|
6.
Process or Product Monitoring and Control
6.6. Case Studies in Process Monitoring 6.6.1. Lithography Process
|
|||
| Case Study for SPC in Batch Processing Environment | |||
| Semiconductor processing creates multiple sources of variability to monitor |
One of the assumptions in using classical Shewhart SPC charts is that
the only source of variation is from part to part (or within subgroup
variation). This is the case for most continuous processing situations.
However, many of today's processing situations have different sources
of variation. The semiconductor industry is one of the areas where the
processing creates multiple sources of variation.
In semiconductor processing, the basic experimental unit is a silicon wafer. Operations are performed on the wafer, but individual wafers can be grouped multiple ways. In the diffusion area, up to 150 wafers are processed in one time in a diffusion tube. In the etch area, single wafers are processed individually. In the lithography area, the light exposure is done on sub-areas of the wafer. There are many times during the production of a computer chip where the experimental unit varies and thus there are different sources of variation in this batch processing environment. The following is a case study of a lithography process. Five sites are measured on each wafer, three wafers are measured in a cassette (typically a grouping of 24 - 25 wafers) and thirty cassettes of wafers are used in the study. The width of a line is the measurement under study. There are two line width variables. The first is the original data and the second has been cleaned up somewhat. This case study uses the raw data. The entire data table is 450 rows long with six columns. |
||
| 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. | ||
| Case study data: wafer line width measurements |
Raw Cleaned
Line Line
Cassette Wafer Site Width Sequence Width
=====================================================
1 1 Top 3.199275 1 3.197275
1 1 Lef 2.253081 2 2.249081
1 1 Cen 2.074308 3 2.068308
1 1 Rgt 2.418206 4 2.410206
1 1 Bot 2.393732 5 2.383732
1 2 Top 2.654947 6 2.642947
1 2 Lef 2.003234 7 1.989234
1 2 Cen 1.861268 8 1.845268
1 2 Rgt 2.136102 9 2.118102
1 2 Bot 1.976495 10 1.956495
1 3 Top 2.887053 11 2.865053
1 3 Lef 2.061239 12 2.037239
1 3 Cen 1.625191 13 1.599191
1 3 Rgt 2.304313 14 2.276313
1 3 Bot 2.233187 15 2.203187
2 1 Top 3.160233 16 3.128233
2 1 Lef 2.518913 17 2.484913
2 1 Cen 2.072211 18 2.036211
2 1 Rgt 2.287210 19 2.249210
2 1 Bot 2.120452 20 2.080452
2 2 Top 2.063058 21 2.021058
2 2 Lef 2.217220 22 2.173220
2 2 Cen 1.472945 23 1.426945
2 2 Rgt 1.684581 24 1.636581
2 2 Bot 1.900688 25 1.850688
2 3 Top 2.346254 26 2.294254
2 3 Lef 2.172825 27 2.118825
2 3 Cen 1.536538 28 1.480538
2 3 Rgt 1.966630 29 1.908630
2 3 Bot 2.251576 30 2.191576
3 1 Top 2.198141 31 2.136141
3 1 Lef 1.728784 32 1.664784
3 1 Cen 1.357348 33 1.291348
3 1 Rgt 1.673159 34 1.605159
3 1 Bot 1.429586 35 1.359586
3 2 Top 2.231291 36 2.159291
3 2 Lef 1.561993 37 1.487993
3 2 Cen 1.520104 38 1.444104
3 2 Rgt 2.066068 39 1.988068
3 2 Bot 1.777603 40 1.697603
3 3 Top 2.244736 41 2.162736
3 3 Lef 1.745877 42 1.661877
3 3 Cen 1.366895 43 1.280895
3 3 Rgt 1.615229 44 1.527229
3 3 Bot 1.540863 45 1.450863
4 1 Top 2.929037 46 2.837037
4 1 Lef 2.035900 47 1.941900
4 1 Cen 1.786147 48 1.690147
4 1 Rgt 1.980323 49 1.882323
4 1 Bot 2.162919 50 2.062919
4 2 Top 2.855798 51 2.753798
4 2 Lef 2.104193 52 2.000193
4 2 Cen 1.919507 53 1.813507
4 2 Rgt 2.019415 54 1.911415
4 2 Bot 2.228705 55 2.118705
4 3 Top 3.219292 56 3.107292
4 3 Lef 2.900430 57 2.786430
4 3 Cen 2.171262 58 2.055262
4 3 Rgt 3.041250 59 2.923250
4 3 Bot 3.188804 60 3.068804
5 1 Top 3.051234 61 2.929234
5 1 Lef 2.506230 62 2.382230
5 1 Cen 1.950486 63 1.824486
5 1 Rgt 2.467719 64 2.339719
5 1 Bot 2.581881 65 2.451881
5 2 Top 3.857221 66 3.725221
5 2 Lef 3.347343 67 3.213343
5 2 Cen 2.533870 68 2.397870
5 2 Rgt 3.190375 69 3.052375
5 2 Bot 3.362746 70 3.222746
5 3 Top 3.690306 71 3.548306
5 3 Lef 3.401584 72 3.257584
5 3 Cen 2.963117 73 2.817117
5 3 Rgt 2.945828 74 2.797828
5 3 Bot 3.466115 75 3.316115
6 1 Top 2.938241 76 2.786241
6 1 Lef 2.526568 77 2.372568
6 1 Cen 1.941370 78 1.785370
6 1 Rgt 2.765849 79 2.607849
6 1 Bot 2.382781 80 2.222781
6 2 Top 3.219665 81 3.057665
6 2 Lef 2.296011 82 2.132011
6 2 Cen 2.256196 83 2.090196
6 2 Rgt 2.645933 84 2.477933
6 2 Bot 2.422187 85 2.252187
6 3 Top 3.180348 86 3.008348
6 3 Lef 2.849264 87 2.675264
6 3 Cen 1.601288 88 1.425288
6 3 Rgt 2.810051 89 2.632051
6 3 Bot 2.902980 90 2.722980
7 1 Top 2.169679 91 1.987679
7 1 Lef 2.026506 92 1.842506
7 1 Cen 1.671804 93 1.485804
7 1 Rgt 1.660760 94 1.472760
7 1 Bot 2.314734 95 2.124734
7 2 Top 2.912838 96 2.720838
7 2 Lef 2.323665 97 2.129665
7 2 Cen 1.854223 98 1.658223
7 2 Rgt 2.391240 99 2.19324
7 2 Bot 2.196071 100 1.996071
7 3 Top 3.318517 101 3.116517
7 3 Lef 2.702735 102 2.498735
7 3 Cen 1.959008 103 1.753008
7 3 Rgt 2.512517 104 2.304517
7 3 Bot 2.827469 105 2.617469
8 1 Top 1.958022 106 1.746022
8 1 Lef 1.360106 107 1.146106
8 1 Cen 0.971193 108 0.755193
8 1 Rgt 1.947857 109 1.729857
8 1 Bot 1.643580 110 1.42358
8 2 Top 2.357633 111 2.135633
8 2 Lef 1.757725 112 1.533725
8 2 Cen 1.165886 113 0.939886
8 2 Rgt 2.231143 114 2.003143
8 2 Bot 1.311626 115 1.081626
8 3 Top 2.421686 116 2.189686
8 3 Lef 1.993855 117 1.759855
8 3 Cen 1.402543 118 1.166543
8 3 Rgt 2.008543 119 1.770543
8 3 Bot 2.139370 120 1.899370
9 1 Top 2.190676 121 1.948676
9 1 Lef 2.287483 122 2.043483
9 1 Cen 1.698943 123 1.452943
9 1 Rgt 1.925731 124 1.677731
9 1 Bot 2.057440 125 1.807440
9 2 Top 2.353597 126 2.101597
9 2 Lef 1.796236 127 1.542236
9 2 Cen 1.241040 128 0.985040
9 2 Rgt 1.677429 129 1.419429
9 2 Bot 1.845041 130 1.585041
9 3 Top 2.012669 131 1.750669
9 3 Lef 1.523769 132 1.259769
9 3 Cen 0.790789 133 0.524789
9 3 Rgt 2.001942 134 1.733942
9 3 Bot 1.350051 135 1.080051
10 1 Top 2.825749 136 2.553749
10 1 Lef 2.502445 137 2.228445
10 1 Cen 1.938239 138 1.662239
10 1 Rgt 2.349497 139 2.071497
10 1 Bot 2.310817 140 2.030817
10 2 Top 3.074576 141 2.792576
10 2 Lef 2.057821 142 1.773821
10 2 Cen 1.793617 143 1.507617
10 2 Rgt 1.862251 144 1.574251
10 2 Bot 1.956753 145 1.666753
10 3 Top 3.072840 146 2.780840
10 3 Lef 2.291035 147 1.997035
10 3 Cen 1.873878 148 1.577878
10 3 Rgt 2.475640 149 2.177640
10 3 Bot 2.021472 150 1.721472
11 1 Top 3.228835 151 2.926835
11 1 Lef 2.719495 152 2.415495
11 1 Cen 2.207198 153 1.901198
11 1 Rgt 2.391608 154 2.083608
11 1 Bot 2.525587 155 2.215587
11 2 Top 2.891103 156 2.579103
11 2 Lef 2.738007 157 2.424007
11 2 Cen 1.668337 158 1.352337
11 2 Rgt 2.496426 159 2.178426
11 2 Bot 2.417926 160 2.097926
11 3 Top 3.541799 161 3.219799
11 3 Lef 3.058768 162 2.734768
11 3 Cen 2.187061 163 1.861061
11 3 Rgt 2.790261 164 2.462261
11 3 Bot 3.279238 165 2.949238
12 1 Top 2.347662 166 2.015662
12 1 Lef 1.383336 167 1.049336
12 1 Cen 1.187168 168 0.851168
12 1 Rgt 1.693292 169 1.355292
12 1 Bot 1.664072 170 1.324072
12 2 Top 2.385320 171 2.043320
12 2 Lef 1.607784 172 1.263784
12 2 Cen 1.230307 173 0.884307
12 2 Rgt 1.945423 174 1.597423
12 2 Bot 1.907580 175 1.557580
12 3 Top 2.691576 176 2.339576
12 3 Lef 1.938755 177 1.584755
12 3 Cen 1.275409 178 0.919409
12 3 Rgt 1.777315 179 1.419315
12 3 Bot 2.146161 180 1.786161
13 1 Top 3.218655 181 2.856655
13 1 Lef 2.912180 182 2.548180
13 1 Cen 2.336436 183 1.970436
13 1 Rgt 2.956036 184 2.588036
13 1 Bot 2.423235 185 2.053235
13 2 Top 3.302224 186 2.930224
13 2 Lef 2.808816 187 2.434816
13 2 Cen 2.340386 188 1.964386
13 2 Rgt 2.795120 189 2.417120
13 2 Bot 2.865800 190 2.485800
13 3 Top 2.992217 191 2.610217
13 3 Lef 2.952106 192 2.568106
13 3 Cen 2.149299 193 1.763299
13 3 Rgt 2.448046 194 2.060046
13 3 Bot 2.507733 195 2.117733
14 1 Top 3.530112 196 3.138112
14 1 Lef 2.940489 197 2.546489
14 1 Cen 2.598357 198 2.202357
14 1 Rgt 2.905165 199 2.507165
14 1 Bot 2.692078 200 2.292078
14 2 Top 3.764270 201 3.362270
14 2 Lef 3.465960 202 3.061960
14 2 Cen 2.458628 203 2.052628
14 2 Rgt 3.141132 204 2.733132
14 2 Bot 2.816526 205 2.406526
14 3 Top 3.217614 206 2.805614
14 3 Lef 2.758171 207 2.344171
14 3 Cen 2.345921 208 1.929921
14 3 Rgt 2.773653 209 2.355653
14 3 Bot 3.109704 210 2.689704
15 1 Top 2.177593 211 1.755593
15 1 Lef 1.511781 212 1.087781
15 1 Cen 0.746546 213 0.320546
15 1 Rgt 1.491730 214 1.063730
15 1 Bot 1.268580 215 0.838580
15 2 Top 2.433994 216 2.001994
15 2 Lef 2.045667 217 1.611667
15 2 Cen 1.612699 218 1.176699
15 2 Rgt 2.082860 219 1.644860
15 2 Bot 1.887341 220 1.447341
15 3 Top 1.923003 221 1.481003
15 3 Lef 2.124461 222 1.680461
15 3 Cen 1.945048 223 1.499048
15 3 Rgt 2.210698 224 1.762698
15 3 Bot 1.985225 225 1.535225
16 1 Top 3.131536 226 2.679536
16 1 Lef 2.405975 227 1.951975
16 1 Cen 2.206320 228 1.750320
16 1 Rgt 3.012211 229 2.554211
16 1 Bot 2.628723 230 2.168723
16 2 Top 2.802486 231 2.340486
16 2 Lef 2.185010 232 1.721010
16 2 Cen 2.161802 233 1.695802
16 2 Rgt 2.102560 234 1.634560
16 2 Bot 1.961968 235 1.491968
16 3 Top 3.330183 236 2.858183
16 3 Lef 2.464046 237 1.990046
16 3 Cen 1.687408 238 1.211408
16 3 Rgt 2.043322 239 1.565322
16 3 Bot 2.570657 240 2.090657
17 1 Top 3.352633 241 2.870633
17 1 Lef 2.691645 242 2.207645
17 1 Cen 1.942410 243 1.456410
17 1 Rgt 2.366055 244 1.878055
17 1 Bot 2.500987 245 2.010987
17 2 Top 2.886284 246 2.394284
17 2 Lef 2.292503 247 1.798503
17 2 Cen 1.627562 248 1.131562
17 2 Rgt 2.415076 249 1.917076
17 2 Bot 2.086134 250 1.586134
17 3 Top 2.554848 251 2.052848
17 3 Lef 1.755843 252 1.251843
17 3 Cen 1.510124 253 1.004124
17 3 Rgt 2.257347 254 1.749347
17 3 Bot 1.958592 255 1.448592
18 1 Top 2.622733 256 2.110733
18 1 Lef 2.321079 257 1.807079
18 1 Cen 1.169269 258 0.653269
18 1 Rgt 1.921457 259 1.403457
18 1 Bot 2.176377 260 1.656377
18 2 Top 3.313367 261 2.791367
18 2 Lef 2.559725 262 2.035725
18 2 Cen 2.404662 263 1.878662
18 2 Rgt 2.405249 264 1.877249
18 2 Bot 2.535618 265 2.005618
18 3 Top 3.067851 266 2.535851
18 3 Lef 2.490359 267 1.956359
18 3 Cen 2.079477 268 1.543477
18 3 Rgt 2.669512 269 2.131512
18 3 Bot 2.105103 270 1.565103
19 1 Top 4.293889 271 3.751889
19 1 Lef 3.888826 272 3.344826
19 1 Cen 2.960655 273 2.414655
19 1 Rgt 3.618864 274 3.070864
19 1 Bot 3.562480 275 3.012480
19 2 Top 3.451872 276 2.899872
19 2 Lef 3.285934 277 2.731934
19 2 Cen 2.638294 278 2.082294
19 2 Rgt 2.918810 279 2.360810
19 2 Bot 3.076231 280 2.516231
19 3 Top 3.879683 281 3.317683
19 3 Lef 3.342026 282 2.778026
19 3 Cen 3.382833 283 2.816833
19 3 Rgt 3.491666 284 2.923666
19 3 Bot 3.617621 285 3.047621
20 1 Top 2.329987 286 1.757987
20 1 Lef 2.400277 287 1.826277
20 1 Cen 2.033941 288 1.457941
20 1 Rgt 2.544367 289 1.966367
20 1 Bot 2.493079 290 1.913079
20 2 Top 2.862084 291 2.280084
20 2 Lef 2.404703 292 1.820703
20 2 Cen 1.648662 293 1.062662
20 2 Rgt 2.115465 294 1.527465
20 2 Bot 2.633930 295 2.043930
20 3 Top 3.305211 296 2.713211
20 3 Lef 2.194991 297 1.600991
20 3 Cen 1.620963 298 1.024963
20 3 Rgt 2.322678 299 1.724678
20 3 Bot 2.818449 300 2.218449
21 1 Top 2.712915 301 2.110915
21 1 Lef 2.389121 302 1.785121
21 1 Cen 1.575833 303 0.969833
21 1 Rgt 1.870484 304 1.262484
21 1 Bot 2.203262 305 1.593262
21 2 Top 2.607972 306 1.995972
21 2 Lef 2.177747 307 1.563747
21 2 Cen 1.246016 308 0.630016
21 2 Rgt 1.663096 309 1.045096
21 2 Bot 1.843187 310 1.223187
21 3 Top 2.277813 311 1.655813
21 3 Lef 1.764940 312 1.140940
21 3 Cen 1.358137 313 0.732137
21 3 Rgt 2.065713 314 1.437713
21 3 Bot 1.885897 315 1.255897
22 1 Top 3.126184 316 2.494184
22 1 Lef 2.843505 317 2.209505
22 1 Cen 2.041466 318 1.405466
22 1 Rgt 2.816967 319 2.178967
22 1 Bot 2.635127 320 1.995127
22 2 Top 3.049442 321 2.407442
22 2 Lef 2.446904 322 1.802904
22 2 Cen 1.793442 323 1.147442
22 2 Rgt 2.676519 324 2.028519
22 2 Bot 2.187865 325 1.537865
22 3 Top 2.758416 326 2.106416
22 3 Lef 2.405744 327 1.751744
22 3 Cen 1.580387 328 0.924387
22 3 Rgt 2.508542 329 1.850542
22 3 Bot 2.574564 330 1.914564
23 1 Top 3.294288 331 2.632288
23 1 Lef 2.641762 332 1.977762
23 1 Cen 2.105774 333 1.439774
23 1 Rgt 2.655097 334 1.987097
23 1 Bot 2.622482 335 1.952482
23 2 Top 4.066631 336 3.394631
23 2 Lef 3.389733 337 2.715733
23 2 Cen 2.993666 338 2.317666
23 2 Rgt 3.613128 339 2.935128
23 2 Bot 3.213809 340 2.533809
23 3 Top 3.369665 341 2.687665
23 3 Lef 2.566891 342 1.882891
23 3 Cen 2.289899 343 1.603899
23 3 Rgt 2.517418 344 1.829418
23 3 Bot 2.862723 345 2.172723
24 1 Top 4.212664 346 3.520664
24 1 Lef 3.068342 347 2.374342
24 1 Cen 2.872188 348 2.176188
24 1 Rgt 3.040890 349 2.342890
24 1 Bot 3.376318 350 2.676318
24 2 Top 3.223384 351 2.521384
24 2 Lef 2.552726 352 1.848726
24 2 Cen 2.447344 353 1.741344
24 2 Rgt 3.011574 354 2.303574
24 2 Bot 2.711774 355 2.001774
24 3 Top 3.359505 356 2.647505
24 3 Lef 2.800742 357 2.086742
24 3 Cen 2.043396 358 1.327396
24 3 Rgt 2.929792 359 2.211792
24 3 Bot 2.935356 360 2.215356
25 1 Top 2.724871 361 2.002871
25 1 Lef 2.239013 362 1.515013
25 1 Cen 2.341512 363 1.615512
25 1 Rgt 2.263617 364 1.535617
25 1 Bot 2.062748 365 1.332748
25 2 Top 3.658082 366 2.926082
25 2 Lef 3.093268 367 2.359268
25 2 Cen 2.429341 368 1.693341
25 2 Rgt 2.538365 369 1.800365
25 2 Bot 3.161795 370 2.421795
25 3 Top 3.178246 371 2.436246
25 3 Lef 2.498102 372 1.754102
25 3 Cen 2.445810 373 1.699810
25 3 Rgt 2.231248 374 1.483248
25 3 Bot 2.302298 375 1.552298
26 1 Top 3.320688 376 2.568688
26 1 Lef 2.861800 377 2.107800
26 1 Cen 2.238258 378 1.482258
26 1 Rgt 3.122050 379 2.364050
26 1 Bot 3.160876 380 2.400876
26 2 Top 3.873888 381 3.111888
26 2 Lef 3.166345 382 2.402345
26 2 Cen 2.645267 383 1.879267
26 2 Rgt 3.309867 384 2.541867
26 2 Bot 3.542882 385 2.772882
26 3 Top 2.586453 386 1.814453
26 3 Lef 2.120604 387 1.346604
26 3 Cen 2.180847 388 1.404847
26 3 Rgt 2.480888 389 1.702888
26 3 Bot 1.938037 390 1.158037
27 1 Top 4.710718 391 3.928718
27 1 Lef 4.082083 392 3.298083
27 1 Cen 3.533026 393 2.747026
27 1 Rgt 4.269929 394 3.481929
27 1 Bot 4.038166 395 3.248166
27 2 Top 4.237233 396 3.445233
27 2 Lef 4.171702 397 3.377702
27 2 Cen 3.04394 398 2.247940
27 2 Rgt 3.91296 399 3.114960
27 2 Bot 3.714229 400 2.914229
27 3 Top 5.168668 401 4.366668
27 3 Lef 4.823275 402 4.019275
27 3 Cen 3.764272 403 2.958272
27 3 Rgt 4.396897 404 3.588897
27 3 Bot 4.442094 405 3.632094
28 1 Top 3.972279 406 3.160279
28 1 Lef 3.883295 407 3.069295
28 1 Cen 3.045145 408 2.229145
28 1 Rgt 3.51459 409 2.696590
28 1 Bot 3.575446 410 2.755446
28 2 Top 3.024903 411 2.202903
28 2 Lef 3.099192 412 2.275192
28 2 Cen 2.048139 413 1.222139
28 2 Rgt 2.927978 414 2.099978
28 2 Bot 3.15257 415 2.322570
28 3 Top 3.55806 416 2.726060
28 3 Lef 3.176292 417 2.342292
28 3 Cen 2.852873 418 2.016873
28 3 Rgt 3.026064 419 2.188064
28 3 Bot 3.071975 420 2.231975
29 1 Top 3.496634 421 2.654634
29 1 Lef 3.087091 422 2.243091
29 1 Cen 2.517673 423 1.671673
29 1 Rgt 2.547344 424 1.699344
29 1 Bot 2.971948 425 2.121948
29 2 Top 3.371306 426 2.519306
29 2 Lef 2.175046 427 1.321046
29 2 Cen 1.940111 428 1.084111
29 2 Rgt 2.932408 429 2.074408
29 2 Bot 2.428069 430 1.568069
29 3 Top 2.941041 431 2.079041
29 3 Lef 2.294009 432 1.430009
29 3 Cen 2.025674 433 1.159674
29 3 Rgt 2.21154 434 1.343540
29 3 Bot 2.459684 435 1.589684
30 1 Top 2.86467 436 1.992670
30 1 Lef 2.695163 437 1.821163
30 1 Cen 2.229518 438 1.353518
30 1 Rgt 1.940917 439 1.062917
30 1 Bot 2.547318 440 1.667318
30 2 Top 3.537562 441 2.655562
30 2 Lef 3.311361 442 2.427361
30 2 Cen 2.767771 443 1.881771
30 2 Rgt 3.388622 444 2.500622
30 2 Bot 3.542701 445 2.652701
30 3 Top 3.184652 446 2.292652
30 3 Lef 2.620947 447 1.726947
30 3 Cen 2.697619 448 1.801619
30 3 Rgt 2.860684 449 1.962684
30 3 Bot 2.758571 450 1.858571
|
||
