Experimental characterization is facing severe difficulties in elucidating the nature of defects at interfaces between silicon and amorphous high-kappa oxides. This motivates recourse to first principle simulation approaches based on density functional theory. A major issue for these approaches is the choice of the model structure. indeed, the most trivial choice of parent crystalline structures may fail in describing the amorphous nature of the oxide or the specific bonding arrangements occurring at the interface. A second critical issue relates to the determination of energy levels with respect to band edges of the semiconductor and the oxide, which often represent the only contact with experimental data. An improved description of the electronic structure is required going beyond standard density functional approaches that severely underestimate electronic band gaps. Here, these issues are illustrated by a comparative study of the oxygen vacancy in monoclinic HfO2, in amorphous HfO2, and at the Si-HfO2 interface.