Anisotropic step stiffness from a kinetic model of epitaxial growth

TL;DR

This paper develops a kinetic model for epitaxial growth to derive a formula for step stiffness as a function of edge orientation, incorporating defect diffusion, kink convection, and flux laws, matching equilibrium results.

Contribution

It introduces a nonequilibrium kinetic model that predicts anisotropic step stiffness in epitaxial growth, extending previous equilibrium-based approaches.

Findings

Step stiffness scales as $ heta^{-1}$ for small angles.

Model aligns with equilibrium calculations for certain parameters.

Provides a kinetic framework for anisotropic step properties.

Abstract

Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson type formula and the associated step stiffness as a function of the step edge orientation angle, $theta$. Basic ingredients of the model are: (i) the diffusion of point defects (``adatoms'') on terraces and along step edges; (ii) the convection of kinks along step edges; and (iii) constitutive laws that relate adatom fluxes, sources for kinks, and the kink velocity with densities via a mean-field approach. This model has a kinetic (nonequilibrium) steady-state solution that corresponds to epitaxial growth through step flow. The step stiffness, $\tbe(\theta)$, is determined via perturbations of the kinetic steady state for small edge Peclet number, P, which is the ratio of the deposition to the diffusive flux along a step edge. In particular, $\tbe$ is found to satisfy $\tbe =O(\theta^{-1})$ for $O(P^{1/3}) <\theta \ll 1$, which is in agreement with independent, equilibrium-based calculations.