E. J. Bawolek, James B. Mohr, E. D. Hirleman, and A. Majumdar, "Light scatter from polysilicon and aluminum surfaces and comparison with surface-roughness statistics by atomic force microscopy," Appl. Opt. 32, 3377-3400 (1993)
Optical-scatter measurements from polysilicon and aluminum surfaces were performed by using 632.8-nm illumination at 45 deg and 488-nm illumination at 76.8 deg. Scatter was recorded up to 60 deg from the specular beam by using a concentric ring photodetector. The results are compared with surface statistics derived from atomic force microscopy. Quantitative predictions of the scatter were derived from power spectral density curves and angle-resolved-scattering theory. The agreement was fair for polysilicon samples with rms surface roughnesses of ∼18 and 42 nm and aluminum with 17-nm rms roughness but poor for other samples. The discrepancy is attributed primarily to internal scatter within the measuring instrument.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Experimental values estimated from measurement of the Brewster angle and extinction on monocrystalline silicon.
Value for bulk aluminum from Schulz.18,19
Table 2
Values of Net Wave-Vector Change |k − k0| for Several Combinations of Incident (θ0) and Scattered (θs) Anglesa
θs
632.8 nm θ0 = 45 deg
488 nm θ0 = 76.8 deg
5
0.0006
0.0003
15
0.0021
0.0012
30
0.0045
0.0031
45
0.0070
0.0058
60
0.0096
0.0088
The units for |k − k0| are inverse nanometers. These results are valid in the plane of incidence only.
Table 3
ABC Parameters for Polysilicon Samples from Least-Squares Fitting of Eq. (17) to the One-Dimensional PSD Curves that Appear in Fig. 12a
Sample
A (nm)
B (nm−1)
C
Polysilicon A
550,000
75
4.2
Polysilicon B
65,000
35
6.1
Polysilicon C
635
22.5
5.5
The two-dimensional PSD curves calculated from these parameters are not shown.
Table 4
Fractal Parameters for Polysilicon Samples
Sample
D (Fractal Dimension)
Polysilicon A
1.17
0.4660
Polysilicon B
1.13
0.0864
Polysilicon C
1.15
0.0209
Table 5
Summary of Polysilicon Sample Characteristics and Optical Scatter Measurements
Integral of (1/P0)(dP/dΩ).
1/e Correlation length determined from autocorrelation function.
Root-mean-square roughness.
Experimental measurements integrated over the range from 6.4 to 61.5 deg, measured from the specular beam, for a total solid angle of 1.434 sr. The value shown is an average of all tests (S pol, P pol, small spot, large spot).
Theoretical value based on the relation, TIS = 1 − exp[−(4πσ cos θ0/λ)2], adjusted for the reduced solid angle captured in the experiment.
Table 6
ABC Parameters for Aluminum Samples Obtained from Least-Squares Fitting of Eq. (17) to the One-Dimensional PSD Curves that Appear in Fig. 25a
Sample
A(nm)
B (nm−1)
C
Aluminum A
135,000
121
4.0
Aluminum B
740
13
6.6
Aluminum C
570
13
6.6
The two-dimensional PSD curves calculated from these parameters are not shown.
Table 7
Fractal Parameters for Aluminum Samples
Sample
D (Fractal Dimension)
Aluminum A
1.15
0.0175
Aluminum B
1.13
0.0221
Aluminum C
1.10
0.0124
Table 8
Summary of Aluminum Sample Characteristics and Optical Scatter Measurements
Integral of (1/P0)(dP/dΩ).
1/e Correlation length determined from the autocorrelation function.
Root-mean-square roughness.
Experimental measurements integrated over the range from 6.4 to 61.5 deg, measured from a specular beam, for a total solid angle of 1.434 sr. The value shown is an average of all tests (S pol, P pol, small spot, large spot).
Theoretical value based on the relation, TIS = 1 − exp[−(4πσ cos θ0/λ)2], adjusted for the reduced solid angle captured in the experiment.
Tables (8)
Table 1
Refractive Indices Assumed in Scattering Computations
Experimental values estimated from measurement of the Brewster angle and extinction on monocrystalline silicon.
Value for bulk aluminum from Schulz.18,19
Table 2
Values of Net Wave-Vector Change |k − k0| for Several Combinations of Incident (θ0) and Scattered (θs) Anglesa
θs
632.8 nm θ0 = 45 deg
488 nm θ0 = 76.8 deg
5
0.0006
0.0003
15
0.0021
0.0012
30
0.0045
0.0031
45
0.0070
0.0058
60
0.0096
0.0088
The units for |k − k0| are inverse nanometers. These results are valid in the plane of incidence only.
Table 3
ABC Parameters for Polysilicon Samples from Least-Squares Fitting of Eq. (17) to the One-Dimensional PSD Curves that Appear in Fig. 12a
Sample
A (nm)
B (nm−1)
C
Polysilicon A
550,000
75
4.2
Polysilicon B
65,000
35
6.1
Polysilicon C
635
22.5
5.5
The two-dimensional PSD curves calculated from these parameters are not shown.
Table 4
Fractal Parameters for Polysilicon Samples
Sample
D (Fractal Dimension)
Polysilicon A
1.17
0.4660
Polysilicon B
1.13
0.0864
Polysilicon C
1.15
0.0209
Table 5
Summary of Polysilicon Sample Characteristics and Optical Scatter Measurements
Integral of (1/P0)(dP/dΩ).
1/e Correlation length determined from autocorrelation function.
Root-mean-square roughness.
Experimental measurements integrated over the range from 6.4 to 61.5 deg, measured from the specular beam, for a total solid angle of 1.434 sr. The value shown is an average of all tests (S pol, P pol, small spot, large spot).
Theoretical value based on the relation, TIS = 1 − exp[−(4πσ cos θ0/λ)2], adjusted for the reduced solid angle captured in the experiment.
Table 6
ABC Parameters for Aluminum Samples Obtained from Least-Squares Fitting of Eq. (17) to the One-Dimensional PSD Curves that Appear in Fig. 25a
Sample
A(nm)
B (nm−1)
C
Aluminum A
135,000
121
4.0
Aluminum B
740
13
6.6
Aluminum C
570
13
6.6
The two-dimensional PSD curves calculated from these parameters are not shown.
Table 7
Fractal Parameters for Aluminum Samples
Sample
D (Fractal Dimension)
Aluminum A
1.15
0.0175
Aluminum B
1.13
0.0221
Aluminum C
1.10
0.0124
Table 8
Summary of Aluminum Sample Characteristics and Optical Scatter Measurements
Integral of (1/P0)(dP/dΩ).
1/e Correlation length determined from the autocorrelation function.
Root-mean-square roughness.
Experimental measurements integrated over the range from 6.4 to 61.5 deg, measured from a specular beam, for a total solid angle of 1.434 sr. The value shown is an average of all tests (S pol, P pol, small spot, large spot).
Theoretical value based on the relation, TIS = 1 − exp[−(4πσ cos θ0/λ)2], adjusted for the reduced solid angle captured in the experiment.