  Intrinsic electron- and hole-phonon interactions are investigated in
monolayer transition metal dichalcogenides MX$_2$ (M=Mo,W; X=S,Se) based on a
density functional theory formalism. Due to their structural similarities, all
four materials exhibit qualitatively comparable scattering characteristics with
the acoustic phonons playing a dominant role near the conduction and valence
band extrema at the K point. However, substantial differences are observed
quantitatively leading to disparate results in the transport properties. Of the
considered, WS$_2$ provides the best performance for both electrons and holes
with high mobilities and saturation velocities in the full-band Monte Carlo
analysis of the Boltzmann transport equation. It is also found that monolayer
MX$_2$ crystals with an exception of MoSe$_2$ generally show hole mobilities
comparable to or even larger than the value for bulk silicon at room
temperature, suggesting a potential opportunity in p-type devices. The analysis
is extended to estimate the effective deformation potential constants for a
simplified treatment as well.
