  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.
