Effect of step anisotropy on crystal growth inhibition by immobile impurity stoppers

Step pinning by immobile stoppers is the most important crystal growth inhibition mechanism. It was first studied by Cabrera and Vermilyea in 1958, who considered the macroscopic effect of a periodic array of pinning sites. However, their analysis (and others since) involved uncontrolled approximations and did not consider what happens when step anisotropy induces faceting. Here we revisit the motion of a step past a periodic array of pinning sites, simulating the evolution numerically using a semi-implicit front-tracking scheme for anisotropic surface energies and kinetic coefficients. We also provide exact formulas for the average step velocity when the anisotropy is such that the interface is fully faceted. We compare the average step velocities obtained numerically to the estimates derived in the isotropic setting by Cabrera & Vermilyea (1958) and Potapenko (1993), and to the exact results obtained in the fully faceted setting. Our results show that while the local geometry of the propagating step varies considerably with anisotropy, the average step velocity is surprisingly insensitive to anisotropy. The behavior starts changing only when the ratio between minimum and maximum values of the surface energy is roughly less than 0.1.