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Phys. Rev. Lett. 64, 772–775 (1990)

[Issue 7 – 12 February 1990 ]

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Scaling theory for the growth of amorphous films

C. Tang, S. Alexander, R. Bruinsma, and Bruce E. Shaw

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106

We present a scaling theory for the time evolution of the morphology of amorphous films, based on the Huygens principle growth algorithm. During the coarsening stage of the growth, the time-dependent correlation length diverges with time as xi (t) [is proportional to] t^p. We calculate p for a range of random and self-similar starting surfaces. When the effect of noise is taken into account, the exponent p reaches a universal value (3/4, in good agreement with experiments.

©1990 The American Physical Society

URL: http://link.aps.org/abstract/PRL/v64/p772
DOI: 10.1103/PhysRevLett.64.772
PACS: 68.55.Jk, 42.10.Dy, 81.15.Cd

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References

1. R. F. Bunshah and D. M. Mattox, Phys. Today 33, No. (5) 50 (1980).
2. Thin Film Process, edited by J. L. Vossen and W. Kern (Academic, New York, 1978).
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8. G. S. Bales, R. Bruinsma, E. Eklund, R. P. U. Karunasiri, J. Rudnick, and A. Zangwill (to be published).
9. For the shadow model of Refs. 6 – 8, it can be shown (see Ref. 7) that if one neglects the shadowing effect from neighboring columns, then in the case of uniform exposure, the broad tops in Fig. 1 evolve with a normal velocity v_n= v ( 1 + cos theta ) / 2, where theta is the angle of the surface normal with respect to the vertical direction. We can decompose v_n as the sum of a uniform translation, with growth velocity v cos theta / 2, and of a normal growth, with growth velocity v / 2. The uniform translation does not affect the growth morphology. The normal growth is the HP term.
10. G. Carter, in Erosion and Growth of Solids Stimulated by Atom and Ion Beams, edited by G. Kiriakidis, G. Carter, and J. L. Whitton (Martinus Nijhoff, Dordrecht, 1986), and references therein.
11. See also J. Krug and H. Spohn, Phys. Rev. A 38, 4271 (1988); E. Medina, T. Hwa, M. Kardar and Y.-C. Zhang, Phys. Rev. A 39, 3053 (1989); M. Kardar, in Proceedings of the 1989 Cargese Meeting on Disorder and Fracture (to be published).
12. This is only valid if we assume that the noise does not produce new groove defects. If that were an allowed process, then a bump would spread as t^p instead of t. For the groove networks of Ref. 3, this appears to be a valid assumption.

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