Emergence of step flow from atomistic scheme of epitaxial growth in 1+1 dimensions

Jianfeng Lu Duke University Jian-Guo Liu Duke University d Dionisios Margetis University of Maryland

Mathematical Physics mathscidoc:1702.22002

Physical Review E, 91, (3), 2015.3
The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling arguments the emergence of the BCF theory for noninteracting steps from a stochastic atomistic scheme of a kinetic restricted solid-on-solid model in one spatial dimension. Our main assumptions are: adsorbed atoms (adatoms) form a dilute system, and elastic effects of the crystal lattice are absent. The step edge is treated as a front that propagates via probabilistic rules for atom attachment and detachment at the step. We formally derive a quasistatic step flow description by averaging out the stochastic scheme when terrace diffusion, adatom desorption, and deposition from above are present.
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@inproceedings{jianfeng2015emergence,
  title={Emergence of step flow from atomistic scheme of epitaxial growth in 1+1 dimensions},
  author={Jianfeng Lu, Jian-Guo Liu, and d Dionisios Margetis},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207235031197747281},
  booktitle={Physical Review E},
  volume={91},
  number={3},
  year={2015},
}
Jianfeng Lu, Jian-Guo Liu, and d Dionisios Margetis. Emergence of step flow from atomistic scheme of epitaxial growth in 1+1 dimensions. 2015. Vol. 91. In Physical Review E. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207235031197747281.
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