We conduct a comprehensive theoretical analysis of wurtzite GaxIn1-xN ternary alloys, focusing on their structural, electronic, elastic, piezoelectric, and dielectric properties through rigorous first-principles calculations. Our investigation systematically explores the influence of varying Ga composition (x = 0%, 25%, 50%, 75%, 100%) on the alloy properties. Remarkably, we observe a distinctive non-linear correlation between the band gap and Ga concentration, attributable to unique slopes in the absolute positions of the valence band maximum and conduction band minimum with respect to Ga concentration. Our effective band structure analysis reveals the meticulous preservation of Bloch characters near band extrema, minimizing charge carrier scattering. Furthermore, we scrutinize deviations from linear Vegard-like dependence in elastic, piezoelectric, and dielectric constants. Additionally, our calculations encompass various optical properties, including absorption coefficient, reflectivity, refractive index, energy loss function, and extinction coefficient. We analyze their trends with photon energy, providing valuable insights into the optical behavior of GaxIn1-xN alloys. Our results, in excellent agreement with available experimental data, significantly contribute to a deeper understanding of the alloys' electronic properties. This study offers valuable insights that may illuminate potential applications of GaxIn1-xN alloys in diverse technological fields.
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