Ballistic thermoelectric transport properties of two-dimensional group III-VI monolayers

Ballistic transport and thermoelectric properties of group III-VI compounds ($XY:X=\mathrm{B}$, Al, Ga, In, Tl; $Y=\mathrm{O}$, S, Se, Te, Po) are investigated based on first-principles calculations and Landauer formalism. This large family is composed of 25 compounds which stands out with their unique electronic band structures. Mexican hat shaped valence band, which exhibits quartic energy-momentum relation gives rise to a sharp peak in the density of states as well as a steplike electronic transmission spectrum near the valence band edge. The intriguing electronic band structure and transport properties motivate us to explore thermoelectric properties of group III-VI monolayers. We find that, in addition to the stepwise transmission at the band edge, flat bands, valley degeneracy, and band degeneracy are the factors that enhance thermoelectric efficiencies. For heavier compounds, better thermoelectric efficiencies are possible for both $n$-type and $p$-type carriers.

Figure 1

Top (a) and lateral (b) views of the crystal lattice structure of monolayer III-VI systems. Reciprocal lattice of the hexagonal symmetry and the high-symmetry points (c). Lattice vectors are represented by ${\mathrm{a}}_1$ and a which are equal in length $a$. Primitive unit cell comprises of four atoms. Group III and VI atoms are shown in blue and yellow, respectively.

Figure 2

The electronic band structures and electronic transmission spectra of the group III-VI compounds calculated at PBE level. Band gap values which are shown as shaded areas are listed in Table 1.

Figure 3

Calculated electronic band structures of selected narrow band gap and oxide compounds; (a) InO, (b) TlO, (c) TlS, (d) TlSe, (e) TlPo, (f) BO, (g) AlO, and (i) GaO based on PBE (red solid line) and $\mathrm{PBE}+\mathrm{HSE}$ (blue dashed line) functional. Fermi level is set to zero for all subfigures.

Figure 4

Phonon dispersion relations and phonon transmission spectra for all studied materials.

Figure 5

Individual phonon mode contributions to total lattice thermal conductance (a) for InSe and (b) for BO at different temperatures. Percentages of the phonon mode contributions are also shown above the bars. The inset shows the contributions at 30 K.

Figure 6

Phonon thermal conductance as a function of maximum frequency of the acoustic branches for all studied III-VI compounds at 300 K.

Figure 7

Electronic band structure, transmission spectra and isoenergy curves at $E_{\mathrm{VBM}}\text{−}E$ and related isoenergy surfaces near the valence band in the entire Brillouin zone of (a) GaS, (b) InSe, and (c) GaTe monolayers. (d) $PF$ and $ZT$ of GaS, InSe, and GaTe are illustrated as a function of chemical potential for various temperatures.

Figure 8

Electronic band structure, transmission spectra isoenergy curves at $E_{\mathrm{VBM}}\text{−}E$ and related isoenergy surfaces near the valence band in the entire Brillouin zone of (a) GaO and (b) TlO monolayers. (c) $PF$ and $ZT$ of GaO and TlO are illustrated as a function of chemical potential for various temperatures.

Figure 9

Electronic band structure, transmission spectra isoenergy curves at $E\text{−}{E}_{\mathrm{CBM}}$ and related isoenergy surfaces near the conduction band in the entire Brillouin zone of (a) GaS, (b) GaTe, and (c) TlTe monolayers. (d) $PF$ and $ZT$ of GaS, GaTe, and TlTe are illustrated as a function of chemical potential for various temperatures.

Figure 10

Electronic band structure, transmission spectra, isoenergy curves at $E\text{−}{E}_{\mathrm{CBM}}$ with a value 0.5 (dashed blue), 0.1 (dashed red), 0.005 (dashed yellow) eV and related isoenergy surfaces near the conduction band in the entire Brillouin zone of (a) BSe and (b) BTe monolayers. (c) $PF$ and $ZT$ of BSe and BTe are illustrated as a function of chemical potential for various temperatures.