Abstract

The polarization and intensity of light scattered by polystyrene latex and copper spheres with diameters of approximately 100 nm deposited onto silicon substrates containing various thicknesses of oxide films were measured with 532-nm light. The results are compared with a theory for scattering by a sphere on a surface, originally developed by others [Physica A 137, 209 (1986)] and extended to include coatings on the substrate. Nonlinear least-squares fits of the theory to the observations yield results that were consistent with differential mobility measurements of the particle diameter.

© 2004 Optical Society of America

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References

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  1. J. C. Stover, Optical Scattering: Measurement and Analysis, Vol. PM24 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1995).
  2. P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
    [CrossRef]
  3. K. B. Nahm, W. L. Wolfe, “Light-scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
  5. G. Videen, “Light scattering from a sphere on or near a surface: errata,” J. Opt. Soc. Am. A 9, 844–845 (1992).
    [CrossRef]
  6. G. Videen, M. G. Turner, V. J. Iafelice, W. S. Bickel, W. L. Wolfe, “Scattering from a small sphere near a surface,” J. Opt. Soc. Am. A 10, 118–126 (1993).
    [CrossRef]
  7. Yu. Eremin, N. Orlov, “Simulation of light scattering from a particle upon a wafer surface,” Appl. Opt. 35, 6599–6604 (1996).
    [CrossRef] [PubMed]
  8. E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
    [CrossRef]
  9. R. Schmehl, B. M. Nebeker, E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A 14, 3026–3036 (1997).
    [CrossRef]
  10. Yu. Eremin, N. Orlov, “Modeling of light scattering by non-spherical particles based on discrete sources method,” J. Quant. Spectrosc. Radiat. Transfer 60, 451–462 (1998).
    [CrossRef]
  11. Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
    [CrossRef]
  12. A. Doicu, Yu. Eremin, T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281–288 (2000).
    [CrossRef]
  13. D. C. Weber, E. D. Hirleman, “Light scattering signatures of individual spheres on optically smooth conducting surfaces,” Appl. Opt. 27, 4019–4026 (1988).
    [CrossRef] [PubMed]
  14. L. Sung, G. W. Mulholland, T. A. Germer, “Polarized light-scattering measurements of dielectric spheres upon a silicon surface,” Opt. Lett. 24, 866–868 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  18. J. C. Stover, C. A. Scheer, “Accurate sizing of deposited PSL spheres from light scatter measurements,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparré, B. Singh, eds., Proc. SPIE4449, 147–150 (2001).
    [CrossRef]
  19. T. A. Germer, G. W. Mulholland, J. H. Kim, S. H. Ehrman, “Measurement of the 100 nm NIST SRM® 1963 by laser surface light scattering,” in Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, A. Duparré, B. Singh, eds., Proc. SPIE4779, 60–71 (2002).
    [CrossRef]
  20. T. A. Germer, “SCATMECH: polarized light scattering C++ class library,” available at http://physics.nist.gov/scatmech (2000).
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  22. C. R. Helms, C.-J. Han, “Parallel oxidation mechanism for Si oxidation in dry O2,” J. Electrochem. Soc. 134, 1297–1302 (1987).
    [CrossRef]
  23. Y. Wang, J. Tao, S. Tong, T. Sun, A. Zhang, S. Feng, “The oxidation kinetics of thin polycrystalline silicon films,” J. Electrochem. Soc. 138, 214–219 (1991).
    [CrossRef]
  24. Unless otherwise noted, we obtained the uncertainties quoted in this paper by estimating the standard uncertainty u for the measurement and multiplying by a coverage factor of k = 2. These values correspond to a confidence level of 95%.
  25. G. W. Mulholland, N. P. Bryner, C. Croarkin, “Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis,” Aerosol Sci. Technol. 31, 39–55 (1999).
    [CrossRef]
  26. J. H. Kim, T. A. Germer, G. W. Mulholland, S. H. Ehrman, “Size-monodisperse metal nanoparticles via hydrogen-free spray pyrolysis,” Adv. Mater. 14, 518–521 (2002).
    [CrossRef]
  27. P. D. Kinney, D. Y. H. Pui, G. W. Mulholland, N. P. Bryner, “Use of the electrostatic classification method to size 0.1 μm SRM particles—a feasibility study,” J. Res. Natl. Inst. Stand. Technol. 96, 147–176 (1991).
    [CrossRef]
  28. E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985).
  29. R. H. Boundy, R. F. Boyer, eds., Styrene, Its Polymers, Copolymers, and Derivatives (Reinhold, New York, 1952).
  30. T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instr. 70, 3688–3695 (1999).
    [CrossRef]
  31. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

2002

2001

2000

A. Doicu, Yu. Eremin, T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281–288 (2000).
[CrossRef]

1999

Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
[CrossRef]

L. Sung, G. W. Mulholland, T. A. Germer, “Polarized light-scattering measurements of dielectric spheres upon a silicon surface,” Opt. Lett. 24, 866–868 (1999).
[CrossRef]

G. W. Mulholland, N. P. Bryner, C. Croarkin, “Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis,” Aerosol Sci. Technol. 31, 39–55 (1999).
[CrossRef]

T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instr. 70, 3688–3695 (1999).
[CrossRef]

1998

Yu. Eremin, N. Orlov, “Modeling of light scattering by non-spherical particles based on discrete sources method,” J. Quant. Spectrosc. Radiat. Transfer 60, 451–462 (1998).
[CrossRef]

1997

1996

1993

1992

1991

G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991).
[CrossRef]

P. D. Kinney, D. Y. H. Pui, G. W. Mulholland, N. P. Bryner, “Use of the electrostatic classification method to size 0.1 μm SRM particles—a feasibility study,” J. Res. Natl. Inst. Stand. Technol. 96, 147–176 (1991).
[CrossRef]

Y. Wang, J. Tao, S. Tong, T. Sun, A. Zhang, S. Feng, “The oxidation kinetics of thin polycrystalline silicon films,” J. Electrochem. Soc. 138, 214–219 (1991).
[CrossRef]

1988

1987

K. B. Nahm, W. L. Wolfe, “Light-scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef] [PubMed]

C. R. Helms, C.-J. Han, “Parallel oxidation mechanism for Si oxidation in dry O2,” J. Electrochem. Soc. 134, 1297–1302 (1987).
[CrossRef]

1986

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

1984

W. Kern, D. A. Puotinen, “Cleaning solutions based on hydrogen peroxide for use in silicon semiconductor technology,” RCA Rev. 30, 187–206 (1984).

Asmail, C. C.

T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instr. 70, 3688–3695 (1999).
[CrossRef]

Bickel, W. S.

Bobbert, P. A.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

Borghese, F.

Bryner, N. P.

G. W. Mulholland, N. P. Bryner, C. Croarkin, “Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis,” Aerosol Sci. Technol. 31, 39–55 (1999).
[CrossRef]

P. D. Kinney, D. Y. H. Pui, G. W. Mulholland, N. P. Bryner, “Use of the electrostatic classification method to size 0.1 μm SRM particles—a feasibility study,” J. Res. Natl. Inst. Stand. Technol. 96, 147–176 (1991).
[CrossRef]

Croarkin, C.

G. W. Mulholland, N. P. Bryner, C. Croarkin, “Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis,” Aerosol Sci. Technol. 31, 39–55 (1999).
[CrossRef]

Denti, P.

Doicu, A.

A. Doicu, Yu. Eremin, T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281–288 (2000).
[CrossRef]

Drevillon, B.

Ehrman, S. H.

J. H. Kim, S. H. Ehrman, G. W. Mulholland, T. A. Germer, “Polarized light scattering by dielectric and metallic spheres on silicon wafers,” Appl. Opt. 41, 5405–5412 (2002).
[CrossRef] [PubMed]

J. H. Kim, T. A. Germer, G. W. Mulholland, S. H. Ehrman, “Size-monodisperse metal nanoparticles via hydrogen-free spray pyrolysis,” Adv. Mater. 14, 518–521 (2002).
[CrossRef]

T. A. Germer, G. W. Mulholland, J. H. Kim, S. H. Ehrman, “Measurement of the 100 nm NIST SRM® 1963 by laser surface light scattering,” in Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, A. Duparré, B. Singh, eds., Proc. SPIE4779, 60–71 (2002).
[CrossRef]

Eremin, Y. A.

Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
[CrossRef]

Eremin, Yu.

A. Doicu, Yu. Eremin, T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281–288 (2000).
[CrossRef]

Yu. Eremin, N. Orlov, “Modeling of light scattering by non-spherical particles based on discrete sources method,” J. Quant. Spectrosc. Radiat. Transfer 60, 451–462 (1998).
[CrossRef]

Yu. Eremin, N. Orlov, “Simulation of light scattering from a particle upon a wafer surface,” Appl. Opt. 35, 6599–6604 (1996).
[CrossRef] [PubMed]

Feng, S.

Y. Wang, J. Tao, S. Tong, T. Sun, A. Zhang, S. Feng, “The oxidation kinetics of thin polycrystalline silicon films,” J. Electrochem. Soc. 138, 214–219 (1991).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Fucile, E.

Germer, T. A.

J. H. Kim, T. A. Germer, G. W. Mulholland, S. H. Ehrman, “Size-monodisperse metal nanoparticles via hydrogen-free spray pyrolysis,” Adv. Mater. 14, 518–521 (2002).
[CrossRef]

J. H. Kim, S. H. Ehrman, G. W. Mulholland, T. A. Germer, “Polarized light scattering by dielectric and metallic spheres on silicon wafers,” Appl. Opt. 41, 5405–5412 (2002).
[CrossRef] [PubMed]

L. Sung, G. W. Mulholland, T. A. Germer, “Polarized light-scattering measurements of dielectric spheres upon a silicon surface,” Opt. Lett. 24, 866–868 (1999).
[CrossRef]

T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instr. 70, 3688–3695 (1999).
[CrossRef]

T. A. Germer, G. W. Mulholland, J. H. Kim, S. H. Ehrman, “Measurement of the 100 nm NIST SRM® 1963 by laser surface light scattering,” in Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, A. Duparré, B. Singh, eds., Proc. SPIE4779, 60–71 (2002).
[CrossRef]

Han, C.-J.

C. R. Helms, C.-J. Han, “Parallel oxidation mechanism for Si oxidation in dry O2,” J. Electrochem. Soc. 134, 1297–1302 (1987).
[CrossRef]

Helms, C. R.

C. R. Helms, C.-J. Han, “Parallel oxidation mechanism for Si oxidation in dry O2,” J. Electrochem. Soc. 134, 1297–1302 (1987).
[CrossRef]

Hirleman, E. D.

Iafelice, V. J.

Kaplan, B.

Kern, W.

W. Kern, D. A. Puotinen, “Cleaning solutions based on hydrogen peroxide for use in silicon semiconductor technology,” RCA Rev. 30, 187–206 (1984).

Kim, J. H.

J. H. Kim, S. H. Ehrman, G. W. Mulholland, T. A. Germer, “Polarized light scattering by dielectric and metallic spheres on silicon wafers,” Appl. Opt. 41, 5405–5412 (2002).
[CrossRef] [PubMed]

J. H. Kim, T. A. Germer, G. W. Mulholland, S. H. Ehrman, “Size-monodisperse metal nanoparticles via hydrogen-free spray pyrolysis,” Adv. Mater. 14, 518–521 (2002).
[CrossRef]

T. A. Germer, G. W. Mulholland, J. H. Kim, S. H. Ehrman, “Measurement of the 100 nm NIST SRM® 1963 by laser surface light scattering,” in Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, A. Duparré, B. Singh, eds., Proc. SPIE4779, 60–71 (2002).
[CrossRef]

Kinney, P. D.

P. D. Kinney, D. Y. H. Pui, G. W. Mulholland, N. P. Bryner, “Use of the electrostatic classification method to size 0.1 μm SRM particles—a feasibility study,” J. Res. Natl. Inst. Stand. Technol. 96, 147–176 (1991).
[CrossRef]

Mulholland, G. W.

J. H. Kim, T. A. Germer, G. W. Mulholland, S. H. Ehrman, “Size-monodisperse metal nanoparticles via hydrogen-free spray pyrolysis,” Adv. Mater. 14, 518–521 (2002).
[CrossRef]

J. H. Kim, S. H. Ehrman, G. W. Mulholland, T. A. Germer, “Polarized light scattering by dielectric and metallic spheres on silicon wafers,” Appl. Opt. 41, 5405–5412 (2002).
[CrossRef] [PubMed]

G. W. Mulholland, N. P. Bryner, C. Croarkin, “Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis,” Aerosol Sci. Technol. 31, 39–55 (1999).
[CrossRef]

L. Sung, G. W. Mulholland, T. A. Germer, “Polarized light-scattering measurements of dielectric spheres upon a silicon surface,” Opt. Lett. 24, 866–868 (1999).
[CrossRef]

P. D. Kinney, D. Y. H. Pui, G. W. Mulholland, N. P. Bryner, “Use of the electrostatic classification method to size 0.1 μm SRM particles—a feasibility study,” J. Res. Natl. Inst. Stand. Technol. 96, 147–176 (1991).
[CrossRef]

T. A. Germer, G. W. Mulholland, J. H. Kim, S. H. Ehrman, “Measurement of the 100 nm NIST SRM® 1963 by laser surface light scattering,” in Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, A. Duparré, B. Singh, eds., Proc. SPIE4779, 60–71 (2002).
[CrossRef]

Nahm, K. B.

Nebeker, B. M.

Orlov, N.

Yu. Eremin, N. Orlov, “Modeling of light scattering by non-spherical particles based on discrete sources method,” J. Quant. Spectrosc. Radiat. Transfer 60, 451–462 (1998).
[CrossRef]

Yu. Eremin, N. Orlov, “Simulation of light scattering from a particle upon a wafer surface,” Appl. Opt. 35, 6599–6604 (1996).
[CrossRef] [PubMed]

Orlov, N. V.

Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Pui, D. Y. H.

P. D. Kinney, D. Y. H. Pui, G. W. Mulholland, N. P. Bryner, “Use of the electrostatic classification method to size 0.1 μm SRM particles—a feasibility study,” J. Res. Natl. Inst. Stand. Technol. 96, 147–176 (1991).
[CrossRef]

Puotinen, D. A.

W. Kern, D. A. Puotinen, “Cleaning solutions based on hydrogen peroxide for use in silicon semiconductor technology,” RCA Rev. 30, 187–206 (1984).

Saija, R.

Scheer, C. A.

J. C. Stover, C. A. Scheer, “Accurate sizing of deposited PSL spheres from light scatter measurements,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparré, B. Singh, eds., Proc. SPIE4449, 147–150 (2001).
[CrossRef]

Schmehl, R.

Sindoni, O. I.

Stover, J. C.

Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
[CrossRef]

J. C. Stover, Optical Scattering: Measurement and Analysis, Vol. PM24 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1995).

J. C. Stover, C. A. Scheer, “Accurate sizing of deposited PSL spheres from light scatter measurements,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparré, B. Singh, eds., Proc. SPIE4449, 147–150 (2001).
[CrossRef]

Sun, T.

Y. Wang, J. Tao, S. Tong, T. Sun, A. Zhang, S. Feng, “The oxidation kinetics of thin polycrystalline silicon films,” J. Electrochem. Soc. 138, 214–219 (1991).
[CrossRef]

Sung, L.

Tao, J.

Y. Wang, J. Tao, S. Tong, T. Sun, A. Zhang, S. Feng, “The oxidation kinetics of thin polycrystalline silicon films,” J. Electrochem. Soc. 138, 214–219 (1991).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Tong, S.

Y. Wang, J. Tao, S. Tong, T. Sun, A. Zhang, S. Feng, “The oxidation kinetics of thin polycrystalline silicon films,” J. Electrochem. Soc. 138, 214–219 (1991).
[CrossRef]

Turner, M. G.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Videen, G.

Vlieger, J.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

Wang, Y.

Y. Wang, J. Tao, S. Tong, T. Sun, A. Zhang, S. Feng, “The oxidation kinetics of thin polycrystalline silicon films,” J. Electrochem. Soc. 138, 214–219 (1991).
[CrossRef]

Weber, D. C.

Wolfe, W. L.

Wriedt, T.

A. Doicu, Yu. Eremin, T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281–288 (2000).
[CrossRef]

Zhang, A.

Y. Wang, J. Tao, S. Tong, T. Sun, A. Zhang, S. Feng, “The oxidation kinetics of thin polycrystalline silicon films,” J. Electrochem. Soc. 138, 214–219 (1991).
[CrossRef]

Adv. Mater.

J. H. Kim, T. A. Germer, G. W. Mulholland, S. H. Ehrman, “Size-monodisperse metal nanoparticles via hydrogen-free spray pyrolysis,” Adv. Mater. 14, 518–521 (2002).
[CrossRef]

Aerosol Sci. Technol.

G. W. Mulholland, N. P. Bryner, C. Croarkin, “Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis,” Aerosol Sci. Technol. 31, 39–55 (1999).
[CrossRef]

Appl. Opt.

J. Electrochem. Soc.

C. R. Helms, C.-J. Han, “Parallel oxidation mechanism for Si oxidation in dry O2,” J. Electrochem. Soc. 134, 1297–1302 (1987).
[CrossRef]

Y. Wang, J. Tao, S. Tong, T. Sun, A. Zhang, S. Feng, “The oxidation kinetics of thin polycrystalline silicon films,” J. Electrochem. Soc. 138, 214–219 (1991).
[CrossRef]

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

Yu. Eremin, N. Orlov, “Modeling of light scattering by non-spherical particles based on discrete sources method,” J. Quant. Spectrosc. Radiat. Transfer 60, 451–462 (1998).
[CrossRef]

J. Res. Natl. Inst. Stand. Technol.

P. D. Kinney, D. Y. H. Pui, G. W. Mulholland, N. P. Bryner, “Use of the electrostatic classification method to size 0.1 μm SRM particles—a feasibility study,” J. Res. Natl. Inst. Stand. Technol. 96, 147–176 (1991).
[CrossRef]

Opt. Commun.

A. Doicu, Yu. Eremin, T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281–288 (2000).
[CrossRef]

Opt. Eng.

Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
[CrossRef]

Opt. Lett.

Physica A

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

RCA Rev.

W. Kern, D. A. Puotinen, “Cleaning solutions based on hydrogen peroxide for use in silicon semiconductor technology,” RCA Rev. 30, 187–206 (1984).

Rev. Sci. Instr.

T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instr. 70, 3688–3695 (1999).
[CrossRef]

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Unless otherwise noted, we obtained the uncertainties quoted in this paper by estimating the standard uncertainty u for the measurement and multiplying by a coverage factor of k = 2. These values correspond to a confidence level of 95%.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985).

R. H. Boundy, R. F. Boyer, eds., Styrene, Its Polymers, Copolymers, and Derivatives (Reinhold, New York, 1952).

J. C. Stover, Optical Scattering: Measurement and Analysis, Vol. PM24 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1995).

J. C. Stover, C. A. Scheer, “Accurate sizing of deposited PSL spheres from light scatter measurements,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparré, B. Singh, eds., Proc. SPIE4449, 147–150 (2001).
[CrossRef]

T. A. Germer, G. W. Mulholland, J. H. Kim, S. H. Ehrman, “Measurement of the 100 nm NIST SRM® 1963 by laser surface light scattering,” in Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, A. Duparré, B. Singh, eds., Proc. SPIE4779, 60–71 (2002).
[CrossRef]

T. A. Germer, “SCATMECH: polarized light scattering C++ class library,” available at http://physics.nist.gov/scatmech (2000).

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Figures (6)

Fig. 1
Fig. 1

Light-scattering parameters for a 100-nm Cu sphere on a silicon substrate having a 160-nm SiO2 film predicted by the MSDI model, the NIA model, and the BV theory in the plane of incidence with θ i = 60° and λ = 532 nm.

Fig. 2
Fig. 2

Light-scattering parameters for 101-nm PSL spheres on a silicon substrate with 18-, 45-, and 66-nm SiO2 films measured in the plane of incidence with θ i = 60° and λ = 532 nm. The curves represent the predictions of the BV theory.

Fig. 3
Fig. 3

Light-scattering parameters for 100-nm Cu spheres on a silicon substrate with 18-, 40-, and 65-nm SiO2 films measured in the plane of incidence with θ i = 60° and λ = 532 nm. The curves represent the predictions of the BV theory.

Fig. 4
Fig. 4

Light-scattering parameters for a 100-nm Cu sphere on a silicon substrate with 18-nm SiO2 film calculated in the plane of incidence with θ i = 60° and λ = 532 nm. Comparison of the scattering parameters is made with the scattering by a 119-nm Cu sphere on a silicon substrate with 1.5-nm native oxide. The cross section for the 119-nm Cu spheres was multiplied by a factor of 0.6.

Fig. 5
Fig. 5

Light-scattering parameters for 101-nm PSL spheres on a silicon substrate with 2077-nm SiO2 films measured in the plane of incidence with θ i = 60° and λ = 532 nm. The curves represent the predictions of the BV theory.

Fig. 6
Fig. 6

Light-scattering parameters for 100-nm Cu spheres on a silicon substrate with 2086-nm SiO2 films measured in the plane of incidence with θ i = 60° and λ = 532 nm. The curves represent the predictions of the BV theory.

Tables (2)

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Table 1 Oxide Growth Conditions and Resulting Film Thicknesses

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Table 2 Results of Nonlinear Least-Squares Fits of the BV Theory to the Dataa

Equations (5)

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Φr=Φr,particle-Φr,witness,
dσdΩΦr,0 cos θiΦiρΩ,
η=12arctanΦr,1, Φr,2,
PC=Φr,3/Φr,0,
P=Φr,12+Φr,22+Φr,321/2/Φr,0.

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