From atoms to steps: The microscopic origins of crystal evolution

TL;DR

This paper derives a microscopic, atomistic basis for the BCF theory of crystal growth, showing its validity in low adatom-density regimes and identifying conditions for its applicability and corrections.

Contribution

It provides a simple 1D derivation of the BCF theory from an atomistic KRSOS model, linking microscopic dynamics to macroscopic surface evolution.

Findings

BCF theory is valid in low adatom-density regimes

Derived conditions for low-density surface states

Identified microscopic origins of BCF model corrections

Abstract

The BCF theory of crystal growth has been successful in describing a wide range of phenomena in surface physics. Typical crystal surfaces are slightly misoriented with respect to a facet plane; thus, the BCF theory views such systems as composed of staircase-like structures of steps separating terraces. Adsorbed atoms (adatoms), which are represented by a continuous density, diffuse on terraces, and steps move by absorbing or emitting these adatoms. Here we shed light on the microscopic origins of the BCF theory by deriving a simple, one-dimensional (1D) version of the theory from an atomistic, kinetic restricted solid-on- solid (KRSOS) model without external material deposition. We define the time-dependent adatom density and step position as appropriate ensemble averages in the KRSOS model, thereby exposing the non-equilibrium statistical mechanics origins of the BCF theory. Our analysis reveals that the BCF theory is valid in a low adatom-density regime, much in the same way that an ideal gas approximation applies to dilute gasses. We find conditions under which the surface remains in a low-density regime and discuss the microscopic origin of corrections to the BCF model.