Consider the plasma etch experiment described in Problem 6-18. Suppose that only a one-half fraction of the design could be run. Set up the design and analyze the data.

Problem 6-18. 

An article in Solid State Technology ("Orthogonal Design for Process Optimization and Its Application in Plasma Etching," May 1987, pp. 127-132) describes the application of factorial designs in developing a nitride etch process on a single-wafer plasma etcher. The process uses C₂F₆ as the reactant gas. Four factors are of interest: anode—cathode gap (A), pressure in the reactor chamber (B), C₂F₆ gas flow (C), and power applied to the cathode (D). The response variable of interest is the etch rate for silicon nitride. A single replicate of a 2⁴ design is run, and the data are shown below:

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Actual Etch Factor Levels Run Run Order Rate Number A B C D (Å/min) Low (-) High (+) 1 13 550 A (cm) 0.80 1.20 2 8 669 B (mTorr) 450 550 - 3 12 604 C (SCCM) 125 200 4 650 D (W) 275 325 5 4 633 15 642 7 16 601 3 635 9. 1 1037 10 14 749 11 5 1052 12 10 868 13 11 1075 14 2 860 15 7 1063 16 6 + + + 729 + + +