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

Abstract

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 $(11\overline{2}2)$ plane under H-rich condition is lower than that of nonpolar $(11\overline{2}0)$ plane. The lower surface energy on the $(11\overline{2}2)$ plane compared with the $(11\overline{2}0)$ plane implies that the semipolar $(11\overline{2}2)$ surface is preferentially formed for high ${\mathrm{H}}_{2}$ 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 $(1\overline{1}01)$ plane in both GaN and AlN, and the absolute surface energy on the $(1\overline{1}01)$ plane is found to be lower than that on the $(11\overline{2}2)$ 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.