Morphological Transition: From Meanders to Mound Structures

TL;DR

This study models the morphological transition from meandered surface patterns to mound structures on crystal surfaces, highlighting the roles of kinetic barriers and mass transport in surface evolution.

Contribution

It introduces a Cellular Automata framework to simulate and analyze the reversible transition between meandered patterns and mounds under various growth conditions.

Findings

Reversible transition occurs under moderate Ehrlich-Schwoebel barriers and high terrace diffusivity.

Surface morphology depends on the interplay between kinetic barriers and mass transport.

Scaling behavior of correlation lengths reveals continuum pathways between different surface structures.

Abstract

Mound formation on flat and miscut crystal surfaces exhibits distinct growth behaviors. While mound structures are the predominant feature on flat surfaces, miscut surfaces display a smooth transition from meandered patterns to three-dimensional mounds, depending on both internal and external conditions. We investigate this morphological evolution-from meander-like surface patterns to faceted pyramidal structures-using a vicinal Cellular Automata modeling framework. The transition is shown to be governed by the competition between the Ehrlich-Schwoebel barrier and adatom mobility on terraces. Under moderate barrier strengths and sufficiently high terrace diffusivity, the system demonstrates a reversible transition from mounded configurations to regular step meandered patterns. This reveals a complex interplay between kinetic barriers and mass transport. Our simulations cover a wide range of growth conditions, including variations in deposition flux, surface diffusion rates, temperature, and miscut angle. By applying the height-height correlation function, we calculate the correlation lengths along and across the steps and analyze their scaling behavior. These results offer insight into the continuum pathways that connect distinct classes of surface structures and provide a unified framework for describing pattern evolution across different crystal growth regimes.