Thermoelectric Properties of Monolayer HfI₂, an Electride with Electrons on The Interstitial Sites

Two-dimensional (2D) thermoelectric materials are particularly suitable for wearable devices due to the flexible monolayer structure, which will supply power for other carried devices.¹ However, the electrical conductivity (σ) of 2D material is usually lower compared with the bulk counterparts because of a lower electron mobility induced by a higher density of scatterings.² Recently, Zhang et el. found that two MoS₂-like structures, ZrI₂ and HfI₂ with long carrier-lattice distance (d_c-l) exhibit a high hole mobility up to 4000 cm²V⁻¹s⁻¹.³ We notice that the ZrI₂-type structures are electrides with excess electrons occupying the interstitial sites increasing the d_c-l.⁴ Such a unique charge distribution should undergo a weaker perturbation under the displacements of atoms, then the carrier mobility and the σ will be high. The figure of merit (ZT) of ZrI₂ reaches 1.2 at 900K under hole doping,⁵ but the relation between the charge distribution and the transport properties is still not clear enough in these electrides.<br/>Here, we investigate the thermoelectric properties of monolayer HfI₂ using first-principles calculations by fully considering the electron-phonon interaction using EPW⁶ code. The thermoelectric properties including Seebeck coefficient (S), σ and electron thermal conductivity (κ_e) are calculated by solving the Boltzmann transport equation beyond the constant relaxation time approximation implemented with BoltzTraP2 code.⁷ The lattice thermal conductivity (κ_l) is calculated by the ShengBTE code.⁸<br/>We found that the hole doping tends to soften the acoustic phonon modes due to the interstitial distributed charge states and low density of states (DOS) near the valence band maximum (VBM), while the electron doping decreases the phonon relaxation time obviously because of a stronger electron-phonon interaction (EPI) induced by the high DOS near conduction band minimum (CBM). The carrier relaxation time at the VBM is obviously higher than that near the CBM due to the weaker lattice perturbation. The p-type σ is also higher than the n-type one under the same concentration. But the p-type S value is lower than the n-type one due to a lower DOS near VBM. The p-type power factor (PF) is larger than the value of n-type more dominated by σ.<br/>The κ_l of HfI₂ is only 9.1 W/m-K within three-phonon interaction at room temperature lower than that of ZrI₂ (20.3 W/m-K⁵). The phonon relaxation time contributed by the electron-phonon scattering is even smaller than that of the three-phonon scattering at low phonon frequency range. The electrons near CBM will scatter the phonons due to the strong EPI. As a result, the κ_l decrease by 1.5 W/m-K when considering the electron-phonon scattering. The final ZT value reaches 0.86 at 1200K under p-type doping.<br/>In summary, the HfI₂ with anionic electrons near the VBM exhibit a high mobility and σ under hole doping due to the weaker lattice perturbation. Our work reveals the role of interstitial distributed anionic electrons on the electron and phonon transport in the electride system, which gives insights for the further design of high-performance thermoelectric materials.<br/><br/>(1) Kanahashi, K.; Pu, J.; Takenobu, T. <i>Adv. Energy Mater. </i><b>2020</b>, <i>10</i> (11), 1902842.<br/>(2) Cheng, L.; Zhang, C.; Liu, Y. <i>Phys. Rev. Lett. </i><b>2020</b>, <i>125</i> (17), 177701.<br/>(3) Zhang, C.; Wang, R.; Mishra, H.; et al. <i>Phys. Rev. Lett. </i><b>2023</b>, <i>130</i> (8), 087001.<br/>(4) He, J.; Chen, Y.; Wang, Z.; et al. <i>J. Mater. Chem. C </i><b>2022</b>, <i>10</i> (19), 7674-7679.<br/>(5) Wen, J.; Peng, J.; Zhang, B.; et al. <i>Nanoscale </i><b>2023</b>, <i>15</i> (9), 4397-4407.<br/>(6) Poncé, S.; Margine, E. R.; Verdi, C.; et al. <i>Comput. Phys. Commun. </i><b>2016</b>, <i>209</i>, 116-133.<br/>(7) Madsen, G. K. H.; Carrete, J.; Verstraete, M. J. <i>Comput. Phys. Commun. </i><b>2018</b>, <i>231</i>, 140-145.<br/>(8) Li, W.; Carrete, J.; A. Katcho, N.; et al. <i>Comput. Phys. Commun. </i><b>2014</b>, <i>185</i> (6), 1747-1758.