A tetragonal phase is predicted for Hf2O3 and Zr2O3 using density functional
theory. Starting from atomic and unit cell relaxations of substoichiometric
monoclinic HfO2 and ZrO2, such tetragonal structures are only reached at zero
temperature by introducing the oxygen vacancy pair with the lowest formation
energy. The tetragonal Hf2O3 and Zr2O3 structures belong to space group P-4m2
and are more stable than their corundum structure counterparts. These phases
are semi-metallic, as confirmed through further G0W0 calculations. The carrier
concentrations are estimated to be 1.77E21 cm^{-3} for both electrons and holes
in tetragonal Hf2O3, and 1.75E21 cm^{-3} for both electrons and holes in
tetragonal Zr2O3. The tetragonal Hf2O3 phase is probably related to the low
resistivity state of hafnia-based resistive random access memory (RRAM)