Ab Initio Velocity-Field Curves in Monoclinic \(β\)-Gatextsubscript{2}Otextsubscript{3}}

We investigate the high-field transport in monoclinic \(\beta\)-Ga\textsubscript{2}O\textsubscript{3}} using a combination of ab initio calculations and full band Monte Carlo (FBMC) simulation. Scattering rate calculation and the final state selection in the FBMC simulation use complete wave-vector (both electron and phonon) and crystal direction dependent electron phonon interaction (EPI) elements. We propose and implement a semi-coarse version of the Wannier-Fourier interpolation method [F. Giustino, M. L. Cohen, and S. G. Louie, Physical Review B, vol. 76, no. 16, 2007] for short-range non-polar optical phonon (EPI) elements in order to ease the computational requirement in FBMC simulation. During the interpolation of the EPI, the inverse Fourier sum over the real-space electronic grids is done on a coarse mesh while the unitary rotations are done on a fine mesh. This paper reports the high field transport in monoclinic \(\beta\)-Ga\textsubscript{2}O\textsubscript{3}} with deep insight on the contribution of electron-phonon interactions, and velocity-field characteristics for electric fields ranging up to 450 kV/cm in different crystal directions. A peak velocity of $2\times10^{7}& cm/s is estimated at an electric field of 200 kV/cm.