimating the Impact of Defects on Yield from In-Line Defect Measurement Data", Semiconductor International Web Exclusive, December 1999, http://www.semiconductor.net/article/206973-Estimating_the_Impact_of_Defects_on_Yield_from_In_Line_Defect_Measurement_Data.php?rssid=20279