Optical properties of AlxGa1−xN/GaN heterostructures on sapphire by spectroscopic ellipsometry

A method of analysis of spectroscopic ellipsometry (SE) measurement data is proposed for ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}\mathrm{N/GaN}$ 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 ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}\mathrm{N}$ 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 ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}\mathrm{N}$ has also been compared with those reported results.