Many-Electron Multiplet Theory Applied to O-Atom Vacancies in High-κ Dielectrics

Abstract

Two-electron multiplet theory has been used to develop a high-spin effective d2 model for O-vacancy spin-allowed and spin-forbidden dipole transitions, and for negative ion state traps. The transition and negative ion states have been detected by X-ray absorption spectroscopy in the O K pre-edge regime of transition metal (TM) elemental oxides and complex oxides. Occupied ground and excited states of the model satisfy Hund's rules by (i) including only high-spin state arrangements and (ii) using many electron state term symbols consistent with Russell–Saunders coupling. Qualitative and quantitative agreement between theory and experiment is demonstrated by using Tanabe–Sugano energy level diagrams for (i) identifying the symmetries and spin states, and (ii) determining the relative energies of intra-d-state transitions that are allowed in the presence of an intermediate strength ligand field. This includes removal of the spin degeneracy for the allowed transitions by a cooperative Jahn–Teller effect. The effective d2 model is applied to nanocrystalline thin films of ZrO2, HfO2, TiO2, and Lu2O3 and to illustrate the agreement between the new d2 model and the X-ray absorption spectroscopy data. The new model has also been applied with the same degree of success to complex TM oxides and SiO2.