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Autocorrelation Function and Roughness Spectrum of a Growing Film Surface

Published online by Cambridge University Press:  15 February 2011

V. I. Trofimov
V. I. Trofimov*
Affiliation:
Institute of Radio Engineering & Electronics of RAS Mokhovaya str., 11, Moscow 103907, Russia, 7(095) 203 8414.
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Abstract

Recently we developed a method that allows to derive a height-height autocorrelation function (ACF) for a randomly rough surface of a thin – film growing by the 3D island mechanism. In this paper, the ACF and roughness spectrum for several versions of the island growth model deduced by this method are presented and discussed. In the model dimension d=1+1 the ACFs are deduced in exact analytical form, and for d=2+1 the ACF' s are calculated numerically. In both model dimensions for the rms roughness the universal analytical expression connecting its with physical deposition parameters is derived. The impact of the growth hillock shape and the hillock space distribution are studied. It is shown that the ACF form is determined by the hillock space distribution and in the cases of an ideally random Poisson distribution and slightly ordered distribution the ACF is nearly gaussian although the surface profile height distribution is non-gaussian. The rms roughness is strongly dependent on the hillock shape while the autocorrelation length is determined by the hillock number density. The theoretical predictions are compared with published TEM and STM-data and the scaling behaviour of the rms roughness is analysed.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 440: Symposia CA – Structure and Evolution of Surfaces , 1996 , 401
Copyright
Copyright © Materials Research Society 1997

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References

1. Surface Polaritons, Electromagnetic Waves at Surfaces and Interfaces, edited by Agranovitch, V.M. and Mills, D.L. (North-Holland, Amsterdam, 1982).Google Scholar
2. Surface Enhanced Raman Scattering, edited by Chang, R.K. and Furtak, T.E. (Plenum Press, New York, 1982).Google Scholar
3. Kardar, M., Parisi, G., and Zhang, Y.-C., Phys. Rev. Lett. 56, 889 (1986).Google Scholar
4. Trofimov, V.I. and Osadchenko, V.A., Growth and Morphology of Thin Films, in Russian ( Energoatomizdat Moscow, 1993), 272pp.Google Scholar
5. Rasigni, G.,Varnier, F.,Rasigni, M. et al.,Phys.Rev.B,25, 2315 (1982); 27, 819(1983); Surface Sci., 162, 985 (1985); J.Vac.Sci. Technol. A, 10, 2869(1992)Google Scholar
6. Salvarezza, R.C., Vazquez, L., Herrasti, P., Ocon, P., Vara, J.M. and Arvia, A.J., Europhys. Lett. 20, 727 (1992).Google Scholar
7. Palasantzas, G. and Krim, J., Phys. Rev. Lett. 73, 3564,1994)Google Scholar
8. Yoshinobu, T., Iwamoto, A. and Iwasaki, H., Jpn.J.Appl.Phys. 33 (Pt.2), L67 (1994).Google Scholar
9. Family, F. and Vicsek, T., Dynamics of Fractal Surfaces (World Scientific, Singapore, 1991).Google Scholar
10. Krug, J., Spohn, H., in Solids Far from Equilibrium: Growth Morphology and Defects, ed. by Gordreche, C. (Cambridge University Press,Cambridge,1991).Google Scholar
11. Meakin, P., Phys. Rep. 235, 191 (1994).Google Scholar