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.