  We conduct comprehensive investigations of both thermal and electrical
transport properties of SnSe and SnS using first-principles calculations
combined with the Boltzmann transport theory. Due to the distinct layered
lattice structure, SnSe and SnS exhibit similarly anisotropic thermal and
electrical behaviors. The cross-plane lattice thermal conductivity $\kappa_{L}$
is 40-60% lower than the in-plane values. Extremely low $\kappa_{L}$ is found
for both materials because of high anharmonicity. It is suggested that
nanostructuring would be difficult to further decrease $\kappa_{L}$ because of
the short mean free paths of dominant phonon modes (1-30 nm at 300 K) while
alloying would be efficient in reducing $\kappa_{L}$ considering that the
relative $\kappa_{L}$ contribution ($\sim$ 65%) of optical phonons is
remarkably large. On the electrical side, the anisotropic electrical
conductivities are mainly due to the different effective masses of holes and
electrons along the $a$, $b$ and $c$ axes. This leads to the highest optimal
$ZT$ values along the $b$ axis and lowest ones along the $a$ axis in both
$p$-type materials. However, the $n$-type ones exhibit the highest $ZT$s along
the $a$ axis due to the enhancement of power factor when the chemical potential
gradually approaches the secondary band valley that causes significant increase
in electron mobility and density of states. SnSe exhibits larger optimal $ZT$s
compared with SnS in both $p$-type and $n$-type materials. For both materials,
the peak $ZT$s of $n$-type materials are much higher than those of $p$-type
ones along the same direction. The predicted highest $ZT$ values at 750 K are
1.0 in SnSe and 0.6 in SnS along the $b$ axis for the $p$-type doping while
those for the $n$-type doping reach 2.7 in SnSe and 1.5 in SnS along the $a$
axis, rendering them among the best bulk thermoelectric materials for
large-scale applications.
