7.15 Level Set Methods for Simulation of Thin Film Growth

The level set method is a general approach to numerical computation for the motion of interfaces. Epitaxial growth of a thin film can be described by the evolution of island boundaries and step edges, so that the level set method is applicable to simulation of thin film growth. In layer-by-layer growth, for example, this includes motion of the island boundaries, merger or breakup of islands, and creation of new islands. A system of size 100× 100 nm may involve hundreds or even thousands of islands. Because it does not require smoothing and or discretization of individual island boundaries, the level set method can accurately and efficiently simulate the dynamics of a system of this size. Moreover, because it does not resolve individual hopping events on the terraces or island boundaries, the level set method can take longer time steps than those of an atomistic method such as kinetic Monte Carlo (KMC). Thus the level set approach can simulate some systems that are computationally intractable for KMC.