How to Estimate the Number of Die Escapes
                            Using In-Line Defect Data

                         ...
Copyright Statement


     Copyright 2009, Stuart L. Riley

     Rights reserved.

     This document may be downloaded fo...
Terms
•     Die – the unit product purchased and shipped to the customer
•     Escapes – number of failing die that were m...
Definition of Escapes
                                                                                                 If ...
Goal

• Find number of escapes using
        –     In-line inspection data
        –     The probability defects will harm...
Benefits

•     Risk analysis
•     Compare excursions to baseline ship / no ship decisions
•     Cost benefit of improvin...
Assume Random Anomaly Distribution Within Die

• Graphical composites of die maps (die stack) may show a tendency
  for an...
Steps

• Determine area of die to be considered
        – Can be entire die, or specific die areas
• Define defect kill ra...
Steps

• Find the probability of escapes, using a probability density function
  (Poisson distribution)
• Apply this proba...
Steps
  Die area of interest (A), may be one area, a combination of different areas, or the entire die area. The
  fractio...
Steps
       If you have classified defect data, the kill ratio for the region can be expressed as a weighted
       avera...
Steps
                Express the fraction of test coverage as a probability of catching a fail at test: PT.

            ...
Steps: Separate Random and Clustered Die
              Because wafers usually have mixed-distributions of anomalies (clust...
Example 1: Use Classification Data
From slide – “Example: Calculate Fractional Die Area”         PArea1 = 0.27            ...
Example 2: Use Estimated Size Data
From slide – “Example: Calculate Fractional Die Area”        PArea1 = 0.27             ...
Example 3: Estimate Escapes Using DLY Data
                                                                               ...
Example 3: Frequency of Escape Ranges From DLY Data




                                                      Excursions

...
Summary

• It is important to know the level of failing die escapes to properly
  manage risk of shipping product to custo...
Appendix




                    Appendix




November 27, 2009   Copyright 2009 Stuart L. Riley   19
Example: Calculate Fractional Die Area
          Die Area = total area of blue square


                                  ...
Example: Classification / Kill Ratios by Area
                       A sub-set of anomalies on the wafer are selected for ...
Example: Classification / Kill Ratios by Area




                     Area 1                                             ...
Example: Classification / Kill Ratios by Area


     K Area1 =
                     ( 7.5 + 9.5) =   17
                  ...
Example: Classification / Kill Ratios by Area
                                         Classification Groupings           ...
Example: Calculate Size Ranges
                    Let critical size range of key defects for Area 1 be in the range 0.4 t...
Example: Die-Based Clustering
Identify die containing significantly more
anomalies, compared to the rest of the die
with a...
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How To Estimate The Number Of Die Escapes Using In Line Defect Data

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Estimate the number of failing die that can be shipped to the customer, using only in-line defect inspection data, and some knowledge of die layout.

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How To Estimate The Number Of Die Escapes Using In Line Defect Data

  1. 1. How to Estimate the Number of Die Escapes Using In-Line Defect Data Stuart L. Riley slriley@valaddsoft.com Member American Society for Quality November 27, 2009 Copyright 2009 Stuart L. Riley 1
  2. 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 November 27, 2009 Copyright 2009 Stuart L. Riley 2
  3. 3. Terms • Die – the unit product purchased and shipped to the customer • Escapes – number of failing die that were missed at test and sent to the customer • Test coverage – Fraction of die, or specific die areas that are tested to detect fails – The smaller the test coverage, the higher the risk of escapes • Anomalies – anything detected by inspection (as seen on a wafer map) – Inspection tool noise – false positives – Cosmetic anomalies • Color, grain, etc. from normal process variation • No negative effect on yield – Defects • Abnormal and potentially harmful • Particle or process-related • Separate from other anomalies using classification (categorization) November 27, 2009 Copyright 2009 Stuart L. Riley 3
  4. 4. Definition of Escapes If test coverage is < 100%, PT < 1 If test coverage = 100%, the probability of capturing a failed die is: PT = 1 There are holes in the fire wall. Test acts like a “fire wall” to prevent failing Some failing die escape test and die going to the customer (escapes). are shipped to the customer. Yield = Y Yield = Y’ In-line data estimates fail potential of defects, assuming 100% coverage. Escape Caught All fails caught Caught Escape Y = Y '× PT If PT < 1, then the true yield may be approximated by multiplying Y’ by PT. November 27, 2009 Copyright 2009 Stuart L. Riley 4
  5. 5. Goal • Find number of escapes using – In-line inspection data – The probability defects will harm specific structures on the die – Some knowledge of the die layout – A known percentage of the die that is testable (test coverage) • Apply knowledge of escapes to – Perform risk management to determine acceptable levels to ship product during excursions – Decide where to focus efforts to address levels that may significantly contribute unacceptable levels of escapes – Determine ROI to address test coverage issues November 27, 2009 Copyright 2009 Stuart L. Riley 5
  6. 6. Benefits • Risk analysis • Compare excursions to baseline ship / no ship decisions • Cost benefit of improving process, or test coverage, or both • Get a running estimate of escapes at any given time, using in-line data as it’s collected November 27, 2009 Copyright 2009 Stuart L. Riley 6
  7. 7. Assume Random Anomaly Distribution Within Die • Graphical composites of die maps (die stack) may show a tendency for anomalies to appear in specific regions – This may be inspector-induced – The inspection tool may have a tendency to detect certain anomalies better in some regions vs. other regions • An exception to this assumption can be made only if there is a physical reason why anomalies can be distributed non-randomly within the die – there must be a reason. November 27, 2009 Copyright 2009 Stuart L. Riley 7
  8. 8. Steps • Determine area of die to be considered – Can be entire die, or specific die areas • Define defect kill ratios based on – Classification data (may change from wafer-wafer / lot-lot) – Estimated defect size data (do not use inspection size data) – Ratio of critical dimensions to circuit area – Educated guess from key engineers – Combination of any of the 3 methods – whatever makes the most sense • Estimate the average number of faults, applied to the average number anomalies in the die areas, with the estimated kill ratios • Apply test coverage (% of die, or % of die area that can be tested) to find the average number of escapes per die November 27, 2009 Copyright 2009 Stuart L. Riley 8
  9. 9. Steps • Find the probability of escapes, using a probability density function (Poisson distribution) • Apply this probability to the number of die with anomalies to find the number of failing die that can escape test • Since distributions are mixed (mix of random and clustered distributions) – We must separate die into 2 groups – random die and clustered die – Find the average number of random anomalies per random die – Find the average number of clustered anomalies per clustered die – Find the number of failing die in each group that can escape test – Combine the 2 groups to get the overall number of failing die that can escape test November 27, 2009 Copyright 2009 Stuart L. Riley 9
  10. 10. Steps Die area of interest (A), may be one area, a combination of different areas, or the entire die area. The fraction of this area to the die area can be expressed as a probability, PA. This is the probability a random defect can fall in this area within the die. If the entire die area is to be used, PA = 1. Area PA = See slide – “Example: Calculate Fractional Die Area” Die Area The probability of finding a fail for an area of the die can be expressed as the product of the probability of finding a defect in the area, and the kill ratio for the expected defect types in the area. (Note – this expression is equivalent to the definition of “critical area”.) PF ( A ) = PA × K A If there are N regions in the die, PF(A) can be expressed as the sum of [PF(A)]i for each ithregion: N PF ( A ) = ∑ ⎡ PF ( A ) ⎤ i ⎣ ⎦ i =1 The estimated average number of faults can be found by multiplying the probability of finding a fail in a die area by the average number of anomalies in the die, d: f ( A ) = PF ( A ) × d November 27, 2009 Copyright 2009 Stuart L. Riley 10
  11. 11. Steps If you have classified defect data, the kill ratio for the region can be expressed as a weighted average: The sum of the count for each defect type (ni), multiplied by the probability of fail for that type in the region (pi(A)), for M groups, divided by the total defects classified (N). M ∑ ( p ( A) × n ) Pi(A) will usually be determined based on i i engineering judgment. KA = i =1 N See slides – “Example: Classification / Kill Ratios by Area” If you don’t have classified defect data, but you do have some idea (or even a good educated guess) about critical size ranges for your defect(s) of interest, you can approximate a size- based kill ratio. N min − max The min – max range of defect sizes may be KA = different for each area of interest. NTotal See slide – “Example: Calculate Size Ranges” For either method, we’ll still use the notation, KA for the kill ratio. November 27, 2009 Copyright 2009 Stuart L. Riley 11
  12. 12. Steps Express the fraction of test coverage as a probability of catching a fail at test: PT. 0 ≤ PT ≤ 1 So the average number of escapes per die can be expressed as the product of the average number of faults and the probability of fails not being caught at test: f esc ( A, PT ) = f ( A ) × (1 − PT ) But, we still need to express this in terms of die (unit product shipped to the customer) that can escape being found to fail at test. We can do this by first using the Poisson distribution function* to find the probability die will escape capture at test: Sanity check: Pesc = 1 − e { − f ( A )×(1− P )} As test coverage approaches 100%: T PT approaches 1, the exponent term approaches 0 and Pesc approaches 0. > No die will escape 100% test coverage. < So the number of failing die that can escape test is: Desc = Pesc × D * - The Poisson dist function can only be applied to random distributions. For mixed distributions (mix of random and clustered anomalies) we need to separate die into random and clustered groups. November 27, 2009 Copyright 2009 Stuart L. Riley 12
  13. 13. Steps: Separate Random and Clustered Die Because wafers usually have mixed-distributions of anomalies (cluster and random), we need to separate each distribution to find the average number of anomalies for each, and combine the results at the end. See slide – “Example: Die-Based Clustering” Random Cluster Avg num fails that can ⎧ N ⎫ ⎛ N ⎞ escape capture at test. N f c ( A ) = ⎨∑ [ PA × K c − A ]i × ( d c − d r ) ⎬ + ⎜ ∑ [ PA × K r − A ]i × d r ⎟ Note – kill ratios may be different for random and f r ( A ) = ∑ [ PA × K r − A ]i × d r ⎩ i =1 N ⎭ ⎝ i =1 ⎠ clustered defects. i =1 or f c ( A ) = ∑ [ PA × K c − A ]i × d c If Kc-a = Kr-a i =1 −{ f r ( A )×(1− P )} Pc −esc = 1 − e { c − f ( A )×(1− P )} Probability of escape Pr −esc = 1 − e T T Number of die that can escape Dr −esc = Pr −esc × Dr Dc −esc = Pc −esc × Dc Number of clustered die Number of random die nr nc dr = dc = Total number of die that can escape: Dr Dc dr and dc are the avg number of defects per random and clustered group. Desc = Dr −esc + Dc −esc nr and nc are the number of defects per group. Dr and Dc are the number of die per group. November 27, 2009 Copyright 2009 Stuart L. Riley 13
  14. 14. Example 1: Use Classification Data From slide – “Example: Calculate Fractional Die Area” PArea1 = 0.27 PArea 2 = 0.07 From slides – “Classification / Kill Ratios by Area” K Area1 = 0.17 K Area 2 = 0.33 PF ( A) = ( 0.27 × 0.17 ) + ( 0.07 × 0.33) = 0.07 From slide – “Example: Die-Based Clustering” Dr = 17 d r = 29 Dc = 3 d c = 167 100 die on the wafer Test coverage = 95% Random Cluster f r ( A ) = 0.07 × 29 = 2.00 f c ( A ) = 0.07 ×167 = 11.52 Pr −esc = 1 − e−{2×0.05} = 0.095 Pc −esc = 1 − e −{11.52×0.05} = 0.438 Dr −esc = 0.095 ×17 = 1.62 Dc −esc = 0.438 × 3 = 1.31 Total number of die that can escape: Desc = 1.62 + 1.31 = 2.93 Wafer has 100 die Pct escaped die = 2.9% November 27, 2009 Copyright 2009 Stuart L. Riley 14
  15. 15. Example 2: Use Estimated Size Data From slide – “Example: Calculate Fractional Die Area” PArea1 = 0.27 PArea 2 = 0.07 From slides – “Calculate Size Ranges” K Area1 = 0.25 K Area 2 = 0.30 PF ( A) = ( 0.27 × 0.25 ) + ( 0.07 × 0.30 ) = 0.09 From slide – “Example: Die-Based Clustering” Dr = 17 d r = 29 Dc = 3 d c = 167 100 die on the wafer Test coverage = 95% Random Cluster f r ( A ) = 0.09 × 29 = 2.57 f c ( A ) = 0.09 ×167 = 14.78 Pr −esc = 1 − e −{2.57×0.05} = 0.120 Pc −esc = 1 − e −{14.78×0.05} = 0.522 Dr −esc = 0.120 × 3 = 2.05 Dc −esc = 0.522 ×12 = 1.57 Total number of die that can escape: Desc = 0.120 + 1.57 = 3.61 Wafer has 100 die Pct escaped die = 3.6% November 27, 2009 Copyright 2009 Stuart L. Riley 15
  16. 16. Example 3: Estimate Escapes Using DLY Data f esc ( A, PT ) = f ( A ) × (1 − PT ) Set test coverage at 95%. f(A) can be extracted from DLY data. f ( A) = ln ( DLY ) Excursion range for escapes “Baseline” range for escapes: < 20 (see next slide) November 27, 2009 Copyright 2009 Stuart L. Riley 16
  17. 17. Example 3: Frequency of Escape Ranges From DLY Data Excursions > 100 November 27, 2009 Copyright 2009 Stuart L. Riley 17
  18. 18. Summary • It is important to know the level of failing die escapes to properly manage risk of shipping product to customers – Know where to focus efforts to address issues – Know if to ship or scrap product during excursions • We have explored several ways to estimate the number of failing die escapes using in-line inspection data based on – Classification data – Defect size estimates – Defect-limited yield data • These procedures, along with applied examples, should provide you with the methods to properly estimate ppm escapes November 27, 2009 Copyright 2009 Stuart L. Riley 18
  19. 19. Appendix Appendix November 27, 2009 Copyright 2009 Stuart L. Riley 19
  20. 20. Example: Calculate Fractional Die Area Die Area = total area of blue square 2 × Area1 2 × Area2 Area 2 PArea1 = PArea 2 = Area 1 Die Area Die Area Area 1 Example: Area 2 Die area = 30 cm2 Area 1 = 4 cm2 Area 2 = 1 cm2 PArea1 = ( 2 × 4) = 8 = 0.27 PArea 2 = ( 2 ×1) = 2 = 0.07 30 30 30 30 • Assume distribution is random within the die • Find ratio of sum of key areas to scan area • Sum the key areas & divide by the scan area November 27, 2009 Copyright 2009 Stuart L. Riley 20
  21. 21. Example: Classification / Kill Ratios by Area A sub-set of anomalies on the wafer are selected for classification. Examples of defects as seen during classification. Some obviously impact the product, others aren’t as obvious. So defects have a probability of affecting the die circuits. November 27, 2009 Copyright 2009 Stuart L. Riley 21
  22. 22. Example: Classification / Kill Ratios by Area Area 1 Area 2 • Same “defects” / same distribution – only circuit layout is different • Array 2 should be more sensitive to defects • Classification captures differences in sensitivities by defect type (kill ratios) • Note how the size of defects can also affect the circuit in different ways November 27, 2009 Copyright 2009 Stuart L. Riley 22
  23. 23. Example: Classification / Kill Ratios by Area K Area1 = ( 7.5 + 9.5) = 17 = 0.17 K Area 2 = (15.5 + 17 ) = 32.5 = 0.33 100 100 100 100 • The weighted kill ratio (overall probability of failure) of defects on array 1 is about ½ that of array 2. • It just so happens that array 1 has about ½ the number of line/space pairs in the same area as array 2. • The differences in kill ratios = the difference in critical areas. • So, armed with just inspection data, a reasonable definition of defect groupings, and consistent application of assumed defect kill ratios, we can capture differences in circuit layout, just like critical area analysis. November 27, 2009 Copyright 2009 Stuart L. Riley 23
  24. 24. Example: Classification / Kill Ratios by Area Classification Groupings Area 1 Area 2 Estimated Fault Fault Type Affect Count Count Kill Ratio Count Count Assume 100 anomalies are Shorts 1 2 2 12 12 classified. Extensions 0.5 11 5.5 7 3.5 Of this, 2 defect types are critical. On Line 0 6 0 1 0 Circles Between We’ll call them “circles” and 0 1 0 0 0 Lines “squares” to match the diagram on Total the previous page. Circular -- 20 7.5 20 15.5 Group Shorts 1 3 3 14 14 Extensions 0.5 13 6.5 6 3 On Line 0 3 0 0 0 Squares Between 0 1 0 0 0 Lines Total Square -- 20 9.5 20 17 Group • Each defect type (group) has an assigned kill ratio. • Multiply the count of each type by the kill ratio to find the fault count. • We can see that the same distributions applied to 2 different circuit layouts have different fault counts, due entirely to the layout differences November 27, 2009 Copyright 2009 Stuart L. Riley 24
  25. 25. Example: Calculate Size Ranges Let critical size range of key defects for Area 1 be in the range 0.4 to 4, and Area 2 be in the range 0.2 to 4. The differences in size ranges are due to differences in circuit layouts in the areas. Defects in this size range can cause a fault, depending where they fall on the circuit. The upper limit to the range can be determined from basic knowledge of defects typically seen. Total area under the curve = 73 (Note – the range on the overall curve can also be bounded) Total area under the size range 0.4 to 4 (Area 1) = 19 Total area under the size range 0.2 to 4 (Area 2) = 22 The ratio of the 2 areas is the probability the total population will fall within the critical size range. size range 0.4 to 4 size range 0.2 to 4 19 22 X-1.5 K Area1 = = 0.25 K Area2 = = 0.30 73 73 November 27, 2009 Copyright 2009 Stuart L. Riley 25
  26. 26. Example: Die-Based Clustering Identify die containing significantly more anomalies, compared to the rest of the die with anomalies. (clusters) Find the average number of anomalies per die for die containing random distributions (dr). Find the average number of anomalies per die for die containing clusters (dc). Clustered die Example: Consider a wafer with 1000 anomalies, 100 die, 20 die with anomalies, 3 die contain 500 anomalies, and 17 die with 500 anomalies. 500 500 dr = = 29 dc = = 167 17 3 Note: All wafer maps were produced using the “KlarfView” application, which can be found at: http://www.valaddsoft.com/ Dark spots: anomalies in clustered die Clustering was defined using the “DBCluster” application. November 27, 2009 Copyright 2009 Stuart L. Riley 26

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