This project concerns kinetic Monte Carlo (KMC) models for the evolution of crystals with phase and grain boundaries. KMC is especially useful for exploring the dynamics of atomistic scale crystal growth problems, many of which have a significant bearing on nanotechnology. The essence of the idea is to coarse-grain a molecular dynamics (MD) simulation. While MD is conceptually simple, robust, and faithful to the underlying physics, it is hopelessly slow in many instances. This problem is particularly apparent when simulating the evolution of crystalline solids, where individual atoms hover for long periods of time in basins of attraction before making occasional transitions to neighboring configurations. When the crystal is well defined, an alternative model that replaces the Newtonian dynamics with a Markov chain readily suggests itself: One replaces the original configuration space with an occupation array for a crystal lattice that idealizes the arrangement of the basins of attraction, and introduces transition probabilities based on transition state theory. Clearly, such a scheme works best when the crystal is uniform -- free of dislocations, grain boundaries, impurities and surface structures. Unlike MD, KMC models have to be carefully adapted to handle these sorts of irregularities. While this is complicated and requires specialized simulation software in each case, the payoff is the ability to perform simulations on the scale of nano-devices -- something that is essentially impossible with MD. In this project, the principal investigator addresses two specific challenges to KMC modeling of crystal growth. The first is modeling of crystal-melt interfaces, melt-vapor interfaces and tri-junctions, with the aim of applying the model to the growth of nanowires. The second is the motion of grain boundaries within a polycrystal.
Technology, particularly within the micro-electronic industries, is increasingly focused on smaller and smaller devices. As a result, it is now important to be able to simulate device manufacturing and performance on atomic length scales. There are relatively few computational tools that can resolve the atomic scale behavior of a complicated system containing, say, a few thousand atoms. One of the more promising approaches is kinetic Monte Carlo -- a model that approximates the atomic scale motion of atoms that have perfect stacking arrangements, i.e., that form perfect crystals. Crystals are, however, idealizations, and they feature many defects that require special consideration. Any atomic scale devices attached to crystals would similarly require special treatment. This project is aimed at extending kinetic Monte Carlo models so that they can handle such irregularities. The project is funded by the Division of Mathematical Sciences and the Division of Materials Research.