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Physical Review B

Fractal character of cold-deposited silver films determined by low-temperature scanning tunneling microscopy

Constantine Douketis, Zhouhang Wang, Tom L. Haslett, and Martin Moskovits

  • Department of Chemistry, University of Toronto and Ontario Laser Lightwave Research Centre, Toronto, Ontario, Canada M5S 1A1

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Phys. Rev. B 51, 11022 – Published 15 April, 1995

DOI: https://doi.org/10.1103/PhysRevB.51.11022

Abstract

High-resolution scanning-tunneling-microscope (STM) topographic images of vacuum-deposited Ag films are reported. Films were formed and imaged at 100 and 300 K. Images of films deposited at 300 K, annealed to 560 K, and then returned to 300 K are also presented. The topographic surfaces of the low-temperature films are found to be self-affine fractals with a local Hausdorff-Besicovitch dimension D=2.5. The low-temperature films exhibit intense surface-enhanced Raman spectra (SERS). Films deposited at 300 K do not possess significant fractal character and are not SERS active. We show that the apparent local fractal dimension obtained by analyzing STM topographic images depends critically on the algorithm used. Three such methods (cube counting, triangulation, and power spectrum analysis) are assessed. A method is proposed for obtaining reliable fractal dimensions by analyzing the experimental STM topographic images using several algorithms and comparing the results to a calibration curve generated by applying the same algorithms to simulated fractal surfaces of known Hausdorff-Besicovitch dimension.

References (22)

  1. D. L. Jeanmarie and R. P. Van Duyne, J. Electroanal. Chem. 84, 1 (1977); M. G. Albrecht and J. A. Creighton, J. Am. Chem. Soc. 99, 5215 (1977); M. Fleischmann, P. J. Hendra and A. J. McQuillan, Chem. Phys. Lett. 26, 163 (1974).
  2. M. Moskovits, Rev. Mod. Phys. 57, 783 (1985), and references therein.
  3. E. V. Albano, S. Daiser, R. Miranda and K. Wandelt, Surf. Sci. 150, 367 (1985); ibid. 150, 386 (1985), and references therein.
  4. J. K. Gimzewski and A. Humbert, IBM J. Res. Dev. 30, 472 (1986).
  5. G. S. Bales, R. Bruinsma, E. A. Eklund, R. P. U. Karunasiri, J. Rudnick and A. Zangwill, Science 249, 264 (1990).
  6. J. T. Stuckless and M. Moskovits, Phys. Rev. B 40, 9997 (1989).
  7. (a) M. I. Stockman, V. M. Shalaev, M. Moskovits, R. Botet and T. F. George, Phys. Rev. B 46, 2821 (1992); (b) V. A. Markel, L. S. Muratov, M. I. Stockman and T. F. George, ibid. 43, 8183 (1991); (c) M. I. Stockman, T. F. George and V. M. Shalaev, ibid. 44, 115 (1991).
  8. A. V. Butenko, P. A. Chubakov, Yu. E. Danilova, S. V. Karpov, A. K. Popov, S. G. Rautian, V. P. Safonov, V. V. Slabko, V. M. Shalaev and M. I. Stockman, Z. Phys. D 17, 283 (1990).
  9. C. Douketis, T. L. Haslett, J. T. Stuckless, M. Moskovits and V. M. Shalaev, Surf. Sci. Lett. 297, L8 (1993); V. M. Shalaev, C. Douketis, and M. Moskovits (unpublished).
  10. R. Chiarello, V. Panella and J. Krim, Phys. Rev. Lett. 67, 3408 (1991).
  11. M. W. Mitchell and D. A. Bonnell, J. Mater. Res. 5, 2244 (1990).
  12. K. Sakamaki, K. Itoh, A. Fujishima and Y. Gohshi, J. Vac. Sci. Technol. A 8, 525 (1990).
  13. D. R. Denley, J. Vac. Sci. Technol. A 8, 603 (1990).
  14. J. M. Gomez-Rodriguez, A. M. Baro and R. C. Salvarezza, J. Vac. Sci. Technol. B 9, 495 (1991).
  15. J. Krim, I. Heyraert, C. Van Haesendonck and Y. Bruynseraede, Phys. Rev. Lett. 70, 57 (1993).
  16. C. Douketis, V. M. Shalaev, T. L. Haslett, Z. Wang and M. Moskovits, J. Electron Spectrosc. Relat. Phenom. 64/65, 167 (1993); Physica A 207, 352 (1994).
  17. R. L. Summers, NASA Technical Report No. D-5285, Washington, DC, 1969 (unpublished).
  18. J. Feder, Fractals (Plenum, New York, 1988), and references therein.
  19. B. B. Mandelbrot, D. E. Passoja and A. J. Paullay, Nature 308, 721 (1984).
  20. (a) W. M. Tong and R. S. Williams, Annu. Rev. Phys. Chem. 45, 401 (1994); (b) E. Courtens, R. Vacher, J. Pelous and T. Woignier, Europhys. Lett. 6, 245 (1988); R. Vacher, T. Woignier, J. Pelous and E. Courtens, Phys. Rev. B 37, 6500 (1988); R. Vacher, E. Courtens, E. Stoll, M. Böffgen and H. Rothuizen, J. Phys.: Condens. Matter 3, 6531 (1991); E. P. Stoll and M. Kolb, Physica A 185, 222 (1992).
  21. R. F. Voss, in Fundamental Algorithms in Computer Graphics, edited by R. A. Earnshaw (Springer-Verlag, Berlin, 1985); also see J. Feder, Fractals (Ref. 18), pp. 221–228.
  22. D. A. Weitz and M. Olivera, Phys. Rev. Lett. 52, 1433 (1984); D. A. Weitz, M. Y. Lin, J. S. Huang, T. A. Witten, S. K. Sinha, J. S. Gertner, and C. Ball, in Scaling Phenomena in Disordered Systems, edited by R. Pynn and A. Skjeltorp (Plenum, New York, 1985), pp. 171–188.