Applied Statistics and Probability for Engineers

14-7 2kFACTORIAL DESIGNS 527

The numerical estimates of the effects indicate that the effect of deposition time is large and

has a positive direction (increasing deposition time increases thickness), since changing dep-

osition time from low to high changes the mean epitaxial layer thickness by 0.836 m. The

effects of arsenic flow rate (B) and the ABinteraction appear small.

The importance of these effects may be confirmed with the analysis of variance. The

sums of squares for A, B, and ABare computed as follows:

3.0672

The analysis of variance is summarized in Table 14-14 and confirms our conclusions obtained

by examining the magnitude and direction of the effects. Deposition time is the only factor

that significantly affects epitaxial layer thickness, and from the direction of the effect esti-

mates we know that longer deposition times lead to thicker epitaxial layers.

Residual Analysis

It is easy to obtain the residuals from a 2kdesign by fitting a regression modelto the data. For

the epitaxial process experiment, the regression model is

Y 0  1 x 1     

SST14.037^2 p14.932^2 

1 56.081p59.156 22

16

SSAB

3 ab 112 ab 42

16



3 0.252 42

16

0.0040

SSB

3 baba 11242

16



3 0.538 42

16

0.0181

SSA

3 aabb 11242

16



3 6.688 42

16

2.7956

Table 14-13 The 2^2 Design for the Epitaxial Process Experiment

Treatment Design Factors Thickness (m)

Combination AB AB Thickness (m) Total Average

112 14.037 14.165 13.972 13.907 56.081 14.020

a 14.821 14.757 14.843 14.878 59.299 14.825

b 13.880 13.860 14.032 13.914 55.686 13.922

ab 14.888 14.921 14.415 14.932 59.156 14.789

Table 14-14 Analysis of Variance for the Epitaxial Process Experiment

Source of Degrees of

Variation Sum of Squares Freedom Mean Square f 0 P-Value

A(deposition time) 2.7956 1 2.7956 134.40 7.07 E-8

B(arsenic flow) 0.0181 1 0.0181 0.87 0.38

AB 0.0040 1 0.0040 0.19 0.67

Error 0.2495 12 0.0208

Total 3.0672 15

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