Coherent Stranski-Krastanov growth in 1+1 dimensions with anharmonic interactions: An equilibrium study

The formation of coherently strained three-dimensional (3D) islands on top of the wetting layer in the Stranski-Krastanov mode of growth is considered in a model in 1 + 1 dimensions accounting for the anharmonicity and noncon vexity of the real interatomic forces. It is shown that coherent 3D islands can be expected to form in compressed rather than expanded overlayers beyo nd a critical lattice misfit. In expanded overlayers the classical Stranski -Krastanov growth is expected to occur because the misfit dislocations can become energetically favored at smaller island sizes. The thermodynamic rea son for coherent 3D islanding is incomplete wetting owing to the weaker adh esion of the edge atoms. Monolayer height islands with a critical size appe ar as necessary precursors of the 3D islands. This explains the experimenta lly observed narrow size distribution of the 3D islands. The 2D-3D transfor mation takes place by consecutive rearrangements of mono-to bilayer, bi- to trilayer islands, etc., after the corresponding critical sizes have been e xceeded. The rearrangements are initiated by nucleation events, each one ne eding to overcome a lower energetic barrier than the one before. The model is in good qualitative agreement with available experimental observations.