Crystal step edges with alternating rows of growth units: 1D nucleation and step velocity

Abstract

Crystals with asymmetric growth units present a ubiquitous challenge for modeling crystal growth. We derive the crystal step edge velocity for steps with alternating rows of growth units (i.e., a row of A followed by a row of B growth units). We construct a free energy model for 1D nucleation of this two-tiered row and show that a single anisotropic interaction parameter and the supersaturation characterize the edge stability. A Fokker–Planck model captures the kinetics of nucleation and seamlessly connects the stable and unstable regimes, whereas previous models diverge near the transition between these cases. The 1D nucleation model leads to an expression that predicts the step velocity as a function of supersaturation and edge stability. We show that the model is in excellent agreement with kinetic Monte Carlo simulations.