Infrared dielectric anisotropy and phonon modes of rutile TiO₂

Spectroscopic ellipsometry in the mid-infrared and far-infrared spectral range and generalized ellipsometry in the mid-infrared spectral range are used to investigate the anisotropic dielectric response of rutile TiO₂. The ordinary and extraordinary dielectric function tensor components and all infrared active phonon mode parameters of single crystalline rutile TiO ₂ are determined with high accuracy for wavelengths from 3 μm to 83 μm. The data were acquired from samples of (001), (100), and (111) surfaces cut from bulk single crystals. A factorized model dielectric function is employed in order to determine the frequencies and damping parameters of the transverse and longitudinal phonon modes with A 2 u and E_u symmetries. The bands of total reflection of s- and p-polarized light in dependence of the angle of incidence for highly symmetric sample cuts and orientations are derived. Excellent agreement with phonon modes reported in literature is obtained. Introduction of two additional modes for ordinary as well as extraordinary component of the dielectric function tensor was necessary to most accurately match the experimental data. The spectral position of the additional modes is compared to the calculated phonon density of states. The low-frequency dielectric constants are calculated from the determined phonon mode parameters and the high-frequency dielectric constants by applying the Lyddanne-Sachs-Teller relation. The presented data revise existing infrared optical function data and will be suitable for interpretation of any kind of infrared spectra for bulk TiO₂ single crystal substrates, thin films, and TiO₂ nanostructures.