  The formation of coherently strained three-dimensional islands on top of the
wetting layer in Stranski-Krastanov mode of growth is considered in a model in
1+1 dimensions accounting for the anharmonicity and non-convexity of the real
interatomic forces. It is shown that coherent 3D islands can be expected to
form in compressed rather than in expanded overlayers beyond a critical lattice
misfit. In the latter case the classical Stranski-Krastanov growth is expected
to occur because the misfit dislocations can become energetically favored at
smaller island sizes. The thermodynamic reason for coherent 3D islanding is the
incomplete wetting owing to the weaker adhesion of the edge atoms. Monolayer
height islands with a critical size appear as necessary precursors of the 3D
islands. The latter explains the experimentally observed narrow size
distribution of the 3D islands. The 2D-3D transformation takes place by
consecutive rearrangements of mono- to bilayer, bi- to trilayer islands, etc.,
after exceeding the corresponding critical sizes. The rearrangements are
initiated by nucleation events each next one requiring to overcome a lower
energetic barrier. The model is in good qualitative agreement with available
experimental observations.
