Example 15.15: Design and Analysis of a Complete Factorial Experiment

Details of the FACTEX Procedure

Example 15.15: Design and Analysis of a Complete Factorial Experiment

See FACTEX16 in the SAS/QC Sample Library

Yin and Jillie (1987) describe an experiment on a nitride etch process for a single wafer plasma etcher. The experiment was run using four factors: cathode power (POWER), gas flow (FLOW), reactor chamber pressure (PRESSURE), and electrode gap (GAP). A single replicate of a 2⁴ design was run, and the etch rate (RATE) was measured.

You can use the following statements to construct a 16-run design in the four factors:

   proc factex;
      factors power flow pressure gap;
      output out=desgndat
             power    nvals=(0.80 1.20)
             flow     nvals=(4.50 550 )
             pressure nvals=(125  200 )
             gap      nvals=(275  325 );
   run;

The design with the actual (decoded) factor levels is saved in the data set DESGNDAT. The experiment using the 16-run design is performed, and the etch rate is measured. The following DATA step updates the data set DESGNDAT with the values of RATE:

   data desgndat;
      set desgndat;
      input rate @@;
      datalines;
      550   669  604   650  633   642  601   635
      1037  749  1052  868  1075  860  1063  729
      ;

The data set DESGNDAT is listed in Output 15.15.1.

Output 15.15.1: A 2⁴ Design with Responses

Nitride Etch Process Experiment

Obs	power	flow	pressure	gap	rate
1	0.8	4.5	125	275	550
2	0.8	4.5	125	325	669
3	0.8	4.5	200	275	604
4	0.8	4.5	200	325	650
5	0.8	550.0	125	275	633
6	0.8	550.0	125	325	642
7	0.8	550.0	200	275	601
8	0.8	550.0	200	325	635
9	1.2	4.5	125	275	1037
10	1.2	4.5	125	325	749
11	1.2	4.5	200	275	1052
12	1.2	4.5	200	325	868
13	1.2	550.0	125	275	1075
14	1.2	550.0	125	325	860
15	1.2	550.0	200	275	1063
16	1.2	550.0	200	325	729

To perform an analysis of variance on the responses, you can use the GLM procedure, as follows:

   proc glm data=desgndat;
      class power flow pressure gap;
      model rate=power|flow|pressure|gap@2 / ss1;
   run;

The factors are listed in both the CLASS and MODEL statements, and the response as a function of the factors is modeled using the MODEL statement. The MODEL statement requests Type I sum of squares (SS1) and lists all effects that contain two or fewer factors. It is assumed that three-factor and higher interactions are not significant.

Part of the output from the GLM procedure is shown in Output 15.15.2. The main effect of the factors POWER and GAP and the interaction between POWER and GAP are significant (their p-values are less than 0.01).

Output 15.15.2: Analysis of Variance for the Nitride Etch Process Experiment

The GLM Procedure

Dependent Variable: rate

Source	DF	Type I SS	Mean Square	F Value	Pr > F
power	1	374850.0625	374850.0625	183.99	<.0001
flow	1	217.5625	217.5625	0.11	0.7571
*powerflow**	1	18.0625	18.0625	0.01	0.9286
pressure	1	10.5625	10.5625	0.01	0.9454
*powerpressure**	1	1.5625	1.5625	0.00	0.9790
*flowpressure**	1	7700.0625	7700.0625	3.78	0.1095
gap	1	41310.5625	41310.5625	20.28	0.0064
*powergap**	1	94402.5625	94402.5625	46.34	0.0010
*flowgap**	1	2475.0625	2475.0625	1.21	0.3206
*pressuregap**	1	248.0625	248.0625	0.12	0.7414

Source	DF	Type III SS	Mean Square	F Value	Pr > F
power	1	374850.0625	374850.0625	183.99	<.0001
flow	1	217.5625	217.5625	0.11	0.7571
*powerflow**	1	18.0625	18.0625	0.01	0.9286
pressure	1	10.5625	10.5625	0.01	0.9454
*powerpressure**	1	1.5625	1.5625	0.00	0.9790
*flowpressure**	1	7700.0625	7700.0625	3.78	0.1095
gap	1	41310.5625	41310.5625	20.28	0.0064
*powergap**	1	94402.5625	94402.5625	46.34	0.0010
*flowgap**	1	2475.0625	2475.0625	1.21	0.3206
*pressuregap**	1	248.0625	248.0625	0.12	0.7414

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