Analysis of the optical constants and bandgap energy in Al _{1- <i>x</i>} In _<i>x</i> N alloys grown on a <i>c</i> -plane freestanding GaN substrate by using spectroscopic ellipsometry

The optical constants and bandgap energy ( E g ) 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 E g in low indium content ( x ) Al 1- x In x N 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 Al 1- x In x N 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 Al 1- x In x N alloys. The accuracy of the E g 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 Al 1- x In x N alloys as well as other III-nitride semiconductors.