Refractive index and dielectric constant evolution of ultra-thin gold from clusters to films

Using high-speed picometrology, the complete cluster-to-film dielectric trajectories of ultra-thin gold films on silica are measured at 488 nm and 532 nm wavelengths for increasing mass-equivalent thickness from 0.2 nm to 10 nm. The trajectories are parametric curves on the complex dielectric plane that consist of three distinct regimes with two turning points. The thinnest regime (0.2 nm – 0.6 nm) exhibits increasing dipole density up to the turning point for the real part of the dielectric function at which the clusters begin to acquire metallic character. The mid-thickness regime (0.6 nm ~2 nm) shows a linear trajectory approaching the turning point for the imaginary part of the dielectric function. The third regime, from 2 nm to 10 nm, clearly displays the Drude circle, with no observable feature at the geometric percolation transition. ©2010 Optical Society of America OCIS codes: (120.3940) Instrument, measurement and metrology; (240.0240) Optics at surfaces; (310.6860) Thin film, optical properties; (260.3910) metal optics. References and links 1. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189– 193 (2006). 2. R. B. Laibowitz, and Y. Gefen, “Dynamic Scaling near the Percolation-Threshold in Thin Au Films,” Phys. Rev. Lett. 53(4), 380–383 (1984). 3. J. J. Tu, C. C. Homes, and M. Strongin, “Optical properties of ultrathin films: evidence for a dielectric anomaly at the insulator-to-metal transition,” Phys. Rev. Lett. 90(1), 017402 (2003). 4. A. Gray, M. Balooch, S. Allegret, S. De Gendt, and W. E. Wang, “Optical detection and characterization of graphene by broadband spectrophotornetry,” J. Appl. Phys. 104(5), 053109 (2008). 5. P. Grosse, and V. Offermann, “Analysis of Reflectance Data Using the Kramers-Kronig Relations,” Appl. Phys., A Mater. Sci. Process. 52(2), 138–144 (1991). 6. D. A. Crandles, F. Eftekhari, R. Faust, G. S. Rao, M. Reedyk, and F. S. Razavi, “Kramers-Kronig-constrained variational dielectric fitting and the reflectance of a thin film on a substrate,” Appl. Opt. 47(23), 4205–4211 (2008). 7. M. Hövel, B. Gompf, and M. Dressel, “Dielectric properties of ultrathin metal films around the percolation threshold,” Phys. Rev. B 81(3), 035402 (2010). 8. F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. Steinber, “Measurememt of Thickness and Refractive Index of Very Thin Films and Optical Properties of Surfaces by Ellipsometry,” J. Res. Natl. Bur. Stand. A 67, 363‒377 (1963). 9. R. J. Archer, “Determination of Properties of Films on Silicon by Method of Ellipsometry,” J. Opt. Soc. Am. 52(9), 970–977 (1962). 10. M. Yamamoto, and T. Namioka, “In situ ellipsometric study of optical properties of ultrathin films,” Appl. Opt. 31(10), 1612–1621 (1992). 11. X. Wang, M. Zhao, and D. D. Nolte, “Common-path interferometric detection of protein monolayer on the BioCD,” Appl. Opt. 46(32), 7836–7849 (2007). 12. X. F. Wang, Y. P. Chen, and D. D. Nolte, “Strong anomalous optical dispersion of graphene: complex refractive index measured by Picometrology,” Opt. Express 16(26), 22105–22112 (2008). 13. O. S. Heavens, Optical Properties of thin solid films (Academic Press Inc., New York, 1955), p. 66~80. 14. V. M. Shalaev, Nonlinear Optics of Random Media: Fractal Composites and Metal-Dielectric Films, Springer Tracts in Modern Physics (Berlin Heidelberg, 2000). 15. H. Y. Li, S. M. Zhou, J. Li, Y. L. Chen, S. Y. Wang, Z. C. Shen, L. Y. Chen, H. Liu, and X. X. Zhang, “Analysis of the drude model in metallic films,” Appl. Opt. 40(34), 6307–6311 (2001). 16. F. Abeles, Optical Properties of Solids (North-Holland, Amsterdam, 1972), p. 103. 17. M. Walther, D. G. Cooke, C. Sherstan, M. Hajar, M. R. Freeman, and F. A. Hegmann, “Terahertz conductivity of thin gold films at the metal-insulator percolation transition,” Phys. Rev. B 76(12), 125408 (2007). #135785 $15.00 USD Received 28 Sep 2010; revised 25 Oct 2010; accepted 26 Oct 2010; published 12 Nov 2010 (C) 2010 OSA 22 November 2010 / Vol. 18, No. 24 / OPTICS EXPRESS 24859 18. U. Kreibig, and C. V. Fragstein, “Limitation of Electron Mean Free Path in Small Silver Particles,” Z. Naturforsch. B 224, 307–323 (1969). 19. M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the Ideal Plasmonic Nanoshell: The Effects of Surface Scattering and Alternatives to Gold and Silver,” J. Phys. Chem. C 113(8), 3041–3045 (2009). 20. C. Noguez, and C. E. Roman-Velazquez, “Dispersive force between dissimilar materials: Geometrical effects,” Phys. Rev. B 70(19), 195412 (2004). 21. M. Kreiter, S. Mittler, W. Knoll, and J. R. Sambles, “Surface plasmon-related resonances on deep and asymmetric gold gratings,” Phys. Rev. B 65(12), 125415 (2002). 22. T. Zychowicz, J. Krupka, and J. Mazierska, “Measurements of Conductivity of Thin Gold Films at Microwave Frequencies Employing Resonant Techniques,” Proceedings of Asia-Pacific Microwave Conference (2006).