Edge-Dependent Step-Flow Growth Mechanism in $\beta$-Ga${}_2$O${}_3$ (100) Facet at the Atomic Level

Homoepitaxial step-flow growth of high-quality $\beta$-Ga${}_2$O${}_3$ thin films is essential for the advancement of high-performance Ga${}_2$O${}_3$-based devices. In this work, the step-flow growth mechanism of $\beta$-Ga${}_2$O${}_3$ (100) facet is explored by machine-learning molecular dynamics simulations and density functional theory calculations. Our results reveal that Ga adatoms and Ga-O adatom pairs, with their high mobility, are the primary atomic species responsible for efficient surface migration on the (100) facet. The asymmetric monoclinic structure of $\beta$-Ga${}_2$O${}_3$ induces a distinct two-stage Ehrlich-Schwoebel barrier for Ga adatoms at the [00$\bar{1}$] step edge, contributing to the suppression of double-step and hillock formation. Furthermore, a miscut towards [00$\bar{1}$] does not induce the nucleation of stable twin boundaries, whereas a miscut towards [001] leads to the spontaneous formation of twin boundaries. This research provides meaningful insights not only for high-quality $\beta$-Ga${}_2$O${}_3$ homoepitaxy but also the step-flow growth mechanism of other similar systems.