Study of Stranski-Krastanov growth using kinetic Monte Carlo simulations with an atomistic model of elasticity

We have analyzed the Stranski-Krastanov growth mode in heteroepitaxial thin films using lattice-based kinetic Monte Carlo simulations with an atomistic model of elasticity. In this growth mode, elastic effects due to the lattice mismatch between the film and the substrate cause a transition from two-dimensional layer-by-layer growth to three-dimensional island growth. In our simulations on a simple cubic lattice model in a 3-dimensional system with nearest neighbor interactions only, we see very little tendency towards islanding. On modifying the anisotropy using next-to-nearest and next-to-next-to-nearest neighbor interactions, the system shows a greater tendency towards islanding. When the calculations are carried out in a 2-dimensional system, islanding is fairly pronounced. To gain insights into the possible reasons for these observations, we evaluate the elastic energy and bond energy of different configurations in a 2-dimensional system. Our calculations show that island growth in 2-dimensions also involves a significant nucleation barrier. This suggests that the barrier for island formation is more easily overcome in a 2-dimensional system as compared to a 3-dimensional system.