Model for the unpolarized infrared reflectivity from uniaxial polar materials: Effects of anisotropy, free carriers, and defects

A rigorous analysis of the unpolarized infrared reflectivity is presented. A randomly reflected electric field from a uniaxial anisotropic material is considered as being the sum of two individual electric field components parallel and perpendicular to the plane defined by the incident photon wavevector and the material optical axis. The harmonicity of the interatomic forces is described by a model that considers the material as coupled damped oscillators. The anharmonic components of these forces associated with interchanges of energies between phonon modes are obtained as functions of frequency and temperature by using perturbation techniques. The enhanced lattice anharmonicity by defects is accounted for by convoluting the point-defect scattering over the intrinsic anharmonic damping. The contribution of the collective plasma oscillation to the infrared reflectivity is described by the classical Drude theory. The importance of all the physical mechanisms we have involved in the model is demonstrated clearly with reference to experimental measurements. Namely the proposed model accounts well for all the features in the experimental infrared reflectivity spectra of sapphire, defect-free 4H–SiC, N-ion-implanted 4H–SiC, and commercial 4H–SiC substrate of poor crystalline quality.