  The transformation of monolayer islands into bilayer islands as a first step
of the overall two-dimensional to three-dimensional (2D-3D) transformation in
the coherent Stranski-Krastanov mode of growth is studied for the cases of
expanded and compressed overlayers. Compressed overlayers display a
nucleation-like behavior: the energy accompanying the transformation process
displays a maximum at some critical number of atoms, which is small for large
enough values of the misfit, and then decreases gradually down to the
completion of the transformation, non-monotonically due to the atomistics of
the process. On the contrary, the energy change in expanded overlayers
increases up to close to the completion of the transformation and then abruptly
collapses with the disappearance of the monoatomic steps to produce low-energy
facets. This kind of transformation takes place only in materials with strong
interatomic bonding. Softer materials under tensile stress are expected to grow
predominantly with a planar morphology until misfit dislocations are
introduced, or to transform into 3D islands by a different mechanism. It is
concluded that the coherent Stranski-Krastanov growth in expanded overlayers is
much less probable than in compressed ones for kinetic reasons.
