Abstract

We investigate the origin of low-level scattering from high-quality coatings produced by ion-assisted deposition and ion plating. For this purpose we use the polarization ratio of light scattering to separate surface and bulk effects that characterize the intrinsic action of the thin-film materials. In the first step the method is tested and validated at scattering levels greater than 10−5. In the second step it is applied at low levels, and the results reveal some anomalies. To conclude, we perform a detailed analysis of scattering resulting from the presence of a few localized defects in the coatings.

© 1996 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
    [CrossRef] [PubMed]
  6. C. Amra, “Light scattering from multilayer optics. Part A: investigation tools,” J. Opt. Soc. Am. A 11, 197–210 (1994).
    [CrossRef]
  7. C. Amra, “Light scattering from multilayer optics. Part B: application to experiment,” J. Opt. Soc. Am. A 11, 211–226 (1994).
    [CrossRef]
  8. C. Amra, C. Grézes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical coatings,” Appl. Opt. 32, 5492–5503 (1993).
    [CrossRef] [PubMed]
  9. C. Amra, C. Grézes-Besset, S. Maure, D. Torricini, “Light scattering from localized and random interface or bulk irregularities in multilayer optics: the inverse problem,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1184–1200 (1994).
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    [CrossRef]
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  12. M. Born, E. Wolf, “Diffraction by a conducting sphere: theory of Mie,” in Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 347–363.
  13. C. Deumié, H. Giovannini, C. Amra, “Ellipsometry of light scattering from multilayer coatings,” Appl. Opt. 35, 5600–5608 (1996).
    [CrossRef] [PubMed]

1996 (1)

1994 (2)

1993 (4)

1992 (2)

1983 (1)

1980 (1)

Amra, C.

Apfel, J. H.

Bennett, J. M.

Born, M.

M. Born, E. Wolf, “Diffraction by a conducting sphere: theory of Mie,” in Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 347–363.

Bruel, L.

Bussemer, P.

Deumié, C.

Duparré, A.

Elson, J. M.

Giovannini, H.

Grézes-Besset, C.

C. Amra, C. Grézes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical coatings,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef] [PubMed]

C. Amra, C. Grézes-Besset, S. Maure, D. Torricini, “Light scattering from localized and random interface or bulk irregularities in multilayer optics: the inverse problem,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1184–1200 (1994).

Helm, K.

Kassam, S.

Maure, S.

C. Amra, C. Grézes-Besset, S. Maure, D. Torricini, “Light scattering from localized and random interface or bulk irregularities in multilayer optics: the inverse problem,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1184–1200 (1994).

Neubert, J.

Pelletier, E.

Rahn, J. P.

Torricini, D.

C. Amra, C. Grézes-Besset, S. Maure, D. Torricini, “Light scattering from localized and random interface or bulk irregularities in multilayer optics: the inverse problem,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1184–1200 (1994).

Wolf, E.

M. Born, E. Wolf, “Diffraction by a conducting sphere: theory of Mie,” in Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 347–363.

Appl. Opt. (8)

J. Opt. Soc. Am. A (3)

Other (2)

M. Born, E. Wolf, “Diffraction by a conducting sphere: theory of Mie,” in Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 347–363.

C. Amra, C. Grézes-Besset, S. Maure, D. Torricini, “Light scattering from localized and random interface or bulk irregularities in multilayer optics: the inverse problem,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1184–1200 (1994).

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Figures (25)

Fig. 1
Fig. 1

Roughness spectra γ(σ) measured for a standard glass substrate (1 nm) and for a supersmooth Si wafer (0.17 nm). These spectra issue from scattering measurements at a 633-nm wavelength. σ/2π is the spatial frequency.

Fig. 2
Fig. 2

Angular scattering measured at λ0 = 633 nm after coating (curve 1) by a 3λ0/4 TiO2 layer produced by ion-assisted deposition. The substrate is a 0.17-nm roughness Si substrate. Curve 2 is the calculation of correlated scattering from a substrate effect that is due to the replication of Si roughness. Curve 3 is the calculation of a material effect that fits the measurements.

Fig. 3
Fig. 3

Angular variations of the polarization ratio at 60° incidence for a λ0/2 low-index SiO2 layer at λ0 = 633 nm and deposited on glass. The curves cor and uncor designate the correlated and the uncorrelated surface scattering, respectively, and the curve bulk is the volume scattering.

Fig. 4
Fig. 4

Same as Fig. 3, except that the substrate is Si. In this case bulk scattering may be confused with uncorrelated surface scattering.

Fig. 5
Fig. 5

Angular variations of the polarization ratio at 60° incidence for a λ0/2 high-index Ta2O5 layer at λ0 = 633 nm and deposited on glass. The curves cor and uncor designate the correlated and the uncorrelated surface scattering, respectively, and the curve bulk is the volume scattering.

Fig. 6
Fig. 6

Same as Fig. 5, except that the substrate is Si.

Fig. 7
Fig. 7

Calculation and measurement of polarization ratio of scattering from a λ0/2 SiO2 layer produced by ion-assisted deposition and deposited on a standard glass substrate. Illumination incidence is 60°, with λ0 = 633 nm. The curves cor and uncor are calculated for the correlated and the uncorrelated surface scattering, respectively, and are rather close to the experiment. The curve bulk is quasi-constant in the angular range.

Fig. 8
Fig. 8

Calculation and measurement of the polarization ratio of scattering of a λ0/2 Ta2O5 layer produced by ion plating and deposited on a standard glass substrate. Illumination incidence is 60°, with λ0 = 633 nm. Measurements are very close to the correlated surface scattering (curve cor).

Fig. 9
Fig. 9

Calculation and measurement of the polarization ratio of a 15-layer TiO2/SiO2 quarter-wave mirror produced by ion-assisted deposition and deposited on glass. Illumination incidence is 60°, with λ0 = 633 nm. Measurements are very close to the correlated surface scattering (curve cor).

Fig. 10
Fig. 10

Calculation and measurement of the polarization ratio of a 2λ0 TiO2 layer produced by ion-assisted deposition and deposited on a Si substrate. Illumination incidence is 60°, with λ0 = 633 nm. Even for a supersmooth substrate, measurements remain very close to the correlated surface scattering (curve cor).

Fig. 11
Fig. 11

Angular scattering measured from a 2λ0 SiO2 layer deposited on a Si substrate, with an angular step of 0.1°. We detect, at levels lower than 10−5, the presence of a particular ripple in the whole angular range, which is characteristic of the presence of a few localized defects.

Fig. 12
Fig. 12

Extension of the scattering models to the case of discrete irregularities: (a) case of a localized defect present at the interface, (b) case of a localized defect present in the bulk.

Fig. 13
Fig. 13

Calculated angular scattering of an 8-μm radius defect present within the bulk of an 8λ0/4 SiO2 layer deposited on a Si substrate. The relative refractive-index inhomogeneity is equal to 6%, and the illuminated area is 2 mm2.

Fig. 14
Fig. 14

Calculated angular scattering of a 28-μm radius defect present within the bulk of an 8λ0/4 SiO2 layer deposited on a Si substrate. The relative refractive-index inhomogeneity is equal to 6%, and the illuminated area is 2 mm2. All minima are very close to each other and will be smoothed in practice by the receiver solid angle.

Fig. 15
Fig. 15

Calculated angular scattering of a 100-nm radius defect present at the surface of an 8λ0/4 SiO2 layer deposited on a Si substrate. The defect height is equal to 70 nm, and the illuminated area is 0.0001 mm2.

Fig. 16
Fig. 16

Calculated angular scattering of 15 identical surface defects of 5-μm diameter and height in a single layer distributed at a period C = 10 μm. We obtain a grating effect. The illuminated area is 2 mm2.

Fig. 17
Fig. 17

Same as Fig. 16, except that the coherent spectrum γcoh is put to zero. In this case, interferences and grating effects vanish.

Fig. 18
Fig. 18

Calculated angular scattering from 16 identical bulk defects randomly distributed within the bulk of an 8λ0/4 SiO2 layer deposited on a Si substrate. The illumination wavelength is λ0 = 633 nm. The defects’ radius is 2.1 μm, and their relative refractive-index inhomogeneity is 4%. The illuminated area is 2 mm2.

Fig. 19
Fig. 19

Same as Fig. 18, except that the coherent spectrum γcoh is put to zero. In this case, interferences effect vanishes.

Fig. 20
Fig. 20

Same as Fig. 18, but a 0.1-nm random roughness is added to the localized defects.

Fig. 21
Fig. 21

Angular scattering of a defect-free Si substrate measured before coating at λ0 = 633 nm.

Fig. 22
Fig. 22

Measurements at λ0 = 633 nm of angular scattering from an 8λ0/4 TiO2 layer deposited on a Si substrate. We observe a ripple in the whole angular range.

Fig. 23
Fig. 23

Calculation of angular scattering from an 8λ0/4 TiO2 layer deposited on a Si substrate. We consider the presence of 25 bulk defects (see the text for the set of parameters) randomly distributed within the bulk of the layer. We also consider the presence of a 0.11-nm random roughness.

Fig. 24
Fig. 24

Measurements of angular scattering from another 8λ0/4 TiO2 layer deposited on a Si substrate. Curves (1) and (2) are measurements at two different locations on the sample. The shape of scattering strongly depends on the location of the illuminated area (see text).

Fig. 25
Fig. 25

Calculation of angular scattering from an 8λ0/4 TiO2 layer deposited on a Si substrate. We consider the presence of 31 bulk defects (see the text for the set of parameters) randomly distributed within the bulk of the layer. We also consider the presence of a 0.11-nm random roughness.

Equations (16)

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I ( θ , ϕ ) = i , j C i j ( θ , ϕ ) α i j ( θ , ϕ ) γ j j ( θ , ϕ ) ,
γ j j = 4 π 2 S h ^ j ( σ ) 2 ,
γ j j = 4 π 2 S p ^ j ( σ ) 2 .
γ j j ( σ ) = TF { δ e , j 2 exp ( - | τ L e , j | ) + δ g , j 2 exp [ - ( τ L g , j ) 2 ] } γ j j ( σ ) = 1 2 π δ e , j 2 L e , j 2 ( 1 + σ 2 L e , j 2 ) 3 / 2 + 1 4 π δ g , j 2 L g , j 2 exp [ - ( σ L g , j 2 ) 2 ] .
μ = I P P I S S = i , j C i j ( P ) α i j γ j j i , j C i j ( S ) α i j γ j j .
μ ( θ ) = i = 0 p C i i ( P ) 2 i = 0 p C i i ( S ) 2 for roughness brought by materials ,
μ ( θ ) = i , j C i j ( P ) α i j a j s i , j C i j ( S ) α i j a j s for substrate roughness replication ,
I ( θ , ϕ ) = i , j C i j α i j γ j j .
γ j j = A j 2 S a j 4 | J 1 ( σ a j ) σ a j | 2 .
γ j j = l S ( 2 Δ n j n j ) 2 a j 4 | J 1 ( σ a j ) σ a j | 2 .
σ m a m π sin θ m m λ 2 a .
γ k k = γ unc + γ coh ,
γ unc = 1 S i = 1 N a i 4 | 2 ( Δ n n ) i J 1 ( σ a i ) σ a i | 2
γ unc = 1 S i = 1 N a i 4 A i 2 | J 1 ( σ a i ) σ a i | 2
γ coh = 1 S i = 1 N - 1 j > i N a i 2 a j 2 | 4 ( Δ n n ) i ( Δ n n ) j J 1 ( σ a i ) σ a i J 1 ( σ a j ) σ a j | × 2 cos [ σ · ( r j - r i ) ]
γ coh = 1 S i = 1 N - 1 j > i N a i 2 a j 2 A i A j | J 1 ( σ a i ) σ a i J 1 ( σ a j ) σ a j | × 2 cos [ σ · ( r j - r i ) ]

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