First-Principles Investigations of the Temperature Dependence of Electronic Structure and Optical Properties of Rutile TiO₂

Abstract

To gain additional insight into high-temperature functional material properties for applications in optical gas sensing, the temperature effects on the band gap and optical properties of rutile TiO2 are investigated using ab initio methods. By analyzing the contributions from electron–phonon interaction and lattice thermal expansion, we show that the electron–phonon interaction is the dominant factor for temperature band-gap renormalization. As the temperature increases, the band gap increases until 300 K and then narrows above 300 K. This behavior results from the acoustic phonons, which widen the band gap, dominate below 300 K, while the optical phonons, which narrow the band gap, dominate above 300 K. Our study suggests that the band gap is narrowed by about 138 meV at 1000 K. We also investigated the temperature effects on the dielectric constants, the refractive index, as well as the extinction coefficient. Both the rate of decrease of the refractive index at 650 and 800 nm as well as the experimentally derived band gap agree with experimentally measured data as the temperature increases. Our results and computational methods are of interest for developing high-temperature functional materials with applications toward gas sensing.

Anharmonicity Explains Temperature Renormalization Effects of the Band Gap in SrTiO3

“…The x -intercept of each linear fit (shown as a dotted line tangent to each curve in the higher inset) was plotted as a function of temperature in the main figure. As shown in the figure the measured band gap is 3.160 eV at 300 K and decreases almost linearly to 2.689 eV at 1000 K. The decrease of the band gap with temperature is consistent with other materials; although for other systems, such as CH 3 NH 3 PbI 3 , the band gap is shown to increase with temperature or even display a nonmonotonic behavior, such as that in TiO 2 …”

“…As shown in the figure the measured band gap is 3.160 eV at 300 K and decreases almost linearly to 2.689 eV at 1000 K. The decrease of the band gap with temperature is consistent with other materials; 25 although for other systems, such as CH 3 NH 3 PbI 3 , the band gap is shown to increase with temperature 26 or even display a nonmonotonic behavior, such as that in TiO 2 . 27 Temperature effects on the electronic structure can be due to thermal expansion and to electron−phonon coupling from quantum zero-point (ZP) motion and thermal motion. The el−ph coupling can be investigated using nonperturbative approaches, such as the finite-displacement (FD) approach 28 or using an analytical perturbative approach based on density functional perturbation theory (DFPT) within the rigid-body approximation.…”

Electron-phonon coupling in d -electron solids: A temperature-dependent study of rutile TiO2 by first-principles theory and two-photon photoemission

“…These different temperature dependences of the CBMs of TiO 2 and SiO 2 confirm the hypsochromic shift of the former and the bathochromic shift for the latter. We note that two recent theoretical studies of TiO 2 by Wu et al [102] and Monserrat [103] found an increase of the gap up to 300 K, followed by a decrease with increasing T [102,103]. By making a careful comparison, we found the differences between Wu's data [102] and our calculations can be attributed to the different phonon frequencies as shown in Ref.…”

“…We note that two recent theoretical studies of TiO 2 by Wu et al [102] and Monserrat [103] found an increase of the gap up to 300 K, followed by a decrease with increasing T [102,103]. By making a careful comparison, we found the differences between Wu's data [102] and our calculations can be attributed to the different phonon frequencies as shown in Ref. [63] as well as different e-p factors for the CBM state.…”

“…[63] as well as different e-p factors for the CBM state. These differences can be attributed to the pseudopotential method adopted by Wu et al [102] and Monserrat [103], whereas we employ an all-electron full-potential method.…”