Shumate and Montgomery (1996) developed a TiW plasma etch process for semiconductor manufacturing by studying a mixture of three gases x1: SR6, x2: He, and x3: N2. The partial pressures of the three gases were forced to add to a constant value of total pressure to form the mixture constraint.

The constraints in micrometers of pressure were 100 B SF6 B 160 100 B He B 160 SF6 + He + N2 = 650 Expressing the components as mixture proportions, these constraints are 0:153846 B x1 B 0:246154 0:153846 B x2 B 0:246154 The authors created a design composed of the extreme vertices of the con-
strained region plus the overall centroid. Six responses were measured for each mixture and the table below shows the responses and their specica-
tions.

(a) Create the design below using functions in the mixexp package and enter data for the six responses that are shown in Table 11.11.

(b) Fit the Schee special cubic model for each response, check the adequacy of the ts, and reduce the model to the quadratic for responses where the ternary mixture coecient is not signicant.

(c) Make contour plots of the tted surface for each response.

(d) By examining your contour plots, nd a region in the constrained space where the tted models predict that all response specications can be met.

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Response Name Specification Delta critical dimension (CD) positive PR <0.25 m Y1 Y2 Positive PR etch uniformity Y3 Delta CD negative PR Y4 Negative PR etch uniformity Y5 Y6 Selectivity (TiW: positive PR.) Selectivity (TiW: negative PR) <2.5% <0.25 m <2.5% > 0.85 > 0.85