A description of how to properly set control limits on defect charts.

1. Control Charts For Semiconductor Defect Management
Stuart L. Riley
slriley@valaddsoft.com
Member American Society for Quality
January 20, 2009 Copyright Stuart L. Riley 1

2. Copyright Statement
Original work by Stuart L. Riley: Copyright 2010
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
slriley@valaddsoft.com or slriley0207@gmail.com
January 20, 2009 Copyright Stuart L. Riley 2

3. Introduction
• We will briefly explore a few ways to create control charts based
on in-line defect inspection data
• Several examples are shown using real defect data
January 20, 2009 Copyright Stuart L. Riley 3

4. Types of Control Charts For Defect Data
• Individuals: XmR Charts
– Continuous data – defect density, defect-limited yield (dly)1
– Used when data cannot be grouped into rational subgroups
– The process distribution may be very skewed or bounded (non-normal)
– May be applied to data with outliers
– Each observation represents the process at a given point in time
– The data is time-ordered and entered in the sequence which it was generated
• C-Chart
– Discrete data - typically used for defect count data2
– Can have problems with outlier data
– Plot the number of defectives (per batch, per day, per machine, etc.)
– Control limits in this chart are computed based on the Poisson distribution
1: http://www.valaddsoft.com/Documents/Semiconductor-Defect-Management---Separating-the-Vital-Few-From-the-Trival-Many.pdf
2: http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc331.htm
January 20, 2009 Copyright Stuart L. Riley 4

5. Types of Control Charts For Defect Data
• Run Charts
– Sometimes used when there is insufficient data to apply SPC charts
– Lacks the benefits of control charts
– Upward and downward trends, cycles, and large aberrations may be spotted
– Can be used to track improvements that have been put into place
– Average centerline can be added to see movement about the average
– The data is time-ordered and entered in the sequence which it was generated
– Try not to depend on these types of charts, unless you really need them
January 20, 2009 Copyright Stuart L. Riley 5

6. Selection Criteria – Which Chart to Use
These are the only charts that
can be used for defect control.
Source: http://peltiertech.com/WordPress/types-of-control-charts/
January 20, 2009 Copyright Stuart L. Riley 6

7. Individuals (XmR) Chart Control Limits
• Mean range is the common method for finding limits for XmR
• Median range can be used for charts with large variation in the
range (outliers)
m
∑x i
X= i =1
m
m
∑ x −x i i −1
Mean of the Range = MR = i =2 Median of the range = MR
m −1
UCLX = X + 2.660 × MR UCLX = X + 3.145 × MR
LCLX = X − 2.660 × MR LCLX = X − 3.145 × MR
UCLR = 3.268 × MR UCLR = 3.865 × MR
January 20, 2009 Copyright Stuart L. Riley 7

8. C-Chart Control Limits
Total number of defects
c=
Total number in sample
UCLc = c + 3 × c
UCLc = c − 3 × c
January 20, 2009 Copyright Stuart L. Riley 8

9. C-Chart Defect Counts Example 1
The UCL for this chart
looks reasonable.
This chart is not too
noisy.
January 20, 2009 Copyright Stuart L. Riley 9

10. XmR Chart Defect Density Example 1: Avg R
The UCLs for these charts look a bit too high.
January 20, 2009 Copyright Stuart L. Riley 10

11. XmR Chart Defect Density Example 1: Median R
The UCLs for these charts look better.
January 20, 2009 Copyright Stuart L. Riley 11

12. XmR Chart DLY Example 1: Avg R
The UCLs on these charts look reasonable.
The same defect data shown in the previous charts has been converted
to defect-limited yields (DLY)*.
The data is not as noisy as with the defect count or density charts.
* http://www.valaddsoft.com/Documents/Semiconductor-Defect-Management---Separating-the-Vital-Few-From-the-Trival-Many.pdf
January 20, 2009 Copyright Stuart L. Riley 12

13. XmR Chart DLY Example 1: Median R
The UCLs on these charts look reasonable.
The same defect data shown in the previous charts has been
converted to defect-limited yields (DLY)*.
The data is not as noisy as with the defect count or density charts.
* http://www.valaddsoft.com/Documents/Semiconductor-Defect-Management---Separating-the-Vital-Few-From-the-Trival-Many.pdf
January 20, 2009 Copyright Stuart L. Riley 13

14. C-Chart Defect Count Example 2
The UCL for this chart
looks too low.
This is an extremely
noisy chart.
January 20, 2009 Copyright Stuart L. Riley 14

15. XmR Chart Defect Density Example 2: Avg R
These charts look too noisy to set a reasonable limit.
January 20, 2009 Copyright Stuart L. Riley 15

16. XmR Chart Defect Density Example 2: Median R
These charts look too noisy to set a reasonable limit.
January 20, 2009 Copyright Stuart L. Riley 16

17. XmR Chart DLY Example 2: Avg R
These limits look reasonable.
The same defect data shown in the previous charts has been converted to
defect-limited yields (DLY)*.
The data is not as noisy as with the defect count or density charts.
* http://www.valaddsoft.com/Documents/Semiconductor-Defect-Management---Separating-the-Vital-Few-From-the-Trival-Many.pdf
January 20, 2009 Copyright Stuart L. Riley 17

18. XmR Chart DLY Example 2: Median R
These limits may be a bit too aggressive, but they are not too bad.
The same defect data shown in the previous charts has been converted to
defect-limited yields (DLY)*.
The data is not as noisy as with the defect count or density charts.
* http://www.valaddsoft.com/Documents/Semiconductor-Defect-Management---Separating-the-Vital-Few-From-the-Trival-Many.pdf
January 20, 2009 Copyright Stuart L. Riley 18

19. Summary
• XmR charts are the typically the best choice for defect control
charts
• C-Charts rarely work well for noisy data, so they should be
avoided
• If the data is too noisy, you can always use a run chart, but you
will loose the benefits of control charts
• The best solution is to use defect-limited yield* control charts
– It is the appropriate metric to track the yield impact of defects on wafers
– It tends to smooth out the noise to focus attention to real issues
– It makes setting up defect control charts much easier
* http://www.valaddsoft.com/Documents/Semiconductor-Defect-Management---Separating-the-Vital-Few-From-the-Trival-Many.pdf
January 20, 2009 Copyright Stuart L. Riley 19