Surface energy and surface stress of polar GaN(0001)

The polar wurtzite GaN(0001) surface has several proposed surface reconstructions whose relative stability is measured by their surface energy and surface stress. However, the polar nature of the surface, together with the slab geometry, fixed layers with pseudohydrogen termination used in calculations, leads to significant difficulties in accurately identifying the numerical value of surface quantities. We show a method to calculate the surface energy of the clean surfaces by separating the contributions due to the pseudohydrogen layer and its interaction with the slab. This yields a value of 368 meV/angstrom(2) for the sum of surface energies of the unreconstructed Ga-polar (0001) surface and the bulk-terminated N-polar (000 (1) over bar) surface, and 359-364 meV/angstrom(2) for the sum of surface energies of reconstructed Ga-polar surfaces and the bulk-terminated N-polar surface. In order to calculate surface stress, we propose a modified plane stress condition that is suitable for slabs with a passivated bottom layer. By detailed analysis of the stress for the reconstructed and unreconstructed slabs of different sizes, we show that the unreconstructed surface is in a state of compressive surface stress with Sigma(xx) < -0.65 N/m. This compressive stress is relieved through surface reconstructions. The method developed here is applicable for other polar materials.