Abstract

A scatterometer is extended and allows us to perform ellipsometric measurements on scattered light in each direction of space. Experimental data are given for single thin-film layers and optical coatings and reveal unexpected results. The phenomena are investigated by means of the electromagnetic theories of surface and bulk scattering that emphasize the role of partial correlation and localized defects.

© 1996 Optical Society of America

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References

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  1. J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
    [Crossref] [PubMed]
  2. J. M. Elson, J. P. Rahn, J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation-length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219 (1983).
    [Crossref] [PubMed]
  3. J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
    [Crossref]
  4. C. Amra, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
    [Crossref] [PubMed]
  5. A. Duparré, S. Kassam, “Relation between light scattering and microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1992).
    [Crossref]
  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. S. Kassam, A. Duparré, K. Helm, P. Bussemer, J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
    [Crossref] [PubMed]
  9. C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
    [Crossref]
  10. C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical coatings,” Appl. Opt. 32, 5492–5503 (1993).
    [Crossref] [PubMed]
  11. C. Amra, D. Torricini, P. Roche, “Multiwavelength (0.45–10.6-mm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
    [Crossref] [PubMed]
  12. C. Amra, J. H. Apfel, E. Pelletier, “The role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
    [Crossref] [PubMed]
  13. C. Amra, C. Grèzes-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).
  14. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 364–416.
  15. J. Rivory, “Ellipsometric measurements,” in Thin Films for Optical Systems, F. Flory, ed. (Dekker, New York, 1995), pp. 299–328.
  16. F. Abélès, “Quelques remarques au sujet de l’utilisation de méthodes optiques pour l’étude des matériaux, de leurs surfaces et interfaces,” Acta Electron. 24, 133–138 (1981).
  17. C. Amra, M. Ranier, C. Grèzes-Besset, R. Mollenhauer, G. Albrand, “Loss anomalies in multilayer planar waveguides,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1005–1020 (1994).

1994 (2)

1993 (4)

1992 (3)

1984 (1)

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[Crossref]

1983 (1)

1981 (1)

F. Abélès, “Quelques remarques au sujet de l’utilisation de méthodes optiques pour l’étude des matériaux, de leurs surfaces et interfaces,” Acta Electron. 24, 133–138 (1981).

1980 (1)

Abélès, F.

F. Abélès, “Quelques remarques au sujet de l’utilisation de méthodes optiques pour l’étude des matériaux, de leurs surfaces et interfaces,” Acta Electron. 24, 133–138 (1981).

Albrand, G.

C. Amra, M. Ranier, C. Grèzes-Besset, R. Mollenhauer, G. Albrand, “Loss anomalies in multilayer planar waveguides,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1005–1020 (1994).

Amra, C.

C. Amra, “Light scattering from multilayer optics. Part A: investigation tools,” J. Opt. Soc. Am. A 11, 197–210 (1994).
[Crossref]

C. Amra, “Light scattering from multilayer optics. Part B: application to experiment,” J. Opt. Soc. Am. A 11, 211–226 (1994).
[Crossref]

C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
[Crossref]

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

C. Amra, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
[Crossref] [PubMed]

C. Amra, D. Torricini, P. Roche, “Multiwavelength (0.45–10.6-mm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
[Crossref] [PubMed]

C. Amra, J. H. Apfel, E. Pelletier, “The role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[Crossref] [PubMed]

C. Amra, M. Ranier, C. Grèzes-Besset, R. Mollenhauer, G. Albrand, “Loss anomalies in multilayer planar waveguides,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1005–1020 (1994).

C. Amra, C. Grèzes-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).

Apfel, J. H.

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 364–416.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 364–416.

Bennett, J. M.

Bruel, L.

Bussemer, P.

Duparré, A.

Elson, J. M.

Grèzes-Besset, C.

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

C. Amra, C. Grèzes-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).

C. Amra, M. Ranier, C. Grèzes-Besset, R. Mollenhauer, G. Albrand, “Loss anomalies in multilayer planar waveguides,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1005–1020 (1994).

Helm, K.

Kassam, S.

Maure, S.

C. Amra, C. Grèzes-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).

Mollenhauer, R.

C. Amra, M. Ranier, C. Grèzes-Besset, R. Mollenhauer, G. Albrand, “Loss anomalies in multilayer planar waveguides,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1005–1020 (1994).

Neubert, J.

Pelletier, E.

Rahn, J. P.

Ranier, M.

C. Amra, M. Ranier, C. Grèzes-Besset, R. Mollenhauer, G. Albrand, “Loss anomalies in multilayer planar waveguides,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1005–1020 (1994).

Rivory, J.

J. Rivory, “Ellipsometric measurements,” in Thin Films for Optical Systems, F. Flory, ed. (Dekker, New York, 1995), pp. 299–328.

Roche, P.

Torricini, D.

C. Amra, D. Torricini, P. Roche, “Multiwavelength (0.45–10.6-mm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
[Crossref] [PubMed]

C. Amra, C. Grèzes-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).

Acta Electron. (1)

F. Abélès, “Quelques remarques au sujet de l’utilisation de méthodes optiques pour l’étude des matériaux, de leurs surfaces et interfaces,” Acta Electron. 24, 133–138 (1981).

Appl. Opt. (8)

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

Phys. Rev. B (1)

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[Crossref]

Other (4)

C. Amra, C. Grèzes-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).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 364–416.

J. Rivory, “Ellipsometric measurements,” in Thin Films for Optical Systems, F. Flory, ed. (Dekker, New York, 1995), pp. 299–328.

C. Amra, M. Ranier, C. Grèzes-Besset, R. Mollenhauer, G. Albrand, “Loss anomalies in multilayer planar waveguides,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 1005–1020 (1994).

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Figures (13)

Fig. 1
Fig. 1

Schematic view of the scatterometer11 that was extended, by means of the addition of a rotating polarizer and analyzer, to an angle-resolved ellipsometer. Ten axis are fully computer controlled in this experimental setup. Specular and diffuse measurements can be performed at different incidence and scattering angles. Several sources can be used with wavelengths from the UV (325 nm) to the mid-IR (10.6 μm).

Fig. 2
Fig. 2

Rotational azimuth angles of polarizer (ψ) and analyzer (ϕ). The angle (α) gives the direction of the incidence linear polarization.

Fig. 3
Fig. 3

Illumination procedure at incidence (i) on the sample. y is the direction of the s polarization, and x′ is that of p polarization. The normal sample is parallel to z.

Fig. 4
Fig. 4

Comparison between theory and measurement for an opaque Al layer. δ is the reflection ellipsometric phase term plotted versus the incidence angle (i) and given between 0° and 80°. The incident source is a He–Ne laser at 633 nm.

Fig. 5
Fig. 5

Same as Fig. 4, but the sample is a multidielectric coating of design HLHLH(6L)HLHLH (see text).

Fig. 6
Fig. 6

Function F(ϕ) measured at i = 20° incidence for the multidielectric sample of Fig. 5, with the corresponding fit. The phase term δ is 0°. Vertical units are arbitrary.

Fig. 7
Fig. 7

Schematic view of scattering ellipsometry. The incidence angle (i) is fixed, while ellipsometric measurements are performed on light scattering at each direction θ in space.

Fig. 8
Fig. 8

Calculation of the scattering phase term η(θ) for a single Ta2O5 layer of optical thickness 8λ0/4, where λ0 = 633 nm is the illumination wavelength. For surface calculation, the two interfaces are identical. The illumination incidence is i = 0°. Surface and bulk scattering can be separated.

Fig. 9
Fig. 9

Same as Fig. 8, except that the design is HLHLH(6L)HLHLH (see text), with materials TiO2 and SiO2. All surface and bulk defects are perfectly correlated for this calculation.

Fig. 10
Fig. 10

Measurements at the 633-nm wavelength of the scattering phase term η(θ) for a single layer of Ta2O5 produced by ion plating. The calculation of Fig. 8 is also reported.

Fig. 11
Fig. 11

Same as Fig. 10, but the sample is an 11-layer interference filter (see text). The calculation of Fig. 9 is also reported.

Fig. 12
Fig. 12

Scattering measurements of F(ϕ) at θ = 72° for the sample of Fig. 11. The experimental data are greater than the 7 × 10−7 system noise. The theoretical fit is superimposed on the measurements.

Fig. 13
Fig. 13

Scattering photograph recorded at θ = 10° on the sample of Fig. 11, with crossed polarizer and analyzer (image size 12 mm × 8 mm).

Tables (2)

Tables Icon

Table 1 Influence of Amplitude ρ of Cross-Polarization Ratio τ = ρ exp(jζ) on the Determination of Scattering Phase Term ηa

Tables Icon

Table 2 Influence of Argument ζ of Cross-Polarization Ratio τ = ρ exp(jζ) on the Determination of Scattering Phase Term ηa

Equations (65)

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E s = E 0 + cos ψ cos ( ψ - α ) ,
E p = E 0 + sin ψ cos ( ψ - α ) .
E * = r s E s cos ϕ + r p E p sin ϕ ,
E * = E 0 + cos ( ψ - α ) ( r S cos ψ cos ϕ + r P sin ψ sin ϕ ) ,
r s = exp ( j δ s ) R s ,
r p = exp ( j δ p ) R p .
I = E * E ¯ * = I 0 ( ψ , α ) F ( R s , R p , ψ , ϕ ) ,
I 0 = E 0 + 2 cos 2 ( ψ - α ) ,
I 0 = E 0 + 2 / 2
F ( ψ , ϕ ) = A ( ψ ) cos 2 ϕ + B ( ψ ) sin 2 ϕ + C ( ψ ) sin ( 2 ϕ ) ,
A ( ψ ) = R s cos 2 ψ ,
B ( ψ ) = R p sin 2 ψ ,
C ( ψ ) = cos δ A B .
δ = δ s - δ p ,
2 F / A = G ( ϕ ) = α + β cos ( 2 ϕ - γ ) ,
α = 1 + u ,
β = ( 1 - u ) / cos γ ,
tan γ = 2 cos δ u / ( 1 - u ) ,
u = B / A .
G extr = α ± β
ϕ m = ( 1 / 2 ) ( γ + k π ) .
cos δ = C / A B = β sin γ / [ 2 ( α - 1 ) 1 / 2 ] .
tan ψ opt = ( R s / R p ) 1 / 2 .
F / A = 1 + cos δ sin 2 ϕ ,
A = R s R p / ( R s + R p )
n = 0.8 + j 6 with j 2 = - 1.
A = i = 0 M C i r h i             for surface scattering ,
A = i = 1 M C i b p i             for bulk scattering ,
h i = ( 1 / 4 π 2 ) a i * h i + 1 + g i ,
h j = α j p h p + k = 0 p - j - 1 α j , j + k g j + k ,
A s = A s s + A s p with A s p = 0 in the incidence plane ,
A p = A p p + A p s with A p s = 0 in the incidence plane .
A s = ν s E s ,
A p = ν p E p ,
A * = ν s E s cos ϕ + ν p E p sin ϕ ,
A * = E 0 + cos ( ψ - α ) ( ν s cos ψ cos ϕ + ν p sin ψ sin ϕ ) ,
ν s = N s exp ( j η s ) ,
ν p = N p exp ( j η p ) .
I = A * A ¯ * = I 0 ( ψ , α ) F ( N s , N p , ψ , ϕ ) ,
I 0 = E 0 + 2 / 2
F ( ψ , ϕ ) = A ( ψ ) cos 2 ϕ + B ( ψ ) sin 2 ϕ + C ( ψ ) sin ( 2 ϕ ) ,
A = N s cos 2 ψ ,
B = N p sin 2 ψ ,
C = cos η A B ,
η = η s - η p
F / A = 1 + cos η sin 2 ϕ
ν s or p = C i ( s or p ) h i ,
C i ( s or p ) = C i r ( s or p ) / E s or p .
ν s = C 0 ( s ) h 0
η = η s - η p = arg [ C 0 ( s ) ] - arg [ C 0 ( p ) ] .
η = η s - η p = arg [ C i ( s ) ] - arg [ C i ( p ) ] for perfect correlation .
η = arg [ C i ( s ) h i ] - arg [ C i ( p ) h i ] with h i h j for i j .
η = arg ( A s A ¯ p ) ,
A s = i A i s ,             A p = i A i p .
η = arg ( i , j D i j γ i j ) ,
D i j = C i r ( s ) C ¯ j r ( p ) ,
γ i j = h i h ¯ j
γ i j = α i j γ i j = α i j α j p 2 γ p p
η = arg ( L )
L = i , j D i j α i j α j p 2 .
L = j α j p 2 .
A * = E 0 + cos ( ψ - α ) [ ( ν s s cos ψ + ν p s sin ψ ) cos ϕ + ( ν p p sin ψ + ν s p cos ψ ) sin ϕ ] ,
A = ν s s cos ψ + ν p s sin ψ 2 ,
B = ν p p sin ψ + ν s p cos ψ 2 ,
C = Re [ ( ν s s cos ψ + ν p s sin ψ ) ( ν p p sin ψ + ν s p cos ψ ) ] .

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