Evolution of the free energy of the GaN(0001) surface based on first-principles phonon calculations

In this paper, we present systematic improvements to a method that allows us to determine the surface phase diagrams based on ab initio calculations and atomistic thermodynamics. In particular, we include a contribution derived from thermal vibrations of the surface, which is usually omitted in such analysis. On the basis of first-principles phonon calculations, we determine a zero-point vibrational energy and thermal dependencies of vibrational entropy and free energy for atoms and molecules adsorbed on the surface. A series of polar GaN(0001) surfaces are examined. Significant changes are observed in the surface phase diagrams compared to the diagrams obtained by standard density-functional theory calculations without phononic contributions.