Modified approach for calculating individual energies of polar and semipolar surfaces of group-III nitrides

We propose an approach for simultaneously calculating absolute surface energies of polar and semipolar planes without invoking the similarity between hexagonal and cubic structures. Our approach is based on the calculations of total energy differences between two identical wedge-shaped geometries with ideal surfaces using density functional calculations in conjunction with the evaluations of surface dangling bonds for various orientations. The calculations demonstrate characteristic features of the surface stability depending on the crystal orientation: For both GaN and AlN, the surface energy of semipolar (11 (2) over bar2) plane under H-rich condition is lower than that of nonpolar (11 (2) over bar0) plane. The lower surface energy on the (11 (2) over bar2) plane compared with the (11 (2) over bar0) plane implies that the semipolar (11 (2) over bar2) surface is preferentially formed for high H-2 pressures during the metal-organic vapor phase epitaxy, consistent with the experimental results of selective-area growth of GaN Similar trends can also be found in the surface energies of semipolar (1 (1) over bar 01) plane in both GaN and AlN, and the absolute surface energy on the (1 (1) over bar 01) plane is found to be lower than that on the (11 (2) over bar2) plane. These calculated results suggest that all of the phenomena related to the stability of polar and semipolar planes of group-III nitrides would benefit from these accurate values of surface energies.