Elastic relaxation during 2D epitaxial growth: a study of in-plane lattice spacing oscillations

The purpose of this paper is to report some new experimental and theoretical results about the analysis of in-plane lattice spacing oscillations during two-dimensional (2D) homo and hetero epitaxial growth. The physical origin of these oscillations comes from the finite size of the strained islands. The 2D islands may thus relax by their edges, leading to in-plane lattice spacing oscillations during the birth and spread of these islands. On the one hand, we formulate the problem of elastic relaxation of a coherent 2D epitaxial deposits by using the concept of point forces and demonstrate that the mean deformation in the islands exhibits an oscillatory behaviour. On the other hand, we calculate the intensity diffracted by such coherently deposited 2D islands by using a mean model of a pile-up of weakly deformed layers. The amplitude of in-plane lattice spacing oscillations is found to depend linearly on the misfit and roughly linearly on the nucleation density. We show that the nucleation density may be approximated from the full-width at half maximum of the diffracted rods at half coverages. The predicted dependence of the in-plane lattice spacing oscillations amplitude with the nucleation density is thus experimentally verified on V/Fe(0 0 1), Mn/Fe(0 0 1), Ni/Fe(0 0 1), Co/Cu(0 0 1) and V/V(0 0 1).