The $alpha$ phase of $Ga_{2}O_{3}$ is an ultra-wideband semiconductor with potential power electronics applications. In this work, we calculate the low field electron mobility in $alpha-Ga_{2}O_{3}$ from first principles. The 10 atom unit cell contributes to 30 phonon modes and the effect of each mode is taken into account for the transport calculation. The phonon dispersion and the Raman spectrum are calculated under the density functional perturbation theory formalism and compared with experiments. The IR strength is calculated from the dipole moment at the $Gamma$ point of the Brillouin zone. The electron-phonon interaction elements (EPI) on a dense reciprocal space grid is obtained using the Wannier interpolation technique. The polar nature of the material is accounted for by interpolating the non-polar and polar EPI elements independently as the localized nature of the Wannier functions are not suitable for interpolating the long-range polar interaction elements. For polar interaction the full phonon dispersion is taken into account. The electron mobility is then calculated including the polar, non-polar and ionized impurity scattering.
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