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

Abstract

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× larger than in-plane. p-type GeTe, however, displays opposite anisotropy with inplane conducting roughly 2× 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 µW/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. * Electronic address: jmaassen@dal.ca arXiv:1904.06439v2 [cond-mat.mtrl-sci]

High‐Performance GeTe‐Based Thermoelectrics: from Materials to Devices

“…For R‐GeTe, S is almost isotropic. [ 98 ] Therefore, the anisotropy of μ and σ results in strong anisotropy of S 2 σ, as shown in Figure 5c. The peak S 2 σ value of R‐GeTe along the a ‐axis is 28 µW cm −1 K −2 which is ≈1.6 times of that along the c ‐axis (18 µW cm −1 K −2 ).…”

“…c) Primitive cell and atomic structure of rhombohedral R‐GeTe along [ 111 ] direction. [ 98 ] d) Unit cell of C‐GeTe. [ 100 ]…”

“…[ 73 ] Such rhombohedral structure of R‐GeTe is a layered quasi‐two‐dimensional structure, composed of two‐atom‐thick layers (in Figure 2c). [ 98 ] The thickness of each two‐atom‐thick layer is ≈1.49 Å with the interlayer distance of ≈2.16 Å. [ 98 ] During the phase transition, due to the displacement of Ge and Te sublattices along [ 111 ] direction, [ 99 ] an angular distortion of 1.65° occurs between the principal axes, resulting in that the angle between the two primitive axes increases from 58.35° of R‐GeTe (Figure 2b) to 60° of C‐GeTe (Figure 2d).…”

“…[ 98 ] The thickness of each two‐atom‐thick layer is ≈1.49 Å with the interlayer distance of ≈2.16 Å. [ 98 ] During the phase transition, due to the displacement of Ge and Te sublattices along [ 111 ] direction, [ 99 ] an angular distortion of 1.65° occurs between the principal axes, resulting in that the angle between the two primitive axes increases from 58.35° of R‐GeTe (Figure 2b) to 60° of C‐GeTe (Figure 2d). [ 100 ] After the phase transition, Ge atoms shift to the center position (1/2, 1/2, 1/2), [ 101 ] leading to the existence of six Ge‐Te bonds with equal length in the cubic structure.…”

“…The low‐temperature R‐GeTe has quasi‐layered crystal structure, weak interlayer coupling along the c ‐axis direction and strong intralayer coupling along the a ‐axis direction, which lead to anisotropic thermoelectric performance. [ 98 ] Figure 5 shows the calculated thermoelectric performance of intrinsic p‐type R‐GeTe at 300 K. [ 98 ] As shown in Figure 5a, μ along a ‐axis direction is higher than that along c ‐axis direction due to weaker interaction between the interlayer atoms comparing with the interaction between the intralayer atoms. [ 98 ] High μ along a ‐axis direction subsequently leads to high σ (Figure 5b).…”