Ab Initio Elucidation of the Nature of the Bonding of Tetrahedral Nitrides (BN, AlN, GaN, and InN), Hexagonal BN, and Graphene

Recent measurements of the band properties of AlN and GaN by fluorescence yield absorption and soft X-ray emission spectroscopies revealed that their valence band (VB) is composed of two separate subbands. The upper VB subband of GaN is composed of gallium <i>sp</i> and nitrogen <i>p</i> orbitals; the lower subband consists of metal <i>d</i> and nitrogen <i>s</i> orbitals. These findings were confirmed by extensive ab initio simulations. These results are not consistent with the standard tetrahedrally coordinated semiconductors, which are bonded by <i>sp</i>³-hybridized orbitals of metal and nonmetal atoms. The new analysis techniques and ab initio simulations create a new picture, allowing the calculation of overlap integrals to determine the bond order in these crystals. According to these results, bonding occurs between resonant <i>p</i>-states of nitrogen and <i>sp</i>³-hybridized metal orbitals in tetrahedral nitrides, allowing tetrahedral symmetry to be maintained. A similar resonant bonding mechanism is observed in hexagonal BN, where the <i>p</i> orbitals of nitrogen create three resonant states necessary for maintaining the planar symmetry of the lattice. In addition, nonresonant π-type bonds in BN are created by the overlap of pz orbitals of boron and nitrogen. BN bonding differs from that in graphene, where carbon states are fully <i>sp</i>²-hybridized. Additionally, π-type bonds in graphene have no ionic contributions, which leads to the formation of Dirac states with linear dispersion close to the <i>K</i> point, closing the band gap.