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