Dielectric properties of crystalline and amorphous transition metal oxides and silicates as potential high-κ candidates: the contribution of density-functional theory

A review is given of various first-principles studies of the dielectric properties of crystalline and amorphous transition metal oxides and silicates, which have drawn considerable attention as potential high-κ materials. After a brief summary of the principal equations of density-functional theory related to the dielectric properties of solids, the results obtained for group IVb M = (Hf,Zr,Ti) and IIIb M = (Y,La,Lu) transition metals crystalline oxides and/or silicates are discussed. For the group IVb transition metals, four crystalline phases (cubic, tetragonal, monoclinic and rutile) of dioxide MO 2 with M = (Hf,Zr,Ti) have been considered in the literature. The results of density-functional theory calculations of the dielectric properties of three crystalline transition metal silicates (hafnon HfSiO 4 , zircon ZrSiO 4 and a hypothetical TiSiO 4 structure) are also presented. For the group IIIb transition metals, two crystalline phases (cubic and hexagonal) of sesquioxides M 2 O 3 with M = Lu have been investigated within density-functional theory. Finally, the first-principles results that have been obtained for the amorphous silicates are discussed. A presentation is given of a scheme recently introduced which relates the dielectric constants to the local bonding of Si and metal atoms. It is based on the definition of parameters characteristic of the basic structural units centred on Si and metals atoms and including their nearest O neighbours. Applied to amorphous Zr silicates, it provides a good description of the measured dielectric constants, both of the optical and the static ones.