Step interaction on a 3D elastic substrate

An elastic lattice model is proposed to study the strain-induced step interactions in atomic levels. In the homoepitaxial case, the behavior predicted by the continuum theory is reproduced asymptotically, even though a large finite size effect is observed such that the interaction across a pit is quite small compared to that across an island at a short step separation. In the heteroepitaxial case, the logarithmic interaction predicted by the continuum theory is reproduced asymptotically, but a step interaction across an island is found to differ from that across a pit. The elastic properties of the substrate also affects the step interaction. For a very hard substrate, the step interaction across a pit is absent. As the substrate softens, the step interaction becomes long-ranged, and a repulsive force between steps across a pit increases.