Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Phys. Rev. ST AB Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article:

Phys. Rev. B 37, 7751–7758 (1988)

[Issue 13 – 1 May 1988 ]

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Scattering by rough surfaces

Po–zen Wong

Schlumberger-Doll Research, Old Quarry Road, Ridgefield, Connecticut 06877-4108

Alan J. Bray

Department of Theoretical Physics, The University, Manchester, M13||9PL United Kingdom

We have used the first Born approximation to derive analytic expressions for the scattering by an oriented solid-on-solid rough surface. The surface roughness is described by a vertical height profile h(r) which is a random function of the positional vector r in the horizontal plane. The mean-square height difference for such surfaces is assumed to diverge either as a power law or a logarithm of r, i.e., w²_r [is proportional to] r^{2 alpha} or w²_r [is proportional to] lnr. We derived expressions for both the specular reflection and the diffuse scattering. Effects due to the surface density profile and to atoms absorbed onto the surface, and relevance to the study of the roughening transition are discussed. We also show that the angular average of our result over all directions of the wave vector q gives a 1/q^{3+ alpha} dependence, in agreement with an earlier calculation for inhomogeneous systems with randomly oriented internal surfaces.

©1988 The American Physical Society

URL: http://link.aps.org/abstract/PRB/v37/p7751
DOI: 10.1103/PhysRevB.37.7751
PACS: 68.35.-p

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