Shape transition in growth of strained islands

Strained islands formed in heteroepitaxy sometimes change shape during growth. Here we show that there is typically a first-order shape transition with island size, with the discontinuous introduction of steeper facets at the island edge. We present a phase diagram for island shape as a function of volume and surface energy, showing how surface energy controls the sequence of island shapes with increasing volume. The discontinuous chemical potential at the shape transition drastically affects island coarsening and size distributions.