  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.
