Symmetry breaking in shape transitions of epitaxial quantum dots

During heteroepitaxial growth, coherently strained islands form. These "self-assembled quantum dots" then undergo a series of shape transitions with increasing size. The best-known examples are the transitions of Ge on Si(001) and InAs on GaAs(001) from pyramidal islands to multifaceted domes. Here we examine the transition pathway, using a simple two-dimensional model. We find that the transition occurs via sequential nucleation of individual facets. While the stable states are symmetrical, the transition states are highly asymmetrical. The calculated transition path can pass through a metastable half-dome island shape, consistent with experimental observations. The broken symmetry of the transition state can be "locked in" by intermixing with substrate material, leading to asymmetrical islands.