Abstract

Accurate angular phase data are extracted from angle-resolved scattering measurements made with polarized light using a technique developed in the laboratory. This Ellipsometry of Angle-Resolved Scattering (E.A.R.S.) technique makes it possible to distinguish surface scattering from bulk scattering independent of the scattering levels for different types of samples. Phase data are also investigated in the speckle pattern.

© 2005 Optical Society of America

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References

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  1. J. M. Elson, J. P. Rahn, and J. M. Bennett, �??Light scattering from multilayer optics: comparison of theory and experiment,�?? Appl. Opt. 19, 669-679 (1980).
    [CrossRef] [PubMed]
  2. C. Amra, �??From light scattering to the microstructure of thin film multilayers,�?? Appl. Opt. 32, 5481-5491 (1993).
    [CrossRef] [PubMed]
  3. P. Bussemer, K. Hehl, and S. Kassam, �??Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,�?? Waves Random Media 1, 207-221 (1991).
    [CrossRef]
  4. R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattson, �??Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,�?? Appl. Opt. 31, 1426-1435 (1992).
    [CrossRef] [PubMed]
  5. C. Amra, �??Light scattering from multilayer optics. Part A: Investigation tools,�?? J. Opt. Soc. Am. A 11, 197-210 (1994).
    [CrossRef]
  6. C. Amra, �??Light scattering from multilayer optics. Part B: Application to experiment,�?? J. Opt. Soc. Am. A 11, 211-226 (1994).
    [CrossRef]
  7. 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]
  8. C. Amra, �??First order vector theory of bulk scattering in optical multilayers,�?? J. Opt. Soc. Am. A 10, 365-374 (1993).
    [CrossRef]
  9. S. Kassam, A. Duparré, K. Hehl, P. Bussemer, and J. Neubert, �??Light scattering from the volume of optical thin films: theory and experiment,�?? Appl. Opt. 31, 1304-1313 (1992).
    [CrossRef] [PubMed]
  10. H. Giovannini, M. Saillard, A. Sentenac, �??Numerical study of scattering from rough inhomogeneous films,�?? J. Opt. Soc. Am. A 15, 1182-1190 (1998).
    [CrossRef]
  11. G. Videen, J-Y Hsu, WS. Bickel, WL. Wolfe, �??Polarized light scattered from rough surfaces,�?? J. Opt. Soc. Am A 9, 1111-1118 (1992).
    [CrossRef]
  12. Germer T.A. and Asmail C. C., �??Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,�?? Review of scientific Instruments 70, 3688-3695 (1999).
    [CrossRef]
  13. N. Destouches, M. Lequime and H. Giovannini and C.A. Guerin, �??Determination of the phase of the diffracted field in the optical domain. Application to the reconstruction of surface profiles,�?? Opt. Comm. 198, 233-239 (2001).
    [CrossRef]
  14. C. Deumié, H. Giovannini and C. Amra, �??Ellipsometry of light scattering from multilayer coatings,�?? Appl. Opt. 35, 5600-5608 (1996).
    [CrossRef] [PubMed]
  15. C. Deumié, H. Giovannini and C. Amra, �??Angle-resolved ellipsometry of light scattering: discrimination of surface and bulk effects in substrates and optical coatings,�?? Appl. Opt. 41, 3362-3369 (2002).
    [CrossRef] [PubMed]
  16. C. Amra, D. Torricini and P. Roche, �??Multiwavelength (0.45-10.6 µm) angle-resolved scatterometer or how to extend the optical window,�?? Appl. Opt. 32, 5462-5474 (1993).
    [CrossRef] [PubMed]
  17. C. Amra, C. Grèzes-Besset, and L. Bruel, �??Comparison of surface and bulk scattering in optical multilayers,�?? Appl. Opt. 32, 5492-5503 (1993).
    [CrossRef] [PubMed]
  18. P. A. Martin and P. Ola, �??Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle,�?? Proc. Roy. Soc. Edinburgh, 123A, 185-208 (1993).
    [CrossRef]
  19. M. Saillard and A. Sentenac, �??Rigorous solution for electromagnetic scattering from rough surfaces,�?? Waves in Random Media 11, 103-137 (2001).
    [CrossRef]
  20. Fang S. J., Chen W., Yamanaka T., and Helms C. R, �??Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry,�?? Applied physics letters 68(20), 2837-2839 (1996).
    [CrossRef]
  21. C. Deumié, R. Richier, P. Dumas, C. Amra, �??Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,�?? Appl. Opt. 35, 5583-5594 (1996).
    [CrossRef] [PubMed]

Appl. Opt. (10)

J. M. Elson, J. P. Rahn, and J. M. Bennett, �??Light scattering from multilayer optics: comparison of theory and experiment,�?? Appl. Opt. 19, 669-679 (1980).
[CrossRef] [PubMed]

C. Amra, �??From light scattering to the microstructure of thin film multilayers,�?? Appl. Opt. 32, 5481-5491 (1993).
[CrossRef] [PubMed]

R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattson, �??Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,�?? Appl. Opt. 31, 1426-1435 (1992).
[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]

S. Kassam, A. Duparré, K. Hehl, P. Bussemer, and J. Neubert, �??Light scattering from the volume of optical thin films: theory and experiment,�?? Appl. Opt. 31, 1304-1313 (1992).
[CrossRef] [PubMed]

C. Deumié, H. Giovannini and C. Amra, �??Ellipsometry of light scattering from multilayer coatings,�?? Appl. Opt. 35, 5600-5608 (1996).
[CrossRef] [PubMed]

C. Deumié, H. Giovannini and C. Amra, �??Angle-resolved ellipsometry of light scattering: discrimination of surface and bulk effects in substrates and optical coatings,�?? Appl. Opt. 41, 3362-3369 (2002).
[CrossRef] [PubMed]

C. Amra, D. Torricini and P. Roche, �??Multiwavelength (0.45-10.6 µm) angle-resolved scatterometer or how to extend the optical window,�?? Appl. Opt. 32, 5462-5474 (1993).
[CrossRef] [PubMed]

C. Amra, C. Grèzes-Besset, and L. Bruel, �??Comparison of surface and bulk scattering in optical multilayers,�?? Appl. Opt. 32, 5492-5503 (1993).
[CrossRef] [PubMed]

C. Deumié, R. Richier, P. Dumas, C. Amra, �??Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,�?? Appl. Opt. 35, 5583-5594 (1996).
[CrossRef] [PubMed]

Applied physics letters (1)

Fang S. J., Chen W., Yamanaka T., and Helms C. R, �??Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry,�?? Applied physics letters 68(20), 2837-2839 (1996).
[CrossRef]

J. Opt. Soc. Am A (1)

G. Videen, J-Y Hsu, WS. Bickel, WL. Wolfe, �??Polarized light scattered from rough surfaces,�?? J. Opt. Soc. Am A 9, 1111-1118 (1992).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Comm. (1)

N. Destouches, M. Lequime and H. Giovannini and C.A. Guerin, �??Determination of the phase of the diffracted field in the optical domain. Application to the reconstruction of surface profiles,�?? Opt. Comm. 198, 233-239 (2001).
[CrossRef]

Proc. Roy. Soc. Edinburgh (1)

P. A. Martin and P. Ola, �??Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle,�?? Proc. Roy. Soc. Edinburgh, 123A, 185-208 (1993).
[CrossRef]

Review of scientific Instruments (1)

Germer T.A. and Asmail C. C., �??Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,�?? Review of scientific Instruments 70, 3688-3695 (1999).
[CrossRef]

Waves in Random Media (1)

M. Saillard and A. Sentenac, �??Rigorous solution for electromagnetic scattering from rough surfaces,�?? Waves in Random Media 11, 103-137 (2001).
[CrossRef]

Waves Random Media (1)

P. Bussemer, K. Hehl, and S. Kassam, �??Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,�?? Waves Random Media 1, 207-221 (1991).
[CrossRef]

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Figures (13)

Fig. 1.
Fig. 1.

Basic principles of EARS. The illumination and scattering angles are denoted by i and θ, respectively.

Fig. 2.
Fig. 2.

Schematic view of the angle-resolved multiwavelength scatterometer

Fig. 3.
Fig. 3.

Angle-resolved scattering measured for three substrates of diffuse reflectance (n°1: dielectric Spectralon, n°2: metallic Infragold, n°3: coarse ground finish glass) and for a polished glass substrate (n°4). Illumination is normal.

Fig. 4.
Fig. 4.

Calculated angular variations of the phase term for a polished glass sample at normal (i=0°) and oblique (i=50°) illumination. Curves are given for surface and bulk scattering.

Fig. 5.
Fig. 5.

Angular phase data measured (bold lines) from a polished glass sample (RG1000 Schott) under normal (i=0°) and oblique (i=50°) illumination. Two calculated curves are superimposed to these experimental data, that are the phase term in the presence of a transition layer (ne=50nm - dashed line), and the phase term resulting from an imaginary index (n”=0.15) of the substrate (+++).

Fig. 6.
Fig. 6.

Angular behavior of the equivalent phase term δ’ measured for 3 samples of diffuse reflectance: (n°1: dielectric Spectralon, n°2: metallic Infragold, n°3: coarse ground finish glass). Illumination is normal (i=0°).

Fig. 7.
Fig. 7.

Same legend as in Fig. 6., but the illumination is oblique (i=50°).

Fig. 8.
Fig. 8.

Angular behavior of the equivalent phase term in the speckle pattern, for the metallic Infragold (dashed line) and dielectric Spectralon (bold line) samples. The angular step of measurements is 0.05°. Illumination is normal.

Fig. 9.
Fig. 9.

Polarimetric phase of specular reflection for glass and the two Spectralon and Infragold samples, versus illumination incidence.

Fig. 10.
Fig. 10.

Angular variations arg(zi) calculated for a glass sample for different cross-polarization ratios T.

Fig. 11.
Fig. 11.

Cross-polarization ratios of angular scattering measured for all diffuse reflectance samples that are dielectric Spectralon (a) and metallic Infragold (b) samples, and glass (c). Illumination is normal.

Fig. 12.
Fig. 12.

Angular scattering measured at a given direction (θ=20°) with crossed polarizers/analyzers, for dielectric Spectralon and metallic Infragold samples. Illumination is normal.

Fig. 13.
Fig. 13.

AFM measurements of the glass sample.

Equations (34)

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E = E s + E p
E = E S + E P = E S exp ( j . η S ) + E P exp ( j . η P )
Δ η = Δ η 0 cos ( Ω . t ) + α 0
A S ( θ ) = ν S ( θ ) E S and A P ( θ ) = ν P ( θ ) E P
I ( θ ) = I C ( θ ) + I Ω ( θ ) sin ( Ω . t ) + I 2 Ω cos ( 2 Ω . t )
I Ω ( θ ) = [ N S ( θ ) . N P ( θ ) ] 1 2 J 1 sin [ δ ( θ ) + α 0 ]
I 2 Ω ( θ ) = [ N S ( θ ) . N P ( θ ) ] 1 2 J 2 cos [ δ ( θ ) + α 0 ]
δ = δ S δ P = arg ( ν S . ν P * )
ν S = N S 1 2 exp ( j . δ S ) and ν P = N P 1 2 exp ( j . δ P )
A S ( θ ) = ν S S ( θ ) E S + ν P S ( θ ) E P
A P ( θ ) = ν S P ( θ ) E S + ν P P ( θ ) E P
I Ω ( θ ) = N ( θ ) J 1 sin [ δ ( θ ) + α 0 ]
I 2 Ω ( θ ) = N ( θ ) J 2 cos [ δ ( θ ) + α 0 ]
N = ( ν S S + ν S P ) . ( ν P S * + ν P P * )
δ = arg [ ( ν S S + ν S P ) . ( ν P S * + ν P P * ) ]
ν 1 , S ( σ ) = C 1 , S ( σ ) h ( σ ) and ν 1 , P ( σ ) = C 1 , P ( σ ) h ( σ ) for surface scattering
ν 2 , S ( σ ) = C 2 , S ( σ ) p ( σ ) and ν 2 , P ( σ ) = C 2 , P ( σ ) p ( σ ) for bulk scattering
δ i = arg ( ν i , S · ν i , P * ) = arg ( C i , S · C i , P * γ i ) = arg ( C i , S · C i , P * )
γ 1 = ( 4 π 2 Σ ) h 2 and γ 2 = ( 4 π 2 Σ ) p 2
δ = arg [ C 1 , S · C 1 , P · h 2 + C 2 , S · C 2 , P · p 2 + C 1 , S · C 2 , P * . h . p * + C 2 , S * . C 1 , P . h * . p ]
± i 1 = i ± β
β > i s ± i
ν x y = N x y 0.5 exp ( j δ x y )
τ x y = T x y 0.5 exp ( j κ x y )
ν S P = τ S P ν S S = T S P 0.5 N S S 0.5 exp [ j ( κ S P + δ S S ) ]
ν P S = τ P S ν P P = T P S 0.5 N P P 0.5 exp [ j ( κ P S + δ P P ) ]
δ = ( δ S S δ P P ) + Arg [ ( 1 + τ S P ) ( 1 + τ P S ) ] = δ + Arg ( z 1 )
T S P T P S
z 1 = 1 + T 0.5 [ exp ( j κ S P ) + exp ( j κ P S ) + T exp [ j ( κ S P κ P S ) ]
ν S S = ν 1 , S S + ν 2 , S S = ν 1 , S S ( 1 + α S S )
ν P P = ν 1 , P P + ν 2 , P P = ν 1 , P P ( 1 + α P P )
δ = δ 1 + Arg ( z 1 ) + Arg ( z 2 )
z 2 = 1 + ρ 0.5 [ exp ( j ξ S P ) + exp ( j ξ P S ) ] + a exp [ j ( ξ S P ξ P S ) ]
α = ρ exp ( j ξ ) and ρ = α

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