title: Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions.
abstract: 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.
authors: Department of Mathematics and Department of Physics, Duke University, Durham, North Carolina 27708, USA.|Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.
authors: Jianfeng
authors: J
authors: Lu
authors: Department of Mathematics and Department of Physics, Duke University, Durham, North Carolina 27708, USA.
authors: Jian-Guo
authors: JG
authors: Liu
authors: Department of Mathematics, and Institute for Physical Science and Technology, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, Maryland 20742, USA.
authors: Dionisios
authors: D
authors: Margetis