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Cost of Misclassification for Non-Contact Sheet Resistance
and Film Thickness Mapping The
cost of misclassified product is often overlooked in the determination of total cost of ownership for measurement systems. In some cases the cost of misclassified product can be several times the total of all other
costs for operating and owning a metrology tool. In order to illustrate this analysis consider a single step manufacturing process such as an epitaxial deposition on a semi-insulating substrate wafer. Following the
deposition the product is tested on Lehighton Electronics 1510 RS sheet resistance measurement system. Following this test a decision is made to either pass the wafer or fail it. Misclassification results when a
defective wafer is passed or when a good wafer is failed.
Let
p1 = the probability that a good wafer will be failed
and
p2
= the probability that a defective wafer will be passed.
and
c1 = the cost of failing a good wafer
c2 = the cost of passing a defective wafer
Then
Total Cost of Misclassification = Total Wafers Measured x (c1p1+c2p2)
We can use the definition of process capability, Cp
where
Cp
= (USL - LSL)/6 STD DEV
USL = Upper Specification Limit
LSL = Lower Specification Limit
STD DEV = the Standard Deviation of the sheet resistance for the epitaxial deposition process
Define
tool accuracy as the average difference between the measured value of sheet resistance and the accurate value as a percentage of USL - LSL.
Also define the (p/T) ratio as
(p/T) = (STD DEV OF MEASURING TOOL)/(STD DEV PROCESS)
Example 1 for marginal process capability and marginal (p/T) ratio
Cp = 1.00
(p/T) = 0.3
Tool Accuracy as % of USL ö LSL = 0%
c1 = $1,000
c2 = $1,000
Total Wafers Measured = 106
For this case using the tabulated results from Table 1 we find
p1 = 0.002015
p2
= 0.00065
Then
Total Cost of Misclassification = 106 x 103 x (0.002015+0.00065)
= $2,665,000
Example 2 for improvements in process capability and (p/T) ratio
Cp = 1.33
(p/T) = 0.1
Tool Accuracy as % of USL ö LSL = 0%
c1 = $1,000
c2 = $1,000
Tool A
Total Wafers Measured = 106
For this case using the tabulated results from Table 1 we find
p1 = 0.000038
p2 = 0.000014
Total Cost of Misclassification = 106 x 103
x (0.000038+0.000014)
= $52,000
The foregoing two examples show how changes in the measuring tool performance and any associated improvement in process capability can have a major impact on the cost
structure of the manufactured product. Consider the Lehighton Electronics sheet resistance measurement system to determine the Cost of Misclassification of your process as follows:
1. Determine the precision of a
1510 system using the LEI brochure or an error of measurement study for your process using your 1510 system on your process. Compute the (p/T) ratio.
2. Use your 1510 system to compute the process capability of your process.
3. Evaluate the cost for c1 and c2 for your product.
4. Use the calibration standards furnished with your
1510 from LEI to keep the average of your measured values near the standard values. You can estimate the cost penalty for a significant calibration error by using the 25% values in Table 1.
5. Use the foregoing information to select appropriate values of p1 and p2.
6. Use the values of p1 and p2
and total number of wafers measured in combination with your sampling plan to estimate your Total Cost of Misclassification.
7. Explore the effect on product cost of additional improvements in process
capability, measurement precision, measurement accuracy, and sampling plan.
8. Use your Cost of Misclassification results to justify the purchase of a new LEI system or an upgrade to a higher performance system
form LEI.
The basic results can be summarized in the following Table 1. Input Parameters for Cost of Misclassification Results
|
Process Capability
(Cp) |
Tool Accuracy
(% of Spec Window) |
(p/T) ratio, % |
p1 |
p2 |
Cost of Misclassification |
|
0.67 |
0 |
60% |
0.028724 |
0.019490 |
$48,214,000 |
|
|
|
30% |
0.011114 |
0.006797 |
$17,911,000 |
|
|
|
10% |
0.004870 |
0.003831 |
$8,701,000 |
|
|
25 |
60% |
0.049291 |
0.029798 |
$79,089,000 |
|
|
|
30% |
0.022331 |
0.017060 |
$39,391,000 |
|
|
|
10% |
0.010112 |
0.009554 |
$19,666,000 |
|
1.00 |
0 |
60% |
0.008309 |
0.000906 |
$9,215,000 |
|
|
|
30% |
0.002015 |
0.000649 |
$2,664,000 |
|
|
|
10% |
0.000720 |
0.000405 |
$1,125,000 |
|
|
25 |
60% |
0.050717 |
0.018252 |
$68,969,000 |
|
|
|
30% |
0.020359 |
0.011726 |
$32,085,000 |
|
|
|
10% |
0.008931 |
0.006715 |
$15,646,000 |
|
1.33 |
0 |
60% |
0.001749 |
0.000025 |
$1,774,000 |
|
|
|
30% |
0.000161 |
0.000020 |
$181,000 |
|
|
|
10% |
0.000038 |
0.000014 |
$52,000 |
|
|
25 |
60% |
0.044081 |
0.007676 |
$51,757,000 |
|
|
|
30% |
0.014362 |
0.005475 |
$19,837,000 |
|
|
|
10% |
0.005557 |
0.003399 |
$8,956,000 |
Conclusions For Process Capability less than 1 it is normally very important to use a high performance metrology
tool. This can often be the case for new product development and the early stages of production manufacturing. In this situation good metrology systems can prevent the shipment of defective
product and provide information needed to improve process capability.
A precise and accurate metrology system from Lehighton Electronics is an important factor in
minimizing the cost of misclassification associated with tool ownership and use.
Improvements in process capability reduce the cost of misclassified product.
As process capability improves the sampling rates for metrology can be reduced. This will also help to facilitate the growth of production as new products are accepted by the market. Monitor rates for
sampling are still advisable to verify that production stays in control while yields are high and quality standards are met.
Please contact Lehighton Electronics if you have any questions. We will be pleased to show you how to minimize your Total Cost of Ownership including the Cost of Misclassified Product. We will
help you to use your process and product specifications to determine your Cost of Misclassified Product and Total Cost of Ownership. Typical Total Cost of Ownership results for Lehighton
Electronics sheet resistance mapping systems are estimated at $.06 per measured wafer for an average manufacturing operation. Reference Copies of the following paper are available on request.
Sudhakar M. Kudva and Randall W. Potter - SEMATECH, 2704 Montopolis Drive, Austin, Texas 7874 |
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