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Forbidden island heights in stress-driven coherent Stranski-Krastanov growth

The observed height distribution of clusters obtained in strained epitaxy has been often interpreted in terms of electronic effects. We show that some aspects can be explained classically by the interplay of strain and edge energies. We find that soft materials can transform directly from monolayer into thicker islands by two-dimensional (2D) multilayer nucleation and growth. There is a critical thickness decreasing with the force constant. Thinner islands are thermodynamically forbidden, due to the insufficient stress relaxation upon clustering particularly under tensile stress. At sufficiently large misfits the barrier for 2D multilayer nucleation is significantly smaller than the barrier for subsequent single-layer nucleation. The effects are found to be quantitatively reasonable and offer a plausible explanation for the absence of thin islands and 2D growth of flattop islands usually attributed to quantum size effects.