Anisotropic Phonon Heat Flow and Thermoelectric Response in Tetragonal GeS and GeSe
arXiv:2608.03478
Abstract
The electronic structure, lattice dynamics, bonding, elastic response, and anisotropic thermoelectric transport properties of tetragonal GeS and GeSe were investigated using density functional theory, density functional perturbation theory, Wannier interpolation, and scattering-aware Boltzmann transport. The relaxed structures are mechanically and dynamically stable within the calculated harmonic description. The HSE03/Wannier band gaps are 2.48 eV for GeS and 1.23 eV for GeSe, while substitution of S by Se lowers the upper phonon frequency from approximately 13.6 to 10.3 THz. The phonon Boltzmann transport calculations reveal pronounced lattice-transport anisotropy. Within the relaxation-time approximation, the 300 K in-plane and cross-plane lattice thermal conductivities are 26.86 and 1.19 W m K for GeS, and 18.74 and 1.52 W m K for GeSe, respectively. At 800 K, these values decrease to 10.22 and 0.46 W m K for GeS, and 7.25 and 0.58 W m K for GeSe. Frequency-resolved analysis shows that low-frequency phonons carry most of the heat, whereas the small cross-plane values reflect restricted out-of-plane phonon transport. Combining the ShengBTE RTA lattice tensors with AMSET electronic coefficients gives for n-type cross-plane GeS at 800 K and cm. The corresponding PBE-AMSET estimate for GeSe is for p-type cross-plane transport at 800 K and cm. LOBSTER analysis identifies mixed covalent--ionic Ge--X bonding, with Ge--S bonds having a larger stabilizing ICOHP magnitude than Ge--Se bonds ( versus eV per bond). These results identify tetragonal GeX compounds as strongly anisotropic thermoelectrics with moderate calculated values whose cross-plane response benefits from suppressed lattice heat transport.
31 pages, 25 figures, and 6 tables. Includes supplementary information