Unusual thermoelectric transport anisotropy in quasi-two-dimensional rhombohedral GeTe

In this study, we calculate the $T$=300 K scattering and thermoelectric\ntransport properties of rhombohedral GeTe using first-principles modeling. The\nroom-temperature phase of GeTe has a layered structure, with cross-plane and\nin-plane directions oriented parallel and perpendicular to [111], respectively.\nBased on rigorous electron-phonon scattering, our transport calculations reveal\nunusual anisotropic properties; n-type GeTe has a cross-plane electrical\nconductivity that is roughly 3$\\times$ larger than in-plane. p-type GeTe,\nhowever, displays opposite anisotropy with in-plane conducting roughly\n2$\\times$ more than cross-plane, as is expected in quasi-2D materials. The\npower factor shows the same anisotropy as the electrical conductivity, since\nthe Seebeck coefficient is relatively isotropic. Interestingly, cross-plane\nn-GeTe shows the largest mobility and power factor approaching 500 cm$^2$/V-s\nand 32 $\\mu$W/cm-K$^2$, respectively. The thermoelectric figure-of-merit, $zT$,\nis enhanced as a result of this unusual anisotropy in n-GeTe since the lattice\nthermal conductivity is minimized along cross-plane. This decouples the\npreferred transport directions of electrons and phonons, leading to a threefold\nincrease in $zT$ along cross-plane compared to in-plane. The n-type anisotropy\nresults from high-velocity electron states formed by Ge p-orbitals that span\nacross the interstitial region. This surprising behavior, that would allow the\npreferential conduction direction to be controlled by doping, could be observed\nin other quasi-2D materials and exploited to achieve higher-performance\nthermoelectrics.\n