Engineering Statistics Handbook Episode 4 Part 6 potx

Pooled level-1 standard deviations ohm.cmGraphs of reproducibility and stability for probe #2362 Averages of the 6 center measurements on each wafer are plotted on a single graph for eac

2.6.1.1.1 Database of resistivity measurements

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (10 of 15) [5/1/2006 10:13:12 AM]

2.6.1.1.1 Database of resistivity measurements

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (11 of 15) [5/1/2006 10:13:12 AM]

2.6.1.1.1 Database of resistivity measurements

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (12 of 15) [5/1/2006 10:13:12 AM]

2.6.1.1.1 Database of resistivity measurements

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (13 of 15) [5/1/2006 10:13:12 AM]

2.6.1.1.1 Database of resistivity measurements

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (14 of 15) [5/1/2006 10:13:12 AM]

2.6.1.1.1 Database of resistivity measurements

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (15 of 15) [5/1/2006 10:13:12 AM]

Pooled level-1 standard deviations (ohm.cm)

Graphs of

reproducibility

and stability for

probe #2362

Averages of the 6 center measurements on each wafer are plotted on

a single graph for each wafer The points (connected by lines) on the left side of each graph are averages at the wafer center plotted over 5 days; the points on the right are the same measurements repeated after one month as a check on the stability of the measurement process The plots show day-to-day variability as well as slight variability from run-to-run.

Earlier work discounts long-term drift in the gauge as the cause of these changes A reasonable conclusion is that day-to-day and run-to-run variations come from random fluctuations in the measurement process.

and pooled over

wafers and runs

Level-2 standard deviations (with K - 1 = 5 degrees of freedom

each) are computed from the daily averages that are recorded in the database Then the level-2 standard deviations are pooled over:

L = 2 runs for L(K - 1) = 10 degrees of freedom

Level-2 standard deviations (ohm.cm) for 5 wafers

2.6.1.2 Analysis and interpretation

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc612.htm (3 of 6) [5/1/2006 10:13:13 AM]

Level-3 standard deviations (ohm.cm) for 5 wafers

2.6.1.2 Analysis and interpretation

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc612.htm (4 of 6) [5/1/2006 10:13:13 AM]

Biases by probe are shown in the following table.

Differences from the mean for each wafer

2.6.1.2 Analysis and interpretation

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc612.htm (5 of 6) [5/1/2006 10:13:13 AM]

Correct all measurements made with probe #2362 to the average

2.6.1.2 Analysis and interpretation

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc612.htm (6 of 6) [5/1/2006 10:13:13 AM]

Wafer 139

Wafer 140

2.6.1.4 Effects of days and long-term stability

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc614.htm (2 of 5) [5/1/2006 10:13:15 AM]

Wafer 141

2.6.1.4 Effects of days and long-term stability

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc614.htm (3 of 5) [5/1/2006 10:13:15 AM]

Wafer 142

2.6.1.4 Effects of days and long-term stability

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc614.htm (4 of 5) [5/1/2006 10:13:15 AM]

2.6.1.4 Effects of days and long-term stability

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc614.htm (5 of 5) [5/1/2006 10:13:15 AM]

2 Measurement Process Characterization

2.6 Case studies

2.6.1 Gauge study of resistivity probes

2.6.1.6 Run gauge study example using

Click on the links below to start Dataplot and

run this case study yourself Each step may use

results from previous steps, so please be patient.

Wait until the software verifies that the current

step is complete before clicking on the next step.

The links in this column will connect you with more detailed information about each analysis step from the case study description.

Graphical analyses of variability Graphs to

standard deviations on days D, E, and F of run 2 are larger in some instances than for the other days.

3 and 4 Interpretation: Probe #2362 appears as

#5 in the plots which show that, for both runs, the precision of this probe is better than for the other probes.

2.6.1.6 Run gauge study example using Dataplot™

http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc616.htm (1 of 2) [5/1/2006 10:13:16 AM]