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I am interested in upper bounds on the coarsening rate for a model of epitaxial growth. The problem I am having with the paper I am reading is that even if "coarsening" is in the title, I can't find anything about it, other than a lower bound on the free energy. The rest of the paper is devoted to finding bounds on the saturation interface width and the corresponding saturation time.

The little I know about coarsening and saturation tells me that these two processes are quite different, but what I said above leads me to think that they are somehow more related than I expect them to be. Can any of you please elaborate on the relation between these two concepts?

I really appreciate your help!

(please, feel free to add any tag that you think would be appropriate)

Giovanni
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1 Answers1

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In a typical layer-by-layer epitaxial growth that begins with a flat substrate, surface morphological instabilities often occur as the film thickness reaches a critical value. As a result, the nucleation of islands starts and many nuclei appear on the film surface. Such nuclei evolve into mounds, and the mound structure coarsens. During the coarsening process, the number of mounds decreases. The interface width $w(t)$, which is the standard deviation of the height profile and measures the roughness of the surface, increases as $w(t) ∝ t^ β$ , where β > 0 is a constant called the growth exponent.

Saturation is reached when this law changes. When the finite size of the underlying system becomes effective, the interface width saturates, and the saturation value $w = w(L)$ now satisfies $w(L) ∝ L^α$ , where L is the linear size of the underlying system and α > 0 is a constant called the roughness exponent. Now the coarsening doesnt change with time as before.

In a graph:

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