IEE 572
Project Report
Electronic Copy
Submitted by :
Brian Benard
Navin Jeyachandran
Hari Jagannathan Balasubramanian
Recognition and statement of the Problem:
The system under consideration is shown above. In a semiconductor-manufacturing environment, wafers have to be tested with the intention of getting repeated measurements as a baseline of system performance, accuracy, and measurement variability.
A series of device test structures is available for testing circuits built on wafers using 0.8-micron technology. There are 3 sites measured on each wafer as shown in the figure, with the sites in the lower left, right, lower right, center, and top sections of the wafer, with the reference as the flat section of the wafer at the bottom. At each site specific electrical parameters are measured and recorded. The recorded data is automatically uploaded to a central factory server for storage after the whole wafer is tested. The normal routine is, after a wafer is robotically loaded onto a vacuum chuck, for the operator to locate the probe needles exactly over the first set of test structures on the first site probed. At each site, 65 sets of test structures are available. A program automatically moves the wafers sequentially through each of these sets, at which a pre-programmed number of electrical tests are done and results, are measured. Then, the program automatically moves the wafer to the second site, with no operator intervention, and the measurements are taken on the same set of test structures. This repeats until the last site is tested, after which the wafer is robotically removed and another wafer can be robotically loaded.
Two testers are available for this purpose. An operator is also present to conduct the tests. Electrical parameters measured give information about the design performance, robustness, fabrication accuracy and variability. A set of response variables, which are called Keithley electrical parameters, is chosen that best reflect the above-enumerated issues (in Italics). For deciding the response variables (as there are many to choose from) people from the design department, quality assurance and the manufacturing department are consulted.
The problem is to understand whether testers, the operators, and wafers produce variability in results. Succinctly stated, we need to find finite source of variation in Keithley electrical parameters. Once the experiment is conducted and analyzed, an exact test procedure can be suggested.
Choice of factors, levels, and ranges:
1. Testers - Currently there are two Keithley Systems used for testing – this factor, therefore, has two fixed levels and is a categorical factor. The variation would be due to differences in calibration of current sources, voltmeters, and resistor networks to traceable standards; and noise factors such as "probe-up capacitance". For example, the programmed value for this is treated as a system constant, at a value of 0.35 pF (picoFarads), but could affect parameters that rely on a measurement of capacitance, such as film thickness (one of the responses chosen). Another effect due to tester, or perhaps operator, is the incidence of "bad " data points; meaning points where the probe needles did not make low-resistance contact with the test structures. Three of the responses (in varying degrees with the leakage parameter being the most sensitive) could be potentially affected due to this source of variation. The number of these bad data points may be added as a response variable; as these points are typically passed to the database as an obvious outlier value; e.g. 2E21 value for data that normally falls between 0 and 2 Volts.
2. Operators - The intention is to perform the experiment using two different operators and see whether variability in the results can be caused if different operators perform the test. This is a fixed factor due to small sample of trained operators for the testers.
3. Wafers - Wafers of the same type and the same technology are used for testing. These wafers can be used as blocks while the other factors are tested randomly within this block. The original design was intending to select a set of wafers (“golden” wafers) as a fixed factor to be used in all the experimental cells, and run a typical gauge study. At the time of this report, due to production constraints out of the control of the experimenters, only half of the originally planned experiment had been run, and the data was unavailable. Instead, randomly selected wafers were used to generate the experimental data. The wafers were of the same device type and technology, run at the same time period through the factory, and were from the same batch of starting material. Therefore we assume they are from the same normally distributed population of samples, even though selected from different fabrication lots.
4. Location of test - 3 points on the wafer are tested. The observations obtained at these points are duplicates and the mean of the observations is taken as the response variable. This factor could have been used as a nested factor within wafer (the data is automatically provided in this manner), but was not. Randomizing testing at all three locations is a tedious task posing a practical difficulty. The dispersion of the data (variance of the wafer average response) can be analyzed.
5. The variation due to a different probe card on the same tester was considered. This might have variation independent of the tester itself, and could be confounded with a tester effect. However, it was difficult to add as a factor for both testers, unless done as a before/after change. The difficulty arises in the execution of the experiment, where excessive setup time would be needed in a random order that varies the probe card. Therefore this factor was not included.
Response Variables:
These responses were chosen as a cross-section of the different types of measurements done in normal production testing, and of the different measurement sub-systems in the tester The following is a list of responses that are most significant:
- Sheet Resistance of N+ active area, ohms/square : The typical variation as a percentage of the mean is 3%. It is subject to all of the temperature variations in the process.
- Sheet Resistance of first layer of metal or width 3μ, ohms : The typical variation as a percentage of the mean is 2%
- Leakage Current of capacitor with electrodes composed of the first and second metal layers, amperes : The typical variation as a percentage of the mean is 10 to 20%. The leakage current can be sensitive to needle contact, therefore to system or operator. The actual measurement is in the nA (nanoampere) range, so coding or transformation of the response may be appropriate.
- Threshold voltage of large W/L n-channel transistor, volts : The typical variation as a percentage of the mean is 1 to 2%.
- Oxide thickness of dielectric between first and second metal layers, Angstroms: The typical variation as a percentage of the mean is 3%. This response could be sensitive to the "probe-up capacitance”. It is a well-controlled process in the factory.
Choice of Design:
There were practical difficulties associated with this experiment, and the choice of design was dictated more by the practical issues than anything else. If wafer were considered as a factor, it would imply randomizing wafer order during the time experiment was run, leading to excessive handling that was deemed too risky to successful completion of the experiment. This, in terms of the experiment, would have meant re-running all combinations again, and also financial losses. Hence, the wafer was to be considered as a block and the treatment combinations were supposed to be run in a randomized fashion on a wafer.
Another possible factor that was considered was the site-location – i.e. the point where the wafer is tested. Considering it as a factor would have meant randomizing the order of points at which the wafer is tested. This implied changing the stepper program and having different run orders for different wafers. Such a modification, though possible, was hardly feasible practically. A natural simplification would be considering only three points, and making the task of randomizing easier. This aspect of the experiment was considered but after considering the set-up of the experiment, it was decided that the observations were actually duplicate observations. Hence the mean of the observations at these points was to be considered as the response. The analysis of the variability of the locations, or the variance of the response by wafer (dispersion effects) could be gained from this data.
The design suggested therefore seems tentative. Each wafer was to be a block and combinations of tester and operator are tested on each wafer. This meant four combinations on each wafer, and the value of a particular response variable is the mean of the observations at the three different sites.
Hence, the experiment under consideration for this project was a general factorial design, with two factors - operator and tester – at two levels. Blocking was to be done by the third factor wafer, and there were supposed to be five blocks.
Number of Replicates:
The number of replicates was decided using a trial an error method on Design Expert. There are fifteen replicates, which means there are three replicates per block. This gave us a power of 96.7% with at a significance level of 5%.
Run Order:
Std / Run / Block / Tester / Operator / Std / Run / Block / Tester / Operator47 / 1 / wafer 1 / t2 / s2 / 52 / 31 / wafer 3 / t2 / s2
48 / 2 / wafer 1 / t2 / s2 / 7 / 32 / wafer 3 / t1 / s1
16 / 3 / wafer 1 / t2 / s1 / 54 / 33 / wafer 3 / t2 / s2
18 / 4 / wafer 1 / t2 / s1 / 37 / 34 / wafer 3 / t1 / s2
46 / 5 / wafer 1 / t2 / s2 / 9 / 35 / wafer 3 / t1 / s1
33 / 6 / wafer 1 / t1 / s2 / 8 / 36 / wafer 3 / t1 / s1
31 / 7 / wafer 1 / t1 / s2 / 57 / 37 / wafer 4 / t2 / s2
1 / 8 / wafer 1 / t1 / s1 / 40 / 38 / wafer 4 / t1 / s2
2 / 9 / wafer 1 / t1 / s1 / 42 / 39 / wafer 4 / t1 / s2
32 / 10 / wafer 1 / t1 / s2 / 27 / 40 / wafer 4 / t2 / s1
3 / 11 / wafer 1 / t1 / s1 / 55 / 41 / wafer 4 / t2 / s2
17 / 12 / wafer 1 / t2 / s1 / 11 / 42 / wafer 4 / t1 / s1
50 / 13 / wafer 2 / t2 / s2 / 10 / 43 / wafer 4 / t1 / s1
34 / 14 / wafer 2 / t1 / s2 / 25 / 44 / wafer 4 / t2 / s1
19 / 15 / wafer 2 / t2 / s1 / 41 / 45 / wafer 4 / t1 / s2
49 / 16 / wafer 2 / t2 / s2 / 12 / 46 / wafer 4 / t1 / s1
4 / 17 / wafer 2 / t1 / s1 / 56 / 47 / wafer 4 / t2 / s2
35 / 18 / wafer 2 / t1 / s2 / 26 / 48 / wafer 4 / t2 / s1
6 / 19 / wafer 2 / t1 / s1 / 15 / 49 / wafer 5 / t1 / s1
21 / 20 / wafer 2 / t2 / s1 / 43 / 50 / wafer 5 / t1 / s2
51 / 21 / wafer 2 / t2 / s2 / 45 / 51 / wafer 5 / t1 / s2
5 / 22 / wafer 2 / t1 / s1 / 30 / 52 / wafer 5 / t2 / s1
20 / 23 / wafer 2 / t2 / s1 / 14 / 53 / wafer 5 / t1 / s1
36 / 24 / wafer 2 / t1 / s2 / 59 / 54 / wafer 5 / t2 / s2
53 / 25 / wafer 3 / t2 / s2 / 28 / 55 / wafer 5 / t2 / s1
23 / 26 / wafer 3 / t2 / s1 / 60 / 56 / wafer 5 / t2 / s2
22 / 27 / wafer 3 / t2 / s1 / 29 / 57 / wafer 5 / t2 / s1
39 / 28 / wafer 3 / t1 / s2 / 58 / 58 / wafer 5 / t2 / s2
38 / 29 / wafer 3 / t1 / s2 / 44 / 59 / wafer 5 / t1 / s2
24 / 30 / wafer 3 / t2 / s1 / 13 / 60 / wafer 5 / t1 / s1
Performing the experiment:
The design that was suggested in previous project proposals was keeping wafers, operators and testers as fixed factors. However, the experiment was run in a different manner. This was because of various factors that affect experiments in industrial settings like availability of time and resources, and understanding of the personnel in-charge of the experiment. Consequently, the experimental design had to be changed in accordance with the way the experiment was run. Wafers were made a random factor nested within operators. The responses considered were the same. The objective was still to find the source of variation in the electrical parameters measured. However, the experiment would now also tell us if any variability existed in the wafer population.
The revised design is shown below:
Operator 1 / Operator 2W1 / W2 / W3 / W4 / W5 / W6 / W7 / W8 / W1 / W2 / W3 / W4 / W5 / W6 / W7 / W8
Tester 1
Tester 2
Eight wafer levels representing the wafer population nested within operators were tested with the two tester levels. One replication was done with these eight levels. This experimental design does not exactly conform to the design initially considered and planned, but it might still be a reasonable model to use in making conclusions. The wafers were selected randomly from the population for each cell of this revised design. However, the conclusions cannot be taken for granted. Follow up experiments need to be conducted to ensure that the results are the same as those predicted by this experiment; e.g. the originally designed gauge study.
Statistical Analysis of Data:
The following represents
Rn - Sheet Resistance of N+ active area, ohms/square
Vtn - Threshold voltage of large W/L n-channel transistor, volts
Leakage - Leakage Current of capacitor with electrodes composed of the first and second metal layers, amperes
Teos - Oxide thickness of dielectric between first and second metal layers, Angstroms
m2snak - Sheet Resistance of first layer of metal or width 3μ, ohms
Statistical analyses are performed for all the five response variables considered; all plots are included in the appendix to the report.
Resposnse 1 Rn: Sheet Resistance of N+ active area, ohms/square
ANOVA: Rn versus tester, operator, wafer
Factor Type Levels Values
wafer(operator) random 8 1 2 3 4 5 6
7 8
tester fixed 2 1 2
operator fixed 2 1 2
Analysis of Variance for rn
Source DF SS MS F P
wafer(operator) 14 0.080143 0.005725 0.57 0.846
tester*operator 1 0.000179 0.000179 0.02 0.895
tester 1 0.000914 0.000914 0.09 0.767
operator 1 0.369728 0.369728 64.59 0.000
Error 14 0.139901 0.009993
Total 31 0.590866
Source Variance Error Expected Mean Square for Each Term
component term (using restricted model)
1 wafer(operator) -0.00213 5 (5) + 2(1)
2 tester*operator 5 (5) + 8Q[2]
3 tester 5 (5) + 16Q[3]
4 operator 1 (5) + 2(1) + 16Q[4]
5 Error 0.00999 (5)
The analysis indicates that the operator effect is a significant. Negative variance component essentially means that the wafer to wafer variability is negligible.
Normal Probability plot, Residuals vs Order plot, and the plot of Residuals vs Predicted values look normal. No violation of assumptions seems to have occurred here.
Resposnse 2 vtn: Threshold voltage of large W/L n-channel transistor, volts
Results for: Worksheet 2
ANOVA: vtn versus tester, operator, wafer
Factor Type Levels Values
wafer(operator) random 8 1 2 3 4 5 6
7 8
tester fixed 2 1 2
operator fixed 2 1 2
Analysis of Variance for vtn
Source DF SS MS F P
wafer(operator) 14 0.00027835 0.00001988 2.93 0.027
tester*operator 1 0.00431134 0.00431134 635.56 0.000
tester 1 0.00281563 0.00281563 415.07 0.000
operator 1 0.00038111 0.00038111 19.17 0.001
Error 14 0.00009497 0.00000678
Total 31 0.00788139
Source Variance Error Expected Mean Square for Each Term
component term (using restricted model)
1 wafer(operator) 0.00001 5 (5) + 2(1)
2 tester*operator 5 (5) + 8Q[2]
3 tester 5 (5) + 16Q[3]
4 operator 1 (5) + 2(1) + 16Q[4]
5 Error 0.00001 (5)
The results show that tester, operator and the tester-operator interaction are significant. The residual graphs seem normal, and no assumptions seem to have been violated. The normality probability plot has some S-shape, but not to an alarming degree.
Response 3 Leakage:
Leakage Current of capacitor with electrodes composed of the first and second metal layers, amperes
Results for: Worksheet 2
ANOVA: leakage versus tester, operator, wafer
Leakage Current of capacitor with electrodes composed of the first and second metal layers, amperes
Factor Type Levels Values
wafer(operator) random 8 1 2 3 4 5 6
7 8
tester fixed 2 1 2
operator fixed 2 1 2
Analysis of Variance for leak
Source DF SS MS F P
wafer(operator) 14 0.10781 0.00770 1.30 0.316
tester*operator 1 1.41536 1.41536 238.70 0.000
tester 1 1.44694 1.44694 244.02 0.000
operator 1 0.07077 0.07077 9.19 0.009
Error 14 0.08301 0.00593
Total 31 3.12389
Source Variance Error Expected Mean Square for Each Term
component term (using restricted model)
1 wafer(operator) 0.00089 5 (5) + 2(1)
2 tester*operator 5 (5) + 8Q[2]
3 tester 5 (5) + 16Q[3]
4 operator 1 (5) + 2(1) + 16Q[4]
5 Error 0.00593 (5)
A log transformation was done on the original readings to make the data conform to the assumptions. The ANOVA table shows that the tester and tester-operator interaction are significant. Wafer to wafer variability is very low as shown by the variance component.
The normal probabilty plot shows a couple of outliers; otherwise the plot passes the fat pencil test. The other graphs show no unusual patterns.
Resposnse 4 m2snak: Sheet Resistance of first layer of metal or width 3μ, ohms
Results for: Worksheet 2
ANOVA: m2sn versus tester, operator, wafer
Factor Type Levels Values
wafer(operator) random 8 1 2 3 4 5 6
7 8
tester fixed 2 1 2
operator fixed 2 1 2
Analysis of Variance for m2sn
Source DF SS MS F P
wafer(operator) 14 51.456 3.675 2.35 0.060
tester 1 0.201 0.201 0.13 0.725
operator 1 140.840 140.840 38.32 0.000
tester*operator 1 32.805 32.805 21.01 0.000
Error 14 21.860 1.561
Total 31 247.162
Source Variance Error Expected Mean Square for Each Term
component term (using restricted model)
1 wafer(operator) 1.057 5 (5) + 2(1)
2 tester 5 (5) + 16Q[2]
3 operator 1 (5) + 2(1) + 16Q[3]
4 tester*operator 5 (5) + 8Q[4]
5 Error 1.561 (5)
The ANOVA table shows that the operator and the tester-operator interaction are significant. There also seems to be some wafer to wafer variability for this response. The residual graphs show no unusual patterns.
Resposnse 5 teos: Oxide thickness of dielectric between first and second metal layers, Angstroms
Results for: Worksheet 2
ANOVA: teos versus tester, operator, wafer
Factor Type Levels Values
wafer(operator) random 8 1 2 3 4 5 6
7 8
tester fixed 2 1 2
operator fixed 2 1 2
Analysis of Variance for teos
Source DF SS MS F P
wafer(operator) 14 5224.7 373.2 0.84 0.630
tester 1 32.0 32.0 0.07 0.793
operator 1 7564.5 7564.5 20.27 0.000
tester*operator 1 150607.2 150607.2 337.01 0.000
Error 14 6256.4 446.9
Total 31 169684.8
Source Variance Error Expected Mean Square for Each Term
component term (using restricted model)
1 wafer(operator) -36.85 5 (5) + 2(1)
2 tester 5 (5) + 16Q[2]
3 operator 1 (5) + 2(1) + 16Q[3]
4 tester*operator 5 (5) + 8Q[4]
5 Error 446.89 (5)
The operator and test*operator interaction are shown as significant. No issues are seen with residuals plots. Originally the data was not entered in enough significant digits, and thus the data appeared on the normal plot on the straight line, as discrete data.
Conclusion
The expected results were that none of the effects would be shown to be significant to the variation of the measurements, except possibly some wafer-to-wafer variation. For the four responses of M2 snake (resistance), leakage, Vtn (threshold voltage),and TEOS thickness (angstroms), the operator*tester interaction is important, indicating a possible violation of the randomness of the wafer samples used in the experiment. This could also be confounded with the time measured for these random samples.
The N+ sheet resistance (ohms per square) showed an effect due to the operator, which is possible, but not expected. The setup procedure for putting the probe needles on the first die under test may be the source of this effect.
The wafer-to-wafer effect on the m2 snake resistance could be due to a single-wafer effect as a result of dry etching variation within a lot. The operator*tester interaction would not be expected to be a result of this source of variation, however.
Recommendations
It is still recommended to do the originally planned gauge study, to verify the operator effect on the N+ Rs, and the interactions on the three responses. It is possible that this will be finished by the end of work week 12/08, and may be submitted as any addendum to this report. If the operator effect is still important, then an analysis of the setup procedure is warranted after review of the training of the chosen operators. If the operator*tester interaction is not seen as important, the assumption of randomness of the wafers chosen could be confirmed as having been violated. If the factory was following a system of electrically testing lots at random, these results would indicate that might not be a good practice.