Quasiparticle calculations of the electronic properties of ${\text{ZrO}}_2$ and ${\text{HfO}}_2$ polymorphs and their interface with Si

Quasiparticle calculations are performed to investigate the electronic band structures of various polymorphs of Hf and Zr oxides. The corrections with respect to density-functional-theory results are found to depend only weakly on the crystal structure. Based on these bulk calculations as well as those for bulk Si, the effect of quasiparticle corrections is also investigated for the band offsets at the interface between these oxides and Si assuming that the lineup of the potential at the interface is reproduced correctly within density-functional theory. On the one hand, the valence-band offsets are practically unchanged with a correction of a few tenths of electron volts. On the other hand, conduction-band offsets are raised by 1.3–1.5 eV. When applied to existing calculations for the offsets at the density-functional-theory level, our quasiparticle corrections provide results in good agreement with the experiment.

Figure 1

(Color online) Theoretical band structure within the LDA [(brown circles) gray in the printed version] and $G{W}_0$ (black circles) along high symmetry axis of the BZ for the (a) cubic, (b) tetragonal, (c) strained, and (d) monoclinic phases of ${\text{ZrO}}_2$ and ${\text{HfO}}_2$. The $G{W}_0$ band structures have been extrapolated from the calculated QP corrections using a linear fit.