Height of a faceted macrostep for sticky steps in a step-faceting zone

Abstract

The driving force dependence of the surface velocity and the average height of faceted merged steps, the terrace-surface-slope, and the elementary step velocity in the non-equilibrium steady-state are studied using the Monte Carlo method. The Monte Carlo study is based on a lattice model, the restricted solid-on-solid model with point-contact type step--step attraction (p-RSOS model). The temperature is selected to be in the step-faceting zone where the surface is surrounded by the (001) terrace and the (111) faceted step at equilibrium. Long time simulations are performed at this temperature to obtain steady-states for the different driving forces that influence the growth/recession of the surface. A Wulff figure of the p-RSOS model is produced through the anomalous surface tension calculated using the density-matrix renormalization group method. Although the p-RSOS model is a simplified model, the model shows a wide variety of dynamics in the step-faceting zone. There are four characteristic driving forces, $\Delta \mu_y$, $\Delta \mu_f$, $\Delta \mu_{co}$, and $\Delta \mu_R$. For $\Delta \mu_{co}<|\Delta \mu|<\Delta \mu_R$, the surface grows/recedes with the successive attachment-detachment of steps to/from a macrostep. When $|\Delta \mu|$ exceeds $\Delta \mu_R $, the macrostep vanishes and the surface roughens kinetically. Classical 2D heterogeneous multi-nucleation was determined to be valid with slight modifications based on the Monte Carlo results of the step velocity and the change in the surface slope of the "terrace". The finite size effects were also determined to be distinctive near equilibrium.