Exploration of a large-scale reconstructed structure on GaN(0001) surface by Bayesian optimization

GaN(0001) surfaces with Ga- and H-adsorbates are fundamental stages for epitaxial growth of semiconductor thin films. We explore stable surface structures with a nanometer scale by the density-functional calculations combined with Bayesian optimization and reach a single structure with satisfactorily low mixing enthalpy among hundreds of thousand possible candidate structures. We find that the obtained structure is free from any postulated high symmetry previously introduced by human intuition, satisfies an electron counting rule locally, and shows a complex adsorbate arrangement, reflecting characteristics of nitride semiconductors. The proposed scheme toward a high-resolution surface phase diagram contributes to a more precise design of GaN epitaxial growth conditions, especially the ratio of Ga and H partial pressures.