Mean-field theory of nucleation and growth on strained surfaces

Mean-field nucleation and growth modeling is important for understanding various adsorbatesubstrate systems, particularly in the context of epitaxial growth. Conventional mean-field theory does not take into account non-local interactions, but adparticles may interact with strained islands via long range elastic interactions mediated by the substrate. We show that recent extensions of mean-field theory to deal with non-local interactions do not describe such processes faithfully. Here we derive a new, generally applicable, mean-field theory of adparticle dynamics on strained surfaces, when interdiffusion is neglected. This approach enables us to determine the transport coefficients from the microscopic physics; in particular we find explicit expressions for the diffusion coefficient and drift velocity at all positions relative to an arbitrarily strained island. We demonstrate the role of strain on island growth, using island strain fields that are dynamically updated, for Ge/Si(001) parameters. This approach has important applications in the modeling of nucleation and growth of many nanostructures, such as metal nanoclusters, semiconductor hut clusters and silicide nanowires.