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

Kinetic Monte Carlo;Nanofabrication;Quantum Dots;Nanorings;Nanowires;Sinterings;Mathematics;Science;Applied and Interdisciplinary Mathematics

Reyes, Kristofer G.Esedoglu, Selim ;

University of Michigan

关键词: Kinetic Monte Carlo;    Nanofabrication;    Quantum Dots;    Nanorings;    Nanowires;    Sinterings;    Mathematics;    Science;    Applied and Interdisciplinary Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/99949/kgre_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This work presents a multi-component kinetic Monte Carlo (KMC) model and its applications to three example systems: Ga droplet epitaxy, nanowires grown bythe 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 redundantcalculations, leading to performance gains.Underlying the cache is a hashtable, indexed by neighborhood patterns of an atom configuration. We presentnumerical evidence that such neighborhood patterns are redundant within and between configurations, justifying the caching procedure.A simulated annealingsearch for optimal, system-specific hash functions is performed.Simulation results and analysis of droplet epitaxy are then described. We detailthe calibration of model parameters, exhibiting a good agreement withhomoepitaxial thin film experiments. Droplet epitaxy simulations capture avariety of nanostrutures seen in experiments, ranging from compact dots tonanorings.The correct trends in growth conditions are also captured, resultingin a phase diagram consistent with what is seen experimentally. Core-shellstructures are also simulated.We present simulations to suggest the existenceof two mechanisms behind the their formation: nucleation at the vapor-liquidinterface and an instability at the vapor-solid interface. An analytical modelis 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 liquidphase is incorporated into the model and perform an energy parameter study.Weexhibit the role of the catalyzed reaction rate and its contribution to growthleading to features such as tapering.The mobility along the liquid-solidinterface is also studied. We show how this affects nanowire growth directionand kinking.In the sintering simulations, we present the KMC model in contrastwith previous simulation work.A similar parameter study is then performed bystudying the effect of parameters on coarsening statistics. Grain statistics are measured as a function of time and captures a power-law behavior for the grainradius.Critical behavior with respect to certain parameters is also presented.