High-Performance GeTe Thermoelectrics in Both Rhombohedral and Cubic Phases.

GeTe Thermoelectrics

Rhombohedral GeTe can be approximated as the directional distortion of the cubic GeTe along [111]. Such a symmetry-breaking of the crystal structure results in an opposite arrangement in energy of the L and Σ valence bands, and a split of them into 3L+1Z and 6Σ+6η, respectively. This enables a manipulation of the overall band degeneracy for thermoelectric enhancements through a precise control of the degree of crystal structure deviating from a cubic structure for the alignment of the split bands. Here, we show the effect of AgBiSe2-alloying on the crystal structure as well as thermoelectric transport properties of rhombohedral GeTe. AgBiSe2-alloying is found to not only finely manipulate the crystal structure for band convergence and thereby an increased band degeneracy, but also flatten the valence band for an increased band effective mass. Both of them result in an increased density of state effective mass and therefore an enhanced Seebeck coefficient along with a decreased mobility. Moreover, a remarkably reduced lattice thermal conductivity of ∼0.4 W/m-K is obtained due to the introduced additional point defect phonon scattering and bond softening by the alloying. With the help of Bi-doping at the Ge site for further optimizing the carrier concentration, thermoelectric figure of merit, zT, of ∼1.7 and average zTave of ∼0.9 are achieved in 5% AgBiSe2-alloyed rhombohedral GeTe, which demonstrates this material as a promising candidate for low-temperature thermoelectric applications.

The authors have investigated the bonding in cubic and rhombohedral GeTe by studying the charge density of each individual valence band, using the Baldereschi method. The calculated charge densities can be interpreted in terms of atomic orbitals. The orbitals that participate in the bonding are s Ge, p Te and p Ge. In cubic GeTe there are p orbitals along the three orthogonal axes forming polar sigma -bonds between the Ge and Te atoms. There is a pronounced admixture of s Ge states with p states in the second and the last valence band. This admixture is responsible for the rise of the last valence band, which makes the GeTe a narrow-gap semiconductor. For rhombohedral GeTe the bonding can be described in terms of one p orbital along the (111) direction and the three p orbitals orthogonal to the (111) direction. These orbitals interact and form an admixture of polar sigma - and pi -bonds. The bonding charge is greater for rhombohedral GeTe, resulting in an increase of the bonding and a lowering of the electronic energy of rhombohedral GeTe with respect to that of cubic GeTe. By calculation they find the dipole moment of the rhombohedral phase to be 1.4 D along the (111) direction.

GeSe is a IV-VI semiconductor, like the excellent thermoelectric materials PbTe and SnSe. Orthorhombic GeSe has been predicted theoretically to have good thermoelectric performance but is difficult to dope experimentally. Like PbTe, rhombohedral GeTe has a multivalley band structure, which is ideal for thermoelectrics and also promotes the formation of Ge vacancies to provide enough carriers for electrical transport. Herein, we investigate the thermoelectric properties of GeSe alloyed with AgSbSe2 , which stabilizes a new rhombohedral structure with higher symmetry that leads to a multivalley Fermi surface and a dramatic increase in carrier concentration. The zT of GeAg0.2 Sb0.2 Se1.4 reaches 0.86 at 710 K, which is 18 times higher than that of pristine GeSe and over four times higher than doped orthorhombic GeSe. Our results open a new avenue towards developing novel thermoelectric materials through crystal phase engineering using a strategy of entropy stabilization of high-symmetry alloys.

We employ first-principles calculations combined with self-consistent phonon theory and Boltzmann transport equations to investigate the thermal transport and thermoelectric properties of full-Heusler compound Na2TlSb. Our findings exhibit that the strong quartic anharmonicity and temperature dependence of the Tl atom with rattling behavior plays an important role in the lattice stability of Na2TlSb. We find that soft Tl-Sb bonding and resonant bonding in the pseudocage composed of the Na and Sb atoms interaction is responsible for ultralow κL. Meanwhile, the multi-valley band structure increases the band degeneracy, results in a high power factor in p-type Na2TlSb. The coexistence of ultralow κL and high power factor presents that Na2TlSb is a potential candidate for thermoelectric applications. Moreover, these findings help to understand the origin of ultralow κL of full-Heusler compounds with strong quartic anharmonicity, leading to the rational design of full-Heusler compounds with high thermoelectric performance.

Low-Symmetry Rhombohedral GeTe Thermoelectrics

Dilute Cu2Te-alloying enables extraordinary performance of r-GeTe thermoelectrics

Anomalous enhancement of thermoelectric performance in GeTe with specific interaxial angle and atomic displacement synergy

High‐performance GeTe‐based thermoelectrics have been recently attracting growing research interest. Here, an overview is presented of the structural and electronic band characteristics of GeTe. Intrinsically, compared to low‐temperature rhombohedral GeTe, the high‐symmetry and high‐temperature cubic GeTe has a low energy offset between L and Σ points of the valence band, the reduced direct bandgap and phonon group velocity, and as a result, high thermoelectric performance. Moreover, their thermoelectric performance can be effectively enhanced through either carrier concentration optimization, band structure engineering (bandgap reduction, band degeneracy, and resonant state engineering), or restrained lattice thermal conductivity (phonon velocity reduction or phonon scattering). Consequently, the dimensionless figure of merit, ZT values, of GeTe‐based thermoelectric materials can be higher than 2. The mechanical and thermal stabilities of GeTe‐based thermoelectrics are highlighted, and it is found that they are suitable for practical thermoelectric applications except for their high cost. Finally, it is recognized that the performance of GeTe‐based materials can be further enhanced through synergistic effects. Additionally, proper material selection and module design can further boost the energy conversion efficiency of GeTe‐based thermoelectrics.

GeTe alloys have attracted wide attention due to their high conversion efficiency. However, pristine GeTe possesses intrinsically massive Ge vacancies, leading to a very high hole concentration (1021 cm−3). Herein, a decreased carrier concentration is realized by alloying NaSbTe2 in GeTe due to the increased formation energy of Ge vacancies. This alloying also lowers energy separation between the valence bands in the rhombohedral GeTe and induces two extra valence band pockets around the Fermi surface along Γ‐L and L‐W in the cubic GeTe, all of which contributes to the higher power factors over a wide temperature range. Combined with the low lattice thermal conductivities due to plenty of dislocations and strains as a result of the crystallographic disorder of Na, Ge, and Sb, a maximum zT ≈ 2.35 at 773 K and a zTave of 1.33 from 300 to 773 K are achieved in (GeTe)90(NaSbTe2)10.

Developing high performance thermoelectrics to convert waste heat into useful electrical power is an important challenge that has the potential to impact our energy future. This requires exploring and discovering new materials with enhanced electronic and thermal (phonon) transport properties. Advances in computational modeling now allow the thermoelectric characteristics of materials to be calculated fully predictively, and thus represents a powerful tool to be partnered with experimental efforts.In this talk, I will present our recent findings on rhombohedral GeTe, a layered quasi-2D material predicted to have unusual anisotropic transport properties [1]. Our approach combines density functional theory with the Boltzmann transport equation, to extract the detailed electron and phonon dispersions along with the electron-phonon scattering rates, in order to predict the thermoelectric transport coefficients. Our results show that the electrons preferentially conduct along the cross-plane direction, while the holes favor the in-plane direction. Interestingly, this feature enhances the thermoelectric figure-of-merit ZT for n-type GeTe, since the conductivity (and power factor) is maximized perpendicular to the atomic layers while the lattice (phonon) thermal conductivity is minimized - leading to a three-fold increase in ZT. The cross-plane power factor and mobility in n-GeTe reach roughly 32 μW/cm-K2 and 500 cm2/V-s, respectively. An analysis of the band structure reveals that the large cross-plane transport originates from high-velocity conduction states, formed by the Ge p-orbitals that span across the interstitial region. These findings illustrate how the dominant electron and phonon transport directions are effectively decoupled in n-GeTe; a feature that can potentially be found in other materials to achieve enhancements in thermoelectric performance.[1] V. Askarpour and J. Maassen, “Unusual thermoelectric transport anisotropy in quasi-two-dimensional rhombohedral GeTe”, Phys. Rev. B 100, 075201 (2019). Figure 1

Exploiting the fascinating properties of materials near soft mode phase transitions is an emerging concept in the quest to increase thermoelectric efficiency [1,2]. The underlying idea is that soft phonons lead to intrinsically low thermal conductivity, while possibly preserving electronic transport properties. Using first principles simulations, we show that driving PbTe near the transition from the rocksalt to a rhombohedral structure will significantly reduce its lattice thermal conductivity. We illustrate this concept by applying biaxial tensile (001) strain to both PbTe and its alloy with rocksalt PbSe, and also by alloying PbTe with rhombohedral GeTe [3]. Moreover, we investigate in detail how tuning the proximity to the soft optical mode phase transition via chemical composition affects the lattice thermal conductivity of (Pb,Ge)Te alloys [4]. We show that the anharmonic contribution to the lattice thermal conductivity is minimized at the phase transition due to the maximized acoustic-optical interaction. Furthermore, mass disorder shifts the conductivity minimum towards the composition at which the scattering due to mass disorder is maximized. The total lattice thermal conductivity and its anharmonic contribution vary continuously between the rocksalt and rhombohedral phases as expected for the second-order phase transition. Our results show that alloys with soft optical mode transitions are promising materials for achieving low thermal conductivity and possibly high thermoelectric efficiency. [1] D. T. Morelli, V. Jovovic, and J. P. Heremans, Phys. Rev. Lett. 101, 035901 (2008). [2] L.-D. Zhao et al, Nature 508, 373 (2014). [3] R. M. Murphy, E. D. Murray, S. Fahy, and I. Savic, Phys. Rev. B 93, 104304 (2016). [4] R. M. Murphy, E. D. Murray, S. Fahy, and I. Savic, Phys. Rev. B 95, 144302 (2017).

The pseudopotential method is used to obtain the band structure and electronic density of states for both cubic and rhombohedral GeTe. We find that the minimum energy gap occurs along the line LK. Our calculations also show that the rhombohedral distortion lowers the electronic energy. In addition the reflectance spectra are obtained for the cubic GeTe and compared with experimental data.

Superior electronic performance due to the highly degenerated Σ valence band (Nv∼12) makes rhombohedral GeTe a promising low-temperature (<600 K) thermoelectric candidate. Minimizing lattice thermal conductivity (κL) is an essential route for enhancing thermoelectric performance, but the temperature-dependent κL, corelated to T-1, makes its reduction difficult at low temperature. In this work, a room-temperature κL of ≈0.55Wm-1-K-1, the lowest ever reported in GeTe-based thermoelectric, is realized in (Ge1- ySbyTe)1- x(Cu8GeSe6)x, primarily due to strong phonon scattering induced by point defects and precipitates. Simultaneously, Cu8GeSe6-alloying effectively suppresses the precipitation of Ge, enabling the optimization of carrier concentration with the additional help of aliovalent Sb doping. As a result, an extraordinary peak zT of up to 2.3 and an average zTavg. of ≈1.2 within 300-625 K are achieved, leading to a conversion efficiency of ≈9% at a temperature difference of 282 K. This work robustly demonstrates its potential as a promising component in thermoelectric generator utilizing low-grade waste heat.

Tin telluride (SnTe) is an IV-VI semiconductor with a topological crystalline insulator band structure, high thermoelectric performance, and in-plane ferroelectricity. Despite its many applications, there has been little work focused on understanding the growth mechanisms of SnTe thin films. In this manuscript, we investigate the molecular beam epitaxy synthesis of SnTe (111) thin films on InP (111)A substrates. We explore the effect of substrate temperature, Te/Sn flux ratio, and growth rate on the film quality. Using a substrate temperature of 340 °C, a Te/Sn flux ratio of 3, and a growth rate of 0.48 Å/s, fully coalesced and single crystalline SnTe (111) epitaxial layers with X-ray rocking curve full-width-at-half-maxima of 0.09° and root-mean-square surface roughness as low as 0.2 nm have been obtained. Despite the 7.5% lattice mismatch between the SnTe (111) film and the InP (111)A substrate, reciprocal space mapping indicates that the 15 nm SnTe layer is fully relaxed. We show that a periodic interfacial misfit (IMF) dislocation array forms at the SnTe/InP heterointerface, where each IMF dislocation is separated by 14 InP lattice sites/13 SnTe lattice sites, providing rapid strain relaxation and yielding the high quality SnTe layer. This is the first report of an IMF array forming in a rock-salt on zinc-blende material system and at an IV-VI on III-V heterointerface, and highlights the potential for SnTe as a buffer layer for epitaxial telluride film growth. This work represents an important milestone in enabling the heterointegration between IV-VI and III-V semiconductors to create multifunctional devices.