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Despite the large number of theoretical III-V semiconductor studies reportedevery year, our atomistic understanding is still limited. The limitations ofthe theoretical approaches to yield accurate structural and electronicproperties on an equal footing, due to the unphysical self-interaction problemthat affects mainly the band gap and spin-orbit splitting (SOC) insemiconductors and, in particular, III-V systems with similar magnitude of theband gap and SOC. In this work, we will report a consistent study of thestructural and electronic properties of the III-V semiconductors employing thescreening hybrid-DFT framework, fitting the $\alpha$ parameters for 12different III-V compounds, namely, AlN, AlP, AlAs, AlSb, GaN, GaP, GaAs, GaSb,InN, InP, InAs, InSb, in order to minimize the deviation between thetheoretical and experimental values of the band gap and SOC. Structuralrelaxation effects were also included. Except for AlP, whose $\alpha = 0.127$,we obtained $\alpha$ values spreading from 0.209 to 0.343, deviating less than0.1 from the universal value of 0.25. Our results for the lattice parameter andelastic constants indicate that the fitting of the $\alpha$ does not affectthose structural parameters when compared with the HSE06 functional, where$\alpha = 0.25$. Our analysis of the band structure based on the$\textbf{k}{\cdot}\textbf{p}$ method shows that the effective masses are inagreement with the experimental values, which can be attributed to thesimultaneous fitting of the band gap and SOC. Finally, we estimate the valuesof $g$-factors, extracted directly from band structure, which are close toexperimental results indicating that the obtained band structure produced arealistic set of $\textbf{k}{\cdot}\textbf{p}$ parameters.

A Comprehensive Study of $g$-Factors, Elastic, Structural and Electronic Properties of III-V Semiconductors using Hybrid-Density Functional Theory