Multiscale modelling of self-organized mono-layer surface atomic clusters

We present here a multi-scale modelling approaches for investigation of self-organized monolayer atomic clusters on atomically flat substrates during epitaxial deposition processes. A phase field model is developed for the free energy of the system, which includes short-range as well as long-range interactions between deposited atoms clusters mediated by the substrate. The way of calculating cluster interactions is the elastic theory of surface stress. The coverage-dependent part in nonlocal interactions is found to have a q3 destabilizing effect, where q is the magnitude of the wave vector for spatial fluctuations in surface atom concentrations. The coverage-independent part associated with the presence of an external elastic field in the substrate is shown to provide an efficient way to control the spatial and size distributions of clusters. Qualitative and quantitative agreements between model predictions and experimental observations on self-organized Ge quantum dots on Si substrate are demonstrated. To precisely determine the influence of periodic strain fields in the substrate on the nucleation of self-organized surface atomic clusters, a Kinetic Monte Carlo model was developed. Island diffusion is found to play a dominant role in the early stage of nucleation.