The Role of Interface Stress for Nanoparticles Embedded in Films

Abstract

We investigate the effect of interface stress on nanoparticles embedded in films, within the framework of continuum and interface elasticity. The study is motivated by the idea that elastic interactions among three-dimensional strained nanoparticles can lead to size and spatial uniformity of islands, during the growth of multilayered superlattices. This presents a promising avenue in the quest of constructing self-organized nanostructures. Islands, adatom-clusters, and quantum dots can be modeled as inhomogeneities embedded in a heterogeneous film substrate. While the film (bulk) is modeled as linearly elastic and isotropic, interfaces are treated according to Gurtin's theory of linear interface elasticity. In order to illustrate the role of a mechanical load, the system is subjected to uniaxial tension, applied at the remote boundary of the substrate. The displacement potentials methodology, i.e. Papkovitch-Neuber, Boussinesq, and Dougall potentials, coupled with interface elasticity yield an analytical solution. The elastic field is expressed in terms of several sets of spherical and cylindrical harmonics. The study illustrates clearly that interface elasticity introduces a size-effect. In addition, local stresses are significantly affected by the size and position of the nanoparticles.