Structural stability, dynamical stability, thermoelectric properties, and elastic properties of GeTe at high pressure

The stability of GeTe in rhombohedral ($R3m$), face centred cubic ($Fm3m$), and simple cubic ($Pm3m$) phases has been studied using density functional perturbation theory. The rhombohedral phase of GeTe is dynamically stable at 0 GPa, while $Fm3m$ and $Pm3m$ phases are stable at 3.1 and 33 GPa, respectively. The pressure-dependent phonon modes are observed in $Fm3m$ and $Pm3m$ phases at \ensuremath{\Gamma} and $M$ points, respectively. The electronic and the thermoelectric properties have been investigated for the stable phases of GeTe. The electronic band gap for rhombohedral and $Fm3m$ phases of GeTe has been observed as 0.66 and 0.17 eV, respectively, while the $Pm3m$ phase shows metallic behavior. We have used the Boltzmann transport equation under a rigid band approximation and constant relaxation time approximation as implemented in boltztrap code for the calculation of thermoelectric properties of GeTe. The metallic behavior of $Pm3m$ phase gives a very low value of Seebeck coefficient compared to the other two phases as a function of temperature and the chemical potential \ensuremath{\mu}. It is observed that the rhombohedral phase of GeTe exhibits higher thermoelectric performance. Due to the metallic nature of $Pm3m$ phase, negligible thermoelectric performance is observed compared to $R3m$ and $Fm3m$-GeTe. The calculated lattice thermal conductivities are low for $Fm3m$-GeTe and high for $R3m$-GeTe. At the relatively higher temperature of 1350 K, the figure of merit $\mathit{ZT}$ is found to be 0.7 for rhombohedral GeTe. The elastic constants satisfy the Born stability criteria for all three phases. The rhombohedral and $Fm3m$ phases exhibits brittleness and the $Pm3m$ phase shows ductile nature.