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

TL;DR

This paper derives the Burton-Cabrera-Frank (BCF) step flow model from an atomistic stochastic scheme in 1+1 dimensions, clarifying its assumptions and emergence from microscopic rules.

Contribution

It provides a formal derivation of the BCF model from a simplified atomistic scheme using scaling arguments, connecting microscopic stochastic rules to macroscopic step flow.

Findings

BCF model emerges from atomistic stochastic scheme under certain conditions

Derivation clarifies assumptions behind the BCF theory

Provides a link between microscopic rules and macroscopic behavior

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 non-interacting steps from a stochastic atomistic scheme of a simplified kinetic 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.