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Title of the problem Polysi Deposition for VLSI
Write an Introduction to the problem Decrease the defects
Team members
Duration start date 27-Sep-06
Date today 08-Apr-23
Last Modified on 2-Mar-2007
password info for P. R. Apte L18**** L18 :- 1 Control factor with 2-Levels and upto 7 control factors with 3 levels each
This Excel Sheet is created by Dr. P. R. Apte, IIT Bombay, Powai, Mumbai-400 076, India e-mail: [email protected] , web-page : http://www.ee.iitb.ac.in/~apte
Polysi Deposition for VLSI
Decrease the defects
L18 :- 1 Control factor with 2-Levels and upto 7 control factors with 3 levels each
This Excel Sheet is created by Dr. P. R. Apte, IIT Bombay, Powai, Mumbai-400 076, India e-mail: [email protected] , web-page : http://www.ee.iitb.ac.in/~apte
YOU MAY OVER-WRITE ON THE 'orange' TEXT
IN ALL THE SHEETS
This Excel Sheet is created by Dr. P. R. Apte, TIFR, Mumbai, India e-mail: [email protected] , web-page : http://www.ee.iitb.ac.in/~apte
USERNAMESTART DATE
STEP 1: Identify Main Function, failure mode and side effects
STEP 3: Identify Quality Characteristics and Objective Function
STEP 4: Identify Control Factors and their Levels
STEP 5: Identify Orthogonal Array (degrees of freedom for error)
Last Modified on 15-Feb-2007
26-Sep-06 TYPE THE DATE HERE
PolySilicon is deposited by "Low-Pressure Chemical Vapor Deposition" Technique. However, there are 3 problems : (1) Thickness Non uniformity, (2) defects (pin holes and/or particulates) and (3) Deposition Rate
STEP 2: Identify Noise factors, testing conditions (to capture the effects of noise)
Internal NoIsE parameters: All process parameters may have 'variations' External NoIsE parameters: power supply, gas pressures, ambient temperature, humidity etc may also have 'variations'
However, there are 3 quality characteristics of interest: (1) Defects (pin holes and/or particulates) : smaller-the-better,(2) Deposition rate : Larger-the-better and(3) Thickness non-uniformity : Nominal-the-Best, ideal value 1000 Ang.,
Assumptions are : All 6 control factors are ORTHOGONAL to each other and hence there would not be any need to study their interactions with each other
L18 array is chosen
1 control factor with 2 levels and upto 7 control factors with 3 levels are allowed.
Interaction AXB can be studied,
Reference : "Quality Engineering using Robust Design" by M.S. Phadke, Prentice Hall 1989, Chapter 4
This Excel Sheet is created by Dr. P. R. Apte, TIFR, Mumbai, India e-mail: [email protected] , web-page : http://www.ee.iitb.ac.in/~apte
TODAY08-Apr-23
PolySilicon is deposited by "Low-Pressure Chemical Vapor Deposition" Technique. However, there are 3 problems : (1) Thickness Non uniformity, (2) defects (pin holes and/or particulates) and (3) Deposition Rate
Internal NoIsE parameters: All process parameters may have 'variations' External NoIsE parameters: power supply, gas pressures, ambient temperature, humidity etc may also have 'variations'
However, there are 3 quality characteristics of interest:
Defects (pin holes and/or particulates) : smaller-the-better,(2) Deposition rate : Larger-the-better and(3) Thickness non-uniformity : Nominal-the-Best, ideal value 1000 Ang.,
Assumptions are : All 6 control factors are ORTHOGONAL to each other and hence there would not be any need to study their interactions with each other
L18 array is chosen
1 control factor with 2 levels and upto 7 control factors with 3 levels are
Interaction AXB can be studied,
TESTS Smaller-the-better Nominal-the-Best Larger-the-Better Mean
Defects YES
Type YES or NOType Quality
Characteristic name/identifier
9 5
Repetitions in each row of expt (due to NoIsE Factor
combinations)Repetitions of confirmation expt
(using the 'best' settings)
You may overtype the number of measurements
for each experiment.(due to NoIsE Factor
combinations)
Type the number of times the 'BEST" experiment (with 'best'
CF levels) is repeated
LEVELSColumn # CONTROL FACTORS \ LEVELS 1 2
1 empty empty empty2 Temperature T1 T23 Pressure P1 P24 Nitrogen N1 N25 Silane S1 S26 Initial Settling time I1 I27 - - -8 Cleaning Method C1 C2
NoIsE FACTORS \ LEVELS NoIsE Level 1 NoIsE Level 2
U NoIsE FACTOR 1 U1 U2
V NoIsE FACTOR 2 V1 V2
W NoIsE FACTOR 3 W1 W2
X NoIsE FACTOR 4 X1 X2
"empty", "-" are reservedfor indicatiing 'blank' columns
Go to a cell, delete contents (using 'delete' key) and write the Control Factor names (necessary) & Level names (optional)
3
T3P3N3S3I3-C3
NoIsE Level 3 NUMBER OF LEVELS
U3 3 Type 2 or 3 V3 3
W3 3
OKAY
L9
Go to a cell, delete contents (using 'delete' key) and write the
Control Factor names (necessary) & Level names (optional)
Go to a cell, delete contents (using 'delete' key) and write the Control Factor names (necessary) & Level names (optional)
WHICH OUTER-ARRAY IS
REQUIRED =
L18 ArrayControl Factors
Expt. No. A B C D E F G H1 1 1 1 1 1 1 1 12 1 1 2 2 2 2 2 23 1 1 3 3 3 3 3 34 1 2 1 1 2 2 3 35 1 2 2 2 3 3 1 16 1 2 3 3 1 1 2 27 1 3 1 2 1 3 2 38 1 3 2 3 2 1 3 19 1 3 3 1 3 2 1 210 2 1 1 3 3 2 2 111 2 1 2 1 1 3 3 212 2 1 3 2 2 1 1 313 2 2 1 2 3 1 3 214 2 2 2 3 1 2 1 315 2 2 3 1 2 3 2 116 2 3 1 3 2 3 1 217 2 3 2 1 3 1 2 318 2 3 3 2 1 2 3 1
9 6repetition number =
repetition number =
Total no. of expts =
18
L18 Array is always the same
and hence no need to
change this - EVER
9
Expt. No.Control Factors Assigned to columns
empty Pressure Nitrogen Silane
1 empty T1 P1 N1 S1 I12 empty T1 P2 N2 S2 I23 empty T1 P3 N3 S3 I34 empty T2 P1 N1 S2 I25 empty T2 P2 N2 S3 I36 empty T2 P3 N3 S1 I17 empty T3 P1 N2 S1 I38 empty T3 P2 N3 S2 I19 empty T3 P3 N1 S3 I2
10 empty T1 P1 N3 S3 I211 empty T1 P2 N1 S1 I312 empty T1 P3 N2 S2 I113 empty T2 P1 N2 S3 I114 empty T2 P2 N3 S1 I215 empty T2 P3 N1 S2 I316 empty T3 P1 N3 S2 I317 empty T3 P2 N1 S3 I118 empty T3 P3 N2 S1 I2
repetition number = 9 6
NUMBER OF MEASUREMENTS
Temperature
Initial Settling time
repetition number =
L9
CHOSEN FACTORIAL OR ORTHOGONAL
ARRAY
1 2 3 4 5 6 7
U NoIsE FACTOR 1 U1 U1 U1 U2 U2 U2 U3V NoIsE FACTOR 2 V1 V2 V3 V1 V2 V3 V1W NoIsE FACTOR 3 W1 W2 W3 W2 W3 W1 W3
Control Factors Assigned to columns
- Cleaning Method
- C1 1.00E+00 0.00E+00 1.00E+00 2.00E+00 0.00E+00 0.00E+00 1.00E+00
- C2 1.00E+00 2.00E+00 8.00E+00 1.80E+02 5.00E+00 0.00E+00 1.26E+02
- C3 3.00E+00 3.50E+01 1.06E+02 3.60E+02 3.80E+01 1.35E+02 3.15E+02
- C3 6.00E+00 1.50E+01 6.00E+00 1.70E+01 2.00E+01 1.60E+01 1.50E+01
- C1 1.72E+03 1.98E+03 2.00E+03 4.87E+02 8.10E+02 4.00E+02 2.02E+03
- C2 1.35E+02 3.60E+02 1.62E+03 2.43E+03 2.07E+02 2.00E+00 2.50E+03
- C3 3.60E+02 8.10E+02 1.22E+03 1.62E+03 1.17E+02 3.00E+01 1.80E+03
- C1 2.70E+02 2.73E+03 5.00E+03 3.60E+02 1.00E+00 2.00E+00 1.00E+04
- C2 5.00E+03 1.00E+03 1.00E+03 3.00E+03 1.00E+03 1.00E+03 3.00E+03
- C1 3.00E+00 0.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00 1.00E+00
- C2 1.00E+00 0.00E+00 1.00E+00 5.00E+00 0.00E+00 0.00E+00 1.00E+00
- C3 3.00E+00 1.62E+03 9.00E+01 2.16E+02 5.00E+00 4.00E+00 2.70E+02
- C2 1.00E+00 2.50E+01 2.70E+02 8.10E+02 1.60E+01 1.00E+00 2.25E+02
- C3 3.00E+00 2.10E+01 1.62E+02 9.00E+01 6.00E+00 1.00E+00 6.30E+01
- C1 4.50E+02 1.20E+03 1.80E+03 2.53E+03 2.08E+03 2.08E+03 1.89E+03
- C2 5.00E+00 6.00E+00 4.00E+01 5.40E+01 0.00E+00 8.00E+00 1.50E+01
- C3 1.20E+03 3.50E+03 3.50E+03 1.00E+03 3.00E+00 1.00E+00 1.00E+04
- C1 8.00E+03 2.50E+03 3.50E+03 5.00E+03 1.00E+03 1.00E+03 5.00E+03
Total no. of expts = 18
CHOSEN FACTORIAL OR ORTHOGONAL
ARRAY==>L9
NoIsE Factor combinations used as repetitions for each (row of) experiment
L4 / F4 F6 F8 / L8 L9 L12
REPETITIONS
NoIsE FACTOR names
meas # 1
meas # 2
meas # 3
meas # 4
meas # 5
meas # 6
meas # 7
L9
F2 EXPT NO. 1 2 3 4 5 6 7A 1 2BCD
F3 EXPT NO. 1 2 3 4 5 6 7A 1 2 3BCD
F4 EXPT NO. 1 2 3 4 5 6 7A 1 1 2 2B 1 2 1 2CD
F6 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 2 2 2B 1 2 3 1 2 3CD
F8 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 1 2 2 2B 1 1 2 2 1 1 2C 1 2 1 2 1 2 1D
F12 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 1 1 1 2B 1 1 1 2 2 2 1C 1 2 3 1 2 3 1D
F16 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 1 1 1 1
B 1 1 1 1 2 2 2C 1 1 2 2 1 1 2D 1 2 1 2 1 2 1
L4 EXPT NO. 1 2 3 4 5 6 7A 1 1 2 2B 1 2 1 2C 1 2 2 1D
L8 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 1 2 2 2B 1 1 2 2 1 1 2C 1 2 1 2 1 2 1D 1 2 1 2 2 1 2
L9 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 2 2 2 3B 1 2 3 1 2 3 1C 1 2 3 2 3 1 3D 1 2 3 3 1 2 2
8 9
U3 U3V2 V3W1 W2
1.00E+00 0.00E+00
3.00E+00 1.00E+00
5.00E+01 1.80E+02
4.00E+01 1.80E+01
3.60E+02 1.20E+01
2.70E+02 3.50E+01
7.20E+02 3.15E+02
2.25E+02 1.00E+00
2.80E+03 2.00E+03
0.00E+00 1.00E+00
0.00E+00 1.00E+00
8.00E+00 3.00E+00
3.00E+00 0.00E+00
1.50E+01 3.90E+01
1.80E+02 2.50E+01
1.00E+00 1.00E+00
6.00E+02 8.00E+00
2.00E+03 2.00E+03
NoIsE Factor combinations used as repetitions for each (row of) experiment
L4 / F4 F6 F8 / L8 L9 L12
meas # 8
meas # 9
8 9 10 11 12 13 14 15 16
8 9 10 11 12 13 14 15 16
8 9 10 11 12 13 14 15 16
8 9 10 11 12 13 14 15 16
8 9 10 11 12 13 14 15 16222
8 9 10 11 12 13 14 15 162 2 2 2 21 1 2 2 22 3 1 2 3
8 9 10 11 12 13 14 15 161 2 2 2 2 2 2 2 2
2 1 1 1 1 2 2 2 22 1 1 2 2 1 1 2 22 1 2 1 2 1 2 1 2
8 9 10 11 12 13 14 15 16
8 9 10 11 12 13 14 15 162221
8 9 10 11 12 13 14 15 163 32 31 23 1
Expt. No. 1 2 3 4 5 6 7 8 9
1 ### ### ### ### ### ### ### ### 0.0E+002 ### ### ### ### ### ### ### ### 1.0E+003 ### ### ### ### ### ### ### ### 1.8E+024 ### ### ### ### ### ### ### ### 1.8E+015 ### ### ### ### ### ### ### ### 1.2E+016 ### ### ### ### ### ### ### ### 3.5E+017 ### ### ### ### ### ### ### ### 3.2E+028 ### ### ### ### ### ### ### ### 1.0E+009 ### ### ### ### ### ### ### ### 2.0E+03
10 ### ### ### ### ### ### ### ### 1.0E+0011 ### ### ### ### ### ### ### ### 1.0E+0012 ### ### ### ### ### ### ### ### 3.0E+0013 ### ### ### ### ### ### ### ### 0.0E+0014 ### ### ### ### ### ### ### ### 3.9E+0115 ### ### ### ### ### ### ### ### 2.5E+0116 ### ### ### ### ### ### ### ### 1.0E+0017 ### ### ### ### ### ### ### ### 8.0E+0018 ### ### ### ### ### ### ### ### 2.0E+03
meas.
4
4
Repetitions or Measurements for each expt.
Feed the data in these rows and columns
You can have upto 16 measurements per expt
2 NF with 2-levels each =
How to use NoIsE Factors for generating
repetitions for each expt
3 NF with 2-levels each =
6
9
How to use NoIsE Factors for generating
repetitions for each expt
1 NF with 2-levels 1 NF with 3-levels=
2-4 NF with 3-levels each =
10 11 12 13 14 15 16
factorial
Blanks will not affect the results of mean, Variance and SN Ratio
L4 Orthogonal Array
factorial
L9 Orthogonal Array
Expt. No. 1 2 3 4 5 6 7
1 1.00E+00 0.00E+00 1.00E+00 2.00E+00 0.00E+00 0.00E+00 1.00E+00
2 1.00E+00 2.00E+00 8.00E+00 1.80E+02 5.00E+00 0.00E+00 1.26E+02
3 3.00E+00 3.50E+01 1.06E+02 3.60E+02 3.80E+01 1.35E+02 3.15E+02
4 6.00E+00 1.50E+01 6.00E+00 1.70E+01 2.00E+01 1.60E+01 1.50E+01
5 1.72E+03 1.98E+03 2.00E+03 4.87E+02 8.10E+02 4.00E+02 2.02E+03
6 1.35E+02 3.60E+02 1.62E+03 2.43E+03 2.07E+02 2.00E+00 2.50E+03
7 3.60E+02 8.10E+02 1.22E+03 1.62E+03 1.17E+02 3.00E+01 1.80E+03
8 2.70E+02 2.73E+03 5.00E+03 3.60E+02 1.00E+00 2.00E+00 1.00E+04
9 5.00E+03 1.00E+03 1.00E+03 3.00E+03 1.00E+03 1.00E+03 3.00E+03
10 3.00E+00 0.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00 1.00E+00
11 1.00E+00 0.00E+00 1.00E+00 5.00E+00 0.00E+00 0.00E+00 1.00E+00
12 3.00E+00 1.62E+03 9.00E+01 2.16E+02 5.00E+00 4.00E+00 2.70E+02
13 1.00E+00 2.50E+01 2.70E+02 8.10E+02 1.60E+01 1.00E+00 2.25E+02
14 3.00E+00 2.10E+01 1.62E+02 9.00E+01 6.00E+00 1.00E+00 6.30E+01
15 4.50E+02 1.20E+03 1.80E+03 2.53E+03 2.08E+03 2.08E+03 1.89E+03
16 5.00E+00 6.00E+00 4.00E+01 5.40E+01 0.00E+00 8.00E+00 1.50E+01
17 1.20E+03 3.50E+03 3.50E+03 1.00E+03 3.00E+00 1.00E+00 1.00E+04
18 8.00E+03 2.50E+03 3.50E+03 5.00E+03 1.00E+03 1.00E+03 5.00E+03
Repetitions or Measurements for each expt.
The data has been brought from previous sheet and
this sheet is protected
You can have upto 16 measurements per
expt
8 9 10 11 12 13 14 15 16
1.00E+00 0.00E+00 8.9E-01 0.51
3.00E+00 1.00E+00 5.4E+03 -37.30
5.00E+01 1.80E+02 3.3E+04 -45.17
4.00E+01 1.80E+01 3.8E+02 -25.76
3.60E+02 1.20E+01 1.8E+06 -62.54
2.70E+02 3.50E+01 1.7E+06 -62.23
7.20E+02 3.15E+02 9.7E+05 -59.88
2.25E+02 1.00E+00 1.5E+07 -71.69
2.80E+03 2.00E+03 6.5E+06 -68.15
0.00E+00 1.00E+00 2.2E+00 -3.47
0.00E+00 1.00E+00 3.2E+00 -5.08
8.00E+00 3.00E+00 3.1E+05 -54.85
3.00E+00 0.00E+00 8.7E+04 -49.38
1.50E+01 3.90E+01 4.5E+03 -36.54
1.80E+02 2.50E+01 2.6E+06 -64.18
1.00E+00 1.00E+00 5.4E+02 -27.33
6.00E+02 8.00E+00 1.4E+07 -71.51
2.00E+03 2.00E+03 1.6E+07 -72.00
S/N Ratio for smaller-the-better
Mean Sum of Squares
SN Ratio (smaller-the-Better)
You can have upto 16 measurements per
expt
Blanks will not affect the results of mean, Variance
and SN Ratio
Main EffectsColumn #1 Column #2
Expt. No. SN Ratio (smaller-the-Better) empty Temperatureempty empty T1 T2 T3
1 0.51 0.51 0.512 -37.30 -37.30 -37.303 -45.17 -45.17 -45.174 -25.76 -25.76 -25.765 -62.54 -62.54 -62.546 -62.23 -62.23 -62.237 -59.88 -59.88 -59.888 -71.69 -71.69 -71.699 -68.15 -68.15 -68.1510 -3.47 -3.47 -3.4711 -5.08 -5.08 -5.0812 -54.85 -54.85 -54.8513 -49.38 -49.38 -49.3814 -36.54 -36.54 -36.5415 -64.18 -64.18 -64.1816 -27.33 -27.33 -27.3317 -71.51 -71.51 -71.5118 -72.00 -72.00 -72.00
Sum -432.2 -384.3 -145.4 -300.6 -370.6-48.02 -42.70 -24.23 -50.10 -61.76
-48.02 -42.70
-24.23 -50.10 -61.76
Ov Mean -45.36 ######-45.36 -45.36 ###-45.36 -45.36 -45.36
OV-Mean -45.36 -45.36 -45.36GrandTotal 47231
Total SSQ 10190
Factor-Effects Factor-Effects for Column #1Factor-Effects for Column #2-#8
Main EffectsInteraction between Column #1 and Column #2 Column #3 Column #4
E1 X T1 E1 X T2 E1 X T3 E2 X T1 E2 X T2 E2 X T3 Pressure NitrogenE1T1 E1T2 E1T3 E2T1 E2T2 E2T3 P1 P2 P3 N10.51 0.51 0.51
-37.30 -37.30-45.17 -45.17
-25.76 -25.76 -25.76-62.54 -62.54-62.23 -62.23
-59.88 -59.88-71.69 -71.69-68.15 -68.15 -68.15
-3.47 -3.47-5.08 -5.08 -5.08
-54.85 -54.85-49.38 -49.38-36.54 -36.54-64.18 -64.18 -64.18
-27.33 -27.33-71.51 -71.51 -71.51-72.00 -72.00
-82.0 -150.5 -199.7 -63.4 -150.1 -170.8 -165.3 -284.7 -366.6 -234.2-27.32 -50.18 -66.57 -21.13 -50.03 -56.94 -27.55 -47.44 -61.10 -39.03
-27.32 -50.18 -66.57 -21.13 -50.03 -56.94 -27.55 -47.44 -61.10 -39.03
###-45.36 -45.36 -45.36 ###-45.36 -45.36 -45.36 ###-45.36 -45.36 -45.36 ###-45.36
-45.36 -45.36
Main EffectsColumn #4 Column #5 Column #6 Column #7Nitrogen Silane Initial Settling time -
N2 N3 S1 S2 S3 I1 I2 I3 - - -0.51 0.51 0.51
-37.30 -37.30 -37.30 -37.30-45.17 -45.17 -45.17 -45.17
-25.76 -25.76 -25.76-62.54 -62.54 -62.54 -62.54
-62.23 -62.23 -62.23 -62.23-59.88 -59.88 -59.88 -59.88
-71.69 -71.69 -71.69 -71.69-68.15 -68.15 -68.15
-3.47 -3.47 -3.47 -3.47-5.08 -5.08 -5.08
-54.85 -54.85 -54.85 -54.85-49.38 -49.38 -49.38 -49.38
-36.54 -36.54 -36.54 -36.54-64.18 -64.18 -64.18
-27.33 -27.33 -27.33 -27.33-71.51 -71.51 -71.51
-72.00 -72.00 -72.00 -72.00
-336.0 -246.4 -235.2 -281.1 -300.2 -309.1 -243.2 -264.2 -248.9 -298.6 -269.1-55.99 -41.07 -39.20 -46.85 -50.04 -51.52 -40.54 -44.03 -41.48 -49.76 -44.85
-55.99 -41.07 -39.20 -46.85 -50.04 -51.52 -40.54 -44.03 -41.48 -49.76 -44.85
-45.36 -45.36 ###-45.36 -45.36 -45.36 ###-45.36 -45.36 -45.36 ###-45.36 -45.36 -45.36 ###
-45.36 -45.36 -45.36 -45.36
Main EffectsColumn #8
Cleaning Method C1 C2 C3 Ov-Mean0.51
#########
######
######
###-3.47
-5.08###
######
######
######
### ### ###### ### ### -45.36
### ### ###
### ### ### ###-45.36
###
YOU CAN MODIFIY THE CHART - PARTICULARLY THE Y-AXIS
empt
yem
pty
T1 T2 T3
E1T
1E
1T2
E1T
3
E2T
1E
2T2
E2T
3
P1
P2
P3
N1
N2
N3
S1
S2
S3 I1 I2 I3 - - -
C1
C2
C3
Ov-
Mea
n
-70.00
-60.00
-50.00
-40.00
-30.00
-20.00
-10.00
0.00
Factor Effect Plot for Quality Char Name
Column #1 Factor Effect Column #2-#8 Factor Effects
Control Factors and Their Levels
S/N
Rat
io (s
mal
ler-
the-
bette
r) in
dB
YOU CAN MODIFIY THE CHART - PARTICULARLY THE Y-AXIS
empt
yem
pty
T1 T2 T3
E1T
1E
1T2
E1T
3
E2T
1E
2T2
E2T
3
P1
P2
P3
N1
N2
N3
S1
S2
S3 I1 I2 I3 - - -
C1
C2
C3
Ov-
Mea
n
-70.00
-60.00
-50.00
-40.00
-30.00
-20.00
-10.00
0.00
Factor Effect Plot for Quality Char Name
Column #1 Factor Effect Column #2-#8 Factor Effects
Control Factors and Their Levels
S/N
Rat
io (s
mal
ler-
the-
bette
r) in
dB
empt
yem
pty
T1 T2 T3
E1T
1E
1T2
E1T
3
E2T
1E
2T2
E2T
3
P1
P2
P3
N1
N2
N3
S1
S2
S3 I1 I2 I3 - - -
C1
C2
C3
Ov-
Mea
n
-70.00
-60.00
-50.00
-40.00
-30.00
-20.00
-10.00
0.00
Ov-Mean
Factor Effect Plot
Column #1 Factor Effect Column #2-#8 Factor Effects
Control Factors and Their Levels
S/N
Rat
io (s
mal
ler-t
he-B
ette
r) in
dB
empt
yem
pty
T1 T2 T3
E1T
1E
1T2
E1T
3
E2T
1E
2T2
E2T
3
P1
P2
P3
N1
N2
N3
S1
S2
S3 I1 I2 I3 - - -
C1
C2
C3
Ov-
Mea
n
-70.00
-60.00
-50.00
-40.00
-30.00
-20.00
-10.00
0.00
Ov-Mean
Factor Effect Plot
Column #1 Factor Effect Column #2-#8 Factor Effects
Control Factors and Their Levels
S/N
Rat
io (s
mal
ler-t
he-B
ette
r) in
dB
LEVELSCONTROL FACTORS \ LEVELS 1 2 3
empty -48.02 -42.70 0 0Temperature -24.23 -50.10 -61.76 2 4428
empty (1) x Temperature (1,2,3) -0.43 2.59 -2.15 0 0empty (2) x Temperature (1,2,3) 0.43 -2.59 2.15
Pressure -27.55 -47.44 -61.10 2 3415Nitrogen -39.03 -55.99 -41.07 2 1029Silane -39.20 -46.85 -50.04 2 372
Initial Settling time -51.52 -40.54 -44.03 2 378- -41.48 -49.76 -44.85 0 0
Cleaning Method -45.56 -41.58 -48.95 2 163
Ov-Mean -45.36 -45.36 -45.36
Total sum of Squares due to Factor Effects 9786
Total sum of Squares = grand Total - 18*mean sq 10190
Error Variance (unpooled) 5 404
Error Variance (unpooled) per degree of freedom
(Error Variance pooled)) 11 1318
Error Variance per degree of freedom
Error Bar for each col #1 CF level = 2*SQRT(error var. per DF / repetition of each level) =
Error Bar for each #2-#8 CF level = 2*SQRT(error var. per DF / repetition of each level) =
95% confidence interval for pred. err = +-2*sqrt(pred err) =
Total Error
OV-MEAN -45.36 -45.36 -45.36 -45.36
Degrees of
Freedom
Sum of Squares
Prediction error variance (for 5 to 6 repititions) = sum of sq for error /neff =
empty
0 - 0 yes yes - +- 7.29 dB2214 43 27 no no 18 +- 8.93 dB
0 - 0 yes yes - +- 8.93 dB +- 8.93 dB
1707 34 21 no no 14 +- 8.93 dB515 10 6 no no 4 +- 8.93 dB186 4 2 no pooled - +- 8.93 dB189 4 2 no pooled - +- 8.93 dB
0 - 0 yes yes - +- 8.93 dB82 2 1 no pooled - +- 8.93 dB
0
3
80.90
119.82
7.30
8.94 0.56
90.53
5
19.03
1.32
Mean Square
Factor Effect (percent)
F before pooling
empty or pooled F=<1.5
F After pooling
Error Bar on each CF Level
NO. OF unpooled 2-LEVEL CFs =
NO. OF unpooled 3-LEVEL CFs =
1/n = 1/(nexpts for mean) + (no of unpooled CF)/(nrepeat for each
level) =
nr = no of repeat expts =
1/neff = 1/n + 1/nrtherefore neff =
Main Effects
Level 1 Level 2 Level 3 SELECTLevelName
Column 1 empty empty empty - -
Column 2 Temperature T1 T2 T3 1 T1
Column 3 Pressure P1 P2 P3 1 P1
Column 4 Nitrogen N1 N2 N3 1 N1
Column 5 Silane S1 S2 S3 -
Column 6 Initial Settling time I1 I2 I3 -
Column 7 - - - - - -
Column 8 Cleaning Method C1 C2 C3 -
-0.1
18.95 -19.11
See the 'RESULTS' here 1.13E-01 to 9.03E+00
Type 'NEW' levels as 1,2 or 3
L18 ASSIGNMENT
Control Factor Names
Opt Level % Factor Effect "F" after Pooling
- - 0 -
T1 43 21.14 18.48
P1 34 17.81 14.25
N1 10 6.34 4.30
- - 0.00 -
- - 0.00 -
- - 0.00 -
- - 0.00 -Ov-Mean -45.36
S/N Ratio -0.08
19.03
Defects
1.01E+00
Contribution of SELECTed Level to S/N Ratio (in dB)
"+-" prediction error (95% confidence) in dB
RangeCenter Value
neutral/negligible-
D O M I N A N T
D O M I N A N T
SIGNIFICANT
neutral/negligible-
neutral/negligible-
neutral/negligible-
neutral/negligible-
D O M I N A N T orSIGNIFICANT orneutral/negligible
Interaction between Columns 1 X 2
LEVELSColumn # CONTROL FACTORS \ LEVELS 1 2 3
1 empty -48.02 -42.702 Temperature -24.23 -50.10 -61.76
1x2 empty (1) x Temperature (1,2,3) -0.43 2.59 -2.151x2 empty (2) x Temperature (1,2,3) 0.43 -2.59 2.15
Ov-Mean -45.36 -45.36 -45.36
The Contribution of SETTINGS empty (1) X Temperature (1) The Contribution of SETTINGS empty (1) X Temperature (2) The Contribution of SETTINGS empty (1) X Temperature (3)
The Contribution of SETTINGS empty (2) X Temperature (1) The Contribution of SETTINGS empty (2) X Temperature (2) The Contribution of SETTINGS empty (2) X Temperature (3)
to objective function for Defects = 18.0 dBto objective function for Defects = -4.8 dBto objective function for Defects = -21.2 dB
=to objective function for Defects = 24.2 dBto objective function for Defects = -4.7 dBto objective function for Defects = -11.6 dB