Patrick J. McMarr and J. R. Blanco, "Measurement of the thickness of the surface layer on amorphous Ge films using spectroscopic ellipsometry: validity of effective medium modeling," Appl. Opt. 27, 4265-4273 (1988)
Amorphous Ge films prepared using rf-diode sputtering were exposed to air for periods from 15 min to several days. These samples were placed in a windowless cell in which an Ar gas flow was maintained and spectroscopic ellipsometry measurements were performed. The surface of each sample was then rinsed with deionized water and in situ measurements obtained. Differences were interpreted as resulting from partial or complete removal of the layer that formed from air exposure. Changes in the thickness of this layer were determined using (i) effective medium modeling and (ii) the exact equations of ellipsometry. Within the limits for each method, the thickness values are identical.
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Best Fit Void Percentage and Oxide Layer Thickness Parameters and Their 90% Confidence Limits for a-Ge Films
a-Ge film thickness (Å)
Bulk region void percentage %
Surface layer (GeO2) thickness (Å)
Unbiased estimator σ
1800
10.0 ± 0.7
7.0 ± 1.6
0.009
3500
6.0 ± 0.6
9.0 ± 1.5
0.008
5000
4.5 ± 0.7
10.0 ± 1.4
0.008
7400
2.0 ± 0.8
13.0 ± 1.2
0.007
11,000
2.0 ± 0.7
14.0 ± 1.2
0.007
Table II
Best Fit Void Percentage Parameter for a-Ge Films with No Oxide Layer. Note that the 90% Confidence Limits and Values of the Unbiased Estimator are Larger than those in Table I.
a-Ge film thickness (Å)
Bulk region void percentage %
Surface layer (GeO2) thickness (Å)
Unbiased estimator σ
1800
13.0 ± 1.1
—
0.015
3500
10.0 ± 1.4
—
0.018
5000
9.0 ± 1.5
—
0.019
7400
8.0 ± 2.0
—
0.025
11,000
9.0 ± 2.1
—
0.026
Table III
Best Fit Oxide Film Thickness Parameter for a-Ge Films with No Voids. Note that the 90% Confidence Limits and Values of the Unbiased Estimator are Larger than those in Table I.
a-Ge film thickness (Å)
Bulk region void percentage %
Surface layer (GeO2) thickness (Å)
Unbiased estimator σ
1800
—
24.0 ± 6.9
0.037
3500
—
19.0 ± 4.6
0.025
5000
—
18.0 ± 3.6
0.019
7400
—
18.0 ± 2.1
0.012
11,000
—
19.0 ± 2.3
0.012
Table IV
Results of Inversion Procedure for a-Ge Films
a-Ge film thickness (Å)
Surface film thickness (Å)
1800
5.1
3500
3.9
5000
3.7
7400
4.7
11,000
4.8
Table V
Best Fit Void Percentage and Oxide Layer Thickness Parameters and Their 90% Confidence Limits for a-Ge Films after Deionized Water Rinse
a-Ge film thickness (Å)
Bulk region void percentage %
Surface layer (GeO2) thickness (Å)
Unbiased estimator σ
1800
10.0 ± 0.8
1.0 ± 1.8
0.010
3500
6.0 ± 0.9
5.0 ± 1.6
0.009
5000
5.0 ± 0.8
6.0 ± 1.6
0.009
7400
2.5 ± 0.8
8.0 ± 1.4
0.008
11,000
2.5 ± 0.7
9.0 ± 1.3
0.008
Table VI
Comparison of Surface Film Thickness Removed using Inversion and Modeling Procedurea
a-Ge film thickness (Å)
Surface film thickness removed
Difference (Inversion—Effective Med.) (Å)
Inversion (Å)
Effective Med. (Å)
1800
5.1
6.0
−0.9
3500
3.9
4.0
−0.1
5000
3.7
4.0
−0.3
7400
4.7
5.0
−0.3
11,000
4.8
5.0
−0.2
Thickness values for column labeled Surface film thickness removed, Inversion are from Table IV, while those listed under Effective Med. were determined by subtracting surface layer thickness values shown in Table V from those in Table I.
Tables (6)
Table I
Best Fit Void Percentage and Oxide Layer Thickness Parameters and Their 90% Confidence Limits for a-Ge Films
a-Ge film thickness (Å)
Bulk region void percentage %
Surface layer (GeO2) thickness (Å)
Unbiased estimator σ
1800
10.0 ± 0.7
7.0 ± 1.6
0.009
3500
6.0 ± 0.6
9.0 ± 1.5
0.008
5000
4.5 ± 0.7
10.0 ± 1.4
0.008
7400
2.0 ± 0.8
13.0 ± 1.2
0.007
11,000
2.0 ± 0.7
14.0 ± 1.2
0.007
Table II
Best Fit Void Percentage Parameter for a-Ge Films with No Oxide Layer. Note that the 90% Confidence Limits and Values of the Unbiased Estimator are Larger than those in Table I.
a-Ge film thickness (Å)
Bulk region void percentage %
Surface layer (GeO2) thickness (Å)
Unbiased estimator σ
1800
13.0 ± 1.1
—
0.015
3500
10.0 ± 1.4
—
0.018
5000
9.0 ± 1.5
—
0.019
7400
8.0 ± 2.0
—
0.025
11,000
9.0 ± 2.1
—
0.026
Table III
Best Fit Oxide Film Thickness Parameter for a-Ge Films with No Voids. Note that the 90% Confidence Limits and Values of the Unbiased Estimator are Larger than those in Table I.
a-Ge film thickness (Å)
Bulk region void percentage %
Surface layer (GeO2) thickness (Å)
Unbiased estimator σ
1800
—
24.0 ± 6.9
0.037
3500
—
19.0 ± 4.6
0.025
5000
—
18.0 ± 3.6
0.019
7400
—
18.0 ± 2.1
0.012
11,000
—
19.0 ± 2.3
0.012
Table IV
Results of Inversion Procedure for a-Ge Films
a-Ge film thickness (Å)
Surface film thickness (Å)
1800
5.1
3500
3.9
5000
3.7
7400
4.7
11,000
4.8
Table V
Best Fit Void Percentage and Oxide Layer Thickness Parameters and Their 90% Confidence Limits for a-Ge Films after Deionized Water Rinse
a-Ge film thickness (Å)
Bulk region void percentage %
Surface layer (GeO2) thickness (Å)
Unbiased estimator σ
1800
10.0 ± 0.8
1.0 ± 1.8
0.010
3500
6.0 ± 0.9
5.0 ± 1.6
0.009
5000
5.0 ± 0.8
6.0 ± 1.6
0.009
7400
2.5 ± 0.8
8.0 ± 1.4
0.008
11,000
2.5 ± 0.7
9.0 ± 1.3
0.008
Table VI
Comparison of Surface Film Thickness Removed using Inversion and Modeling Procedurea
a-Ge film thickness (Å)
Surface film thickness removed
Difference (Inversion—Effective Med.) (Å)
Inversion (Å)
Effective Med. (Å)
1800
5.1
6.0
−0.9
3500
3.9
4.0
−0.1
5000
3.7
4.0
−0.3
7400
4.7
5.0
−0.3
11,000
4.8
5.0
−0.2
Thickness values for column labeled Surface film thickness removed, Inversion are from Table IV, while those listed under Effective Med. were determined by subtracting surface layer thickness values shown in Table V from those in Table I.