Monte Carlo simulation of three-dimensional islands

The usual kinetic Monte Carlo method is adapted, to treat off-lattice problems of multilayer growth (coverage θ>1) by molecular-beam epitaxy. This method takes into account the Schwoebel barrier, which comes out as a result of the choice of the potential interaction between the atoms. This method allows a free choice of the lattice mismatch, temperature, deposition flux rate, and interfacial energies. A particular choice of these parameters leads to the three-dimensional (3D) (Volmer-Weber) growth mode, whereas another choice of these parameters leads to the 2D-3D growth mode (Stranski-Krastanov). The 3D islands seem to obey scaling only approximately. Using this method, the surface stress inside a substrate and a (pyramidal) coherent 3D island is computed. Strong relaxations appear, not only at the edges of the 3D island (which is expected), but also in the proximity of the edges, and inside the 3D island. These particular sites inside the 3D island are located just beneath a step site of the upper layer. Moreover, these particular sites develop strong corrugations, which later are propagating along the layer. Strain-induced modulation of layers is thermally activated, so the steps could act as defects and nucleation sites for propagating roughness, in agreement with some theories and experimental facts.