The electronic structure of O-vacancy at the interface between Si and HfO$_{2}$*

We study the electronic properties of oxygen vacancy (V$_{O})$ at the interface structure between Si and HfO$_{2}$ through local density functional calculations. We consider a device model, where HfO$_{2}$ layers are placed on the Si (001) surface. For monoclinic and amorphous HfO$_{2}$, the valence band offsets are estimated to be 2.0--3.0 eV. The defect properties of V$_{O}$ are affected by the local bonding geometry and band offset at the interface. We find that V$_{O}$ defects at the interface, which are surrounded by a mixture of the Hf and Si atoms, have lower formation energies than those in the oxide region. For various interface structures, we find that the defect levels of V$_{O}$ are generally higher in the amorphous phase than in the monoclinic phase due to the smaller valence band offset. Our calculations suggest that the Fermi level pinning in $p$-MOS devices is caused by O-vacancies in the oxide region, more significantly in the amorphous oxide. On the other hand, O-vacancies formed at the interface, which have the unoccupied levels in the Si band gap, are responsible for the Fermi level pinning in $n$-MOS devices.