Terahertz permittivity of rutile TiO2 single crystal measured by anisotropic far-infrared ellipsometry (original) (raw)
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Infrared dielectric anisotropy and phonon modes of rutile TiO2
Journal of Applied Physics, 2013
Spectroscopic ellipsometry in the infrared spectral range is used for comprehensive analysis of the anisotropic dielectric response of sapphire. We determine the ordinary and extraordinary infrared complex dielectric functions as well as all infrared-active phonon modes of single crystal ␣-Al 2 O 3 for wavelengths from 3 to 30 m. Data were acquired from high-symmetry orientations of a-plane and c-plane surfaces cut from bulk crystals. A simple classification scheme is developed, which allows identification of the total reflection bands for p-and s-polarized light in anisotropic materials with multiple phonon branches. We employ a factorized form of the dielectric function for superior best-fit calculation of the infrared ellipsometry spectra adjusting frequencies and damping parameters of the transverse and longitudinal phonon modes with A 2u and E u symmetry separately. A generalized Lowndes condition for the damping parameters is derived and found satisfied for the A 2u and E u branches. Excellent agreement with phonon mode literature values is obtained, and improper use of selection rules reported previously for calculation of the sapphire dielectric functions is revised ͓Harman, Ninomiya, and Adachi, J. Appl. Phys. 76, 8032 ͑1994͔͒. The dielectric function model will become useful for infrared ellipsometry investigation of multiple-layer structures grown on ␣-Al 2 O 3 substrates such as group-III nitride heterostructures. PRB 61 8189 INFRARED DIELECTRIC ANISOTROPY AND PHONON . . .
arXiv (Cornell University), 2022
We calculate the lattice dielectric function of strongly anharmonic rutile TiO2 from ab initio anharmonic lattice dynamics methods. Since an accurate calculation of the Γ point phonons is essential for determining optical properties, we employ the modified self-consistent approach, including third-order anharmonicity as well as fourth-order anharmonicity. The resulting optical phonon frequencies and linewidths at the Γ point much better agree with experimental measurements than those from a perturbative approach. We show that the four-phonon scattering process contributes as much as the third-order anharmonic term to phonon linewidths. Furthermore, incorporating the frequency dependence of phonon linewidth reveals that experimentally known but unidentified peaks of the dielectric function are due to two-phonon process. This work emphasizes the importance of a self-consistent approach in predict the optical properties of highly anharmonic materials.
Measurement of rutile TiO2 dielectric tensor from 0.148 to 33 μm using generalized ellipsometry
We have determined the complex uniaxial dielectric tensor of bulk rutile titanium dioxide (110), (100) and (111) samples using reflection generalized ellipsometry, which measures both the diagonal and off-diagonal elements of the reflection Jones matrix. Data were acquired using three commercially available ellipsometers, each covering the following spectral ranges: 0.148 to 0.292, 0.200 to 1.7 µm; and 1.7 to 33 µm. Generalized ellipsometry measures three complex ratios involving all four Jones matrix elements. In principle, this means that the complex dielectric tensor of a uniaxial crystal can be determined in a single measurement, provided that the sample is oriented such that the off-diagonal components of the Jones matrix are non-zero. To improve our results, we measure the samples at several rotational orientations around the surface normal. This insures that the probing electric fields vibrate along substantially different directions with respect to the optic axis. In some cases, we also varied the angle of incidence. The dielectric tensor was determined at every wavelength directly from a simultaneous fit to data from all rotational orientations and incident angles. A similar methodology should be applicable to a wide range of anisotropic optical materials.
Effect of oxygen vacancies on intrinsic dielectric permittivity of strontium titanate ceramics
Journal of the Ceramic Society of Japan, 2018
We prepared oxygen-deficient strontium titanate ceramics and measured the THz dielectric spectra to discuss the effect of oxygen vacancies on the intrinsic dielectric permittivity. In the presence of oxygen vacancies, the lattice volume of strontium titanate increased. First-principles calculation revealed that the expansion of the lattice originated from repulsion between the oxygen vacancies and cations, causing a decrease in the covalency of the TiO bonding. THz dielectric measurement using a far-infrared spectroscopic ellipsometer made it clear that the Slater-type phonon mode hardened and then the intrinsic permittivity of strontium titanate decreased in the presence of oxygen vacancies.
Anisotropic complex permittivity measurements of mono-crystalline rutile between 10 and 300 K
Journal of Applied Physics, 1998
The dielectric properties of a single crystal rutile (TiO 2 ) resonator have been measured using whispering gallery modes. Q factors and resonant frequencies were measured from 300 to 10 K. Q factors as high as 10 4 , 10 5 , and 10 7 were obtained at 300, 80, and 10 K, respectively. Using the whispering gallery mode technique we have determined accurately the loss tangent and dielectric constant of monocrystalline rutile and obtained much more sensitive measurements than previously reported. We show that rutile exhibits anisotropy in both the loss tangent and permittivity over the range from 10 to 300 K.
On the permittivity of titanium dioxide
Scientific Reports
Conductive rutile TiO2 has received considerable attention recently due to multiple applications. However, the permittivity in conductive, reduced or doped TiO2 appears to cause controversy with reported values in the range 100–10,000. In this work, we propose a method for measurements of the permittivity in conductive, n-type TiO2 that involves: (i) hydrogen ion-implantation to form a donor concentration peak at a known depth, and (ii) capacitance–voltage measurements for donor profiling. We cannot confirm the claims stating an extremely high permittivity of single crystalline TiO2. On the contrary, the permittivity of conductive, reduced single crystalline TiO2 is similar to that of insulating TiO2 established previously, with a Curie–Weiss type temperature dependence and the values in the range 160–240 along with the c-axis.
Journal of the Ceramic Society of Japan, 2016
Sr 0.7 Bi 0.2)TiO 3 ceramics were fabricated by a solid state reaction, and a wideband dielectric spectrum was measured for understanding the microscopic polarization mechanism of (Sr 0.7 Bi 0.2)TiO 3 ceramics. It was revealed that the dielectric permittivity of (Sr 0.7 Bi 0.2)TiO 3 ceramics at 25°C was determined by dipole polarization as well as ionic polarization, whereas the permittivity of SrTiO 3 is mainly determined only by ionic polarization. The temperature dependence of permittivity suggested that (Sr 0.7 Bi 0.2)TiO 3 ceramics belongs to ferroelectric relaxor, in which off-center Bi 3+ ions contribute to the formation of polar nanoregions (PNRs). The origin of the dipole polarization is considered the dipole fluctuations of PNRs. On the other hand, the ionic polarization of (Sr 0.7 Bi 0.2)TiO 3 ceramics was suppressed by an influence of Sr-site vacancy, compared to that of SrTiO 3. High permittivity of (Sr 0.7 Bi 0.2)TiO 3 ceramics is mainly due to the dipole polarization associated with dipole fluctuation of PNRs.
Physical Review B, 2011
We use first principles density functional theory to investigate the softening of polar phonon modes in rutile TiO2 under tensile (110)-oriented strain. We show that the system becomes unstable against a ferroelectric distortion with polarization along (110) for experimentally accessible strain values. The resulting polarization, estimated from the Born effective charges, even exceeds the bulk polarization of BaTiO3. Our calculations demonstrate the different strain dependence of polar modes polarized along (110) and (001) directions, and we discuss the possibility of strain engineering the polarization direction, and the resulting dielectric and piezoelectric response, in thin films of TiO2 grown on suitable substrates. PACS numbers: 77.22.-d,77.80.-e,77.80.bn,77.84.-s