We report a direct approach for calculating individual energy of polar semiconductor surfaces and interfaces using density functional theory calculations. This approach is applied to polar surfaces and interfaces of group-III nitrides (AlN, GaN, and InN) and clarifies the interplay of chemical bonding and charge neutrality at the interface, which is crucial for the stability and polarity of group-III nitrides. Furthermore, using the surface and interface energies we demonstrate phase diagrams as functions of temperature and pressure. For AlN on Si-face SiC substrate under H-rich condition, we find that Al-polar AlN surfaces with substitutional Al atoms at AlN/SiC interface are stabilized over the wide range of Al pressure. In contrast, the H-terminated Ga-polar GaN surface on N-polar AlN(0001) substrate with two monolayers of Al olverlayers is favorable over the entire growth conditions. These results suggest that the stability of interface between III-nitride and substrate rather than surface stability is crucial for the polarity of III-nitrides.
