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.