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, $\theta$. 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, $\tilde{\beta}(\theta)$, 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, $\tilde{\beta}$ is found to satisfy $\tilde{\beta} =O(\theta^{-1})$ for $O(P^{1/3})