Strain-driven instability of a single island and a hexagonal island array on solid substrates

Ordered arrays of two-dimensional (2D) strained islands on a solid surface have been generated recently by mask deposition or self-organization. Their feature sizes and shapes can be controlled in a broad way. Due to the competing effect of edge energy of islands and elastic energy caused by misfit strain, the morphological stability of such ordered island arrays becomes a critical issue. In this paper, we show, by a linear stability analysis, that an isolated circular island may undergo shape transition of various modes which are determined by the island size. We also perform a dynamical simulation for the morphological evolution of a hexagonal array of circular islands based on a continuum phase-field model. Numerical results indicate that long-range elastic interaction between islands mediated through the underlying substrate can significantly influence island shape. The hexagonal island array can be either stable or unstable, critically depending on the initial radius and spacing of the islands as well as the amplitude of thermal fluctuation localized at the island edge.