Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-15T00:22:39.345Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic Scaling in Electrochemical Deposition

Published online by Cambridge University Press:  03 September 2012

Hiroshi Iwasaki ,
Atsushi Iwamoto ,
Koichi Sudoh  and
Tatsuo Yoshinobu
Hiroshi Iwasaki
Affiliation:
The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567, Japan
Atsushi Iwamoto
Affiliation:
The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567, Japan
Koichi Sudoh
Affiliation:
The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567, Japan
Tatsuo Yoshinobu
Affiliation:
The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567, Japan
Get access

Abstract

Static and dynamic scaling behavior in copper electrochemical deposition in the stable growth condition (non-bulk fractal growth) was studied by atomic force microscopy and numerical simulation. We found two distinct scaling regimes with roughness exponent α of 0.6 and 0.87α0.05 corresponding to the concentrations of the “brightener” organic additive higher and lower than 1 mℓ/ℓ, respectively. The rms surface width of the whole measured area of the surfaces in the former regime was smaller than that in the latter regime. For the latter rougher surface, we observed dynamic scaling behavior for longer length scales as well as the stationary scaling behavior for shorter length scales: surface width did not further increase with linear size of the area for longer length scales than a characteristic correlation length and increased as a power of deposition time with the dynamic exponent β of 0.45. The sum of α + (α/β) was larger than the value expected for KPZ local growth, 2. This was understood that in electrochemical deposition there is enhancement of growth at protrusions owing to non-local Laplacian field effect. The smoother (α =0.6) and the rougher (0.87) surfaces were reproduced by numerical solutions of KPZ + (the growth term proportional to height) for the shorter and the longer growth times, respectively. Bifurcation of the surface morphology is understood as a result of decrease of weight of the additional term owing to increase of the additive.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 367: Symposium P – Fractal Aspects of Materials , 1994 , 159
Copyright
Copyright © Materials Research Society 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Family, F. and Vicsek, T., eds., Dynamics of Fractals Surfaces (World Scientific, Singapore, 1991).Google Scholar
2. Krug, J. and Spohn, H., in Solids Far From Equilibrium: Growth, Morphology, and Defects, ed. Godreche, C. (Cambridge University Press, Cambridge, 1990) pp. 479–582.Google Scholar
3. Iwasaki, H. and Yoshinobu, T., Phase Transitions, to be published.Google Scholar
4. Iwasaki, H. and Yoshinobu, T., Phys. Rev. B 48, 8282 (1993).Google Scholar
5. Kahanda, G. L. M. K. S., Zou, X., Farrell, R., and Wong, P., Phys. Rev. Lett. 68, 3741 (1992).Google Scholar
6. Iwamoto, A., Yoshinobu, T. and Iwasaki, Hiroshi, Phys. Rev. Lett. 72, 4025 (1994).Google Scholar
7. Brady, R. M. and Ball, R. C., Nature 309, 225, (1984).Google Scholar
8. Sawada, Y., Dougherty, A., and Gollub, J. P., Phys. Rev. Lett. 56, 1260, (1986).Google Scholar
9. Halsey, T. C., Phys. Rev. A36, 3512 (1987).Google Scholar
10. Garic, P., Barkey, D., Jacob, E. B., Bochner, E., Broxholm, N., Miller, B., Orr, B., and Zamir, R., Phys. Rev. Lett. 62, 2703, (1989).Google Scholar
11. Haak, R., Ogden, C. and Tench, D., Plat. and Surf. Finishing 69, 62 (1982).Google Scholar
12. Barkey, D. P., Muller, R. H., and Tobias, C. W., J. Electrochem. Soc. 136, 2199, (1989) and, 136, 2207, (1989).Google Scholar
13. Pritzker, M. D. and Fahidy, T. Z., Electrochim. Acta, 37, 103, (1992).Google Scholar
14. Mullins, W. W. and Sekerka, R. F., J. Appl. Phys. 34, 323 (1963); 35, 444 (1964).Google Scholar
15. In ref. [9], Halsey analyzed electrodeposition without convective transport and supporting electrolyte. Here we use Halsey's result with only replacing the separation distance of the electrodes by the boundary layer thickness.Google Scholar
16. Kardar, M., Parisi, G., and Zhang, Y. C., Phys. Rev. Lett. 56, 889 (1986).Google Scholar
17. Villain, J., J. Phys. 11, 19 (1991).Google Scholar
18. He, Y. L., Yang, H. N., Lu, T. M., and Wang, G. C., Phys. Rev. Lett. 69, 3770 (1992).Google Scholar
19. Yoshinobu, T., Iwamoto, A. and Iwasaki, H., Jpn. J. Appl. Phys. 33, L67 (1994).Google Scholar
20. Amar, Jacques G. and Family, Fereydoon, Physical Review A, 41, 6 (1990).Google Scholar
21. Iwamoto, A., Sudoh, K., Yoshinobu, T., and Iwasaki, H., unpublished.Google Scholar