The interactions between electrons and lattice vibrational modes play the key role in determining the carrier transport properties, thermoelectric performance and other physical quantities related to phonons in semiconductors. However, for two-dimensional (2D) materials, the widely-used models for carrier transport only consider the interactions between electrons and some specific phonon modes, which usually leads to inaccruate predictions of electrons/phonons transport properties. In this work, comprehensive investigations on full electron-phonon couplings and their influences on carrier mobility and thermoelectric performances of 2D group-IV and V elemental monolayers were performed, and we also analyzed in details the selection rules on electron-phonon couplings using group-theory arguments. Our calculations revealed that, for the cases of shallow dopings where only intravalley scatterings are allowed, the contributions from optical phonon modes are significantly larger than those from acoustic phonon modes in group-IV elemental monolayers, and LA and some specific optical phonon modes contribute significantly to the total intravalley scatterings. When the doping increases and intervalley scatterings are allowed, the intervalley scatterings are much stronger than intravalley scatterings, and ZA/TA/LO phonon modes dominate the intervalley scatterings in monolayer Si, Ge and Sn. The dominant contributions to the total intervalley scatterings are ZA/TO in monolayer P, ZA/TO in monolayer As and TO/LO in monolayer Sb. Based on the thorough investigations on the full electron-phonon couplings, we predict accurately the carrier mobilities and thermoelectric figure of merits in these two elemental crystals, and reveal significant reductions when compared with the calculations based on the widely-used simplified model.
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