Many-Electron Multiplet Theory Applied to O-Atom Vacancies in High-$\kappa$ Dielectrics

• Published in: Japanese Journal of Applied Physics 2011-04, Vol.50 (4), p.04DA15-04DA15-8
• Main Authors: Lucovsky, Gerald, Miotti, Leonardo, Bastos, Karen Paz
• Format: Article
• Language: English
• ISSN: 0021-4922; 1347-4065
• DOI: 10.1143/JJAP.50.04DA15

Two-electron multiplet theory has been used to develop a high-spin effective d$^{2}$ 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 d 2 model is applied to nanocrystalline thin films of ZrO 2 , HfO 2 , TiO 2 , and Lu 2 O 3 and to illustrate the agreement between the new d 2 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 SiO 2 .