Anisotropic incoherent reflection model for spectroscopic ellipsometry of a thick semitransparent anisotropic substrate

An anisotropic incoherent reflection model for the Mueller matrix elements of an optically thick uniaxial anisotropic semitransparent substrate with its anisotropy axis along its surface normal is developed. The Mueller matrix elements are measured by phase-modulated spectroscopic ellipsometry (SE) and compared with incoherent reflection model simulations. In the case of a sapphire substrate the oscillations observed are accurately modeled, and, in addition, the oscillating degree of polarization is correctly predicted. A straightforward generalization of the optical model, in the case of an arbitrary stack of layers containing a thick anisotropic semitransparent substrate, is also proposed and experimentally validated. The model is further applied to study the anisotropic dielectric function of a semi-insulating 4H-SiC wafer. An approximation based on a simple variation in the optical transition element is proposed to model the SiC birefringence. In conclusion, SE is shown to be a powerful alternative for investigating and predicting the behavior of optically thick birefringent materials.