Supplement Number 1

Detailed information regarding computational details, the validation of Wannierization, PBE and HSE electronic band structures, phonon dispersion, convergence tests on the drift and Hall mobilities, carrier concentration impact on hole mobility, band structure with and without spin-orbit coupling, band structures of diamond and 3C-SiC via shear strain, temperature-dependent lattice parameter and strain effects on hole mobility, the impact of shear strain on hole mobility, average electron group velocity, mode-resolved and spectral decomposed hole scattering rates with shear strain, intraband electron-phonon scattering rates, hole effective masses without and with shear strain.