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Accounting for the anharmonicity of the real interatomic potentials in a model in 1+1 dimensions shows that coherent three-dimensional (3D) islands can be formed on the wetting layer in a Stranski-Krastanov growth mode predominantly in compressed overlayers. Coherent 3D islanding in expanded overlayers could be expected as an exception rather than as a rule. The thermodynamic driving force of formation of coherent 3D islands on the wetting layer of the same material is the weaker adhesion of the atoms near the island edges. The average adhesion gets weaker with increasing island thickness but reaches a saturation after several monolayers. A misfit greater than a critical value is a necessary condition for coherent 3D islanding. Monolayer height islands with a critical size appear as necessary precursors of the 3D islands. The transformation from monolayer-high islands to three-dimensional pyramids takes place through a series of stable intermediate 3D islands with discretely increasing thickness.

Dislocation-Free 3D Islands in Highly Mismatched Epitaxy: An Equilibrium Study With Anharmonic Interactions