The physical origin of the two-dimensional towards three-dimensional coherent epitaxial Stranski-Krastanov transition

Epitaxial two-dimensional layer growth (2D) relayed by three-dimensional (3D) growth, characterizes the Stranski-Krastanov growth mode. The physical origin of this transition is not well understood up to now. We show for a coherent epitaxy that three conditions are necessary and sufficient to rationalize the problem: (i) the perfect wetting condition of Bauer's criterion expressed in terms of long range forces (ii) an elastic misfit energy of the so produced layers (iii) an elastic striction energy induced in the substrate by appearing islands. The three associated energies may compete each other. A single layer island may spontaneously thicken when it grows over a number of A layers greater than a critical one z* provided it has reached a critical size R(z)*. At this point striction opposes to wetting and spends the necessary energy for creating new edges. The kinetics of 2D --> 3D transition is surface diffusion dependent and driven by the striction giving a very abrupt transition around R(z)*, which is of mesoscopic size. The Ge(111)/Si(111)7 x 7 system is treated numerically since most of the necessary data are known.