6.
Process or Product Monitoring and Control
6.6. Case Studies in Process Monitoring 6.6.1. Lithography Process
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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. |
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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 |