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 correspondsto epitaxial growth through step flow. The step stiffness, (beta) over tilde(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, (beta) over tilde is found to satisfy (beta) over tilde = O(theta(-1)) for O(P-1/3) < theta << 1, which is in agreement with independent, equilibrium-based calculations.