High Thermoelectric Performance of New Rhombohedral Phase of GeSe stabilized through Alloying with AgSbSe2

Two-Dimensional-Like Phonons in Three-Dimensional-Structured Rhombohedral GeSe-Based Compounds with Excellent Thermoelectric Performance

The coupling of charge and phonon transport in solids is a long-standing issue for thermoelectric performance enhancement. Herein, two new narrow-gap semiconductors with the same chemical formula of GeSe0.65Te0.35 (GST) are rationally designed and synthesized: one with a layered hexagonal structure (H-GST) and the other with a non-layered rhombohedral structure (R-GST). Thanks to the three-dimensional (3D) network structure, R-GST possesses a significantly larger weighted mobility than H-GST. Surprisingly, 3D-structured R-GST displays an extremely low lattice thermal conductivity of ∼0.5 W m-1 K-1 at 523 K, which is comparable to that of layered H-GST. The two-dimensional (2D)-like phonon transport in R-GST stems from the unique off-centering Ge atoms that induce ferroelectric instability, yielding soft polar phonons, as demonstrated by the Boson peak detected by the low-temperature specific heat and calculated phonon spectra. Furthermore, 1 mol % doping of Sb is utilized to successfully suppress the undesired phase transition of R-GST toward H-GST at elevated temperatures. Consequently, a peak ZT of 1.1 at 623 K is attained in the rhombohedral Ge0.99Sb0.01Se0.65Te0.35 sample, which is 1 order of magnitude larger than that of GeSe. This work demonstrates the feasibility of exploring high-performance thermoelectric materials with decoupled charge and phonon transport in off-centering compounds.

High Thermoelectric Performance in Rhombohedral GeSe-LiBiTe2

GeSe, an analogue of SnSe, shows promise in exhibiting exceptional thermoelectric performance in the Pnma phase. The constraints on its dopability, however, pose challenges in attaining optimal carrier concentrations and improving ZT values. This study demonstrates a crystal structure evolution strategy for achieving highly doped samples and promising ZTs in GeSe via LiBiTe2 alloying. A rhombohedral phase (R3m) can be stabilized in the GeSe-LiBiTe2 system, further evolving into a cubic (Fm3̅m) phase with a rising temperature. The band structures of GeSe-LiBiTe2 in the rhombohedral and cubic phases feature a similar multiple-valley energy-converged valence band of L and Σ bands. The observed high carrier concentration (∼1020 cm-3) reflects the effective convergence of these bands, enabling a high density-of-states effective mass and an enhanced power factor. Moreover, a very low lattice thermal conductivity of 0.6-0.5 W m-1 K-1 from 300 to 723 K is achieved in 0.9GeSe-0.1LiBiTe2, approaching the amorphous limit value. This remarkably low lattice thermal conductivity is related to phonon scattering from point defects, planar vacancies, and ferroelectric instability-induced low-energy Einstein oscillators. Finally, a maximum ZT value of 1.1 to 1.3 at 723 K is obtained, with a high average ZT value of over 0.8 (400-723 K) in 0.9GeSe-0.1LiBiTe2 samples. This study establishes a viable route for tailoring crystal structures to significantly improve the performance of GeSe-related compounds.

Two-step phase manipulation by tailoring chemical bonds results in high-performance GeSe thermoelectrics

In thermoelectrics, phase engineering serves a crucial function in determining the power factor by affecting the band degeneracy. However, for low-symmetry compounds, the mainstream one-step phase manipulation strategy, depending solely on the valley or orbital degeneracy, is inadequate to attain a high density-of-states effective mass and exceptional zT. Here, we employ a distinctive two-step phase manipulation strategy through stepwise tailoring chemical bonds in GeSe. Initially, we amplify the valley degeneracy via CdTe alloying, which elevates the crystal symmetry from a covalently bonded orthorhombic to a metavalently bonded rhombohedral phase by significantly suppressing the Peierls distortion. Subsequently, we incorporate Pb to trigger the convergence of multivalence bands and further enhance the density-of-states effective mass by moderately restraining the Peierls distortion. Additionally, the atypical metavalent bonding in rhombohedral GeSe enables a high Ge vacancy concentration and a small band effective mass, leading to increased carrier concentration and mobility. This weak chemical bond along with strong lattice anharmonicity also reduces lattice thermal conductivity. Consequently, this unique property ensemble contributes to an outstanding zT of 0.9 at 773 K for Ge0.80Pb0.20Se(CdTe)0.25. This work underscores the pivotal role of the two-step phase manipulation by stepwise tailoring of chemical bonds in improving the thermoelectric performance of p-bonded chalcogenides.

Doping by Design: Enhanced Thermoelectric Performance of GeSe Alloys Through Metavalent Bonding

Doping is usually the first step to tailor thermoelectrics. It enables precise control of the charge-carrier concentration and concomitant transport properties. Doping should also turn GeSe, which features an intrinsically a low carrier concentration, into a competitive thermoelectric. Yet, elemental doping fails to improve the carrier concentration. In contrast, alloying with Ag-V-VI₂ compounds causes a remarkable enhancement of thermoelectric performance. This advance is closely related to a transition in the bonding mechanism, as evidenced by sudden changes in the optical dielectric constant ε_∞ , the Born effective charge, the maximum of the optical absorption ε₂ (ω), and the bond-breaking behavior. These property changes are indicative of the formation of metavalent bonding (MVB), leading to an octahedral-like atomic arrangement. MVB is accompanied by a thermoelectric-favorable band structure featuring anisotropic bands with small effective masses and a large degeneracy. A quantum-mechanical map, which distinguishes different types of chemical bonding, reveals that orthorhombic GeSe employs covalent bonding, while rhombohedral and cubic GeSe utilize MVB. The transition from covalent to MVB goes along with a pronounced improvement in thermoelectric performance. The failure or success of different dopants can be explained by this concept, which redefines doping rules and provides a "treasure map" to tailor p-bonded chalcogenides.

Regulating the Configurational Entropy to Improve the Thermoelectric Properties of (GeTe)1-x(MnZnCdTe3)x Alloys

In thermoelectrics, entropy engineering as an emerging paradigm-shifting strategy can simultaneously enhance the crystal symmetry, increase the solubility limit of specific elements, and reduce the lattice thermal conductivity. However, the severe lattice distortion in high-entropy materials blocks the carrier transport and hence results in an extremely low carrier mobility. Herein, the design principle for selecting alloying species is introduced as an effective strategy to compensate for the deterioration of carrier mobility in GeTe-based alloys. It demonstrates that high configurational entropy via progressive MnZnCdTe₃ and Sb co-alloying can promote the rhombohedral-cubic phase transition temperature toward room temperature, which thus contributes to the enhanced density-of-states effective mass. Combined with the reduced carrier concentration via the suppressed Ge vacancies by high-entropy effect and Sb donor doping, a large Seebeck coefficient is attained. Meanwhile, the severe lattice distortions and micron-sized Zn_0.6Cd_0.4Te precipitations restrain the lattice thermal conductivity approaching to the theoretical minimum value. Finally, the maximum zT of Ge_0.82Sb_0.08Te_0.90(MnZnCdTe₃)_0.10 reaches 1.24 at 723 K via the trade-off between the degraded carrier mobility and the improved Seebeck coefficient, as well as the depressed lattice thermal conductivity. These results provide a reference for the implementation of entropy engineering in GeTe and other thermoelectric materials.

Suppressing Charged Cation Antisites via Se Vapor Annealing Enables p-Type Dopability in AgBiSe2 -SnSe Thermoelectrics

Cation disordering is commonly found in multinary cubic compounds, but its effect on electronic properties has been neglected because of difficulties in determining the ordered structure and defect energetics. An absence of rational understanding of the point defects present has led to poor reproducibility and uncontrolled conduction type. AgBiSe₂ is a representative compound that suffers from poor reproducibility of thermoelectric properties, while the origins of its intrinsic n-type conductivity remain speculative. Here, it is demonstrated that cation disordering is facilitated by Bi_Ag charged antisite defects in cubic AgBiSe₂ which also act as a principal donor defect that greatly controls the electronic properties. Using density functional theory calculations and in situ Raman spectroscopy, how saturation annealing with selenium vapor can stabilize p-type conductivity in cubic AgBiSe₂ alloyed with SnSe at high temperatures is elucidated. With stable and controlled hole concentration, a peak is observed in the weighted mobility and the density-of-states effective mass in AgBiSnSe₃ , implying an increased valley degeneracy in this system. These findings corroborate the importance of considering the defect energetics for exploring the dopability of ternary thermoelectric chalcogenides and engineering electronic bands by controlling self-doping.

Enhancing Thermoelectric Performance of AgSbTe2-Based Compounds via Microstructure Modulation Combining with Entropy Engineering

Modulation of the microstructure and configurational entropy tuning are the core stratagem for improving thermoelectric performance. However, the correlation of evolution among the preparation methods, chemical composition, structural defects, configurational entropy, and thermoelectric properties is still unclear. Herein, two series of AgSbTe₂-based compounds were synthesized by an equilibrium melting-slow-cooling method and a nonequilibrium melting-quenching-spark plasma sintering (SPS) method, respectively. The equilibrium method results in coarse grains with a size of >300 μm in the samples and a lower defect concentration, leading to higher carrier mobility of 10.66 cm² V^-1 s^-1 for (Ag₂Te)_0.41(Sb₂Te₃)_0.59 compared to the sample synthesized by nonequilibrium preparation of 1.83 cm² V^-1 s^-1. Moreover, tuning the chemical composition of nonstoichiometric AgSbTe₂ effectively improves the configurational entropy and creates a large number of cation vacancies, which evolve into dense dislocations in the samples. Owing to all of these in conjunction with the strong inharmonic vibration of lattice, an ultralow thermal conductivity of 0.51 W m^-1 K^-1 at room temperature is achieved for the (Ag₂Te)_0.42(Sb₂Te₃)_0.58 sample synthesized by the equilibrium preparation method. Due to the enhanced carrier mobility, optimized carrier concentration, and low thermal conductivity, the (Ag₂Te)_0.42(Sb₂Te₃)_0.58 sample synthesized by the equilibrium preparation method possesses the highest ZT of 1.04 at 500 K, more than 60% higher than 0.64 at 500 K of the same composition synthesized by nonequilibrium preparation.

Synergistic Optimization of the Electronic and Phonon Transports of N-Type Argyrodite Ag8Sn1-xGaxSe6 (x = 0-0.6) through Entropy Engineering

The argyrodite compound, Ag₈SnSe₆ (ATS), which is one of the promising thermoelectric (TE) candidates, is receiving growing attention in thermoelectrics recently. However, its TE performance is still low and phases are unstable as the temperature varies. In this work, inspired by entropy engineering, we eliminate the β/γ phase transformation at ∼355 K via alloying Ga, thus extending its high-temperature cubic phase from 320 to 730 K. In the meantime, the power factor (PF) enhances by 10% and lattice thermal conductivity (κ_L) reduces by 40% at 723 K. As a result, the ZT value is boosted to ∼1.15 for Ag₈Sn_0.5Ga_0.5Se₆, which stands high among the ATS systems. This proves that the entropy engineering is an effective approach to extend the high-temperature range for the cubic γ-phase and improve its TE performance simultaneously.

Surface-Defect States in Photovoltaic Absorber GeSe

GeSe is an emerging promising light-harvesting material for photovoltaics due to its excellent optoelectronic properties, nontoxic and earth-abundant constituents, and high stability. In particular, perovskite-like antibonding states at the valence band maximum arising from Ge-4s and Se-4p coupling enable the bulk-defect-tolerant properties in GeSe. However, a fundamental understanding of surface-defect states in GeSe, another important factor for high-performance photovoltaics, is still lacking. Here, we investigate the surface-defect properties of GeSe through first-principle calculations. We find that different from common semiconductors possessing numerous surface dangling bonds, some GeSe surfaces are prone to reconstruction, thus eliminating the dangling bonds. The rearranged armchair edges exhibit unexpected benign defect properties, similar to those of bulk GeSe, arising from the formation of bulk-like [GeSe₃] tetrahedrons. We further show that the stable exposed (111) surfaces are hard to reconstruct due to the stiff structure but are effectively passivated by the addition of H.

Metavalent Bonding in GeSe Leads to High Thermoelectric Performance

Orthorhombic GeSe is a promising thermoelectric material. However, large band gap and strong covalent bonding result in a low thermoelectric figure of merit, zT≈0.2. Here, we demonstrate a maximum zT≈1.35 at 627 K in p-type polycrystalline rhombohedral (GeSe)_0.9 (AgBiTe₂ )_0.1  , which is the highest value reported among GeSe based materials. The rhombohedral phase is stable in ambient conditions for x=0.8-0.29 in (GeSe)_1-x (AgBiTe₂ )_x  . The structural transformation accompanies change from covalent bonding in orthorhombic GeSe to metavalent bonding in rhombohedral (GeSe)_1-x (AgBiTe₂ )_x  . (GeSe)_0.9 (AgBiTe₂ )_0.1 has closely lying primary and secondary valence bands (within 0.25-0.30 eV), which results in high power factor 12.8 μW cm^-1  K^-2 at 627 K. It also exhibits intrinsically low lattice thermal conductivity (0.38 Wm^-1  K^-1 at 578 K). Theoretical phonon dispersion calculations reveal vicinity of a ferroelectric instability, with large anomalous Born effective charges and high optical dielectric constant, which, in concurrence with high effective coordination number, low band gap and moderate electrical conductivity, corroborate metavalent bonding in (GeSe)_0.9 (AgBiTe₂ )_0.1 . We confirmed the presence of low energy phonon modes and local ferroelectric domains using heat capacity measurement (3-30 K) and switching spectroscopy in piezoresponse force microscopy, respectively.

Boosting Thermoelectric Properties of AgBi3(SeyS1-y)5 Solid Solution via Entropy Engineering

AgBi₃S₅ is an environmentally friendly n-type thermoelectric material composed of earth-abundant and nontoxic elements. It has a complex monoclinic structure with distorted NaCl-type fragments, which provide its intrinsically low thermal conductivity. However, poor electrical properties limit its overall performance. Configurational entropy engineering is an effective method to enhance thermoelectric properties. With the increase of configurational entropy, phonon point defect scattering is amplified, yielding lower lattice thermal conductivity, while the structure symmetry can also be improved, which leads to the enhanced electrical transport property. In this study, we combine carrier modulation and entropy engineering, utilizing melting-annealing and spark plasma sintering, to synthesize a series of AgBi₃(Se_yS_1-y)_5.08 bulks. Se substitution effectively increases the configurational entropy and thus dramatically decreases the thermal conductivity. Moreover, anion deficiency modulation effectively optimizes the carrier concentration and the electrical transport properties. Due to a power factor of 2.7 μW/(cm·K²) and a low thermal conductivity of 0.45 W/(m·K) at 723 K, the AgBi₃(Se_0.9S_0.1)_5.08 sample possesses the highest ZT of 0.42 at 723 K, nearly double the value of AgBi₃S_5.08 or pristine AgBi₃S₅. Our work demonstrates that apart from carrier optimization, entropy engineering opens a new avenue for enhancing the thermoelectric properties of a given material.

Structure-Dependent Thermoelectric Properties of GeSe1-xTex (0 ≤ x ≤ 0.5)

GeSe was theoretically predicted to have thermoelectric (TE) performance as high as SnSe. However, the relatively high TE performance was not achieved experimentally in doped GeSe samples with an original orthorhombic structure but observed in Ag(Sb,Bi)(Se,Te)₂ alloyed samples that crystalize in either a rhombohedral or cubic structure. Herein, to clarify the crystal structure-dependent properties, the electrical and thermal transport properties of GeSe_1-xTe_x (0 ≤ x ≤ 0.5), where orthorhombic, hexagonal, and rhombohedral phases are stable at room temperature for different Te content, have been studied, without any intentional manipulation on carrier concentration. It is found that the three phases show intrinsically different hole concentrations: ∼10¹⁶ cm^-3 for the orthorhombic phase but as high as 10²¹ cm^-3 for the hexagonal and rhombohedral phases. Ge-rich status in the orthorhombic phase and Ge-poor status in hexagonal and rhombohedral phases may be responsible for the huge difference in hole concentrations. The rhombohedral phase shows a much higher Seebeck coefficient than the hexagonal phase with similar hole concentration, indicating that the profile of valance band maximum for the rhombohedral structure is more favorable for high TE performance than the hexagonal phase in GeSe_1-xTe_x. The highest zT of 0.69 has been obtained in GeSe_0.55Te_0.45 at 778 K, at which temperature the rhombohedral phase has already transformed to a cubic phase; however, a zT value of 1.74 at 628 K is predicted by the quality factor analysis for rhombohedral GeSe_0.55Te_0.45 if optimum hole concentration can be achieved.

A first-principles study of the thermoelectric properties of rhombohedral GeSe

Manipulation of crystal symmetry is an important strategy to tune the thermoelectric performance. High-symmetry thermoelectric materials benefit from high band degeneracy. With first-principles calculations and Boltzmann transport theory, we systematically investigate the electronic and phononic transport properties of rhombohedral GeSe with higher symmetry. At optimized carrier concentrations, the maximum power factors are found to be 5.86 mW m-1 K-2 for the p-type and 4.45 mW m-1 K-2 for the n-type, respectively. The high p-type power factor originates from the highly degenerated L and Σ bands and small energy offset between them, while the n-type one results from the weak electron-phonon coupling. More importantly, rhombohedral GeSe possesses anisotropic and low lattice thermal conductivities of 3.58 W m-1 K-1 and 1.96 W m-1 K-1 at room temperature in the intralayer and interlayer directions, respectively, which is associated with the giant phonon anharmonicity driven by the resonant bonding. Combining the high power factor and low thermal conductivity, the predicted ZT values for p-type and n-type doping can reach 2.02 and 2.37 at 800 K. This study offers insights into the thermal and charge transport properties in rhombohedral GeSe, and demonstrates that both p-type and n-type GeSe are potential high-performance thermoelectric materials.

Realization of High Thermoelectric Figure of Merit in Solution Synthesized 2D SnSe Nanoplates via Ge Alloying

Recently single crystals of layered SnSe have created a paramount importance in thermoelectrics owing to their ultralow lattice thermal conductivity and high thermoelectric figure of merit ( zT). However, nanocrystalline or polycrystalline SnSe offers a wide range of thermoelectric applications for the ease of its synthesis and machinability. Here, we demonstrate high zT of ∼2.1 at 873 K in two-dimensional nanoplates of Ge-doped SnSe synthesized by a simple hydrothermal route followed by spark plasma sintering (SPS). Anisotropic measurements also show a high zT of ∼1.75 at 873 K parallel to the SPS pressing direction. Ge doping (3 mol %) in SnSe nanoplates significantly enhances the p-type carrier concentration, which results in high electrical conductivity and power factor of ∼5.10 μW/cm K² at 873 K. High lattice anharmonicity, nanoscale grain boundaries, and Ge precipitates in the SnSe matrix synergistically give rise to the ultralow lattice thermal conductivity of ∼0.18 W/mK at 873 K.

Stabilizing n-Type Cubic GeSe by Entropy-Driven Alloying of AgBiSe2 : Ultralow Thermal Conductivity and Promising Thermoelectric Performance

The realization of n-type Ge chalcogenides is elusive owing to intrinsic Ge vacancies that make them p-type semiconductors. GeSe crystallizes into a layered orthorhombic structure similar to SnSe at ambient conditions. The high-symmetry cubic phase of GeSe is predicted to be stabilized by applying 7 GPa external pressure or by enhancing the entropy by increasing to temperature to 920 K. Stabilization of the n-type cubic phase of GeSe at ambient conditions was achieved by alloying with AgBiSe₂ (30-50 mol %), enhancing the entropy through solid solution mixing. The interplay of positive and negative chemical pressure anomalously changes the band gap of GeSe with increasing the AgBiSe₂ concentration. The band gap of n-type cubic (GeSe)_1-x (AgBiSe₂ )_x (0.30≤x≤0.50) has a value in the 0.3-0.4 eV range, which is significantly lower than orthorhombic GeSe (1.1 eV). Cubic (GeSe)_1-x (AgBiSe₂ )_x exhibits an ultralow lattice thermal conductivity (κ_L ≈0.43 W m^-1  K^-1 ) in the 300-723 K range. The low κ_L is attributed to significant phonon scattering by entropy-driven enhanced solid-solution point defects.

Soft Phonon Modes Leading to Ultralow Thermal Conductivity and High Thermoelectric Performance in AgCuTe

Crystalline solids with intrinsically low lattice thermal conductivity (κ_L ) are crucial to realizing high-performance thermoelectric (TE) materials. Herein, we show an ultralow κ_L of 0.35 Wm^-1  K^-1 in AgCuTe, which has a remarkable TE figure-of-merit, zT of 1.6 at 670 K when alloyed with 10 mol % Se. First-principles DFT calculation reveals several soft phonon modes in its room-temperature hexagonal phase, which are also evident from low-temperature heat-capacity measurement. These phonon modes, dominated by Ag vibrations, soften further with temperature giving a dynamic cation disorder and driving the superionic transition. Intrinsic factors cause an ultralow κ_L in the room-temperature hexagonal phase, while the dynamic disorder of Ag/Cu cations leads to reduced phonon frequencies and mean free paths in the high-temperature rocksalt phase. Despite the cation disorder at elevated temperatures, the crystalline conduits of the rigid anion sublattice give a high power factor.