Morphological stability of islands upon thin-film condensation

The stability of shape of a disklike cluster growing on a substrate from supersaturated vapor of adsorbed particles is studied. The investigation is carried out by expansion in terms of cosines of a minor deflection of island shape from a disk and subsequent evaluation of expansion coefficient relations in time. In addition to diffusion of adatoms towards an island and the relation between an equilibrium concentration and curvature, some kinetic phenomena on the surface of an island, the interface energy anisotropy, and surface diffusion are taken into account. It is shown that the reevaporation process of adatoms from a substrate leads to a considerable change in the criteria of instability initiation of the island shape as compared to the three-dimensional case. The mode with number $\nu$ starts to be excited only in the case where the radius of a cluster lies within a certain interval, $R_1\left(\nu \right)<R<\mathrm{}{R}_2\left(\nu \right)$. The criterion of island faceting is derived as well.