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2. Measurement Process Characterization
2.6. Case studies
2.6.1. Gauge study of resistivity probes

2.6.1.1.

Background and data

Description of measurements Measurements of resistivity on 100 ohm.cm wafers were made according to an ASTM Standard Test Method (ASTM F84) to assess the sources of uncertainty in the measurement system. Resistivity measurements have been studied over the years, and it is clear from those data that there are sources of variability affecting the process beyond the basic imprecision of the gauges. Changes in measurement results have been noted over days and over months and the data in this study are structured to quantify these time-dependent changes in the measurement process.
Gauges The gauges for the study were five probes used to measure resistivity of silicon wafers. The five gauges are assumed to represent a random sample of typical 4-point gauges for making resistivity measurements. There is a question of whether or not the gauges are essentially equivalent or whether biases among them are possible.
Check standards The check standards for the study were five wafers selected at random from the batch of 100 ohm.cm wafers.
Operators The effect of operator was not considered to be significant for this study.
Database of measurements The 3-level nested design consisted of:
  • J = 6 measurements at the center of each wafer per day
  • K = 6 days
  • L = 2 runs
To characterize the probes and the influence of wafers on the measurements, the design was repeated over:
  • Q = 5 wafers (check standards 138, 139, 140, 141, 142)
  • I = 5 probes (1, 281, 283, 2062, 2362)
The runs were separated by about one month in time. The J = 6 measurements at the center of each wafer are reduced to an average and repeatability standard deviation and recorded in a database with identifications for wafer, probe, and day.
Software The analyses used in this case study can be generated using both Dataplot code and R code. The reader can download the data as a text file.
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