Step meandering: Balance between the potential well and the Ehrlich-Schwoebel barrier

This study presents a comprehensive and innovative exploration of how the surface potential energy landscape influences meander formation. Using the vicinal cellular automaton model, which distinguishes surface diffusion from adatom incorporation into the crystal, the research delves into various factors affecting surface pattern dynamics. By isolating the diffusion process within a defined energy potential, the study provides a detailed analysis of how changes in the potential energy well and the barrier at the top of the step contribute to meander formation. Remarkably, the results reveal that the mere presence of a potential well at the step's bottom is sufficient to induce meandering. The role of the Ehrlich-Schwoebel barrier on formed meanders is further investigated, and a mechanism for meander formation is proposed to clarify this process. The derived relation successfully reflects the wavelength of the meandered patterns observed in the simulations, emphasizing its reliability. Overall, the results highlight the essential role of the surface energy potential's landscape in governing surface pattern formation.