Infrared dielectric anisotropy and phonon modes of rutile TiO2 (original) (raw)
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Infrared dielectric anisotropy and phonon modes of sapphire
Physical Review B, 2000
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.
Solid State Communications, 2009
We have used spectroscopic ellipsometry to determine the complex dielectric function of a series of ternary Be x Zn 1−x Te thin films grown by molecular beam epitaxy. The II-VI semiconductor alloys were grown on InP substrates that had an InGaAs buffer layer. After the growth, X-ray diffraction experiments were performed in order to determine the alloy concentration. A standard inversion technique was used to obtain the dielectric functions from the measured ellipsometric spectra, obtained between 2000 nm (5000 cm −1) and 40,000 nm (250 cm −1). By modelling the dielectric function as a collection of oscillators, representing longitudinal and transverse optical phonons of the Be x Zn 1−x Te lattice, we were able to recover the phonon spectra for this alloy system. It is argued that the additional phonon modes that are obtained from ellipsometry are best understood from the recently-proposed percolation model.
Journal of the Ceramic Society of Japan, 2015
Rutile structured TiO 2 has very high dielectric permittivities in non-ferroelectric materials. To understand the reason why rutile TiO 2 has high ionic polarizabilities, it is essential to analyze accurate dielectric spectra of rutile TiO 2 in the THz region. In this study, the complex permittivity of rutile TiO 2 single crystal in the range 30700 cm ¹1 (0.9021 THz) was directly measured using the anisotropic far-infrared spectroscopic ellipsometer. The three E u modes and one A 2u mode, which are all infrared-active phonon modes in rutile TiO 2 , were observed. Moreover, the resonance frequencies of the phonon modes approximately were coincident with a calculation result of first-principles and the analysis data by a harmonic oscillator model. From the examination of the dielectric response, it was found that E u (1) mode, which indicates the oscillation of Ti ions against O ions in the same phase, was dominant contributor to the static permittivity for a-axis. On the other hand, the high permittivity for c-axis was due to "soft" A 2u mode.
Physical Review B, 2005
The optical properties of hexagonal Al x Ga 1−x N ͑x from 0.05 to 0.42͒ epitaxial films with Si doping concentrations up to 10 18 cm −3 grown on c-plane sapphire substrates by metal-organic chemical vapor deposition have been investigated using infrared reflectance spectra. The dielectric functions ͑ = 1 + i 2 ͒ of the Al x Ga 1−x N films are determined in the wavelength region of 1.54-50 m at room temperature. The experimental reflectance spectra are analyzed using classical harmonic Lorentz oscillators and Drude model in the transparent, reststrahlen, and free carrier absorption regions. GaN-like E 1 transverse-optical ͑TO͒ phonon frequency linearly decreases and its strength increases with decreasing Al composition. However, AlN-like E 1 ͑TO͒ phonon frequency shows a relatively weak composition dependence and its strength increases with increasing composition. At a wavelength of 1.54 m, 1 varies between 4.86 and 5.2 when the composition x changes from 0.05 to 0.42 and 2 is close to zero. The longitudinal-optical phonon plasmon ͑LPP͒ coupled modes of n-type hexagonal Al x Ga 1−x N films are also discussed. For samples with higher concentrations beyond 10 18 cm −3 the upper LPP coupled mode frequencies increase with increasing carrier concentration indicating the transition from phononlike to plasmonlike behavior.
Vibrational Spectroscopy, 2002
Spectroscopic ellipsometry (SE) for infrared wavelengths is presented as a novel technique for contactless and nondestructive measurement of free-carrier and crystal-structure properties of complex semiconductor heterostructures for device applications. Infrared (IR)-active lattice vibrations and LO phonon±plasmon coupled modes dominate the infrared dielectric response of semiconductor materials. Analysis of ellipsometry data from 2 to 33 mm can precisely determine thin-®lm dielectric functions (DF) without numerical Kramers±Kronig analysis and thus provides information on phonon mode frequencies and broadening parameters, static dielectric constants, and free-carrier parameters, even for ®lms with thicknesses only a fraction of the probing wavelengths. Alloy composition, ®lm strain, and crystal quality of sample constituents in thin-®lm heterostructures can be derived. An infrared dielectric function database, which was established by analysis of simple heterostructures, is used for the investigation of complex device structures. As an example, we demonstrate the characterization of a laser diode (LD) structure based on group-III-nitride materials, where information such as concentration and mobility of free carriers in the n-and p-type regions, thickness, alloy composition, and quality of device constituents are accessible. #
Local field effect on infrared phonon frequencies of thin dielectric films
Opto-Ireland 2002: Optics and Photonics Technologies and Applications, 2003
A number of thin dielectric films deposited onto aluminated glass substrates and onto the materials transparent in the IR range (silicon, KRS-5 and CsI) were investigated using infrared transmission and reflection-absorption techniques. The application of these techniques to thin dielectric films at normal and oblique incidence of light allows the observation of both the longitudinal and transverse optical phonons. The longitudinal (LO)-transverse (TO) optical phonons splitting is analysed in terms of a dispersive local field effect. It has been shown that the results of LO-TO splitting obtained from dispersive local field effect are in a good agreement with the results obtained from the dynamical theory of crystalline lattices.
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.
Soft-Mode Phonons in SrTiO3 Thin Films Studied by Far-Infrared Ellipsometry and Raman Scattering
MRS Proceedings
We report the experimental studies of the vibrational spectra of SrTiO3 films with the thickness of 1 µm grown by pulsed laser deposition. Fourier-transform infrared ellipsometry between 30 and 700 cm−1 and electric field-induced Raman scattering have been utilized for investigation of the phonon behavior. These results can be used for comparison with the low-frequency measurements of the static dielectric constant. In the films, the soft mode reveals hardening compared to that in bulk crystals. This observation is in agreement with the Lyddane-Sachs-Teller formalism.
Infrared reflectance of optical phonon modes in AlGaN epitaxial layers grown on sapphire substrates
Proceedings of SPIE - The International Society for Optical Engineering, 2008
We reported the systematical study of optical properties of hexagonal Al x Ga 1−x N epitaxial films grown on c-sapphire substrate using metal-organic chemical vapor deposition. By performing Fourier transform infrared spectroscopy measurements, the high-frequency dielectric constants and phonon frequencies can be obtained by theoretically fitting the experimental infrared reflectance spectra using a four-phase layered model. The high-frequency dielectric constant of Al x Ga 1−x N varies between 4.98 and 4.52 for ε ∞,⊥ (polarization perpendicular to the optical axis) and between 4.95 and 4.50 for ε ∞,// (polarization parallel to the optical axis) respectively when the aluminum composition changes from 0.15 to 0.24. Furthermore, from experimental infrared reflectance spectra of Al x Ga 1−x N films, a specific absorption dip at 785 cm −1 was observed when the aluminum composition is larger than 0.24. The dip intensity increases and the dip frequency shifts from 785 to 812 cm −1 as aluminum composition increases from 0.24 to 0.58. According to the reciprocal space map of x-ray diffraction measurements, the emergence of this dip could be resulted from the effects of strain relaxation in AlGaN epitaxial layers due to the large lattice mismatch between GaN and AlGaN epitaxial film.