Modeling the optical constants of hexagonal GaN, InN, and AlN

Optical constants of hexagonal GaN (in the range 1.5–10 eV), InN (in the range 2–10 eV), and AlN (in the range 6–20 eV) for $\mathrm{E\perp c}$ are modeled using a modification of Adachi’s model of optical properties of semiconductors. Model parameters are determined using the acceptance-probability-controlled simulated annealing method. The employed model uses an adjustable broadening function instead of the conventional Lorentzian one. The broadening can vary over a range of functions with similar kernels but different wings. Therefore, excessive absorption inherent to Lorentzian broadening due to the large wings of a Lorentz function can be reduced, yielding better agreement with experimental data. As a result, excellent agreement with experimental data is obtained; the relative rms errors for the real part of the index of refraction are below 2% for all three materials, and, for the imaginary part, below 5% for GaN and below 3% for InN and AlN.