Electronic structure of strongly reduced ( 1 ‾ 1 1 ) surface of monoclinic HfO 2

Highlights: • Oxygen vacancy (Vo) tends to segregate onto the surface and attracts each other when forming pairs, enabling the possibility of developing a Vo-controlled functional area/device on the surface. • In this work, a conductivity-stability dilemma for the surface Vo-chains is found, and a semiconductor to metal transition is demonstrated in metastable Vo-chain with formation energy increased by 0.25 eV per Vo. • Application of Hubbard U correction to Density Functional Theory is necessary when discussing the conductance mechanism (metallic/semiconducting/polaron-hopping) of Vo-contained HfO₂. Material surface is playing an increasingly important role in electronic devices as their size down to nanoscale. Here, by first-principles calculations we studied the surface oxygen-vacancies (Vos) induced electronic-structure variation of ${\text{HfO}}_2$, in order to explore its potential applications in surface-controlled electronic devices. Firstly, it is found that single Vo tends to segregate onto the surface and attracts each other as they form pairs, making the formation of vacancies-contained functional surface possible. Then extensive Vo-chains whose formation/rupture can represent the high/low conductivity state are constructed. The electronic states induced by the Vos remain localized in the band-gap region for most of the Vo-chains studied here. A transition to a metallic conductance is found in metastable Vo-chain with formation energy increased by 0.25 eV per Vo. Moreover, we highlight the significance of the Hubbard U correction for density functional theory when studying the electronic-structure based conductance in the oxides. By comprehensive calculations, we find a conductivity-stability dilemma of the Vo-chains, providing guideline for understanding and designing the electronic devices based on ${\text{HfO}}_2$ surface.