  Scattering of carriers with ionized impurities governs charge transport in
doped semiconductors. However, electron interactions with ionized impurities
cannot be fully described with quantitative first-principles calculations, so
their understanding relies primarily on simplified models. Here we show an ab
initio approach to compute the interactions between electrons and ionized
impurities or other charged defects. It includes the short- and long-range
electron-defect (e-d) interactions on equal footing, and allows for efficient
interpolation of the e-d matrix elements. We combine the e-d and
electron-phonon interactions in the Boltzmann transport equation to compute the
carrier mobilities in doped silicon over a wide range of temperature and doping
concentrations, spanning seamlessly the defect- and phonon-limited transport
regimes. The individual contributions of the defect- and phonon-scattering
mechanisms to the carrier relaxation times and mean-free paths are analyzed.
Our method provides a powerful tool to study electronic interactions in doped
materials. It broadens the scope of first-principles transport calculations,
enabling studies of a wide range of doped semiconductors and oxides with
application to electronics, energy and quantum technologies.
