Analysis of an Energy Localization Approximation applied to three-dimensional Kinetic Monte Carlo simulations of heteroepitaxial growth

Heteroepitaxial growth involves depositing one material onto another with a different lattice spacing. This misfit leads to long-range elastic stresses that affect the behavior of the film. Previously, an Energy Localization Approximation was applied to Kinetic Monte Carlo simulations of two-dimensional growth in which the elastic field is updated using a sequence of nested domains. We extend the analysis of this earlier work to a three-dimensional setting and show that while it scales with the increase in dimensionality, a more intuitive Energy Truncation Approximation does not.