pg_0200
5.
Process Improvement
5.4.
Analysis of DOE data
5.4.7.
Examples of DOE's
5.4.7.3.
Response surface model example
Data Source
A
CCD
DOE
with two
responses
This example uses experimental data published in
Czitrom and Spagon, (1997)
, Statistical Case
Studies for Industrial Process Improvement. This material is copyrighted by the American
Statistical Association and the Society for Industrial and Applied Mathematics, and used with
their permission. Specifically, Chapter 15, titled "Elimination of TiN Peeling During Exposure to
CVD Tungsten Deposition Process Using Designed Experiments", describes a semiconductor
wafer processing experiment (labeled Experiment 2).
Goal,
response
variables,
and factor
variables
The goal of this experiment was to fit response surface models to the two responses, deposition
layer Uniformity and deposition layer Stress, as a function of two particular controllable factors
of the chemical vapor deposition (CVD) reactor process. These factors were Pressure (measured
in torr) and the ratio of the gaseous reactants H
2
and WF
6
(called H
2
/WF
6
). The experiment also
included an important third (categorical) response - the presence or absence of titanium nitride
(TiN) peeling. That part of the experiment has been omitted in this example, in order to focus on
the response surface model aspects.
To summarize, the goal is to obtain a response surface model for each response where the
responses are: "Uniformity" and "Stress". The factors are: "Pressure" and "H
2
/WF
6
".
Experiment Description
The design is
a 13-run
CCI
design with 3
centerpoint
runs
The maximum and minimum values chosen for pressure were 4 torr and 80 torr. The lower and
upper H
2
/WF
6
ratios were chosen to be 2 and 10. Since response curvature, especially for
Uniformity, was a distinct possibility, an experimental design that allowed estimating a second
order (quadratic) model was needed. The experimenters decided to use a
central composite
inscribed (CCI)
design. For two factors, this design is typically recommended to have
13 runs
with 5 centerpoint runs.
However, the experimenters, perhaps to conserve a limited supply of
wafer resources, chose to include only 3 centerpoint runs. The design is still
rotatable
, but the
uniform precision
property has been sacrificed.
5.4.7.3. Response surface model example
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