Comparisons between intrinsic bonding defects in d⁰ transition metal oxide such as HfO₂, and impurity atom defects in d⁰ complex oxides such as GdScO₃

This article addresses O-atom vacancy defects in the d⁰ transition metal (TM) oxides HfO₂ and TiO₂, and Ti substitutions for Sc in the d⁰ complex oxide GdScO₃. In each instance this results in occupied TM atoms with d¹ state representations. These are important for different aspects of the ultimate scaling limits for performance and functionality in nano-scale Si devices. The occupancy of d¹ states is cast in terms of many-electron theory in order to determine the effects of correlation on device performance and functionality. The first section of this article identifies equivalent d-state representations using on an ionic model for the effective valence states of Ti and Hf atoms bordering on O-atom vacancy defects. Removal of an O atom to create a neutral vacancy; this is equivalent to the bonding of two electrons to each vacancy site. This give rise to two coupled d¹ states for a mono-vacancy defect. Transitions from these occupied states generate spectroscopic features in the (i) pre-edge shake-up, and (ii) virtual bound state (VBS) shake-off energy regimes in O K edge XAS spectra. The number of states confirm that these are mono-vacancy defects. The second section addresses incorporation of Ti tetravalent impurities into trivalent GdScO₃, forcing Ti into a Ti³⁺ state and generating a d¹ electronic structure. Vacancy defect concentrations in HfO₂ are generally <10¹⁹ cm^-3. However, the Ti solubility in GdScO₃ is higher, and relative concentrations in excess of 16-17% lead to an insulator to metal transition with a ferri-magnetic electronic structure.