Relaxation of the (0 0 1) surface in binary Sc, Ti and V nitrides: a first principles density functional study

Density functional calculations with periodic boundary conditions of the structure of ScN, TiN and VN(0 0 1) surfaces are reported. Using slabs of different thickness to model the surface, the rippling relaxation of outermost layer is estimated to be 0.011, 0.178 and 0.256 Å, respectively. Calculations show that on nitrogen atoms there is a significant surface core-level shift arising from both the lack of periodicity and the rippling relaxation. For the TiN(0 0 1) surface, the rippling contribution to the N 1s surface core-level shift is estimated to be −0.20 eV (35%), with a final value of −0.56 eV, in excellent agreement with photoemission experiments. The analysis of the electronic band structure of TiN(0 0 1) surface along the Γ–X and X–M directions confirms that the experimentally surface state observed in the angle-resolved photoemission spectra at −2.9 eV is due to a Tamm surface state pulled off the top of the Δ5 bulk band. The shift of the state is also clearly enhanced by the rippling relaxation.