Abstract

The polarization and intensity of light scattered by monodisperse polystyrene latex and copper spheres, with diameters ranging from 92 to 218 nm, deposited on silicon substrates were measured with 442-, 532-, and 633-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 sphere and the substrate. The results show that accurate calculation of the scattering of light by a metal sphere requires that the near-field interaction between the sphere and its image be included in a complete manner. The normal-incidence approximation does not suffice for this interaction, and the existence of any thin oxide layer on the substrate must be included in the calculation.

© 2002 Optical Society of America

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  1. J. C. Stover, ed., Optical Scattering: Measurement and Analysis, Vol. PM24 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1995).
  2. 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]
  3. P. R. Spyak, W. L. Wolfe, “Scatter from particulate-contaminated mirrors. Part 1: Theory and experiment for polystyrene spheres and λ = 0.6328 µm,” Opt. Eng. 31, 1746–1756 (1992).
    [CrossRef]
  4. G. W. Starr, E. D. Hirleman, “Comparison of experimentally measured differential scattering cross sections of PSL spheres on flat surfaces and patterned surfaces,” in Flatness, Roughness, and Discrete Defect Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE2862, 130–138 (1996).
    [CrossRef]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. T. A. Germer, “Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness,” Appl. Opt. 36, 8798–8805 (1997).
    [CrossRef]
  10. T. A. Germer, C. C. Asmail, “Polarization of light scattered by microrough surfaces and subsurface defects,” J. Opt. Soc. Am. A 16, 1326–1332 (1999).
    [CrossRef]
  11. T. A. Germer, C. C. Asmail, B. W. Scheer, “Polarization of out-of-plane scattering from microrough silicon,” Opt. Lett. 22, 1284–1286 (1997).
    [CrossRef]
  12. P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
    [CrossRef]
  13. G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991).
    [CrossRef]
  14. G. Videen, “Light scattering from a sphere on or near a surface: errata,” J. Opt. Soc. Am. A 9, 844–845 (1992).
    [CrossRef]
  15. P. A. Bobbert, J. Vlieger, R. Greef, “Light reflection from a substrate sparsely seeded with spheres—comparison with an ellipsometric experiment,” Physica A 137, 243–257 (1986).
    [CrossRef]
  16. T. A. Germer, “Light scattering by slightly nonspherical particles on surfaces,” Opt. Lett. 27, 1159–1161 (2002).
    [CrossRef]
  17. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  18. T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
    [CrossRef]
  19. 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]
  20. G. Videen, “Light scattering from a particle on or near a perfectly conducting surface,” Opt. Commun. 115, 1–7 (1995).
    [CrossRef]
  21. T. A. Germer, “SCATMECH: polarized light scattering C++ class library,” available at http://physics.nist.gov/scatmech (2000).
  22. 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]
  23. 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]
  24. We obtained the uncertainties quoted in this paper by estimating the standard uncertainty σ 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. Dixkens, H. Fissan, “Development of an electrostatic precipitator for off-line particle analysis,” Aerosol Sci. Technol. 30, 438–453 (1999).
    [CrossRef]
  27. W. Kern, D. A. Puotinen, “Cleaning solutions based on hydrogen peroxide for use in silicon semiconductor technology,” RCA Rev. 30, 187–206 (1984).
  28. M. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, M. Ohwada, “Growth of native oxide on a silicon surface,” J. Appl. Phys. 68, 1272–1281 (1990).
    [CrossRef]
  29. E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985).
  30. R. H. Boundy, R. F. Boyer, S. M. Stoesser, STYRENE: Its Polymers, Copolymers and Derivatives (Reinhold, New York, 1952), Chap. 11, pp. 523–525.
  31. T. A. Germer, C. C. Asmail, “A goniometric optical scatter instrument for bidirectional reflectance distribution function measurements with out-of-plane and polarimetry capabilities,” in Scattering and Surface Roughness, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3141, 220–231 (1997).
    [CrossRef]
  32. T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
    [CrossRef]
  33. F. Zenhausern, Y. Martin, H. K. Wickramasinghe, “Scanning interferometric apertureless microscopy: optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
    [CrossRef] [PubMed]
  34. C. Girard, C. Joachim, S. Gauthier, “The physics of the near-field,” Rep. Prog. Phys. 63, 893–938 (2000).
    [CrossRef]

2002

T. A. Germer, “Light scattering by slightly nonspherical particles on surfaces,” Opt. Lett. 27, 1159–1161 (2002).
[CrossRef]

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]

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]

C. Girard, C. Joachim, S. Gauthier, “The physics of the near-field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

1999

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

J. Dixkens, H. Fissan, “Development of an electrostatic precipitator for off-line particle analysis,” Aerosol Sci. Technol. 30, 438–453 (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]

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]

T. A. Germer, C. C. Asmail, “Polarization of light scattered by microrough surfaces and subsurface defects,” J. Opt. Soc. Am. A 16, 1326–1332 (1999).
[CrossRef]

1998

T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

1997

1995

F. Zenhausern, Y. Martin, H. K. Wickramasinghe, “Scanning interferometric apertureless microscopy: optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
[CrossRef] [PubMed]

G. Videen, “Light scattering from a particle on or near a perfectly conducting surface,” Opt. Commun. 115, 1–7 (1995).
[CrossRef]

1992

P. R. Spyak, W. L. Wolfe, “Scatter from particulate-contaminated mirrors. Part 1: Theory and experiment for polystyrene spheres and λ = 0.6328 µm,” Opt. Eng. 31, 1746–1756 (1992).
[CrossRef]

G. Videen, “Light scattering from a sphere on or near a surface: errata,” J. Opt. Soc. Am. A 9, 844–845 (1992).
[CrossRef]

1991

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]

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

1990

M. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, M. Ohwada, “Growth of native oxide on a silicon surface,” J. Appl. Phys. 68, 1272–1281 (1990).
[CrossRef]

1988

1987

1986

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

P. A. Bobbert, J. Vlieger, R. Greef, “Light reflection from a substrate sparsely seeded with spheres—comparison with an ellipsometric experiment,” Physica A 137, 243–257 (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, “Polarization of light scattered by microrough surfaces and subsurface defects,” J. Opt. Soc. Am. A 16, 1326–1332 (1999).
[CrossRef]

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

T. A. Germer, C. C. Asmail, B. W. Scheer, “Polarization of out-of-plane scattering from microrough silicon,” Opt. Lett. 22, 1284–1286 (1997).
[CrossRef]

T. A. Germer, C. C. Asmail, “A goniometric optical scatter instrument for bidirectional reflectance distribution function measurements with out-of-plane and polarimetry capabilities,” in Scattering and Surface Roughness, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3141, 220–231 (1997).
[CrossRef]

Bobbert, P. A.

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

P. A. Bobbert, J. Vlieger, R. Greef, “Light reflection from a substrate sparsely seeded with spheres—comparison with an ellipsometric experiment,” Physica A 137, 243–257 (1986).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Boundy, R. H.

R. H. Boundy, R. F. Boyer, S. M. Stoesser, STYRENE: Its Polymers, Copolymers and Derivatives (Reinhold, New York, 1952), Chap. 11, pp. 523–525.

Boyer, R. F.

R. H. Boundy, R. F. Boyer, S. M. Stoesser, STYRENE: Its Polymers, Copolymers and Derivatives (Reinhold, New York, 1952), Chap. 11, pp. 523–525.

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]

Dixkens, J.

J. Dixkens, H. Fissan, “Development of an electrostatic precipitator for off-line particle analysis,” Aerosol Sci. Technol. 30, 438–453 (1999).
[CrossRef]

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]

T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

Ehrman, S. H.

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]

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]

Fissan, H.

J. Dixkens, H. Fissan, “Development of an electrostatic precipitator for off-line particle analysis,” Aerosol Sci. Technol. 30, 438–453 (1999).
[CrossRef]

Gauthier, S.

C. Girard, C. Joachim, S. Gauthier, “The physics of the near-field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

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]

T. A. Germer, “Light scattering by slightly nonspherical particles on surfaces,” Opt. Lett. 27, 1159–1161 (2002).
[CrossRef]

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

T. A. Germer, C. C. Asmail, “Polarization of light scattered by microrough surfaces and subsurface defects,” J. Opt. Soc. Am. A 16, 1326–1332 (1999).
[CrossRef]

T. A. Germer, C. C. Asmail, B. W. Scheer, “Polarization of out-of-plane scattering from microrough silicon,” Opt. Lett. 22, 1284–1286 (1997).
[CrossRef]

T. A. Germer, “Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness,” Appl. Opt. 36, 8798–8805 (1997).
[CrossRef]

T. A. Germer, C. C. Asmail, “A goniometric optical scatter instrument for bidirectional reflectance distribution function measurements with out-of-plane and polarimetry capabilities,” in Scattering and Surface Roughness, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3141, 220–231 (1997).
[CrossRef]

Girard, C.

C. Girard, C. Joachim, S. Gauthier, “The physics of the near-field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

Greef, R.

P. A. Bobbert, J. Vlieger, R. Greef, “Light reflection from a substrate sparsely seeded with spheres—comparison with an ellipsometric experiment,” Physica A 137, 243–257 (1986).
[CrossRef]

Hasegawa, E.

M. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, M. Ohwada, “Growth of native oxide on a silicon surface,” J. Appl. Phys. 68, 1272–1281 (1990).
[CrossRef]

Hirleman, E. D.

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]

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]

G. W. Starr, E. D. Hirleman, “Comparison of experimentally measured differential scattering cross sections of PSL spheres on flat surfaces and patterned surfaces,” in Flatness, Roughness, and Discrete Defect Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE2862, 130–138 (1996).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Joachim, C.

C. Girard, C. Joachim, S. Gauthier, “The physics of the near-field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

Kawakami, M.

M. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, M. Ohwada, “Growth of native oxide on a silicon surface,” J. Appl. Phys. 68, 1272–1281 (1990).
[CrossRef]

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, 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]

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]

Martin, Y.

F. Zenhausern, Y. Martin, H. K. Wickramasinghe, “Scanning interferometric apertureless microscopy: optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
[CrossRef] [PubMed]

Morita, M.

M. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, M. Ohwada, “Growth of native oxide on a silicon surface,” J. Appl. Phys. 68, 1272–1281 (1990).
[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]

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]

Nahm, K. B.

Nebeker, B. M.

Ohmi, T.

M. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, M. Ohwada, “Growth of native oxide on a silicon surface,” J. Appl. Phys. 68, 1272–1281 (1990).
[CrossRef]

Ohwada, M.

M. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, M. Ohwada, “Growth of native oxide on a silicon surface,” J. Appl. Phys. 68, 1272–1281 (1990).
[CrossRef]

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).

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).

Scheer, B. W.

Schmehl, R.

Spyak, P. R.

P. R. Spyak, W. L. Wolfe, “Scatter from particulate-contaminated mirrors. Part 1: Theory and experiment for polystyrene spheres and λ = 0.6328 µm,” Opt. Eng. 31, 1746–1756 (1992).
[CrossRef]

Starr, G. W.

G. W. Starr, E. D. Hirleman, “Comparison of experimentally measured differential scattering cross sections of PSL spheres on flat surfaces and patterned surfaces,” in Flatness, Roughness, and Discrete Defect Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE2862, 130–138 (1996).
[CrossRef]

Stoesser, S. M.

R. H. Boundy, R. F. Boyer, S. M. Stoesser, STYRENE: Its Polymers, Copolymers and Derivatives (Reinhold, New York, 1952), Chap. 11, pp. 523–525.

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]

Sung, L.

Videen, G.

Vlieger, J.

P. A. Bobbert, J. Vlieger, R. Greef, “Light reflection from a substrate sparsely seeded with spheres—comparison with an ellipsometric experiment,” Physica A 137, 243–257 (1986).
[CrossRef]

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

Weber, D. C.

Wickramasinghe, H. K.

F. Zenhausern, Y. Martin, H. K. Wickramasinghe, “Scanning interferometric apertureless microscopy: optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
[CrossRef] [PubMed]

Wolfe, W. L.

P. R. Spyak, W. L. Wolfe, “Scatter from particulate-contaminated mirrors. Part 1: Theory and experiment for polystyrene spheres and λ = 0.6328 µm,” Opt. Eng. 31, 1746–1756 (1992).
[CrossRef]

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]

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]

T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

Zenhausern, F.

F. Zenhausern, Y. Martin, H. K. Wickramasinghe, “Scanning interferometric apertureless microscopy: optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
[CrossRef] [PubMed]

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]

J. Dixkens, H. Fissan, “Development of an electrostatic precipitator for off-line particle analysis,” Aerosol Sci. Technol. 30, 438–453 (1999).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

M. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, M. Ohwada, “Growth of native oxide on a silicon surface,” J. Appl. Phys. 68, 1272–1281 (1990).
[CrossRef]

J. Opt. Soc. Am. A

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.

T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

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]

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Figures (9)

Fig. 1
Fig. 1

Schematic of the scattering problem.

Fig. 2
Fig. 2

Light-scattering parameters for a 155-nm PSL sphere on a silicon substrate predicted by the MSDI model, NIA model, and the BV theory in the plane of incidence with θ i = 60° and λ = 633 nm. The substrate is assumed to have a 1.5-nm native oxide layer.

Fig. 3
Fig. 3

Same as Fig. 2, except for a 155-nm copper sphere.

Fig. 4
Fig. 4

Light-scattering parameters for a 155-nm PSL sphere on a silicon substrate predicted by the BV theory for different SiO2 layer thicknesses, calculated in the plane of incidence with θ i = 60° and λ = 633 nm.

Fig. 5
Fig. 5

Same as Fig. 4, except for a 155-nm copper sphere.

Fig. 6
Fig. 6

Light-scattering parameters for 101-, 155-, and 218-nm PSL spheres measured in the plane of incidence with θ i = 60° and λ = 442 nm. The solid curves represent the predictions of the BV theory.

Fig. 7
Fig. 7

Same as Fig. 6, except for 92-, 123-, and 155-nm copper spheres.

Fig. 8
Fig. 8

Light-scattering parameters for 155-nm PSL spheres measured in the plane of incidence with θ i = 60° and three different wavelengths (λ = 442, 532, and 633 nm). The curves represent the predictions of the BV theory.

Fig. 9
Fig. 9

Same as Fig. 8, except for 155-nm copper spheres.

Tables (2)

Tables Icon

Table 1 Modal Diameters, Distribution Widths, and Number Densities of PSL and Copper Spheres Used in This Study

Tables Icon

Table 2 Complex Indices of Refraction for the Materials Used in the Calculations

Equations (5)

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

rkθ=r˜kθ, 1, n1+r˜kθ, n1, n2exp2iqθt/1+r˜kθ, 1, n1r˜kθ, n1, n2exp2iqθt,
r˜sθ, N1, N2=N12-sin2 θ1/2-N22-sin2 θ1/2/N12-sin2 θ1/2+N22-sin2 θ1/2,
r˜pθ, N1, N2=N22N12-sin2 θ1/2-N12N22-sin2 θ1/2/N22N12-sin2 θ1/2+N12N22-sin2 θ1/2
qθ=2πn12-sin2 θ1/2/λ.
dσdΩ=dΦrdΩcos θiΦiρ,

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