The $p$-type Cu${}_2$Sn$X_3$ ($X$ $=$ Se, S) compounds are known experimentally to be good thermoelectric materials, although the reasons for this good performance in an adamantine-derived crystal structure are not well understood. Here, we demonstrate the existence of a three-dimensional (3D) hole conductive network in these ternary diamondlike Cu${}_2$Sn$X_3$ ($X$ $=$ Se, S) semiconductors using ab initio calculations, and identify the features of the electronic structure responsible for this good performance. We also provide results as a function of doping level to find the regime where the highest performance will be realized and estimate the maximum figure of merit, $ZT$. Our results clearly show that the strong hybridization between 3$d$ orbitals from copper and $p$ orbitals from selenium or sulfur at the upper valence band leads to the 3D $p$-type hole transport channel, mainly consisting of Cu-$X$ and $X$-$X$ networks in Cu${}_2$Sn$X_3$ ($X$ $=$ Se, S). The resulting heavy, but still conductive, hybridized bands of Cu $d$–chalcogen $p$ character are highly favorable for thermoelectric performance. The electrical transport properties of these $p$-type materials are mainly determined by these bands and have been investigated by Boltzmann transport methods. The optimal doping levels of Cu${}_2$Sn$X_3$ are estimated to be around 0.1 holes per unit cell at 700 K. The theoretical figure of merit $ZT$ has been predicted.

• Received 20 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.155201