  We present a first-principles framework to investigate the electron
scattering channels and transport properties for polar material by combining
the exact solution of linearized electron-phonon (e-ph) Boltzmann transport
equation in its integral-differential form associated with the e-ph coupling
matrices obtained from polar Wannier interpolation scheme. No ad hoc parameter
is required throughout this calculation, and GaAs, a well-studied polar
material, is used as an example to demonstrate this method. In this work, the
long-range and short-range contributions as well as the intravalley and
intervalley transitions in the e-ph interactions (EPIs) have been
quantitatively addressed. Promoted by such mode-by-mode analysis, we find that
in GaAs, the piezoelectric scattering is comparable to deformation-potential
scattering for electron scatterings by acoustic phonons in EPI even at room
temperature and makes a significant contribution to mobility. Furthermore, we
achieved good agreements with experimental data for the mobility, and
identified that electrons with mean free paths between 130 and 210 nm
contribute dominantly to the electron transport at 300 K. Such information
provides deeper understandings on the electron transport in GaAs, and the
presented framework can be readily applied to other polar materials.
