1. A spin coater is used to apply photoresist to a bare silicon wafer. This operation usually occurs early in the semiconductor manufacturing process, and the average coating thickness and the variability in the coating thickness have an important impact on the downstream manufacturing steps. Six variables are used in the experiment. The variables and the high and low levels are as follows:

Factor	Low Level	High Level
Final spin speed	7350 rpm	6650 rpm
Acceleration rate	5	20
Volume of resist applied	3cc	5cc
Time of spin	14 sec	6 sec
Resist batch variation	Batch 1	Batch 2
Exhaust pressure	Cover off	Cover on

The experimenter decides to use a 2^6-1 design and to make three readings on resist thickness on each test wafer. The experimenter uses the default defining relation .

1. Verify that the default relation is indeed used in the fractional factorial design and discuss the alias relationship in this design and list all aliasing terms.
2. What factors appear to affect average resist thickness?
3. Project this design into a smaller design involving only the significant factors. Graphically display the results.

Table 1: Data for problem 2.

	Volume	Batch	Time	Speed	Acc	Cover	Thick Avg
1	3	Batch 2	14	6650	5	Off	7036.05
2	3	Batch 2	14	7350	20	Off	6475.95
3	3	Batch 2	14	7350	5	On	6802.5
4	3	Batch 1	14	6650	5	On	6984
5	5	Batch 2	14	7350	20	On	6393
6	5	Batch 1	6	6650	20	Off	6728.55
7	3	Batch 2	6	6650	20	Off	6782.55
8	5	Batch 2	14	7350	5	Off	6788.55
9	5	Batch 1	14	7350	5	On	6574.05
10	5	Batch 2	6	7350	20	Off	6450.45
11	3	Batch 1	6	7350	5	On	6739.95
12	3	Batch 1	6	7350	20	Off	6335.55
13	5	Batch 1	14	6650	20	On	6676.5
14	3	Batch 2	6	7350	20	On	6330.45
15	3	Batch 2	6	7350	5	Off	6795.45
16	3	Batch 2	14	6650	20	On	6718.05
17	3	Batch 1	14	7350	20	On	6298.05
18	3	Batch 1	6	6650	20	On	6700.5
19	3	Batch 1	14	6650	20	Off	6746.55
20	5	Batch 2	14	6650	20	Off	6813.45
21	5	Batch 1	14	6650	5	Off	6938.55
22	5	Batch 1	14	7350	20	Off	6352.5
23	5	Batch 1	6	7350	20	On	6295.05
24	3	Batch 2	6	6650	5	On	6997.05
25	5	Batch 2	6	7350	5	On	6773.55
26	5	Batch 2	14	6650	5	On	7001.55
27	5	Batch 1	6	6650	5	On	6940.05
28	3	Batch 1	6	6650	5	Off	6697.05
29	5	Batch 2	6	6650	20	On	6712.05
30	5	Batch 2	6	6650	5	Off	7016.55
31	5	Batch 1	6	7350	5	Off	6669
32	3	Batch 1	14	7350	5	Off	6445.5