Density Functional Theory Modeling of Low-Loss Electron Energy-Loss Spectroscopy in Wurtzite III-Nitride Ternary Alloys

In the present work, the dielectric response of III-nitride semiconductors is studied using density functional theory (DFT) band structure calculations. The aim of this study is to improve our understanding of the features in the low-loss electron energy-loss spectra of ternary alloys, but the results are also relevant to optical and UV spectroscopy results. In addition, the dependence of the most remarkable features with composition is tested, i.e. applying Vegard's law to band gap and plasmon energy. For this purpose, three wurtzite ternary alloys, from the combination of binaries AlN, GaN, and InN, were simulated through a wide compositional range (i.e., AlxGa1 (-) N-x, InxAl1 (-) (x) N, and InxGa1 (-) (x) N, with x = [0,1]). For this DFT calculations, the standard tools found in Wien2k software were used. In order to improve the band structure description of these semiconductor compounds, the modified Becke-Johnson exchange-correlation potential was also used. Results from these calculations are presented, including band structure, density of states, and complex dielectric function for the whole compositional range. Larger, closer to experimental values, band gap energies are predicted using the novel potential, when compared with standard generalized gradient approximation. Moreover, a detailed analysis of the collective excitation features in the dielectric response reveals their compositional dependence, which sometimes departs from a linear behavior (bowing). Finally, an advantageous method for measuring the plasmon energy dependence from these calculations is explained.