  Recently, it has been found that crystalline tin selenide (SnSe) holds great
potential as a thermoelectric material due to its ultralow thermal conductivity
and moderate electronic transport performance. As thermoelectric application
usually requires doped material, charge carriers can play a role in the thermal
transport in doped SnSe, but such an effect has not been clearly elucidated in
previous theoretical and experimental studies. Here we performed a fully
first-principles study on the effects of electrons to the thermal transport in
doped SnSe. The electron-phonon coupling (EPC) effects on both phonons and
charge carriers were considered using the mode specific calculation in our
work. It is found that for phonons, EPC are weak compared to the intrinsic
phonon-phonon scattering even at high carrier concentrations and thus have
negligible effects on the lattice thermal conductivity. The electronic thermal
conductivity is not negligible when the carrier concentration is higher than
$10^{19} cm^{-3}$ and the values can be as high as 1.55, 1.45 and 1.77
$Wm^{-1}K^{-1}$ on a, b and c axes, respectively, for $10^{20} cm^{-3}$
electron concentration at 300K. The Lorenz number of SnSe is also calculated
and it is dependent on crystal orientations, carrier concentrations, and
carrier types. The simple estimation of electronic thermal conductivity using
Wiedemann-Franz law can cause large uncertainties for doped SnSe.
