Light Scattering from Fused Polycrystalline Aluminum Oxide Surfaces

D. H. Hensler

doi:10.1364/AO.11.002522

Applied Optics
Vol. 11,
Issue 11,
pp. 2522-2528
(1972)
•https://doi.org/10.1364/AO.11.002522

Light Scattering from Fused Polycrystalline Aluminum Oxide Surfaces

D. H. Hensler

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D. H. Hensler, "Light Scattering from Fused Polycrystalline Aluminum Oxide Surfaces," Appl. Opt. 11, 2522-2528 (1972)

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Abstract

The results of a study of the topography of fused polycrystalline aluminum oxide surfaces using reflected coherent light of 6328-Å wavelength are reported. It is shown that the wavelength and angular dependences of the specular intensity can be understood in terms of optical scattering theory in the Kirchhoff approximation for a surface with a Gaussian roughness distribution. The values of the rms roughness obtained optically by fitting the experimental observations to the theory agree well with those obtained from Talysurf measurements. Estimates of the rms slope and correlation distance of the surface structure are obtained from a treatment of the specular and diffuse components of the reflected light intensity using the Beckmann model. An empirical relationship is shown to exist between the mean surface grain size as determined by microscopic observation using the line intercept method and the rms surface roughness. These results have formed the basis of an optical technique for rapidly estimating the mean surface grain size on high alumina substrates used in the microelectronics industry.

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Sample	Optical roughness from angular dependence, σ_θ (μ)	Optical roughness from dependence σ_λ (μ)	Center line average Talysurf roughness (μ)	Mean grain size (μ)
1	0.10		0.09	0.7
2	0.11	0.12	0.10	0.7
3	0.15	0.17	0.14	1.1
4	0.11		0.12	1.05
5	0.25		0.25	2.86
6	0.24		0.20	2.9
7	0.24	0.24	0.24	2.8
8	0.25		0.23	2.9
9	0.25		0.19	2.9
10	0.24	0.25	0.27	3.4
11	0.26		0.27	3.7
12	0.30		0.35	3.7
13	0.26	0.26	0.30	3.8
14	0.26	0.25		3.9
15	0.29		0.27	4.05
16	0.31		0.29	4.45
17	0.30	0.31	0.28	4.8
18	0.29		0.29	5.0
19	0.31		0.29	5.6
20	0.30		0.32	6.0
21	0.33		0.27	6.0
22	0.34		0.33	6.5
23	0.38		0.36	8.2
24	0.42		0.36	8.5

Sample	σ_θ (μ)	T(μ)	M(θ)	M
5	0.25	0.88	0.40	0.35
7	0.24	1.26	0.27	0.34
8	0.25	1.46	0.24	0.35
11	0.26	1.83	0.20	0.28
12	0.30	1.00	0.42	0.32
14	0.26	1.60	0.23	0.27
15	0.29	1.11	0.37	0.29
16	0.31	1.36	0.34	0.28
18	0.29	0.80	0.51	0.23
19	0.31	1.24	0.35	0.22
20	0.30	1.68	0.25	0.20
22	0.34	1.13	0.43	0.21
24	0.42	1.76	0.34	0.20

Sample	Optical roughness from angular dependence, σ_θ (μ)	Optical roughness from dependence σ_λ (μ)	Center line average Talysurf roughness (μ)	Mean grain size (μ)
1	0.10		0.09	0.7
2	0.11	0.12	0.10	0.7
3	0.15	0.17	0.14	1.1
4	0.11		0.12	1.05
5	0.25		0.25	2.86
6	0.24		0.20	2.9
7	0.24	0.24	0.24	2.8
8	0.25		0.23	2.9
9	0.25		0.19	2.9
10	0.24	0.25	0.27	3.4
11	0.26		0.27	3.7
12	0.30		0.35	3.7
13	0.26	0.26	0.30	3.8
14	0.26	0.25		3.9
15	0.29		0.27	4.05
16	0.31		0.29	4.45
17	0.30	0.31	0.28	4.8
18	0.29		0.29	5.0
19	0.31		0.29	5.6
20	0.30		0.32	6.0
21	0.33		0.27	6.0
22	0.34		0.33	6.5
23	0.38		0.36	8.2
24	0.42		0.36	8.5

Sample	σ_θ (μ)	T(μ)	M(θ)	M
5	0.25	0.88	0.40	0.35
7	0.24	1.26	0.27	0.34
8	0.25	1.46	0.24	0.35
11	0.26	1.83	0.20	0.28
12	0.30	1.00	0.42	0.32
14	0.26	1.60	0.23	0.27
15	0.29	1.11	0.37	0.29
16	0.31	1.36	0.34	0.28
18	0.29	0.80	0.51	0.23
19	0.31	1.24	0.35	0.22
20	0.30	1.68	0.25	0.20
22	0.34	1.13	0.43	0.21
24	0.42	1.76	0.34	0.20

Abstract

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Equations (9)

Applied Optics