Fig. 1: Configurations and band structures of HfO₂ phases.
From: Extra hole threshold in HfO2 ferroelectric phase stabilization
a Crystal structures of paraelectric monoclinic (M-phase), and (b) ferroelectric orthorhombic (O-phase) phase. Hafnium (Hf) atoms are represented by gray spheres, and oxygen atoms are color-coded by coordination: red spheres denote fourfold-coordinated oxygen (OIV, bonded to four Hf atoms), and yellow spheres indicate threefold-coordinated oxygen (OIII, bonded to three Hf atoms). The spatial distribution of excess extra holes in the HfO₂ lattice is visualized as green iso-surfaces (1/10 of the maximum value). Oxygen vacancies located at threefold-coordinated (c) and fourfold-coordinated (d) oxygen lattice sites, respectively, demonstrate the modulation effect of vacancy-hole couplings on the relative stability between ferroelectric O-phase and paraelectric M-phase. e–h Band structures of M-phase and O-phase systems containing oxygen vacancies at tetragonal-coordinated (VOⅣ) and trigonal-coordinated (VOⅢ) oxygen lattice sites, the red curve represents the defect energy level where oxygen vacancies are located.
