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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 3 — Feb. 11, 2013
  • pp: 3091–3102

Effect of clustering on ellipsometric spectra of randomly distributed gold nanoparticles on a substrate

Huai-Yi Xie, Yia-Chung Chang, Guangwei Li, and Shih-Hsin Hsu  »View Author Affiliations

Optics Express, Vol. 21, Issue 3, pp. 3091-3102 (2013)

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We present a theoretical model for describing light scattering from randomly distributed Au nanoparticles on a substrate, including the clustering effect. By using the finite-element Green’s function method and spherical harmonic basis functions, we are able to calculate the polarization-dependent reflectivity spectra of the system (modeled by randomly distributed nanoparticles coupled with clusters) efficiently and accurately. The calculated ellipsometric spectra of the system with clusters can adequately describe the experimental data for the whole frequency range. We find that the clustering effect leads to some prominent features in the low frequency range of the ellipsometric spectra, which are attributed to plasmonic resonances associated with the coupling of Au nanoparticles and clusters.

© 2013 OSA

OCIS Codes
(120.3940) Instrumentation, measurement, and metrology : Metrology
(290.5820) Scattering : Scattering measurements
(290.5825) Scattering : Scattering theory
(240.2130) Optics at surfaces : Ellipsometry and polarimetry

ToC Category:

Original Manuscript: December 6, 2012
Revised Manuscript: January 4, 2013
Manuscript Accepted: January 7, 2013
Published: January 31, 2013

Virtual Issues
Vol. 8, Iss. 3 Virtual Journal for Biomedical Optics

Huai-Yi Xie, Yia-Chung Chang, Guangwei Li, and Shih-Hsin Hsu, "Effect of clustering on ellipsometric spectra of randomly distributed gold nanoparticles on a substrate," Opt. Express 21, 3091-3102 (2013)

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  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer Tracts in Modern Physics, Vol. 111 (Springer-Verlag, New York, 1988).
  2. J. T. Krug, G. D. Wang, S. R. Emory, and S. Nie, “Efficient Raman enhancement and intermittent light emission observed in single gold nanocrystals,” J. Am. Chem. Soc.121(39), 9208–9214 (1999). [CrossRef]
  3. H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics62(33 Pt B), 4318–4324 (2000). [CrossRef] [PubMed]
  4. A. M. Michaels, J. Jiang, and L. Brus, “Ag nanocrystal junctions as the site for surface-enhanced Raman scattering of single rhodamine 6G molecules,” J. Phys. Chem. B104(50), 11965–11971 (2000). [CrossRef]
  5. A. Wokaun, J. P. Gordon, and P. F. Liao, “Radiation Damping in Surface-Enhanced Raman Scattering,” Phys. Rev. Lett.48(14), 957–960 (1982). [CrossRef]
  6. S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science275(5303), 1102–1106 (1997). [CrossRef] [PubMed]
  7. S. V. Gaponenko, A. A. Gaiduk, O. S. Kulakovich, S. A. Maskevich, N. D. Strekal, O. A. Prokhorov, and V. M. Shelekhina, “Raman scattering enhancement using crystallographic surface of a colloidal crystal,” JETP Lett.74(6), 309–311 (2001). [CrossRef]
  8. B. Kaplan, T. Novikova, A. De Martino, and B. Drévillon, “Characterization of bidimensional gratings by spectroscopic ellipsometry and angle-resolved Mueller polarimetry,” Appl. Opt.43(6), 1233–1240 (2004). [CrossRef] [PubMed]
  9. H. Wormeester, E. Stefan Kooij, A. Mewe, S. Rekveld, and B. Poelsema, “Ellipsometric characterisation of heterogeneous 2D layers,” Thin Solid Films455–456, 323–334 (2004). [CrossRef]
  10. S.-H. Hsu, E.-S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G. R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A205(4), 876–879 (2008). [CrossRef]
  11. D. Schmidt, B. Booso, T. Hofmann, E. Schubert, A. Sarangan, and M. Schubert, “Monoclinic optical constants, birefringence, and dichroism of slanted titanium nanocolumns determined by generalized ellipsometry,” Appl. Phys. Lett.94(1), 011914 (2009). [CrossRef]
  12. G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys.330(3), 377–445 (1908). [CrossRef]
  13. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  14. S. Asano and G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt.14(1), 29–49 (1975). [PubMed]
  15. G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A8(3), 483–489 (1991). [CrossRef]
  16. I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling ot the optical response of supported metallic particles,” Phys. Rev. B61(11), 7722–7733 (2000). [CrossRef]
  17. R. Lazzari, I. Simonsen, D. Bedeaux, J. Vlieger, and J. Jupille, “Polarizability of truncated spheroidal particles supported by a substrate: model and applications,” Eur. Phys. J. B24(2), 267–284 (2001). [CrossRef]
  18. D. Bedeaux and J. Vlieger, Optical Properties of Surfaces (Imperial College Press, London, UK, 2002).
  19. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A12(5), 1068–1076 (1995). [CrossRef]
  20. Y. C. Chang, S. H. Hsu, P. K. Wei, and Y. D. Kim, “Optical nanometrology of Au nanoparticles on a multilayer film,” Phys. Status Solidi C5(5), 1194–1197 (2008). [CrossRef]
  21. Y. C. Chang, G. Li, H. Chu, and J. Opsal, “Efficient finite-element, Green’s function approach for critical-dimension metrology of three-dimensional gratings on multilayer films,” J. Opt. Soc. Am. A23(3), 638–645 (2006). [CrossRef] [PubMed]
  22. S. H. Hsu, Y. C. Chang, Y. C. Chen, P. K. Wei, and Y. D. Kim, “Optical metrology of randomly-distributed Au colloids on a multilayer film,” Opt. Express18(2), 1310–1315 (2010). [CrossRef] [PubMed]
  23. R. Lazzari and I. Simonsen, “GRANFILM: a software for calculating thin-layer dielectric properties and Fresnel coefficients,” Thin Solid Films419(1-2), 124–136 (2002). [CrossRef]
  24. G. R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, “Low refractive index Si nanopillars on Si substrate,” Appl. Phys. Lett.90(18), 181923 (2007). [CrossRef]
  25. R. S. Moirangthem, Y. C. Chang, and P.-K. Wei, “Investigation of surface plasmon biosensing using gold nanoparticles enhanced ellipsometry,” Opt. Lett.36(5), 775–777 (2011). [CrossRef] [PubMed]
  26. R. S. Moirangthem, Y. C. Chang, and P. K. Wei, “Ellipsometry study on gold-nanoparticle-coated gold thin film for biosensing application,” Biomed. Opt. Express2(9), 2569–2576 (2011). [CrossRef] [PubMed]
  27. E. D. Palik, ed., Handbook of Optical Constants of Solids, vol. 1 (Academic, Orlando, FL, USA, 1985).
  28. See for example, Fayyazuddin and Riazuddin, Quantum Mechanics (World Scientific, 1990), p. 368.

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