Anisotropic Step Stiffness from a Kinetic Model of Epitaxial Growth

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, θ. 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 meanfield approach. This model has a kinetic (nonequilibrium) steady-state solution that corresponds to epitaxial growth through step flow. The step stiffness, β̃(θ), is determined via perturbations of the kinetic steady state for small edge Péclet number, P , which is the ratio of the deposition to the diffusive flux along a step edge. In particular, β̃ is found to satisfy β̃ = O(θ−1) for O(P 1/3) < θ 1, which is in agreement with independent, equilibrium-based calculations.