Abstract

Angular dependencies of the scattered light intensity were measured on Si wafers that have different crystallographic orientations by using a He–Ne laser (λ = 632.8 nm, 80 μm spot diameter). During the experiment the Si wafer was fixed relative to the incident beam. Regular patterns were found in the azimuthal-angle-resolved scattering curves. Such patterns seem to be caused by the faceted shallow atomic structures of the surface.

© 1995 Optical Society of America

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References

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  1. 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]
  2. J. M. Bennett, J. M. Elson, J. P. Rahn, “Angle-resolved scattering: comparison of theory and experiment,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 401, 234–246 (1983).
  3. H.-G. Walther, G. Schirmer, “Untersuchung von Lichtstreuung von transparenten Einfachschichten auf Glassubstraten,” Ann. Phys. 7(41), 12–22 (1984).
    [CrossRef]
  4. D. J. Janeczko, “Power spectrum standard for surface roughness,” in Scatter from Optical Components, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1165, 175–183 (1989).
  5. P. Roche, P. Bousquet, F. Flory, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. 1, 1028–1031 (1984).
    [CrossRef]
  6. A. J. Pidduck, D. J. Robbins, A. G. Cullis, D. B. Gasson, J. L. Glasper, “In situ laser light scattering. Part II. Relationship to silicon surface topography,” J. Electrochem. Soc. 136, 3089–3094 (1989).
  7. P. O. Hahn, M. Kerstan, “Elastic light scattering measurements on Si surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1009, 172–180 (1988).
  8. H. Wang, “Light-scattering method for characterizing optical surface,” Opt. Eng. 32, 2904–2910 (1993).
    [CrossRef]
  9. E. Bauer, “Surface processes studied by LEEM,” presented at the Workshop on Frontiers of Surface Diffraction and Imaging, Hong Kong University of Science and Technology, Hong Kong, August 1993.
  10. M. Iwatsuki, S. Kitamura, T. Sato, T. Snejoshi, “Nanofabrication on silicon at high temperature in a UHV-STM,” Nanotechnology 3, 137–141 (1992).
    [CrossRef]

1993

H. Wang, “Light-scattering method for characterizing optical surface,” Opt. Eng. 32, 2904–2910 (1993).
[CrossRef]

1992

M. Iwatsuki, S. Kitamura, T. Sato, T. Snejoshi, “Nanofabrication on silicon at high temperature in a UHV-STM,” Nanotechnology 3, 137–141 (1992).
[CrossRef]

1989

A. J. Pidduck, D. J. Robbins, A. G. Cullis, D. B. Gasson, J. L. Glasper, “In situ laser light scattering. Part II. Relationship to silicon surface topography,” J. Electrochem. Soc. 136, 3089–3094 (1989).

1984

H.-G. Walther, G. Schirmer, “Untersuchung von Lichtstreuung von transparenten Einfachschichten auf Glassubstraten,” Ann. Phys. 7(41), 12–22 (1984).
[CrossRef]

P. Roche, P. Bousquet, F. Flory, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. 1, 1028–1031 (1984).
[CrossRef]

1983

Bauer, E.

E. Bauer, “Surface processes studied by LEEM,” presented at the Workshop on Frontiers of Surface Diffraction and Imaging, Hong Kong University of Science and Technology, Hong Kong, August 1993.

Bennett, J. M.

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]

J. M. Bennett, J. M. Elson, J. P. Rahn, “Angle-resolved scattering: comparison of theory and experiment,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 401, 234–246 (1983).

Bousquet, P.

P. Roche, P. Bousquet, F. Flory, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. 1, 1028–1031 (1984).
[CrossRef]

Cullis, A. G.

A. J. Pidduck, D. J. Robbins, A. G. Cullis, D. B. Gasson, J. L. Glasper, “In situ laser light scattering. Part II. Relationship to silicon surface topography,” J. Electrochem. Soc. 136, 3089–3094 (1989).

Elson, J. M.

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]

J. M. Bennett, J. M. Elson, J. P. Rahn, “Angle-resolved scattering: comparison of theory and experiment,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 401, 234–246 (1983).

Flory, F.

P. Roche, P. Bousquet, F. Flory, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. 1, 1028–1031 (1984).
[CrossRef]

Gasson, D. B.

A. J. Pidduck, D. J. Robbins, A. G. Cullis, D. B. Gasson, J. L. Glasper, “In situ laser light scattering. Part II. Relationship to silicon surface topography,” J. Electrochem. Soc. 136, 3089–3094 (1989).

Glasper, J. L.

A. J. Pidduck, D. J. Robbins, A. G. Cullis, D. B. Gasson, J. L. Glasper, “In situ laser light scattering. Part II. Relationship to silicon surface topography,” J. Electrochem. Soc. 136, 3089–3094 (1989).

Hahn, P. O.

P. O. Hahn, M. Kerstan, “Elastic light scattering measurements on Si surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1009, 172–180 (1988).

Iwatsuki, M.

M. Iwatsuki, S. Kitamura, T. Sato, T. Snejoshi, “Nanofabrication on silicon at high temperature in a UHV-STM,” Nanotechnology 3, 137–141 (1992).
[CrossRef]

Janeczko, D. J.

D. J. Janeczko, “Power spectrum standard for surface roughness,” in Scatter from Optical Components, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1165, 175–183 (1989).

Kerstan, M.

P. O. Hahn, M. Kerstan, “Elastic light scattering measurements on Si surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1009, 172–180 (1988).

Kitamura, S.

M. Iwatsuki, S. Kitamura, T. Sato, T. Snejoshi, “Nanofabrication on silicon at high temperature in a UHV-STM,” Nanotechnology 3, 137–141 (1992).
[CrossRef]

Pidduck, A. J.

A. J. Pidduck, D. J. Robbins, A. G. Cullis, D. B. Gasson, J. L. Glasper, “In situ laser light scattering. Part II. Relationship to silicon surface topography,” J. Electrochem. Soc. 136, 3089–3094 (1989).

Rahn, J. P.

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]

J. M. Bennett, J. M. Elson, J. P. Rahn, “Angle-resolved scattering: comparison of theory and experiment,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 401, 234–246 (1983).

Robbins, D. J.

A. J. Pidduck, D. J. Robbins, A. G. Cullis, D. B. Gasson, J. L. Glasper, “In situ laser light scattering. Part II. Relationship to silicon surface topography,” J. Electrochem. Soc. 136, 3089–3094 (1989).

Roche, P.

P. Roche, P. Bousquet, F. Flory, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. 1, 1028–1031 (1984).
[CrossRef]

Sato, T.

M. Iwatsuki, S. Kitamura, T. Sato, T. Snejoshi, “Nanofabrication on silicon at high temperature in a UHV-STM,” Nanotechnology 3, 137–141 (1992).
[CrossRef]

Schirmer, G.

H.-G. Walther, G. Schirmer, “Untersuchung von Lichtstreuung von transparenten Einfachschichten auf Glassubstraten,” Ann. Phys. 7(41), 12–22 (1984).
[CrossRef]

Snejoshi, T.

M. Iwatsuki, S. Kitamura, T. Sato, T. Snejoshi, “Nanofabrication on silicon at high temperature in a UHV-STM,” Nanotechnology 3, 137–141 (1992).
[CrossRef]

Walther, H.-G.

H.-G. Walther, G. Schirmer, “Untersuchung von Lichtstreuung von transparenten Einfachschichten auf Glassubstraten,” Ann. Phys. 7(41), 12–22 (1984).
[CrossRef]

Wang, H.

H. Wang, “Light-scattering method for characterizing optical surface,” Opt. Eng. 32, 2904–2910 (1993).
[CrossRef]

Ann. Phys.

H.-G. Walther, G. Schirmer, “Untersuchung von Lichtstreuung von transparenten Einfachschichten auf Glassubstraten,” Ann. Phys. 7(41), 12–22 (1984).
[CrossRef]

Appl. Opt.

J. Electrochem. Soc.

A. J. Pidduck, D. J. Robbins, A. G. Cullis, D. B. Gasson, J. L. Glasper, “In situ laser light scattering. Part II. Relationship to silicon surface topography,” J. Electrochem. Soc. 136, 3089–3094 (1989).

J. Opt. Soc. Am.

P. Roche, P. Bousquet, F. Flory, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. 1, 1028–1031 (1984).
[CrossRef]

Nanotechnology

M. Iwatsuki, S. Kitamura, T. Sato, T. Snejoshi, “Nanofabrication on silicon at high temperature in a UHV-STM,” Nanotechnology 3, 137–141 (1992).
[CrossRef]

Opt. Eng.

H. Wang, “Light-scattering method for characterizing optical surface,” Opt. Eng. 32, 2904–2910 (1993).
[CrossRef]

Other

E. Bauer, “Surface processes studied by LEEM,” presented at the Workshop on Frontiers of Surface Diffraction and Imaging, Hong Kong University of Science and Technology, Hong Kong, August 1993.

P. O. Hahn, M. Kerstan, “Elastic light scattering measurements on Si surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1009, 172–180 (1988).

J. M. Bennett, J. M. Elson, J. P. Rahn, “Angle-resolved scattering: comparison of theory and experiment,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 401, 234–246 (1983).

D. J. Janeczko, “Power spectrum standard for surface roughness,” in Scatter from Optical Components, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1165, 175–183 (1989).

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Figures (5)

Fig. 1
Fig. 1

Optical schematic of the equipment used: L, He–Ne laser; BCh, beam chopper; MOb, microobjective; Ob’s, objectives; D’s, diaphragms; M, Al mirror; S, Si wafer; SM’s, stepper motors; PM, photomultiplier.

Fig. 2
Fig. 2

3-D dependence of BRDF(θ, ϕ) in cylindrical coordinates for Si(100) surface. A sketch of the applied reference system is shown in the upper-right-hand corner.

Fig. 3
Fig. 3

Isophote map of log[BRDF(θ, ϕ)] for a Si(100) surface. Contour line labels are the values of the BRDF.

Fig. 4
Fig. 4

Same as Fig. 3 except for a Si(111) surface.

Fig. 5
Fig. 5

Power spectral density function for the Si(100) surface S 1 versus spatial frequency f x . The rms roughness was calculated from that in Eqs. (1) and (2).

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

BRDF ( θ , ϕ ) = 1 I 0 d I ( θ , ϕ ) d Ω .
TIS = 1 I 0 d I d Ω sin ( θ ) d Ω .
d I d θ = const .
σ = λ 4 π TIS .
BRDF ( θ ) 16 π 2 λ 4 cos ( θ ) R ( θ ) S 1 ( f ) ,
S 1 ( f ) = A f B ,
σ 2 = A B - 1 1 C B - 1 1 D B - 1 ,

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