Hybrid functional versus quasiparticle calculations for the Schottky barrier and effective work function at TiN/HfO2interface

We investigate the Schottky barrier and effective work function (EWF) at TiN/HfO${}_{2}$ interface through density functional calculations. For different interfaces that consist of either Ti-O or N-Hf interface bonds, the intrinsic metal-induced gap states are nearly independent of the interface structure, with similar decay lengths into the oxide. Due to the weak Fermi-level pinning, the EWF is more sensitive to the extrinsic effect of interface bonding. As N-rich interface bonds are replaced by O-rich bonds, the EWF decreases by up to 0.36 eV, which is attributed to the formation of opposing interface dipoles. To improve the band gap and EWF, we perform both hybrid functional and quasiparticle (QP) calculations. In the $G{W}_{0}$ approximation, in which the Green's function is self-consistently calculated by updating only QP energies and the full frequency-dependent dielectric function is used, the agreement of the EWF with experiment is greatly improved, while QP calculations at the ${G}_{0}{W}_{0}$ level or using the plasmon-pole dielectric function tend to overestimate the EWF. In the self-consistent $GW$ approach, in which both QP energies and wave functions are updated in iterations, the band gap is overestimated, resulting in the lower EWF. On the other hand, the EWF is severely underestimated with the hybrid functional because of the larger shift of the valence band edge level of HfO${}_{2}$.