Ballistic thermoelectric properties of monolayer semiconducting transition metal dichalcogenides and oxides

Combining first-principles calculations with Landauer-Büttiker formalism, ballistic thermoelectric transport properties of semiconducting two-dimensional transition metal dichalcogenides (TMDs) and oxides (TMOs) (namely ${\mathrm{MX}}_2$ with M = Cr, Mo, W, Ti, Zr, Hf; X = O, S, Se, Te) are investigated in their 2H and 1T phases. Having computed structural, as well as ballistic electronic and phononic transport properties for all structures, we report the thermoelectric properties of the semiconducting ones. We find that 2H phases of four of the studied structures have very promising thermoelectric properties, unlike their 1T phases. The maximum room temperature $p$-type thermoelectric figure of merit ($ZT$) of 1.57 is obtained for $2\mathrm{H}-{\mathrm{HfSe}}_2$, which can be as high as 3.30 at $T=800$ K. Additionally, $2\mathrm{H}-{\mathrm{ZrSe}}_2, 2\mathrm{H}-{\mathrm{ZrTe}}_2$, and $2\mathrm{H}-{\mathrm{HfS}}_2$ have considerable $ZT$ values (both $n$- and $p$-type), that are above 1 at room temperature. The 1T phases of Zr and Hf-based oxides possess relatively high power factors, however their high lattice thermal conductance values limit their $ZT$ values to below 1 at room temperature.

Figure 1

Crystal structures of TMDs and TMOs. The 2H phase (a) and the 1T phase (b). The Brillouin zone, reciprocal lattice vectors, and the high symmetry points are given in (c).

Figure 2

Calculated electronic band structures of selected $2\mathrm{H}-{\mathrm{MX}}_2$ compounds; ${\mathrm{CrO}}_2, {\mathrm{TiTe}}_2, {\mathrm{ZrTe}}_2, {\mathrm{HfTe}}_2$ based on PBE (red solid line) and $\text{PBE}+\text{HSE}$ (blue dashed line) functional. Fermi level is set to zero for all subfigures.

Figure 3

Phonon dispersion relations, phonon transmission spectra, and phonon thermal conductance as a function of temperature of ${\mathrm{ZrSe}}_2, {\mathrm{ZrTe}}_2, {\mathrm{HfS}}_2$, and ${\mathrm{HfSe}}_2$ are shown, respectively.

Figure 4

Heat capacities at various temperatures from 300 K to 1000 K are shown for the semiconducting compounds in the 2H phase.

Figure 5

Heat capacities at various temperatures from 300 K to 1000 K are shown for the semiconducting compounds in the 1T phase.

Figure 6

Electronic transmission, Seebeck coefficient, power factor, and thermoelectric figure of merit are plotted around the Fermi level for $2\mathrm{H}-{\mathrm{ZrSe}}_2, 2\mathrm{H}-{\mathrm{ZrTe}}_2, 2\mathrm{H}-{\mathrm{HfS}}_2$, and $2\mathrm{H}-{\mathrm{HfSe}}_2$.

Figure 7

Electronic band structure of $1\mathrm{T}-{\mathrm{TiS}}_2$ with PBE (solid red) and hybrid HSE06 (dashed blue) functionals. Transition from semimetallic to semiconducting phase occurs with the hybrid functional.