Decay characteristics of two-dimensional islands on strongly anisotropic surfaces

We investigate analytically the decay characteristics of two-dimensional islands on strongly anisotropic surfaces. We show that a generic scaling law can always be established in describing the dynamical evolution of such islands, given by Lα(t₀-t)^β where L is the island width, and to is the lifetime of the islands. The value of the scaling exponent β in the fast-decay direction is always 1/2 in the low-temperature regime where the decay is quasi-one-directional, irrespective of the specific dominant decaying mechanism involved. At higher temperatures where the decay proceeds effectively in both directions, β is again a good measure of the dominant microscopic decaying mechanism involved, just like the isotropic case. We discuss these results in connection with recent experiments.