Response Surface Methodology RSM

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• Response Surface Methodology (RSM)
• Process optimization (maximize, minimize or hit a
  target)
• Resolution III (screening) designs w/ curvature
  check
• Path of steepest ascent/descent
• Resolution V designs with 2nd order axial runs

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Gap (cm) Power (W) A B Etch Rate 1.20 275 -1
-1 775 1.60 275 1 -1 670 1.20 325
-1 1 890 1.60 325 1 1 730 1.40 300 0
0 745 1.40 300 0 0 760 1.40 300 0
0 780 1.40 300 0 0 720
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Standard Parameter Estimate
Error t Value Pr gt t Intercept
766.2500000 12.64499242 60.60
lt.0001 a -66.2500000
12.64499242 -5.24 0.0135 b
43.7500000 12.64499242 3.46
0.0406 curvature -15.0000000
17.88271978 -0.84 0.4632
Gradient vector (path of steepest ascent)
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Path of steepest ascent
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Take steps along path of steepest ascent

Predicted m A B Gap Power
Etch Rate 1 -0.83446 0.55106 1.23 314
845 2 -1.66893 1.10212 1.07 328
925 3 -2.50339 1.65318 0.90 341
1004 4 -3.33786 2.20425 0.73 355
1084 5 -4.17232 2.75531 0.57 369
1163
Gap 1.40 (1.60 1.20)A/2 Power 300 (325
275)B/2
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Central Composite Design (CCD)

• Resolution V fractional factorial
• Center runs
• Axial runs

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A B 1 1 1 1 1 -1 1
1 0 0 0 0 0 0 0
0 -1.414 0 1.414 0 0 -1.414 0
1.414
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A B Y -1 -1 78.5 -1
1 76.7 1 -1 75.8 1 1
82.6 0 0 81.1 0 0
82.2 0 0 79.8 0 0 83.4
1.414 0 77.8 -1.414 0 79.3 0
1.414 79.0 0 -1.414 77.2
A Time (80, 90) B Temperature (170, 180)
Time 855A Temperature 1755B
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Quadratic model
proc rsreg datachemical model yield a b /
nocode run
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Stationary point Process
optimum A 0.418256 Time
855(0.418256) 87.1 B 0.528245
Temp 1755(0.528245) 177.6