Surface-dependent band structure variations and bond deviations of GaN.

Density functional theory (DFT) calculations on a tunable number of GaN (0001) planes give an invariant band structure, density of states (DOS) diagram, and band gap of the GaN unit cell. Dissimilar band structures and DOS diagrams are obtained for 1, 3, 5, 7, and 9 layers of GaN (101̄0) planes, but the same band structure as that of the (0001) plane returns for 2, 4, 6, and 8 (101̄0) planes. Furthermore, 1 to 4 layers of GaN (101̄1) planes exhibit dissimilar band structures, but the GaN unit cell band structure is obtained for 5 (101̄1) planes. While there are no changes to the Ga-N bond length and bond geometry for the (0001) planes, the (101̄0) planes present bond length variation and bond distortion with odd numbers of layers. Bond length and bond direction deviations are also obtained for 1 to 4 (101̄1) planes. These results suggest that slight structural deviations may be present near the GaN surface to produce facet-dependent properties, and such atomic position deviations in the surface layer can be observed in various semiconductors.