Critical nuclei shapes in the stress-driven 2D-to-3D transition

We investigate the kinetic pathways to coherent island formation during the stress-driven roughening of strained films, and specifically examine the role of facets during island nucleation. Despite the ubiquitous appearance of {501} facets in the Si-Ge system, we show that for ${\mathrm{Ge}}_{0.5}{\mathrm{Si}}_{0.5}$ strained layers, the initial islanding pathway does not involve discrete {501} facets. A kinetic model based on interacting surface steps is developed, which explains the observed pathway and is consistent with the sensitive dependence of the 2D-3D transition on temperature and the sign of misfit.