An article in Solid State Technology 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 interests: 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: factor A B C D etch rate – – – – 550 + – – – 669 – + – – 604 + + – – 650 – – + – 633 + – + – 642 – + + – 601 + + + – 635 – – – + 1037 + – – + 749 – + – + 1052 + + – + 868 – – + + 1075 + – + + 860 – + + + 1063 + + + + 729
(a) Estimate the factorial effects. Use QQ plot to identify potentially significant effects.
(b) Conduct an analysis of variance to confirm your findings in (a).
(c) What is the regression model relating etch rate to the significant process variables?
d) Analyze the residuals from this experiment. Comment on the model adequacy.
(e) If not all factors are important,project the 24 design into a 2k design with k < 4 and conduct the analysis of variance.
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