Nonequilibrium Kink Density from One-Dimensional Nucleation for Step Velocity Predictions

Crystal growth rates depend on the density of kink sites along step edges, ρ. The supersaturation-dependence of the kink density, ρ(S), is often ignored despite available nonequilibrium models for centrosymmetric crystals. The aim of this work is to derive ρ(S) from a rather simple one-dimensional nucleation framework in a manner that accounts for multiheight kinks. These become more prevalent at higher S and/or lower kink energies where the step front roughens (i.e., higher ρ). We arrive at a density of kinetic kinks that contribute to the step velocity and make comparisons with other models and simulations. Our model almost entirely eliminates systematic errors in predicted step velocities and crystal growth rates.