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One of the initial steps in fabricating integrated circuit (IC) devices is to grow an epitaxial layer on polished silicon wafers. The wafers are mounted on a six-faceted cylinder (two wafers per facet), called a susceptor, which is spun inside a metal bell jar. The jar is injected with chemical vapors through nozzles at the top of the jar and heated. The process continues until the epitaxial layer grows to a desired thickness




A tibble with 16 observations, 4 factors (A,B,C,D), and three responses (ybar,s2,lns2)

Factor A

Susceptor-rotation method. Low level is oscillating and high level is continuous

Factor B

Nozzle position. Low level is 2 and high level is 6

Factor C

Deposition temperature (Celsius). Low level is 1210 and high level is 1220

Factor D

Deposition time. Low level is low and high level is high


average thickness


variance of thickness


log variance of thickness


Wu, CF Jeff, and Michael S. Hamada. Experiments: planning, analysis, and optimization. John Wiley & Sons, 2011


In the epitaxial layer growth process, suppose that the four experimental factors, susceptor rotation method, nozzle position, deposition temperature, and deposition time (labeled A, B, Cand D) are to be investigated at the two levels each.

The purpose of this experiment is to find process conditions, that is, combinations of factor levels for A, B, C, and D, under which the average thickness is close to the target 14.5 micrometre with variation as small as possible. The most basic experimental design or plan is the full factorial design, which studies all possible combinations of factors at two levels.