期刊
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
卷 57, 期 3, 页码 521-538出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2008.11.007
关键词
Heteroepitaxy; Strained thin films; Kinetic Monte Carlo
资金
- NSF [DMS-0553487, DMS-0509124, NSF-DMS-0707443, DE-FG02-03ER25586]
- Direct For Mathematical & Physical Scien [0810113] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [0810113] Funding Source: National Science Foundation
Simulation of heteroepitaxial growth using kinetic Monte Carlo (KMC) is often based on rates determined by differences in elastic energy between two configurations. This is computationally challenging due to the long range nature of elastic interactions. A new method is introduced in which the elastic field is updated using a local approximation technique. This involves an iterative method that is applied in a sequence of nested domains until a convergence criteria is satisfied. These localized calculations yield energy differences that are highly accurate despite the fact that the energies themselves are far less accurate: an effect referred to as the principle of energy localization. This is explained using the continuum analogue of the discrete model and error estimates are found. In addition, a rejection algorithm that relies on a computationally inexpensive estimate of hopping rates is used to avoid a substantial fraction of the elastic updates. These techniques are applied to 1 + 1-dimensional KMC simulations in physically interesting regimes. (C) 2008 Elsevier Ltd. All rights reserved.
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