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 3.7 eV, while the optical gap is estimated to 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.

Accurate prediction of band gaps and optical properties of HfO2

“…A similar approach is often applied to experimental optical measurements, in which the band gap upper energy is traditionally obtained by extrapolating the linear part of √ αEn near the absorption onset (i.e., so-called Tauc plot), where α is the absorption coefficient, E is the photon energy, and n is the refractive index [47]. The same approach has been already applied to simulated amorphous cells of TiO 2 [48]. The optical band gap of amorphous cells was estimated by an equivalent procedure, fitting the linear part of J(E), where J(E) is the joint density of occupied and unoccupied states as calculated by Wien2k.…”

Practice-oriented optical thin film growth simulation via multiple scale approach

“…From this, the refractive index in x-direction can be calculated using Eq. (2) [7], in which ε 1 (ω) is the real part and ε 2 (ω) is the imaginary part of the dielectric function. In order to achieve a significant comparison to experimental data of pure amorphous solids, the average refractive index is calculated using the notation n av = (n x + n y + n z ) / 3.…”

“…In order to determine the optical properties of the simulated thin film structures, techniques based on quantum mechanics have to be applied. In contrast to the classical atomistic approaches, the quantum mechanical techniques are limited to few hundred of atoms [7].…”

“…Furthermore, TiO 2 has proven to be an expressive model in classical and quantum mechanical simulations in order to investigate in structural and optical layer properties [7].…”

Synthesis and Catalytic Applications of Non-Metal Doped Mesoporous Titania

“…The first challenge results from the wide band gap of TiO 2 (3.0-3.5 eV [23]), which allows the absorption of light mainly in the ultraviolet (UV) range. UV light corresponds to only 4%-5% of the whole solar spectrum, while visible light constitutes 40% [24].…”