Analysis of the optical constants and bandgap energy in Al1-x In x N alloys grown on a c-plane freestanding GaN substrate by using spectroscopic ellipsometry

The optical constants and bandgap energy (Eg) of semiconductors, characterized by spectroscopic ellipsometry (SE), are highly affected by the applied model dielectric function (MDF). In this study, we investigated the optical constants and Eg in low indium content (x) Al1-xInxN alloys grown on a c-plane freestanding GaN substrate by using SE, and their applied MDF dependence was investigated. The tanΨ and cosΔ spectra, in a photon energy range of 1.5–5.0 eV, of high-quality crystalline Al1-xInxN alloys were well fitted by Adachi's critical-point (ACP) model. The ACP model exhibited better spectral fitting results than did the Tauc–Lorentz model, which has often been adopted for Al1-xInxN alloys. The accuracy of the Eg values obtained by the ACP model was confirmed by optical reflectance measurements. It is suggested that the ACP model is a suitable MDF for recent high-quality crystalline Al1-xInxN alloys as well as other III-nitride semiconductors.