First-principles study of anisotropic thermoelectric transport properties of IV-VI semiconductor compounds SnSe and SnS

We conduct comprehensive investigations of both thermal and electrical\ntransport properties of SnSe and SnS using first-principles calculations\ncombined with the Boltzmann transport theory. Due to the distinct layered\nlattice structure, SnSe and SnS exhibit similarly anisotropic thermal and\nelectrical behaviors. The cross-plane lattice thermal conductivity $\\kappa_{L}$\nis 40-60% lower than the in-plane values. Extremely low $\\kappa_{L}$ is found\nfor both materials because of high anharmonicity. It is suggested that\nnanostructuring would be difficult to further decrease $\\kappa_{L}$ because of\nthe short mean free paths of dominant phonon modes (1-30 nm at 300 K) while\nalloying would be efficient in reducing $\\kappa_{L}$ considering that the\nrelative $\\kappa_{L}$ contribution ($\\sim$ 65%) of optical phonons is\nremarkably large. On the electrical side, the anisotropic electrical\nconductivities are mainly due to the different effective masses of holes and\nelectrons along the $a$, $b$ and $c$ axes. This leads to the highest optimal\n$ZT$ values along the $b$ axis and lowest ones along the $a$ axis in both\n$p$-type materials. However, the $n$-type ones exhibit the highest $ZT$s along\nthe $a$ axis due to the enhancement of power factor when the chemical potential\ngradually approaches the secondary band valley that causes significant increase\nin electron mobility and density of states. SnSe exhibits larger optimal $ZT$s\ncompared with SnS in both $p$-type and $n$-type materials. For both materials,\nthe peak $ZT$s of $n$-type materials are much higher than those of $p$-type\nones along the same direction. The predicted highest $ZT$ values at 750 K are\n1.0 in SnSe and 0.6 in SnS along the $b$ axis for the $p$-type doping while\nthose for the $n$-type doping reach 2.7 in SnSe and 1.5 in SnS along the $a$\naxis, rendering them among the best bulk thermoelectric materials for\nlarge-scale applications.\n