Stability of a Circular Epitaxial Island

The morphological stability of a single, epitaxially growing, circular adatom island with a radially symmetric adatom distribution is studied using a BurtonCabrera-Frank type island dynamics model. Various kinds of boundary conditions for the adatom density that include the thermodynamic equilibrium value, line tension, and attachment-detachment kinetics, and different velocity formulas with or without the one-dimensional “surface” diffusion are examined. Rigorous analysis shows that the circular island is always stable if its normalized area A is larger than a critical value. If A is less than such a critical value, and if neither the line tension nor surface diffusion is present, then there exists a critical wavenumber kc = kc(A) such that the island is only stable for wavenumbers less than kc. When the line tension or surface diffusion is present, small islands are always stable. In particular, the Bales-Zangwill instability for straight steps due to the kinetic asymmetry does not exist for small circular islands. PACS numbers: 68.35.J (Surface dynamics); 68.55.a (Thin film structure and morphology); 81.10.Aj (Theory and models of crystal growth).