A flexible kinetic Monte Carlo framework for GaN molecular beam epitaxy with adaptive on-the-fly barrier evaluation

We present a lattice-based kinetic Monte Carlo (KMC) framework for simulating GaN(0001) growth by molecular beam epitaxy. The framework captures the key microscopic processes governing epitaxial growth, including temperature-dependent surface diffusion, flux-driven deposition, Ehrlich--Schwoebel (ES) step-edge barriers, Ostwald ripening, and species-specific desorption, within a scalable architecture that enables systematic exploration of experimentally relevant growth conditions. In addition to predefined activation-energy catalogs, the framework supports adaptive on-the-fly barrier evaluation using machine-learned interatomic potentials. When previously unencountered local atomic configurations arise, activation barriers are computed via nudged elastic band, potential energy scans, or Br{\o}nsted--Evans--Polanyi methods, and cached for reuse. Predefined-barrier simulations reproduce compact triangular island formation, and further capture Ostwald ripening during growth interruptions and ES barrier-induced multilayer nucleation. At elevated temperatures, desorption drives an island ``walking'' regime, in which N--Ga exchange generates weakly bound Ga adatoms (AdGa) at trailing edges; preferential desorption of AdGa leads to asymmetric edge retreat and net island translation. Our KMC framework provides a flexible platform for predictive simulations of GaN epitaxy at the atomic scale and, more broadly, non-equilibrium growth of compound semiconductors.