Towards efficient band structure and effective mass calculations for III-V direct band-gap semiconductors

The band structures and effective masses of III-V semiconductors (InP, InAs, InSb, GaAs, and GaSb) are calculated using the $GW$ method, the Heyd, Scuseria, and Ernzerhof hybrid functional, and modified Becke-Johnson combined with the local-density approximation (MBJLDA)---a local potential optimized for the description of the fundamental band gaps [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)]. We find that MBJLDA yields an excellent description of the band gaps at high-symmetry points, on par with the hybrid functional and $GW$. However, the effective masses are generally overestimated by $20--30\text{ }\mathrm{%}$ using the MBJLDA local multiplicative potential. We believe this to be related to incorrect nearest-neighbor hopping elements, which are little affected by the choice of the local potential. Despite these shortcomings, the MBJLDA method might be a suitable approach for predicting or interpolating the full band dispersion, if only limited experimental data are available. Furthermore, the method is applicable to systems containing several thousand atoms where accurate quasiparticle methods are not applicable.