3. Line yield and defect density are very important variables in the semiconductor industry as they are directly correlated with production cost and quality. A small pilot study considered the effect of three factors, “PMOS transistor threshold voltage,” “polysilicon sheet resistance,”

and “N-sheet contact chain resistance,” on the defect density in batches of wafers (determined by synchrotron X-ray topographs and etch pit micrographs). The design considered two levels for each factor with one replication.

Using the system of coding the factor-level combinations explained in Example 11.3-1, the data are

(a) Which are the observations denoted by x221, x112, and x122?

(b) Construct a table of signs similar to Table 11-2.

(c) Use the table of signs constructed in part

(b) to estimate the main effects and interactions.

(d) Compute the sum of squares for each effect.

(e) Assuming all interactions are zero, test for the significance of the main effects at level 0.05.

(f) Enter the estimates of the seven main and interaction effects in the R object eff and use an R command to produce a probability plot of the effects. Comment on the assumption that the three interaction effects are zero.

Treatment Code 1 a b ab ac bc abc 11 10 8 16 12 15 18 19