  Significant progress on parameter-free calculations of carrier mobilities in
real materials has been made during the past decade; however, the role of
various approximations remains unclear and a unified methodology is lacking.
Here, we present and analyse a comprehensive and efficient approach to compute
the intrinsic, phonon-limited drift and Hall carrier mobilities of
semiconductors, within the framework of the first-principles Boltzmann
transport equation. The methodology exploits a novel approach for estimating
quadrupole tensors and including them in the electron-phonon interactions, and
capitalises on a rigorous and efficient procedure for numerical convergence.
The accuracy reached in this work allows to assess common approximations,
including the role of exchange and correlation functionals, spin-orbit
coupling, pseudopotentials, Wannier interpolation, Brillouin-zone sampling,
dipole and quadrupole corrections, and the relaxation-time approximation. A
detailed analysis is showcased on ten prototypical semiconductors, namely
diamond, silicon, GaAs, 3C-SiC, AlP, GaP, c-BN, AlAs, AlSb, and SrO. By
comparing this extensive dataset with available experimental data, we explore
the intrinsic nature of phonon-limited carrier transport and magnetotransport
phenomena in these compounds. We find that the most accurate calculations
predict Hall mobilities up to a factor of two larger than experimental data;
this could point to promising experimental improvements in the samples quality,
or to the limitations of density-function theory in predicting the carrier
effective masses and overscreening the electron-phonon matrix elements. By
setting tight standards for reliability and reproducibility, the present work
aims to facilitate validation and verification of data and software towards
predictive calculations of transport phenomena in semiconductors.
