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3. Production Process Characterization
3.5. Case Studies
3.5.1. Furnace Case Study

3.5.1.1.

Background and Data

Introduction In a semiconductor manufacturing process flow, we have a step whereby we grow an oxide film on the silicon wafer using a furnace. In this step, a cassette of wafers is placed in a quartz "boat" and the boats are placed in the furnace. The furnace can hold four boats. A gas flow is created in the furnace and it is brought up to temperature and held there for a specified period of time (which corresponds to the desired oxide thickness). This study was conducted to determine if the process was stable and to characterize sources of variation so that a process control strategy could be developed.
Goal The goal of this study is to determine if this process is capable of consistently growing oxide films with a thickness of 560 Angstroms +/- 100 Angstroms. An additional goal is to determine important sources of variation for use in the development of a process control strategy.
Software The analyses used in this case study can be generated using both Dataplot code and R code.
Process Model In the picture below we are modeling this process with one output (film thickness) that is influenced by four controlled factors (gas flow, pressure, temperature and time) and two uncontrolled factors (run and zone). The four controlled factors are part of our recipe and will remain constant throughout this study. We know that there is run-to-run variation that is due to many different factors (input material variation, variation in consumables, etc.). We also know that the different zones in the furnace have an effect. A zone is a region of the furnace tube that holds one boat. There are four zones in these tubes. The zones in the middle of the tube grow oxide a little bit differently from the ones on the ends. In fact, there are temperature offsets in the recipe to help minimize this problem.
diagram of process model
Sensitivity Model The sensitivity model for this process is fairly straightforward and is given in the figure below. The effects of the machine are mostly related to the preventative maintenance (PM) cycle. We want to make sure the quartz tube has been cleaned recently, the mass flow controllers are in good shape and the temperature controller has been calibrated recently. The same is true of the measurement equipment where the thickness readings will be taken. We want to make sure a gauge study has been performed. For material, the incoming wafers will certainly have an effect on the outgoing thickness as well as the quality of the gases used. Finally, the recipe will have an effect including gas flow, temperature offset for the different zones, and temperature profile (how quickly we raise the temperature, how long we hold it and how quickly we cool it off).
diagram of sensitivity model
Sampling Plan Given our goal statement and process modeling, we can now define a sampling plan. The primary goal is to determine if the process is capable. This just means that we need to monitor the process over some period of time and compare the estimates of process location and spread to the specifications. An additional goal is to identify sources of variation to aid in setting up a process control strategy. Some obvious sources of variation are incoming wafers, run-to-run variability, variation due to operators or shift, and variation due to zones within a furnace tube. One additional constraint that we must work under is that this study should not have a significant impact on normal production operations.

Given these constraints, the following sampling plan was selected. It was decided to monitor the process for one day (three shifts). Because this process is operator independent, we will not keep shift or operator information but just record run number. For each run, we will randomly assign cassettes of wafers to a zone. We will select two wafers from each zone after processing and measure two sites on each wafer. This plan should give reasonable estimates of run-to-run variation and within zone variability as well as good overall estimates of process location and spread.

We are expecting readings around 560 Angstroms. We would not expect many readings above 700 or below 400. The measurement equipment is accurate to within 0.5 Angstroms which is well within the accuracy needed for this study.

Data The following are the data that were collected for this study.
RUN   ZONE    WAFER    THICKNESS
--------------------------------
 1       1       1       546
 1       1       2       540
 1       2       1       566
 1       2       2       564
 1       3       1       577
 1       3       2       546
 1       4       1       543
 1       4       2       529
 2       1       1       561
 2       1       2       556
 2       2       1       577
 2       2       2       553
 2       3       1       563
 2       3       2       577
 2       4       1       556
 2       4       2       540
 3       1       1       515
 3       1       2       520
 3       2       1       548
 3       2       2       542
 3       3       1       505
 3       3       2       487
 3       4       1       506
 3       4       2       514
 4       1       1       568
 4       1       2       584
 4       2       1       570
 4       2       2       545
 4       3       1       589
 4       3       2       562
 4       4       1       569
 4       4       2       571
 5       1       1       550
 5       1       2       550
 5       2       1       562
 5       2       2       580
 5       3       1       560
 5       3       2       554
 5       4       1       545
 5       4       2       546
 6       1       1       584
 6       1       2       581
 6       2       1       567
 6       2       2       558
 6       3       1       556
 6       3       2       560
 6       4       1       591
 6       4       2       599
 7       1       1       593
 7       1       2       626
 7       2       1       584
 7       2       2       559
 7       3       1       634
 7       3       2       598
 7       4       1       569
 7       4       2       592
 8       1       1       522
 8       1       2       535
 8       2       1       535
 8       2       2       581
 8       3       1       527
 8       3       2       520
 8       4       1       532
 8       4       2       539
 9       1       1       562
 9       1       2       568
 9       2       1       548
 9       2       2       548
 9       3       1       533
 9       3       2       553
 9       4       1       533
 9       4       2       521
10       1       1       555
10       1       2       545
10       2       1       584
10       2       2       572
10       3       1       546
10       3       2       552
10       4       1       586
10       4       2       584
11       1       1       565
11       1       2       557
11       2       1       583
11       2       2       585
11       3       1       582
11       3       2       567
11       4       1       549
11       4       2       533
12       1       1       548
12       1       2       528
12       2       1       563
12       2       2       588
12       3       1       543
12       3       2       540
12       4       1       585
12       4       2       586
13       1       1       580
13       1       2       570
13       2       1       556
13       2       2       569
13       3       1       609
13       3       2       625
13       4       1       570
13       4       2       595
14       1       1       564
14       1       2       555
14       2       1       585
14       2       2       588
14       3       1       564
14       3       2       583
14       4       1       563
14       4       2       558
15       1       1       550
15       1       2       557
15       2       1       538
15       2       2       525
15       3       1       556
15       3       2       547
15       4       1       534
15       4       2       542
16       1       1       552
16       1       2       547
16       2       1       563
16       2       2       578
16       3       1       571
16       3       2       572
16       4       1       575
16       4       2       584
17       1       1       549
17       1       2       546
17       2       1       584
17       2       2       593
17       3       1       567
17       3       2       548
17       4       1       606
17       4       2       607
18       1       1       539
18       1       2       554
18       2       1       533
18       2       2       535
18       3       1       522
18       3       2       521
18       4       1       547
18       4       2       550
19       1       1       610
19       1       2       592
19       2       1       587
19       2       2       587
19       3       1       572
19       3       2       612
19       4       1       566
19       4       2       563
20       1       1       569
20       1       2       609
20       2       1       558
20       2       2       555
20       3       1       577
20       3       2       579
20       4       1       552
20       4       2       558
21       1       1       595
21       1       2       583
21       2       1       599
21       2       2       602
21       3       1       598
21       3       2       616
21       4       1       580
21       4       2       575
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