E. Korutcheva et al., Coherent Stranski-Krastanov growth in 1+1 dimensions with anharmonic interactions: An equilibrium study, PHYS REV B, 61(24), 2000, pp. 16890-16901
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.