Chemical trends in the high thermoelectric performance of the pyrite-type dichalcogenides ${\mathrm{ZnS}}_2, {\mathrm{CdS}}_2$, and ${\mathrm{CdSe}}_2$

The thermoelectric (TE) properties of the three pyrite-type IIB-${\mathrm{VIA}}_2$ dichalcogenides (${\mathrm{ZnS}}_2, {\mathrm{CdS}}_2$, and ${\mathrm{CdSe}}_2$) are systematically investigated and compared with those of the prototype ${\mathrm{ZnSe}}_2$ to optimize their TE properties. Using the phonon Boltzmann transport equation, we find that they all have ultralow lattice thermal conductivities. By analyzing their vibrational properties, this is attributed to soft phonon modes derived from the loosely bound rattlinglike metal atoms and to strong anharmonicity caused by the vibrations of all atoms perpendicular to the strongly bound nonmetallic dimers. Additionally, by correlating those properties along the series, we elucidate several chemical trends. We find that the heavier atom masses, larger atomic displacement parameters, and longer bond lengths between metal and nonmetal atoms can be beneficial to the looser rattling behaviors of the metal atoms and therefore lead to the softer phonon modes and that the stronger nonmetallic dimer bonds can boost the anharmonicities, both leading to the lower thermal conductivities. Furthermore, we find that all three compounds have complex energy isosurfaces at valence and conduction band edges that simultaneously allow for large density-of-states effective masses and small conductivity effective masses for both $p$- and $n$-type carriers. Consequently, the calculated TE figures of merit ($ZT$) can reach large values for both $p$- and $n$-type doping. In this paper, we illustrate the effects of the rattlinglike metal atoms and the localized nonmetallic dimers on the thermal transport properties and the importance of different carrier effective masses to electrical transport properties in these pyrite-type dichalcogenides, which can be used to predict and optimize the TE properties of other TE compounds in the future.

Figure 1

(a) Crystal structures and bonds between atoms in the pyrite-type IIB-${\mathrm{VIA}}_2$ dichalcogenides [$\mathrm{Pa}\overline{3}-{MX}_2, M=$ transition metal (Zn and Cd), $X=\mathrm{S}$ and Se]. The Wyckoff positions are $4a$ (0,0,0) for $M$ and $8c$ ($u,u,u$) for $X$, where $u$ is the Wyckoff pyrite parameter. In this structure, each $M$ atom has six $X$ neighbors, whereas each $X$ atom binds with three $M$ and one $X$ atoms, and the neighboring $X$ atoms form the $X\text{−}X$ dimers. (b) The corresponding first Brillouin zone and its high-symmetry points.

Figure 2

Calculated phonon dispersions of ${\mathrm{ZnS}}_2, {\mathrm{CdS}}_2$, and ${\mathrm{CdSe}}_2$ (from left to right), respectively. The red, green, and blue lines highlight two transverse (TA, TA′) and one longitudinal (LA) acoustic phonon modes, respectively. The black lines represent optical (O) phonon modes.

Figure 3

(a) Calculated partial phonon densities of states (PDOSs), (b) projected two-dimensional (2D) electron localization function (ELF) in (001) plane, and (c) atomic displacement parameters (ADPs) along different directions of different atoms in ${\mathrm{ZnS}}_2, {\mathrm{CdS}}_2$, and ${\mathrm{CdSe}}_2$ (from left to right), respectively.

Figure 4

Calculated anharmonicity parameters ($\gamma$) at different phonon modes (the color denotes the values of $\gamma$) for ${\mathrm{ZnS}}_2, {\mathrm{CdS}}_2$, and ${\mathrm{CdSe}}_2$ (from left to right), respectively.

Figure 5

Calculated lattice thermal conductivities (${\kappa }_l$) at different temperatures for ${\mathrm{ZnS}}_2$ (black line), ${\mathrm{CdS}}_2$ (red line), and ${\mathrm{CdSe}}_2$ (blue line), respectively.

Figure 6

(a) The PBE-calculated and (b) the HSE06-calculated electronic band structures of ${\mathrm{ZnS}}_2, {\mathrm{CdS}}_2$, and ${\mathrm{CdSe}}_2$ (from left to right), respectively.

Figure 7

(a) Calculated Seebeck coefficients $S$ and (b) electrical conductivities with respect to relaxation time $\sigma /\tau$ in ${\mathrm{ZnS}}_2, {\mathrm{CdS}}_2$, and ${\mathrm{CdSe}}_2$ (from left to right) as functions of the carrier concentration for $p$- and $n$-type doping at 300, 500, and 700 K, respectively.

Figure 8

(a) Calculated acoustic phonon scatterings (${\tau }_a$), (b) polar optical phonon scatterings (${\tau }_o$), and (c) total carrier relaxation times ($\tau$) in ${\mathrm{ZnS}}_2, {\mathrm{CdS}}_2$, and ${\mathrm{CdSe}}_2$ (from left to right) as functions of the carrier concentration for $p$- and $n$-type doping at 300, 500, and 700 K, respectively.

Figure 9

Calculated power factors ($PF$) as functions of the carrier concentration for $p$- and $n$-type doping at 300 K in ${\mathrm{ZnS}}_2, {\mathrm{CdS}}_2$, and ${\mathrm{CdSe}}_2$ (from left to right), respectively.

Figure 10

Calculated figures of merit ($ZT$) as functions of the carrier concentration for $p$- and $n$-type doping at 300 K in ${\mathrm{ZnS}}_2, {\mathrm{CdS}}_2$, and ${\mathrm{CdSe}}_2$ (from left to right), respectively.