Optical properties of Al_xGa_1-xN/GaN heterostructures on sapphire by spectroscopic ellipsometry

A method of analysis of spectroscopic ellipsometry (SE) measurement data is proposed for Al_xGa_1-xN/GaN heterostructures grown on sapphire substrates. The SE data measured at three angles of incidence, 40°, 50°, and 60°, are simultaneously fitted assuming the dielectric function to consist of a Sellmeir dispersion equation and a free-exciton absorption term. The refractive index n and the extinction coefficient k of undoped Al_xGa_1-xN films are determined in the spectral range of 1.5-4.13 eV of photon energy. The transition energy of the free exciton, which is in excellent agreement with the reported results for GaN in a previous paper, is found to vary from 3.44 to 3.95 eV when the composition x varies from 0 to 0.151. The refractive index n of Al_xGa_1-xN has also been compared with those reported results.