Tight-binding model and electronic structure of tetrahedral zirconium silicate

Abstract

We present a tight-binding model of Zr silicate in the limit that every Zr and Si atom is bonded to four O atoms. We view the material as being composed of small, relatively uncoupled collections of atoms, called bonding units, with stoichiometries SiSiO4 and ZrSiO4. The SiSiO4 bonding unit constitutes a model for pure SiO2, and the ZrSiO4 bonding unit represents the fundamental element distinguishing tetrahedral Zr silicate from pure SiO2. In the first part of this article we look at the electronic structure of “ideal” bonding units in which the O atoms are arranged in a perfect tetrahedron and the M–O–Si angle is 180° (M=Si or Zr). We find the valence levels of both bonding units to be dominated by O p states, and the lowest conduction levels of the ZrSiO4 bonding unit to derive primarily from Zr d states, whose energy depends sensitively upon the charge transfer to the O atoms. The energy gap of the ideal ZrSiO4 bonding unit is found to be 5.9 eV, compared to 8.0 eV for the SiSiO4 bonding unit. Finally, for the ZrSiO4 bonding unit, we present a simplification which allows the energy levels of the ZrSiO4 bonding unit to be obtained approximately in terms of decoupled Zr–O and Si–O interactions. In the next part of the article we investigate how bond angle and bond length distortions affect the electronic structure of the ZrSiO4 bonding unit. In particular, we note that significant distortions of the Zr–O–Si angle could produce Zr-based localized states that could act as traps for electrons tunneling through the material. In the last part of the article we discuss the basic principles governing band lineups for Si/silicate interfaces constructed by substituting Zr atoms for Si atoms on the SiO2 side of crystalline Si/SiO2 interfaces. We calculate the band lineups as a function of Zr concentration for one particular interface.