Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2

Abstract

We have investigated the structural and electronic properties as well as the linear optical response of amorphous TiO${}_{2}$ within density functional theory and a numerically efficient density functional based tight-binding approach as well as many-body perturbation theory. The disordered TiO${}_{2}$ phase is modeled by molecular dynamics. The equivalence to experimentally characterized amorphous phases is demonstrated by atomic structure factors and radial pair-distribution functions. By density functional theory calculations, using both the semilocal Perdew-Burke-Ernzerhof functional and the nonlocal Heyd-Scuseria-Ernzerhof screened hybrid functional, the electronic energy gap is found to be larger than in the crystalline TiO${}_{2}$ phases rutile and brookite but close to the anatase band gap. The quasiparticle energy gap of amorphous TiO${}_{2}$ is determined to be $\ensuremath{\gtrsim}$3.7 eV, while the optical gap is estimated to $\ensuremath{\lesssim}$3.5 eV. The disorder-induced formation of localized electronic states has been analyzed by the information entropy of the charge density distributions. The frequency-dependent optical constants, calculated from the complex dielectric function, have been determined in independent particle approximation. Besides similar absorption characteristics between the most common crystalline phases and amorphous TiO${}_{2}$, we find distinct differences in the optical spectra in the energy region between 5 eV and 8 eV. These differences can be assigned to the loss of symmetry in the local atomic structure of the disordered material. While the composition of the crystalline phases rutile, anatase, and brookite is well described by periodic arrangements of distorted TiO${}_{6}$ octahedra building blocks, the amorphous phase is characterized by partial loss of this octahedral coordination and the disorder-induced formation of under- and over-coordinated Ti ions. This leads to the absence of the characteristic crystal-field splitting of unoccupied Ti${}_{3d}$ states into ${e}_{g}$ and ${t}_{2g}$ like subbands. The optical characteristics of the amorphous phase are interpreted as a superposition of optical transitions that reflect the various local symmetries of the manifold of synthesizable crystalline TiO${}_{2}$ phases. The linear optical properties, calculated within the independent-particle approximation, are found to be in good agreement with the available experimental data.