Next Page Previous Page Home Tools & Aids Search Handbook
6. Process or Product Monitoring and Control
6.6. Case Studies in Process Monitoring
6.6.1. Lithography Process

6.6.1.1.

Background and Data

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.
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
Home Tools & Aids Search Handbook Previous Page Next Page