Fast Kinetic Monte Carlo Simulations: Implementation, Application, and Analysis.

Abstract

This work presents a multi-component kinetic Monte Carlo (KMC) model and its applications to three example systems: Ga droplet epitaxy, nanowires grown by the Vapor-Liquid-Solid (VLS) method, and sintering of porous granular material. The first two systems are examples of liquid mediated growth. We detail how the liquid phase is modeled. A caching technique is proposed to eliminate redundant calculations, leading to performance gains. Underlying the cache is a hash table, indexed by neighborhood patterns of an atom configuration. We present numerical evidence that such neighborhood patterns are redundant within and between configurations, justifying the caching procedure. A simulated annealing search for optimal, system-specific hash functions is performed.

Simulation results and analysis of droplet epitaxy are then described. We detail the calibration of model parameters, exhibiting a good agreement with homoepitaxial thin film experiments. Droplet epitaxy simulations capture a variety of nanostrutures seen in experiments, ranging from compact dots to nanorings. The correct trends in growth conditions are also captured, resulting in a phase diagram consistent with what is seen experimentally. Core-shell structures are also simulated. We present simulations to suggest the existence of two mechanisms behind the their formation: nucleation at the vapor-liquid interface and an instability at the vapor-solid interface. An analytical model is developed and isolates the relevant processes behind the formation of the phenomena seen throughout the simulations and in experiments.

In the VLS nanowire simulations, we present how the catalyzed role of the liquid phase is incorporated into the model and perform an energy parameter study. We exhibit the role of the catalyzed reaction rate and its contribution to growth leading to features such as tapering. The mobility along the liquid-solid interface is also studied. We show how this affects nanowire growth direction and kinking. In the sintering simulations, we present the KMC model in contrast with previous simulation work. A similar parameter study is then performed by studying the effect of parameters on coarsening statistics. Grain statistics are measured as a function of time and captures a power-law behavior for the grain radius. Critical behavior with respect to certain parameters is also presented.