Abstract

We have previously shown that macroscopic roughness spectra measured with light scattering at visible wavelengths were perfectly extrapolated at high spatial frequencies by microscopic roughness spectra measured with atomic force microscopy [Europhys. Lett. 22, 717 (1993); Proc. SPIE 2253, 614 (1994)]. These results have been confirmed by numerous experiments [Proc. SPIE 2253, 614 (1994)] and allow us today to characterize thin films microstructure from a macroscopic to a microscopic scale. In the first step the comparison of light scattering and atomic force microscopy is completed by optical measurements at UV wavelengths that allow us to superimpose (and no longer extrapolate) the spectra measured by the two techniques. In the second step we extract multiscale parameters that describe the action of thin-film coatings on substrate roughness in all bandwidths. The results obviously depend on materials and substrates and deposition techniques. Electron-beam evaporation, ion-assisted deposition, and ion plating are compared, and the conclusions are discussed in regard to the deposition parameters. Finally, special attention is given to the limits and performances of the two characterization techniques (light scattering and atomic force microscopy) that may be sensitive to different phenomena.

© 1996 Optical Society of America

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References

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  1. Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness using near field microscopies and optical,” Europhys. Lett. 22, 717–722 (1993).
    [CrossRef]
  2. C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).
  3. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).
  4. 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]
  5. J. M. Elson, “Angle resolved light scattering from composite optical surfaces,” in Periodic Structures, Gratings, Moire Patterns, and Diffraction Phenomena I, C. H. Chin, ed., Proc. SPIE240, 296–306 (1980).
  6. 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]
  7. S. Kassam, A. Duparré, K. Hehl, P. Bussemer, J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
    [CrossRef] [PubMed]
  8. C. Amra, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
    [CrossRef] [PubMed]
  9. C. Amra, “Light scattering from multilayer optics. Part A: investigation tools,” J. Opt. Soc. Am. A 11, 197–210 (1994).
    [CrossRef]
  10. C. Amra, “Light scattering from multilayer optics. Part B: Application to experiment,” J. Opt. Soc. Am. A 11, 211–226 (1994).
    [CrossRef]
  11. 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]
  12. C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
    [CrossRef]
  13. C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical coatings,” Appl. Opt. 32, 5492–5503 (1993).
    [CrossRef] [PubMed]
  14. C. Amra, D. Torricini, P. Roche, “Multiwavelength (0.45–10.6 μm) angle-resolved scatterometer or how to extend the optic window,” Appl. Opt. 32, 5462–5474 (1993).
    [CrossRef] [PubMed]

1994 (2)

1993 (5)

1992 (2)

1983 (1)

1980 (1)

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]

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness using near field microscopies and optical,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

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

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]

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

André, E.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness using near field microscopies and optical,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

Apfel, J. H.

Bennett, J. M.

Bouffakhreddine, B.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness using near field microscopies and optical,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

Bruel, L.

Bussemer, P.

Deumié, C.

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

Dumas, Ph.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness using near field microscopies and optical,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

Duparré, A.

Elson, J. M.

Galindo, R.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness using near field microscopies and optical,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

Grèzes-Besset, C.

Hehl, K.

Kassam, S.

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).

Neubert, J.

Pelletier, E.

Rahn, J. P.

Roche, P.

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

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

Salvan, F.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness using near field microscopies and optical,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

Torricini, D.

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

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

Vatel, O.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness using near field microscopies and optical,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

Appl. Opt. (7)

Europhys. Lett. (1)

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness using near field microscopies and optical,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

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

Other (3)

C. Amra, C. Deumié, D. Torricini, P. Roche, R. Galindo, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwidths,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 614–630 (1994).

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).

J. M. Elson, “Angle resolved light scattering from composite optical surfaces,” in Periodic Structures, Gratings, Moire Patterns, and Diffraction Phenomena I, C. H. Chin, ed., Proc. SPIE240, 296–306 (1980).

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Figures (21)

Fig. 1
Fig. 1

Roughness spectra measured in two frequency bandwidths obtained with visible (633-nm) and near-IR (1.06-μm) illumination wavelengths. The sample is an uncoated glass surface, and the measurement technique is light scattering.

Fig. 2
Fig. 2

AFM pictures of a fused-silica substrate with current polish, a glass substrate (RG 1000 Schott) with current polish, and a supersmooth silicon substrate. The scan lengths are 5 μm in the fused silica and glass and 0.5 μm in the silicon, with height scales equal to 20 nm/div in the fused silica, 40 nm/div in the glass, and 2 nm/div in the silicon. In the silicon the slight anisotropy originates from an AFM artifact.

Fig. 3
Fig. 3

Calculation of the spectra γ ¯ 0(σ) [curve (1)], γ ¯ 1(σ) [curve (2)], and γ ¯ 2(σ) [curve (3)] for a glass substrate (see text). Removing one frequency is enough to obtain a correct spectrum. The scan length is 15 μm.

Fig. 4
Fig. 4

Spectra of a numerical random surface [curve (1)], the curvature surface [curve (2)] whose axes are deduced from sections of AFM pictures, and the random surface plus the curvature [curve (3)]. The average curvature radius is approximately 0.5 mm.

Fig. 5
Fig. 5

Section of curvature surface emphasized by a Si surface measured on a rather large area (L = 10 μm). For this size, AFM sensitivity is not sufficient enough for us to gain access to the roughness, but it permits us to obtain a picture of the piezoelectric curvature surface. The vertical distance between repairs is 10.5 nm. The horizontal distance between repairs is 5.6 μm, so that the equivalent curvature radius is approximately 1.5 mm. Note that the curvature radius is relative to the best circle that fits the partial curve.

Fig. 6
Fig. 6

Spectra obtained for a Si substrate by AFM measurements [curve (1)] with different lag lengths, by optical measurements at the 633-nm visible wavelength [curve (2)], and the spectrum of a surface of curvature [curve (3)] obtained by measurement of a Si surface for a large scan length (10 μm) (see Fig. 5). Curve (3) is due only to curvature and does not overlap or extrapolate the optical measurements.

Fig. 7
Fig. 7

AFM picture of (left) a localized defect, (right) its roughness spectrum. The defect diameter is ~0.08 μm.

Fig. 8
Fig. 8

Roughness spectrum of a glass substrate issued from light-scattering measurements at 633 and 325 nm. The curves overlap at the intersection of the bandwidths.

Fig. 9
Fig. 9

Roughness spectrum of an Al substrate issued from light-scattering measurements at 633 and 325 nm. The curves overlap at the intersection of the bandwidths.

Fig. 10
Fig. 10

Average roughness spectra of a glass surface calculated from AFM measurements, with a scan length of L = 3 μm and 256 × 256 data points. Measurements were performed over two different regions of the sample in order to check the stationarity of roughness. The two curves are quasi-identical.

Fig. 11
Fig. 11

Roughness spectra calculated from AFM and light-scattering data for a glass substrate of current polish. The AFM measurements were performed with different scan lengths (Li = 25, 10, 5, 1, and 0.7 μm) and the same number of data points (N × N = 256 × 256), resulting in upper frequency limits equal to N/Li = 5.1, 12.8, 25.6, 128, and 182 μm−1. These AFM spectra overlap at the intersection of bandwidths. Note that the spectra are very close to a straight line with a σ−2.7 frequency variation. Light-scattering measurements were performed at the 633-nm visible wavelength so that the upper frequency limit is given by 1/λ. The optical spectrum agrees well with AFM spectra. Note that the abscissa is the spatial frequency ν in inverse micrometers.

Fig. 12
Fig. 12

Roughness spectra calculated from AFM and light-scattering data for an Al substrate. AFM measurements were performed with 128 × 28 data points and a scan length of L = 5 μm, which gives an upper frequency equal to 0.16 nm−1. Light-scattering measurements were performed at 633 and 325 nm, so that the upper frequency limits are, respectively, 1/633 nm = 1.5 × 10−3 nm−1 and 1/325 nm = 3 × 10−3 nm−1. The optical spectra agree well with AFM spectra. Note that the abscissa is σ = 2πν in inverse nanometers.

Fig. 13
Fig. 13

Roughness spectra calculated from AFM and light-scattering data for a supersmooth Si substrate. The AFM measurements were performed with different scan lengths (Li = 5 μm, 1 μm, and 500 nm) and the same number of data points (N × N = 256 × 256), resulting in upper frequency limits equal to 2πN/Li = 0.16, 0.8, and 1.6 nm−1. These AFM spectra overlap at the intersection of bandwidths. Light-scattering measurements were performed at 633 nm, so that the upper frequency limit is given by 1/λ. The optical spectrum agrees well with AFM spectra. Note that the abscissa is σ = 2πν in inverse nanometers.

Fig. 14
Fig. 14

AFM pictures of a Si substrate with L = 500 nm and a vertical scale of 2 nm/div, a TiO2 layer produced by IAD on a Si substrate with L = 500 nm and a vertical scale of 2 nm/div, a TiO2 layer produced by EBD on a Si substrate with L = 500 nm and a vertical scale of 20 nm/div.

Fig. 15
Fig. 15

AFM roughness spectra that correspond to the pictures of Fig. 14: Si substrate [curve (1)], TiO2 layer produced by IAD on a Si substrate [curve (2)], and TiO2 layer produced by EBD on a Si substrate [curve (3)]. Obviously the IAD spectrum is very close to the uncoated Si spectrum in all bandwidths, whereas the EBD spectrum is much rougher.

Fig. 16
Fig. 16

AFM pictures of ZnS deposited by EBD on a Si substrate for different substrate temperatures: (top left) 35 °C, (middle left) 70 °C, (bottom left) 110 °C, (top right) 150 °C, (bottom right) 200 °C. The scan length is 500 nm, with 512 × 512 data points.

Fig. 17
Fig. 17

AFM roughness spectra that correspond to the case of Figs. 16(top left) [curve (1)], 16(middle left) [curve (2)], 16(bottom left) [curve (3)], and 16(top right) [curve (4)]. Several lag lengths were used for each substrate temperature.

Fig. 18
Fig. 18

Roughness spectra obtained for numerical surfaces with bumps of diameter s and height h, with s = 40 nm and h = 3 nm [curve (1)]; s = 80 nm and h = 5 nm [curve (2)]; s = 140 nm and h = 10 nm [curve (3)]; s = 300 nm and h = 75 nm [curve (4)]. The scan length is equal to 500 nm for 128 × 128 data points.

Fig. 19
Fig. 19

AFM pictures of different materials obtained by EBD on a Si substrate: (top left) for an uncoated silicon substrate, (bottom left) for a TiO2 layer, (top right) for a ZnS layer, (bottom right) for an Al layer. The scan length is 500 nm, with 512 × 512 data points.

Fig. 20
Fig. 20

Roughness spectra issued from the AFM measurements of Fig. 19. Curve (1) is for an uncoated Si substrate, curve (2) for a TiO2 layer, and curve (3) for a ZnS layer. Several scan lengths, from 1 to 0.5 μm, are used for each sample measurement, with 256 × 256 data points.

Fig. 21
Fig. 21

AFM pictures of (left) a TiO2 layer deposited by EBD on a Si substrate, (right) the same layer after bombardment by an ion beam. Left, the scan length is 1 μm and the vertical scale is 5 nm/div. Right, the scan length is 500 nm and the vertical scale is 3 nm/div.

Tables (1)

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Table 1 Refractive Index n and Extinction Coefficient k for a ZnS Layer Produced by EBD at Different Temperatures

Equations (22)

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sin θ min λ < ν < 1 λ ,
I ( θ , ϕ ) = C ( θ , ϕ ) γ ( θ , ϕ ) ,
C ( θ , ϕ ) = C ( θ ) = 1 2 ( 2 π n o λ ) 2 [ cos 2 θ q s 2 + q p 2 ] ,
q s ( θ ) = j ( 2 π λ ) 2 n o ( n o - n s ) ( n o cos θ o + n s cos θ s ) - 1 ,
q p ( θ ) = j ( 2 π λ ) 2 n o ( n o - n s ) ( n o / cos θ o + n s / cos θ s ) - 1 ,
n o sin θ o = n s sin θ s .
γ ( σ ) = 4 π 2 S h ^ ( σ ) 2 ,
h ^ ( σ ) = 1 4 π 2 r S h ( r ) exp ( - j σ · r ) d r .
σ B ( λ ) sin θ min / λ ν = σ / ( 2 π ) 1 / λ ,
δ 2 = 1 S S h 2 ( r ) d r = σ B ( λ ) γ ( σ ) d σ .
δ 2 = ( 2 π λ ) 2 0 θ π / 2 0 ϕ 2 π γ ( θ , ϕ ) sin θ cos θ d θ d ϕ .
γ ¯ ( σ ) = 1 2 π ϕ = 0 2 π γ ( θ , ϕ ) d ϕ ,
δ 2 = 2 π 2 π sin θ min / λ 2 π / λ σ γ ¯ ( σ ) d σ .
γ p q = γ ( p Δ σ x , q Δ σ y ) = ( 2 π L ) 2 h ^ ( p Δ σ x , q Δ σ y ) 2 ,
Δ σ x = Δ σ y = π N Δ x = π L .
h ^ ( σ ) = 1 4 π 2 - + - + h ( r ) exp ( - j σ · r ) d r ,
h ^ ( p 2 π L , q 2 π L ) = 1 4 π 2 L 2 N 2 m , n h ( m L N , n L N ) × exp [ - j 2 π N ( m p + m q ) ] ,
γ ( p 2 π L , q 2 π L ) = ( L 2 4 π 2 N 4 ) | m , n h ( m L N , n L N ) × exp [ - j 2 π N ( m p + n q ) ] | 2 .
δ 2 = 2 π σ min σ max σ γ ¯ ( σ ) d σ .
B ( 633 nm ) = ( 8.2 × 10 - 5 nm - 1 , 10 - 2 nm - 1 ) , B ( 325 nm ) = ( 1.6 × 10 - 4 nm - 1 , 2 × 10 - 2 nm - 1 ) .
γ ¯ ( σ ) = β / σ α ,
D = ( 8 - α ) / 2.

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