Interaction of small diamond islands on iridium: A finite element simulation study

Finite element simulations using the code ABAQUS have been performed to model the elastic interaction of small heteroepitaxial diamond islands on iridium. The simulations predict a huge relaxation of the elastic energy density for a thin two-dimensional diamond layer when it splits into individual islands. They show that the interaction of neighbouring islands increases their elastic energy. For the modelled islands with lateral dimensions of 2 nm this mutual rejection works only within a distance of a few nanometers.The results of the simulation allow the following conclusions with respect to potential nucleation models: 1) The repulsive elastic interaction between neighbouring grains rather suppresses nucleation in the vicinity of an existing grain than enhancing it. Thus, it cannot provide an explanation for the agglomeration of the grains in areas of extremely high nucleation density, the so called “domains”. 2) For an alternative model of two-dimensional lateral diamond growth followed by splitting into isolated grains the simulations can explain the splitting and the subsequent repulsion. 3) The rapid drop of the interaction strength with distance indicates that further interaction mechanisms are required to account for the final distance of the grains found experimentally.