Three-dimensional elastic lattice model of heteroepitaxy

If the overlayer consists of two adatoms at a separation r, they interact asymptotically with a repulsive energy proportional to r−3, in agreement to the continuum elasticity theory but with a strength weakened due to the atomic relaxation. If the overlayer consists of two parallel steps with alternating signs, the interaction is proportional to the logarithm of the separation, and depends strongly on the softness of the substrate. As the substrate softens, steps around monolayer islands induce strong island repulsion. If an island becomes three-dimensional, its large portion relaxes to recover its natural lattice constant. The force balances for an island, but the force dipole remains to produce a repulsive interaction between two islands which decays as r−3, similar to the adatom interaction. The interaction strength, however, is large, proportional to the product of two island sizes.