Reduction Strategies for Kinetic Monte Carlo Models of Thin Film Growth

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Martha A. Gallivan, Richard M. Murray, David G. Goodwin
Electrochemical Society, May 2001

Thin film deposition encompasses a variety of physical processes, which occur over a wide range of length and time scales. A major challenge in modeling and simulating thin film deposition is this disparity in scales. In this study we focus on an atomic-scale lattice model of surface processes. Kinetic Monte Carlo simulations provide stochastic realizations of the surface evolution, which may then inform a reacting flow or heat transfer model. Unfortunately, these simulations are extremely computationally intensive, particularly for design and optimization studies in which many cases are considered.

We develop reduced-order models of thin film growth using two techniques: balanced truncation and eigensystem realization. After identifying the underlying structure of the lattice model as a linear differential equation, we apply the reduction techniques to obtain reduced-order models of root-mean-square roughness and step edge density. Three modes are needed for a very small model system, while only five modes capture the evolution of a 200x200-site system over a range of growth modes, from stochastic roughening to island nucleation and coalescence.

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