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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
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| The check standards are five wafers chosen at random from a batch of wafers | Measurements of resistivity (ohm.cm) were made according to an ASTM Standard Test Method (F4) at NIST to assess the sources of uncertainty in the measurement system. The gauges for the study were five probes owned by NIST; the check standards for the study were five wafers selected at random from a batch of wafers cut from one silicon crystal doped with phosphorous to give a nominal resistivity of 100 ohm.cm. | ||
| Measurements on the check standards are used to estimate repeatability, day effect, and run effect |
The effect of operator was not considered to be significant for
this study; therefore, 'day' replaces 'operator' as a factor in
the nested design. Averages and standard deviations from
J = 6 measurements at the center of each wafer are shown
in the table.
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Run Wafer Probe Month Day Op Temp Average Std Dev 1 138. 1. 3. 15. 1. 22.98 95.1772 0.1191 1 138. 1. 3. 17. 1. 23.02 95.1567 0.0183 1 138. 1. 3. 18. 1. 22.79 95.1937 0.1282 1 138. 1. 3. 21. 1. 23.17 95.1959 0.0398 1 138. 1. 3. 23. 2. 23.25 95.1442 0.0346 1 138. 1. 3. 23. 1. 23.20 95.0610 0.1539 1 138. 281. 3. 16. 1. 22.99 95.1591 0.0963 1 138. 281. 3. 17. 1. 22.97 95.1195 0.0606 1 138. 281. 3. 18. 1. 22.83 95.1065 0.0842 1 138. 281. 3. 21. 1. 23.28 95.0925 0.0973 1 138. 281. 3. 23. 2. 23.14 95.1990 0.1062 1 138. 281. 3. 23. 1. 23.16 95.1682 0.1090 1 138. 283. 3. 16. 1. 22.95 95.1252 0.0531 1 138. 283. 3. 17. 1. 23.08 95.1600 0.0998 1 138. 283. 3. 18. 1. 23.13 95.0818 0.1108 1 138. 283. 3. 21. 1. 23.28 95.1620 0.0408 1 138. 283. 3. 22. 1. 23.36 95.1735 0.0501 1 138. 283. 3. 24. 2. 22.97 95.1932 0.0287 1 138. 2062. 3. 16. 1. 22.97 95.1311 0.1066 1 138. 2062. 3. 17. 1. 22.98 95.1132 0.0415 1 138. 2062. 3. 18. 1. 23.16 95.0432 0.0491 1 138. 2062. 3. 21. 1. 23.16 95.1254 0.0603 1 138. 2062. 3. 22. 1. 23.28 95.1322 0.0561 1 138. 2062. 3. 24. 2. 23.19 95.1299 0.0349 1 138. 2362. 3. 15. 1. 23.08 95.1162 0.0480 1 138. 2362. 3. 17. 1. 23.01 95.0569 0.0577 1 138. 2362. 3. 18. 1. 22.97 95.0598 0.0516 1 138. 2362. 3. 22. 1. 23.23 95.1487 0.0386 1 138. 2362. 3. 23. 2. 23.28 95.0743 0.0256 1 138. 2362. 3. 24. 2. 23.10 95.1010 0.0420 1 139. 1. 3. 15. 1. 23.01 99.3528 0.1424 1 139. 1. 3. 17. 1. 23.00 99.2940 0.0660 1 139. 1. 3. 17. 1. 23.01 99.2340 0.1179 1 139. 1. 3. 21. 1. 23.20 99.3489 0.0506 1 139. 1. 3. 23. 2. 23.22 99.2625 0.1111 1 139. 1. 3. 23. 1. 23.22 99.3787 0.1103 1 139. 281. 3. 16. 1. 22.95 99.3244 0.1134 1 139. 281. 3. 17. 1. 22.98 99.3378 0.0949 1 139. 281. 3. 18. 1. 22.86 99.3424 0.0847 1 139. 281. 3. 22. 1. 23.17 99.4033 0.0801 1 139. 281. 3. 23. 2. 23.10 99.3717 0.0630 1 139. 281. 3. 23. 1. 23.14 99.3493 0.1157 1 139. 283. 3. 16. 1. 22.94 99.3065 0.0381 1 139. 283. 3. 17. 1. 23.09 99.3280 0.1153 1 139. 283. 3. 18. 1. 23.11 99.3000 0.0818 1 139. 283. 3. 21. 1. 23.25 99.3347 0.0972 1 139. 283. 3. 22. 1. 23.36 99.3929 0.1189 1 139. 283. 3. 23. 1. 23.18 99.2644 0.0622 1 139. 2062. 3. 16. 1. 22.94 99.3324 0.1531 1 139. 2062. 3. 17. 1. 23.08 99.3254 0.0543 1 139. 2062. 3. 18. 1. 23.15 99.2555 0.1024 1 139. 2062. 3. 18. 1. 23.18 99.1946 0.0851 1 139. 2062. 3. 22. 1. 23.27 99.3542 0.1227 1 139. 2062. 3. 24. 2. 23.23 99.2365 0.1218 1 139. 2362. 3. 15. 1. 23.08 99.2939 0.0818 1 139. 2362. 3. 17. 1. 23.02 99.3234 0.0723 1 139. 2362. 3. 18. 1. 22.93 99.2748 0.0756 1 139. 2362. 3. 22. 1. 23.29 99.3512 0.0475 1 139. 2362. 3. 23. 2. 23.25 99.2350 0.0517 1 139. 2362. 3. 24. 2. 23.05 99.3574 0.0485 1 140. 1. 3. 15. 1. 23.07 96.1334 0.1052 1 140. 1. 3. 17. 1. 23.08 96.1250 0.0916 1 140. 1. 3. 18. 1. 22.77 96.0665 0.0836 1 140. 1. 3. 21. 1. 23.18 96.0725 0.0620 1 140. 1. 3. 23. 2. 23.20 96.1006 0.0582 1 140. 1. 3. 23. 1. 23.21 96.1131 0.1757 1 140. 281. 3. 16. 1. 22.94 96.0467 0.0565 1 140. 281. 3. 17. 1. 22.99 96.1081 0.1293 1 140. 281. 3. 18. 1. 22.91 96.0578 0.1148 1 140. 281. 3. 22. 1. 23.15 96.0700 0.0495 1 140. 281. 3. 22. 1. 23.33 96.1052 0.1722 1 140. 281. 3. 23. 1. 23.19 96.0952 0.1786 1 140. 283. 3. 16. 1. 22.89 96.0650 0.1301 1 140. 283. 3. 17. 1. 23.07 96.0870 0.0881 1 140. 283. 3. 18. 1. 23.07 95.8906 0.1842 1 140. 283. 3. 21. 1. 23.24 96.0842 0.1008 1 140. 283. 3. 22. 1. 23.34 96.0189 0.0865 1 140. 283. 3. 23. 1. 23.19 96.1047 0.0923 1 140. 2062. 3. 16. 1. 22.95 96.0379 0.2190 1 140. 2062. 3. 17. 1. 22.97 96.0671 0.0991 1 140. 2062. 3. 18. 1. 23.15 96.0206 0.0648 1 140. 2062. 3. 21. 1. 23.14 96.0207 0.1410 1 140. 2062. 3. 22. 1. 23.32 96.0587 0.1634 1 140. 2062. 3. 24. 2. 23.17 96.0903 0.0406 1 140. 2362. 3. 15. 1. 23.08 96.0771 0.1024 1 140. 2362. 3. 17. 1. 23.00 95.9976 0.0943 1 140. 2362. 3. 18. 1. 23.01 96.0148 0.0622 1 140. 2362. 3. 22. 1. 23.27 96.0397 0.0702 1 140. 2362. 3. 23. 2. 23.24 96.0407 0.0627 1 140. 2362. 3. 24. 2. 23.13 96.0445 0.0622 1 141. 1. 3. 15. 1. 23.01 101.2124 0.0900 1 141. 1. 3. 17. 1. 23.08 101.1018 0.0820 1 141. 1. 3. 18. 1. 22.75 101.1119 0.0500 1 141. 1. 3. 21. 1. 23.21 101.1072 0.0641 1 141. 1. 3. 23. 2. 23.25 101.0802 0.0704 1 141. 1. 3. 23. 1. 23.19 101.1350 0.0699 1 141. 281. 3. 16. 1. 22.93 101.0287 0.0520 1 141. 281. 3. 17. 1. 23.00 101.0131 0.0710 1 141. 281. 3. 18. 1. 22.90 101.1329 0.0800 1 141. 281. 3. 22. 1. 23.19 101.0562 0.1594 1 141. 281. 3. 23. 2. 23.18 101.0891 0.1252 1 141. 281. 3. 23. 1. 23.17 101.1283 0.1151 1 141. 283. 3. 16. 1. 22.85 101.1597 0.0990 1 141. 283. 3. 17. 1. 23.09 101.0784 0.0810 1 141. 283. 3. 18. 1. 23.08 101.0715 0.0460 1 141. 283. 3. 21. 1. 23.27 101.0910 0.0880 1 141. 283. 3. 22. 1. 23.34 101.0967 0.0901 1 141. 283. 3. 24. 2. 23.00 101.1627 0.0888 1 141. 2062. 3. 16. 1. 22.97 101.1077 0.0970 1 141. 2062. 3. 17. 1. 22.96 101.0245 0.1210 1 141. 2062. 3. 18. 1. 23.19 100.9650 0.0700 1 141. 2062. 3. 18. 1. 23.18 101.0319 0.1070 1 141. 2062. 3. 22. 1. 23.34 101.0849 0.0960 1 141. 2062. 3. 24. 2. 23.21 101.1302 0.0505 1 141. 2362. 3. 15. 1. 23.08 101.0471 0.0320 1 141. 2362. 3. 17. 1. 23.01 101.0224 0.1020 1 141. 2362. 3. 18. 1. 23.05 101.0702 0.0580 1 141. 2362. 3. 22. 1. 23.22 101.0904 0.1049 1 141. 2362. 3. 23. 2. 23.29 101.0626 0.0702 1 141. 2362. 3. 24. 2. 23.15 101.0686 0.0661 1 142. 1. 3. 15. 1. 23.02 94.3160 0.1372 1 142. 1. 3. 17. 1. 23.04 94.2808 0.0999 1 142. 1. 3. 18. 1. 22.73 94.2478 0.0803 1 142. 1. 3. 21. 1. 23.19 94.2862 0.0700 1 142. 1. 3. 23. 2. 23.25 94.1859 0.0899 1 142. 1. 3. 23. 1. 23.21 94.2389 0.0686 1 142. 281. 3. 16. 1. 22.98 94.2640 0.0862 1 142. 281. 3. 17. 1. 23.00 94.3333 0.1330 1 142. 281. 3. 18. 1. 22.88 94.2994 0.0908 1 142. 281. 3. 21. 1. 23.28 94.2873 0.0846 1 142. 281. 3. 23. 2. 23.07 94.2576 0.0795 1 142. 281. 3. 23. 1. 23.12 94.3027 0.0389 1 142. 283. 3. 16. 1. 22.92 94.2846 0.1021 1 142. 283. 3. 17. 1. 23.08 94.2197 0.0627 1 142. 283. 3. 18. 1. 23.09 94.2119 0.0785 1 142. 283. 3. 21. 1. 23.29 94.2536 0.0712 1 142. 283. 3. 22. 1. 23.34 94.2280 0.0692 1 142. 283. 3. 24. 2. 22.92 94.2944 0.0958 1 142. 2062. 3. 16. 1. 22.96 94.2238 0.0492 1 142. 2062. 3. 17. 1. 22.95 94.3061 0.2194 1 142. 2062. 3. 18. 1. 23.16 94.1868 0.0474 1 142. 2062. 3. 21. 1. 23.11 94.2645 0.0697 1 142. 2062. 3. 22. 1. 23.31 94.3101 0.0532 1 142. 2062. 3. 24. 2. 23.24 94.2204 0.1023 1 142. 2362. 3. 15. 1. 23.08 94.2437 0.0503 1 142. 2362. 3. 17. 1. 23.00 94.2115 0.0919 1 142. 2362. 3. 18. 1. 22.99 94.2348 0.0282 1 142. 2362. 3. 22. 1. 23.26 94.2124 0.0513 1 142. 2362. 3. 23. 2. 23.27 94.2214 0.0627 1 142. 2362. 3. 24. 2. 23.08 94.1651 0.1010 2 138. 1. 4. 13. 1. 23.12 95.1996 0.0645 2 138. 1. 4. 15. 1. 22.73 95.1315 0.1192 2 138. 1. 4. 18. 2. 22.76 95.1845 0.0452 2 138. 1. 4. 19. 1. 22.73 95.1359 0.1498 2 138. 1. 4. 20. 2. 22.73 95.1435 0.0629 2 138. 1. 4. 21. 2. 22.93 95.1839 0.0563 2 138. 281. 4. 14. 2. 22.46 95.2106 0.1049 2 138. 281. 4. 18. 2. 22.80 95.2505 0.0771 2 138. 281. 4. 18. 2. 22.77 95.2648 0.1046 2 138. 281. 4. 20. 2. 22.80 95.2197 0.1779 2 138. 281. 4. 20. 2. 22.87 95.2003 0.1376 2 138. 281. 4. 21. 2. 22.95 95.0982 0.1611 2 138. 283. 4. 18. 2. 22.83 95.1211 0.0794 2 138. 283. 4. 13. 1. 23.17 95.1327 0.0409 2 138. 283. 4. 18. 1. 22.67 95.2053 0.1525 2 138. 283. 4. 19. 2. 23.00 95.1292 0.0655 2 138. 283. 4. 21. 2. 22.91 95.1669 0.0619 2 138. 283. 4. 21. 2. 22.96 95.1401 0.0831 2 138. 2062. 4. 15. 1. 22.64 95.2479 0.2867 2 138. 2062. 4. 15. 1. 22.67 95.2224 0.1945 2 138. 2062. 4. 19. 2. 22.99 95.2810 0.1960 2 138. 2062. 4. 19. 1. 22.75 95.1869 0.1571 2 138. 2062. 4. 21. 2. 22.84 95.3053 0.2012 2 138. 2062. 4. 21. 2. 22.92 95.1432 0.1532 2 138. 2362. 4. 12. 1. 22.74 95.1687 0.0785 2 138. 2362. 4. 18. 2. 22.75 95.1564 0.0430 2 138. 2362. 4. 19. 2. 22.88 95.1354 0.0983 2 138. 2362. 4. 19. 1. 22.73 95.0422 0.0773 2 138. 2362. 4. 20. 2. 22.86 95.1354 0.0587 2 138. 2362. 4. 21. 2. 22.94 95.1075 0.0776 2 139. 1. 4. 13. 2. 23.14 99.3274 0.0220 2 139. 1. 4. 15. 2. 22.77 99.5020 0.0997 2 139. 1. 4. 18. 2. 22.80 99.4016 0.0704 2 139. 1. 4. 19. 1. 22.68 99.3181 0.1245 2 139. 1. 4. 20. 2. 22.78 99.3858 0.0903 2 139. 1. 4. 21. 2. 22.93 99.3141 0.0255 2 139. 281. 4. 14. 2. 23.05 99.2915 0.0859 2 139. 281. 4. 15. 2. 22.71 99.4032 0.1322 2 139. 281. 4. 18. 2. 22.79 99.4612 0.1765 2 139. 281. 4. 20. 2. 22.74 99.4001 0.0889 2 139. 281. 4. 20. 2. 22.91 99.3765 0.1041 2 139. 281. 4. 21. 2. 22.92 99.3507 0.0717 2 139. 283. 4. 13. 2. 23.11 99.3848 0.0792 2 139. 283. 4. 18. 2. 22.84 99.4952 0.1122 2 139. 283. 4. 18. 2. 22.76 99.3220 0.0915 2 139. 283. 4. 19. 2. 23.03 99.4165 0.0503 2 139. 283. 4. 21. 2. 22.87 99.3791 0.1138 2 139. 283. 4. 21. 2. 22.98 99.3985 0.0661 2 139. 2062. 4. 14. 2. 22.43 99.4283 0.0891 2 139. 2062. 4. 15. 2. 22.70 99.4139 0.2147 2 139. 2062. 4. 19. 2. 22.97 99.3813 0.1143 2 139. 2062. 4. 19. 1. 22.77 99.4314 0.1685 2 139. 2062. 4. 21. 2. 22.79 99.4166 0.2080 2 139. 2062. 4. 21. 2. 22.94 99.4052 0.2400 2 139. 2362. 4. 12. 1. 22.82 99.3408 0.1279 2 139. 2362. 4. 18. 2. 22.77 99.3116 0.1131 2 139. 2362. 4. 19. 2. 22.82 99.3241 0.0519 2 139. 2362. 4. 19. 1. 22.74 99.2991 0.0903 2 139. 2362. 4. 20. 2. 22.88 99.3049 0.0783 2 139. 2362. 4. 21. 2. 22.94 99.2782 0.0718 2 140. 1. 4. 13. 1. 23.10 96.0811 0.0463 2 140. 1. 4. 15. 2. 22.75 96.1460 0.0725 2 140. 1. 4. 18. 2. 22.78 96.1582 0.1428 2 140. 1. 4. 19. 1. 22.70 96.1039 0.1056 2 140. 1. 4. 20. 2. 22.75 96.1262 0.0672 2 140. 1. 4. 21. 2. 22.93 96.1478 0.0562 2 140. 281. 4. 15. 2. 22.71 96.1153 0.1097 2 140. 281. 4. 14. 2. 22.49 96.1297 0.1202 2 140. 281. 4. 18. 2. 22.81 96.1233 0.1331 2 140. 281. 4. 20. 2. 22.78 96.1731 0.1484 2 140. 281. 4. 20. 2. 22.89 96.0872 0.0857 2 140. 281. 4. 21. 2. 22.91 96.1331 0.0944 2 140. 283. 4. 13. 2. 23.22 96.1135 0.0983 2 140. 283. 4. 18. 2. 22.85 96.1111 0.1210 2 140. 283. 4. 18. 2. 22.78 96.1221 0.0644 2 140. 283. 4. 19. 2. 23.01 96.1063 0.0921 2 140. 283. 4. 21. 2. 22.91 96.1155 0.0704 2 140. 283. 4. 21. 2. 22.94 96.1308 0.0258 2 140. 2062. 4. 15. 2. 22.60 95.9767 0.2225 2 140. 2062. 4. 15. 2. 22.66 96.1277 0.1792 2 140. 2062. 4. 19. 2. 22.96 96.1858 0.1312 2 140. 2062. 4. 19. 1. 22.75 96.1912 0.1936 2 140. 2062. 4. 21. 2. 22.82 96.1650 0.1902 2 140. 2062. 4. 21. 2. 22.92 96.1603 0.1777 2 140. 2362. 4. 12. 1. 22.88 96.0793 0.0996 2 140. 2362. 4. 18. 2. 22.76 96.1115 0.0533 2 140. 2362. 4. 19. 2. 22.79 96.0803 0.0364 2 140. 2362. 4. 19. 1. 22.71 96.0411 0.0768 2 140. 2362. 4. 20. 2. 22.84 96.0988 0.1042 2 140. 2362. 4. 21. 1. 22.94 96.0482 0.0868 2 141. 1. 4. 13. 1. 23.07 101.1984 0.0803 2 141. 1. 4. 15. 2. 22.72 101.1645 0.0914 2 141. 1. 4. 18. 2. 22.75 101.2454 0.1109 2 141. 1. 4. 19. 1. 22.69 101.1096 0.1376 2 141. 1. 4. 20. 2. 22.83 101.2066 0.0717 2 141. 1. 4. 21. 2. 22.93 101.0645 0.1205 2 141. 281. 4. 15. 2. 22.72 101.1615 0.1272 2 141. 281. 4. 14. 2. 22.40 101.1650 0.0595 2 141. 281. 4. 18. 2. 22.78 101.1815 0.1393 2 141. 281. 4. 20. 2. 22.73 101.1106 0.1189 2 141. 281. 4. 20. 2. 22.86 101.1420 0.0713 2 141. 281. 4. 21. 2. 22.94 101.0116 0.1088 2 141. 283. 4. 13. 2. 23.26 101.1554 0.0429 2 141. 283. 4. 18. 2. 22.85 101.1267 0.0751 2 141. 283. 4. 18. 2. 22.76 101.1227 0.0826 2 141. 283. 4. 19. 2. 22.82 101.0635 0.1715 2 141. 283. 4. 21. 2. 22.89 101.1264 0.1447 2 141. 283. 4. 21. 2. 22.96 101.0853 0.1189 2 141. 2062. 4. 15. 2. 22.65 101.1332 0.2532 2 141. 2062. 4. 15. 1. 22.68 101.1487 0.1413 2 141. 2062. 4. 19. 2. 22.95 101.1778 0.1772 2 141. 2062. 4. 19. 1. 22.77 101.0988 0.0884 2 141. 2062. 4. 21. 2. 22.87 101.1686 0.2940 2 141. 2062. 4. 21. 2. 22.94 101.3289 0.2072 2 141. 2362. 4. 12. 1. 22.83 101.1353 0.0585 2 141. 2362. 4. 18. 2. 22.83 101.1201 0.0868 2 141. 2362. 4. 19. 2. 22.91 101.0946 0.0855 2 141. 2362. 4. 19. 1. 22.71 100.9977 0.0645 2 141. 2362. 4. 20. 2. 22.87 101.0963 0.0638 2 141. 2362. 4. 21. 2. 22.94 101.0300 0.0549 2 142. 1. 4. 13. 1. 23.07 94.3049 0.1197 2 142. 1. 4. 15. 2. 22.73 94.3153 0.0566 2 142. 1. 4. 18. 2. 22.77 94.3073 0.0875 2 142. 1. 4. 19. 1. 22.67 94.2803 0.0376 2 142. 1. 4. 20. 2. 22.80 94.3008 0.0703 2 142. 1. 4. 21. 2. 22.93 94.2916 0.0604 2 142. 281. 4. 14. 2. 22.90 94.2557 0.0619 2 142. 281. 4. 18. 2. 22.83 94.3542 0.1027 2 142. 281. 4. 18. 2. 22.80 94.3007 0.1492 2 142. 281. 4. 20. 2. 22.76 94.3351 0.1059 2 142. 281. 4. 20. 2. 22.88 94.3406 0.1508 2 142. 281. 4. 21. 2. 22.92 94.2621 0.0946 2 142. 283. 4. 13. 2. 23.25 94.3124 0.0534 2 142. 283. 4. 18. 2. 22.85 94.3680 0.1643 2 142. 283. 4. 18. 1. 22.67 94.3442 0.0346 2 142. 283. 4. 19. 2. 22.80 94.3391 0.0616 2 142. 283. 4. 21. 2. 22.91 94.2238 0.0721 2 142. 283. 4. 21. 2. 22.95 94.2721 0.0998 2 142. 2062. 4. 14. 2. 22.49 94.2915 0.2189 2 142. 2062. 4. 15. 2. 22.69 94.2803 0.0690 2 142. 2062. 4. 19. 2. 22.94 94.2818 0.0987 2 142. 2062. 4. 19. 1. 22.76 94.2227 0.2628 2 142. 2062. 4. 21. 2. 22.74 94.4109 0.1230 2 142. 2062. 4. 21. 2. 22.94 94.2616 0.0929 2 142. 2362. 4. 12. 1. 22.86 94.2052 0.0813 2 142. 2362. 4. 18. 2. 22.83 94.2824 0.0605 2 142. 2362. 4. 19. 2. 22.85 94.2396 0.0882 2 142. 2362. 4. 19. 1. 22.75 94.2087 0.0702 2 142. 2362. 4. 20. 2. 22.86 94.2937 0.0591 2 142. 2362. 4. 21. 1. 22.93 94.2330 0.0556 |
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