In-plane and out-of-plane shape transitions of heteroepitaxially self-assembled nanostructures

In this work, shapes and shape transitions of several types of self-assembled heteroepitaxial nanostructures, as observed in in situ scanning tunneling microscopy experiments during growth, are examined in the framework of several equilibrium and kinetic models. In particular, heteroepitaxial TiSi₂ and CoSi₂ islands on Si(1 1 1) are shown to behave in accordance with generalized Wulff-Kaishew theorem of equilibrium strained and supported crystal shapes. More specifically, these silicide nanocrystals exhibit out-of-plane thickening shape transition by increasing their vertical aspect ratio with growth, as long as they are strained, and inverse (flattening) transition upon relaxation by misfit dislocations. On the other hand, heteroepitaxial Ge and CoSi₂ islands on Si(0 0 1) are well-known for their in-plane anisotropic elongation. Plausible energetic and kinetic reasons for such elongation, based on the unique nucleation features of Ge-hut/Si(0 0 1) and non-planar CoSi₂-hut/Si(0 0 1) interface, are discussed.