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2. Measurement Process Characterization
2.6. Case studies
2.6.3. Evaluation of type A uncertainty

Background and data

Description of measurements The measurements in question are resistivities ( of silicon wafers. The intent is to calculate an uncertainty associated with the resistivity measurements of approximately 100 silicon wafers that were certified with probe #2362 in wiring configuration A, according to ASTM Method F84 (ASTM F84) which is the defined reference for this measurement. The reported value for each wafer is the average of six measurements made at the center of the wafer on a single day. Probe #2362 is one of five probes owned by the National Institute of Standards and Technology that is capable of making the measurements.
Sources of uncertainty in NIST measurements The uncertainty analysis takes into account the following sources of variability:
Database of 3-level nested design -- for estimating time-dependent sources of uncertainty The certification measurements themselves are not the primary source for estimating uncertainty components because they do not yield information on day-to-day effects and long-term effects. The standard deviations for the three time-dependent sources of uncertainty are estimated from a 3-level nested design. The design was replicated on each of Q = 5 wafers which were chosen at random, for this purpose, from the lot of wafers. The certification measurements were made between the two runs in order to check on the long-term stability of the process. The data consist of repeatability standard deviations (with J - 1 = 5 degrees of freedom each) from measurements at the wafer center.
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