Plasma etching is essential to the fine-line pattern transfer in current semicon
ID: 3225848 • Letter: P
Question
Plasma etching is essential to the fine-line pattern transfer in current semiconductor processes. An article gives the accompanying data (read from a graph) on chlorine flow (x, in SCCM) through a nozzle used in the etching mechanism and etch rate (y, in 100 A/min).
x 1.5 1.5 2.0 2.5 2.5 3.0 3.5 3.5 4.0
y 22.5 24.5 25.0 31.0 33.5 39.0 40.5 46.5 49.0
(A)Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
(B)Estimate the true average change in etch rate associated with a 1-SCCM increase in flow rate using a 95% confidence interval. (Round your answers to three decimal places.)
(C)Calculate a 95% CI for Y · 3.0,the true average etch rate when flow = 3.0. (Round your answers to three decimal places.)
(D)Calculate a 95% PI for a single future observation on etch rate to be made when flow = 3.0. (Round your answers to three decimal places.)
Explanation / Answer
Using Minitab:
Regression Analysis: y versus x
Method
Rows unused 4
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 723.64 723.642 147.91 0.000
x 1 723.64 723.642 147.91 0.000
Error 7 34.25 4.892
Lack-of-Fit 4 11.12 2.780 0.36 0.825
Pure Error 3 23.13 7.708
Total 8 757.89
Model Summary
S R-sq R-sq(adj) R-sq(pred)
2.21188 95.48% 94.84% 92.60%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 6.47 2.43 2.67 0.032
x 10.551 0.868 12.16 0.000 1.00
Regression Equation
y = 6.47 + 10.551 x
(A)Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
Answer:
From above output: test statistic: 2.67 P-value 0.032
(B)Estimate the true average change in etch rate associated with a 1-SCCM increase in flow rate using a 95% confidence interval.
Prediction for y
Regression Equation
y = 6.47 + 10.551 x
Variable Setting
x 1
Fit SE Fit 95% CI 95% PI
17.0256 1.62307 (13.1877, 20.8636) (10.5383, 23.5130)
C and D :
Prediction for y
Regression Equation
y = 6.47 + 10.551 x
Variable Setting
x 3
Fit SE Fit 95% CI 95% PI
38.1282 0.791979 (36.2555, 40.0009) (32.5728, 43.6836)
Hope this will be helpful. Thanks and god Bless You :-)