Elastic lattice Green's function in three dimensions

The elastic lattice Green's function for a simple cubic substrate with a semi-infinite thickness is obtained numerically in the isotropic case. This allows us to replace the bulk substrate by a single surface layer in the study of epitaxial adsorption. Its application to the homoepitaxial adsorption systems with various surface defects, as adatoms, steps or islands, results in the evaluation of their formation and interaction energies. Interactions approach to the asymptotic limit by the continuum elasticity theory even at short distances, except the step-step interaction. The latter has a large transient region before the final asymptotics sets in. This shows that the continuum elasticity is insufficient to describe the structural details of the atomic scale when forces are distributed over two atomic layers, such as, at the step edge.