Hidden link between atomic radius difference and optimal HSE exchange fraction for wurtzite III-V semiconductor bandgap prediction

In first-principles calculations of semiconductor bandgaps, the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional’s exchange fraction a is often retroactively fitted to experiments or fixed at 0.25, which may introduce methodological limitations. This study systematically investigates the bandgaps of wurtzite III-V semiconductors (from BN to InSb) using the HSE06 hybrid functional with varying exchange fractions (from 0.05 to 0.45), confirming a linear increase of the bandgap with exchange fraction a, as rigorously derived from the formal definition of the HSE functional and the Kohn-Sham framework. Comparison with experimental bandgaps indicates that materials with wider bandgaps, such as AlN, require larger exchange fractions, while those with narrower bandgaps, such as InSb, perform better with smaller values. A clear trend is identified, showing that the optimal exchange fraction, ranging from 0.1 to 0.5, increases linearly with the atomic radius difference between group-III and group-V elements. This study establishes a reliable guideline for selecting appropriate exchange fractions in HSE bandgap calculations, thereby improving the accuracy of first-principles predictions and providing valuable support for the design of III-V semiconductor-based optoelectronic devices.