538 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORSEXAMPLE 14-5 An article in Solid State Technology(“Orthogonal Design for Process Optimization and Its
Application in Plasma Etching,” May 1987, pp. 127–132) describes the application of facto-
rial designs in developing a nitride etch process on a single-wafer plasma etcher. The process
uses C 2 F 6 as the reactant gas. It is possible to vary the gas flow, the power applied to the cath-
ode, the pressure in the reactor chamber, and the spacing between the anode and the cathode
(gap). Several response variables would usually be of interest in this process, but in this
example we will concentrate on etch rate for silicon nitride.
We will use a single replicate of a 2^4 design to investigate this process. Since it is unlikely
that the three- and four-factor interactions are significant, we will tentatively plan to combine
them as an estimate of error. The factor levels used in the design are shown below:Table 14-19 presents the data from the 16 runs of the 2^4 design. Table 14-20 is the table of plus
and minus signs for the 2^4 design. The signs in the columns of this table can be used to esti-
mate the factor effects. For example, the estimate of factor Ais101.625 550 604 633 601 1037 1052 1075 106341
83669 650 642 635 749 868 860 729cbcdbdcdbcd 4A1
83 aabacabcadabdacdabcd 112 bDesign Factor
Gap Pressure C 2 F 6 Flow Power
Level (cm) (mTorr) (SCCM) (w)
Low () 0.80 450 125 275
High () 1.20 550 200 325Table 14-19 The 2^4 Design for the Plasma Etch Experiment
AB C DEtch Rate
(Gap) (Pressure) (C 2 F 6 Flow) (Power) (Å/min)
1 1 1 1 550
1 1 1 1 669
11 1 1 604
11 1 1 650
1 11 1 633
1 11 1 642
11 1 1 601
11 1 1 635
1 1 1 1 1037
1 1 1 1 749
11 1 1 1052
11 1 1 868
1 1 1 1 1075
1 1 1 1 860
1 1 1 1 1063
1 1 1 1 729c 14 .qxd 5/9/02 7:54 PM Page 538 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH112 FIN L: