Metal halide thermoelectrics: prediction of high-performance CsCu2I3

Thermoelectric devices can directly convert waste heat into electricity, which makes them an important clean energy technology. The underlying materials performance can be evaluated by the dimensionless figure of merit ZT. Metal halides are attractive candidates due to their chemical flexibility and ease of processing; however, the maximum ZT realized (ZT = 0.15) falls far below the level needed for commercialization (ZT>1). Using a first-principles procedure we assess the thermoelectric potential of copper halide CsCu2I3, which features 1D Cu-I connectivity. The n-type crystal is predicted to exhibit a maximum ZT of 2.2 at 600 K along the b-axis. The strong phonon anharmonicity of this system is shown by locally stable non-centrosymmetric Amm2 structures that are averaged to form the observed centrosymmetric Cmcm space group. Our work provides insights into the structure-property relations in metal halide thermoelectrics and suggests a path forward to engineer higher-performance heat-to-electricity conversion.


I. INTRODUCTION
Thermoelectric materials -which enable the direct conversion of waste heat to electricity -have received great attention as one of the most promising renewable energy technologies [1].The performance of thermoelectric materials is evaluated by the dimensionless figure of merit, ZT : where S is the Seebeck coefficient, σ is the electrical conductivity, T is the temperature, κ elec is the electronic thermal conductivity, and κ latt is the lattice thermal conductivity (power factor, P F , is defined as S 2 σ).Due to the recent progress in calculation methods for electron (hole) and phonon transport in solid crystals, computational studies have been made to discover novel compounds that possess a high ZT [2][3][4][5].Although the trade-off effect between the parameters that control ZT makes the optimization challenging, search for an intrinsically low κ latt material is still crucial to maximize performance [6].In other words, high thermoelectric performance requires the phonons to be disrupted like in a glass but the electrons to have a high mobility like in crystalline semiconductors (i.e.phonon-glass electroncrystal) [7].
However, the highest maximum ZT of 0.15 achieved from a halide perovskite CsSnI 3 [18] is far to compete with top thermoelectric materials such as SnSe whose maximum ZT is > 2.6 [29].In addition, studies were mainly conducted on conventional halide perovskites, while emerging low-dimensional metal halides have yet to be explored.Recently, we reported a high thermoelectric potential in metal halide Cs 3 Cu 2 I 5 for the first time where asymmetric heat and charge transport in the material enables a high maximum ZT of 2.6 at 600 K [28].
In this article, we present CsCu 2 I 3 as a candidate for thermoelectric applications on the basis of first-principles predictions.CsCu 2 I 3 is one of the copper-based lowdimensional halide compounds where 1D [Cu 2 I 3 ] -anionic chains are separated by Cs + cations.By performing lattice dynamics simulations, we found that heat transport in the material is highly anisotropic where the κ latt in the ab-plane (perpendicular to the chains) is about 2 times lower than that along the c-axis (chain direction).We also confirmed that the experimentally reported Cmcm structure of the material is not dynamically stable but an average of Amm2 structures during our phonon analysis.Interestingly, electron transport in the material shows an opposite anisotropy compared to the phonon transport; electron mobility in the ab-plane is 1.5 times higher than that along the c-axis.Due to this unique anisotropy of heat and electron transport in a single material, we predict that the CsCu 2 I 3 in Amm2 structure reaches a ZT of 2.2 at 600 K along the b-axis, having potential as a next-generation thermoelectric material.

A. First-principles thermoelectrics workflow
The workflow to predict ZT from first principles is shown in Fig. 1.In principle, this only requires prior knowledge of a crystal structure and all other properties can be directly calculated in turn.As the first step, the crystal structure of a compound of interest should be optimized to a local minimum in the potential energy surface.If the compound shows imaginary phonon modes, additional crystal structure optimization and/or anharmonic corrections should be applied to obtain dynamically stable structure, so that reliable thermal properties can be calculated [30].With the dynamically stable crystal structure, bulk properties can be assessed.Results from steps 2-4 are given as inputs for calculating carrier lifetimes and transport properties -S, σ, and κ elec (step 5), while lattice thermal conductivity, κ latt is obtained from anharmonic phonon calculations (steps 6 and 7).Finally, thermoelectric properties such as ZT and thermodynamic efficiency (η) are predicted by combining the outputs from steps 5 and 7. Computational details are provided in section IV.

B. Structural analysis
CsCu 2 I 3 has been reported in a Cmcm space group, [31,32] where 1D [Cu 2 I 3 ] -anionic chains are separated by Cs + cations as shown in Fig. 2. When the experimentally known structure was adopted and optimized, we found that imaginary phonon modes are persistent across the first Brillouin zone (see Fig. 3(a)), which confirms dynamic structural instability of the Cmcm structure.(This will be further discussed in section II C).To obtain a dynamically stable crystal structure, we deformed the Cmcm structure along the eigenvector of its imaginary Γ phonon mode, which results in a structural transition to new lower-symmetry Amm2 phase.The structural transition from Cmcm to Amm2 occurs with atomic positions shifted along the directions indicated by the arrows in Fig. 2(a), (c).Cs and I atoms move within the b-axis and ab-plane, respectively, while Cu atoms move along the c-axis.The Cu-I-Cu bond angle for Cmcm is alternately 71.54 • and 71.16 • , while polyhedra distortion in Amm2 results in a bond angle of 61.39 • and 81.42 • , as shown in Fig. 2(e).In Cmcm, the Cu-I bond lengths in the [CuI 4 ] 3− tetrahedron are of a similar value (2.62 and 2.61 Å, two each), as opposed to the bonds in Amm2 all having a different value (2.66, 2.65, 2.58, and 2.61 Å).Thus, while the crystal system is maintained as orthorhombic, the crystal symmetry is lowered from centrosymmetric Cmcm to non-centrosymmetric Amm2.Comparison of the calculated lattice parameters of Cmcm and Amm2, as well as experimental value from X-ray diffraction measurement are provided in Table II.The structural transition results in a 0 decreasing 0.30 % while b 0 increasing 0.84 %, both changes due to the movement of Cs and I atoms.In contrast, c 0 is equivalent in both structures, as the shift of Cu atoms even out macroscopically.Amm2 has an expanded volume of 0.70 % compared to Cmcm.The elastic and dielectric tensors calculated from Cmcm and Amm2 phases are provided in Table S1.

C. Dynamic structural instability
The phonon dispersion of Cmcm and Amm2 is illustrated together with the atom-projected phonon density of states (PDOS) in Fig. 3(a), (b), respectively.While the Materials Project [34] repository, as well as computational [35] and experimental [33] reports, indicate CsCu 2 I 3 as a Cmcm structure, dynamic structural instability of Cmcm is evident by the numerous imaginary modes shown in Fig. 3  ModeMap [36], the corresponding energy as a function of the distortion amplitude along the eigenvectors illustrated in Fig. 2(a), (c) is shown in Fig. 4. A characteristic double-well potential-energy curve is shown.The saddle point corresponds to the Cmcm structure, while the two wells indicate the lower symmetry Amm2 structure as a local minimum.Thus, the energy-lowering distortion causes a structural transition to a ground-state polymorph, Amm2, with an energy 2.84 meV/atom lower than Cmcm.As shown in Fig. 3(b), the absence of imaginary phonon modes indicates the dynamic stability of Amm2.Hence, we propose that the previously reported centrosymmetric Cmcm structure is a macroscopic average over locally non-centrosymmetric Amm2 structures.In addition, in the Amm2 structure, a lack of inversion symmetry causes a spontaneous electric polarization.As shown in Fig. 2(a), (c), polarization mainly occurs within the ab-plane by the shift of Cs and I atoms, while minute polarization along the c-axis corresponds to the movement of Cu atoms.The corresponding piezoelectric tensor of the Amm2 structure is provided in Table S1.

D. Ultra-low lattice thermal conductivity
Fig. 5 shows the κ latt of Amm2 CsCu 2 I 3 , as a function of temperature along different crystallographic directions.Because CsCu 2 I 3 is experimentally reported to have a melting point at ∼644 K [33,37], the temperature range for calculating κ latt as well as transport and thermoelectric properties discussed later is set up to 600 K. Amm2 shows an unexpectedly low κ latt (i.e.ultralow κ latt ) of a value under 0.1 W/m•K for all directions even at 300 K; 0.05, 0.03, and 0.08 W/m•K for the a-, b-, and c-axes, respectively.The isotropically averaged κ latt (κ avg ) at 300 K is 0.05 W/m•K, which is lower than one of the top thermoelectric materials, SnSe (0.2 W/m•K at 300 K [38]).The value is slightly higher compared to Cs 3 Cu 2 I 5 (κ avg = 0.02 W/m•K at room temperature (RT) [28]), which was calculated at a similar level of theory.At 600 K, the κ latt values are 0.02 W/m•K along the a-and b-axes, and 0.04 W/m•K along the c-axis (κ avg being 0.03 W/m•K).The anisotropy of CsCu 2 I 3 , having a higher κ latt along the c-axis, can be ascribed to a weaker chemical bonding towards the c-axis of the unit cell [39].It is noteworthy that the c-axis is parallel to the [Cu 2 I 3 ] − chains.Acoustic phonon modes and low-frequency optic modes act as the primary heat carriers in crystals, mainly contributing to κ latt .As shown in Fig. 3(b), the low-lying optic modes of Amm2 are relatively flat, which leads to low group velocities (v λ ), one of the reasons for its ultralow κ latt .In addition, the high density of the low-lying optic modes produces a large number of scattering channels at this frequency range, causing short phonon lifetimes (τ λ ).Fig. S1 shows avoided crossings of the acoustic and low-frequency optic modes at the Γ-Y direction.Avoided crossing is a characteristic feature shown when a 'rattler' is present in the material [40].PDOS shown in Fig. 3(b) indicates that lower-frequency phonon modes mostly comprise motions of Cs atoms.Thus, we can infer that Cs atoms behave as the rattler, rattling within the space between [Cu 2 I 3 ] − chains.Fig. S2 shows the Cs-I bonds (total 10), and the broad range of bond lengths being from 3.81 to 4.21 Å contributes to the anharmonicity of CsCu 2 I 3 .This is similar to the origin of anharmonicity of SnSe [41].We note that fluctuations between Cmcm and Amm2 could also contribute to the scattering of the heat transport, but such higher-order anharmonicity is not considered here.
To further understand the origins of the ultra-low κ latt of CsCu 2 I 3 , we analyzed the modal contributions to the net transport (Fig. 6).The net transport, κ latt , is a sum of the individual phonon modes (λ): where N is the number of unit cells in the crystal (equivalent to the number of wavevectors included in the Brillouin zone summation), V 0 is the volume of the crystallographic unit cell, and C λ is the modal heat capacity.The frequency spectra of v λ , τ λ , and phonon mean free path (Λ λ = v λ × τ λ ) at 300 K is shown in Fig. 6(a)-(c), respec-tively [42].In the entire frequency range, the majority of v λ fall within the range between 1 and 10 3 m/s, and the fastest modes are seen at the 0-0.2THz frequency range.The fastest modes correspond to the acoustic phonon bands that are relatively dispersive compared to the optic modes.The overall spectra is comparable to (CH 3 NH 3 )PbI 3 (MAPbI 3 ) [43], a 3D perovskite reported to have a ultra-low κ latt of 0.05 W/m•K at 300 K, while the fastest modes have a lower v λ in CsCu 2 I 3 .In addition, a number of modes have a very low v λ , from 10 −12 to 10 −10 m/s, unseen in the v λ spectra of MAPbI 3 [43] and Cs 3 Cu 2 I 5 [28].These modes correspond to the low-lying optic modes at the 0.2-2.4THz frequency range that are relatively flat.The low v λ attribute to the heavy elements that constitute CsCu 2 I 3 .τ λ mostly falls into the range of 10 −1 to 10 1 ps, while a number of phonon modes within the 0-0.2THz frequency range (acoustic phonon modes) have a τ λ longer than 10 ps.The overall spectra is similar to MAPbI 3 [43] and Cs 3 Cu 2 I 5 [28], while the longest τ λ of CsCu 2 I 3 are longer compared to Cs 3 Cu 2 I 5 (longest being 11 ps).The combination of a low v λ and τ λ leads to the majority of the modes having Λ λ shorter than 10 0 nm, which is why CsCu 2 I 3 shows an ultra-low κ latt .The low-frequency modes (acoustic and low-lying optic modes) have a relatively faster v λ and longer τ λ resulting in a longer Λ λ compared to the high-frequency modes.This matches with the fact that acoustic and low-lying optic modes are the primary heat carriers.

E. Electronic structure and transport properties
The electronic band structure of Cmcm and Amm2 is illustrated in Fig. 7(a) and (b), respectively.Both Cmcm and Amm2 phases have a direct band gap (E g ) at the Γ-point, with a E g value of 3.23 eV and 3.08 eV, respectively.The calculated E g is similar to the experimental value estimated from the optical absorption spectrum, 3.49 eV [37].As shown in Fig. S3, upper valence bands are dominated by Cu 3d and I 5p orbitals, while lower conduction bands arise from the hybridization of Cu 4s and I 5p orbitals.For the conduction band minimum, I 5s contributes more compared to I 5p.Calculation of the orbitals that comprise band edges are in good agreement with previous reports [33,37].The contribution of Cs orbitals on those band edges is negligible, which is the wellknown feature of low dimensional metal halides [44,45].The corresponding orbitals are also equivalent to the electronic band structure of Cs 3 Cu 2 I 5 [28].The upper valence band is relatively flat, having a hole effective mass of 0.83 m e at the valence band maximum, while the lower conduction band is relatively dispersive with an electron effective mass of 0.31 m e at the conduction band minimum.Conduction band has multiple valleys (Γ-point, Z-point, and along the S-R and Y-T direction), and the energy difference between the first and second conduction band edge is 0.57 eV for Amm2.The dispersive nature and multiple valleys lead to a high σ and S, respectively, suggesting the possibility of CsCu 2 I 3 as a promising ntype thermoelectric material.Fig. 8 shows the calculated electron mobility, µ, of Amm2 as a function of temperature along different crystallographic directions at the optimal electron concentration, n e , (6 × 10 18 cm −3 ) at which thermoelectric properties are maximized (n e will be further discussed in Fig. 10(a)).Similar to κ latt , µ is anisotropic, with µ being lower along the c-axis.The isotropically averaged µ is 21.4 cm 2 /V•s at 300 K, which is slightly higher than the µ of Cs 3 Cu 2 I 5 [28] (18.2 cm 2 /V•s at RT). Fig. S4 shows µ of Cmcm and Amm2 by the individual scattering mechanisms.Acoustic deformation potential (ADP), ionized impurity (IMP), and polar optical phonon (POP) scattering mechanisms were considered for both structures, and for Amm2 (non-centrosymmetric), piezoelectric (PIE) scattering mechanism was considered as well.
µ is limited by POP scattering for both structures, followed by IMP and ADP scattering.POP scattering is dominant in many of the top thermoelectric materials including SnSe [46] and Cs 3 Cu 2 I 5 [28].In Amm2, PIE scattering has the smallest contribution to the total µ, as its polarization is minute.
The electronic transport -σ, S, P F , and κ elec -of Amm2 as a function of temperature and n e are shown in Fig. S5.σ and κ elec are proportional to n e , but have an inverse relationship with temperature.On the other hand, |S| is disproportionate with n e , and increases with temperature.Fig. 9 shows σ, S, P F , and κ elec as a function of temperature along different crystallographic directions (n e = 6 × 10 18 cm −3 ).σ, κ elec , and P F is higher along the a-and b-axes, which reflects the anisotropy of µ. |S| is almost equivalent along all axes.Along the b-axis, the P F goes up to 109.66 µW/m•K 2 at 470 K.

F. Thermoelectric properties
By combining the phonon and electron transport properties using Eq. ( 1), ZT for CsCu 2 I 3 as a function of temperature along different crystallographic axes is predicted (Fig. 9(e)).Due to the anisotropy of σ, κ latt , κ elec , ZT is also anisotropic, showing a lower value along the c-axis.At 600 K, it reaches a value of 2.2 along the b-axis, while the a-and c-axes has a ZT of 1.7 and 0.8, respectively.Notably, a high ZT is obtained at a lower temperature compared to the state-of-the-art thermoelectric material, n-type SnSe, which has a ZT of 2.0 above 700 K [47].The origin of a high ZT is a combination of ultralow κ latt and high P F .Fig. 10(a) shows the isotropically averaged ZT of CsCu 2 I 3 as a function of temperature and n e .ZT is maximized at n e of 6 × 10 18 cm −3 , and the maximum ZT achievable at this condition is 1.5 at 600 K.As mentioned above, the highest ZT from a conventional halide perovskite was only 0.15, so this work may derive more attention towards CsCu 2 I 3 and other low-dimensional metal halides.
Thermodynamic efficiency, η, of thermoelectric generators can be calculated by the following equation: where T H and T C are the hot side and cold side temperature of the generator, respectively.The average ZT (ZT ) is defined as follows: Using these equations, we plotted η as a function of T H , while T C is fixed to 200 K (Fig. 10(b)).Maximum η of 13.1 % is achieved when the temperature difference is 400 K (T H = 400 K), and ZT being 0.8.The main concern when fabricating CsCu 2 I 3 for thermoelectric applications would be whether the optimal n e could be achieved by doping.Currently, doping of perovskite derivatives is underexplored, but below we address some of the doping strategies that can be implemented.Similar to the doping approaches of 3D perovskites, doping in perovskite derivatives could be achieved either by (1) adding dopant sources to the precursor solution; (2) post-synthesis solution doping; and (3) post-synthesis vapor doping [48].The specific methods could be adding atomic dopants, and molecular dopants by surface doping.In general, the B-site metals (Cu for CsCu 2 I 3 ) mainly contribute to the edge of the band structure [48] (c.f.Fig. S3).Thus, substituting Cu + with +2 charged ions is more likely to produce the necessary states to tune n e , compared to the doping of Cs and I.
ZT of CsCu 2 I 3 is relatively low compared to Cs 3 Cu 2 I 5 .However, it is reported that CsCu 2 I 3 is more stable than Cs 3 Cu 2 I 5 when dopants are added, and the unstable Cs 3 Cu 2 I 5 decompose and form into CsCu 2 I 3 [49].Thus, although a higher optimal n e is required for CsCu 2 I 3 (6×10 18 cm −3 , compared to 4×10 18 cm −3 for Cs 3 Cu 2 I 5 ), it may be achieved more easily.In addition, whether this high thermoelectric performance is shown only for CsCu 2 I 3 and Cs 3 Cu 2 I 5 , or from perovskite derivatives in general requires further investigation.Through our initial calculations, copper-based metal halides K 2 CuX 3 and CsCu 2 X 3 (X = Cl, Br) are also expected to have a high potential as an n-type thermoelectric material.Changing the A-site or X-site elements to the ones in the same group of the periodic table is also worth a try.Thus, investigating Cs 3 Cu 2 X 5 and Rb 2 CuX 3 (X = Cl, Br) as well as RbCu 2 Y 3 (Y = Br, I) could be possible.

III. CONCLUSIONS
In this paper, we report a new direction for metal halide thermoelectrics with a predictive study on the structure, properties, and performance of CsCu 2 I 3 .
The dynamic structural instability of the previously known Cmcm structure of CsCu 2 I 3 was investigated.We report a new, ground-state Amm2 structure of CsCu 2 I 3 , and compared its basic bulk properties with Cmcm.The ultra-low κ latt of Amm2 and its origins were studied in detail.Additionally, the electronic transport properties as well as ZT were first reported in this work.We predict that CsCu 2 I 3 is a new promising n-type thermoelectric material, and require further investigations in lowdimensional metal halides.
The centrosymmetric Cmcm structure is a macroscopic average over locally non-centrosymmetric Amm2 structures.The octahedra distortion leads to an energylowering structural transition from Cmcm to Amm2, and the energy being 2.84 meV/atom lower.The lack of in- version symmetry in Amm2 results in a spontaneous tice polarization mainly within the ab-plane.
Amm2 shows an ultra-low κ latt with κ avg at 300 K being 0.05 W/m•K, and the values being higher along the c-axis (i.e.anisotropic).The low v λ is due to the low-frequency optic modes being relatively flat.Avoided crossings of the acoustic and low-lying optic modes are shown from the dispersion, which is the cause of short τ λ .Cs atoms between the [Cu 2 I 3 ] − chains behave as rattlers, and the inequivalent Cs-I bond lengths give rise to a strong anharmonicity.The structural transition between Cmcm and Amm2 could also contribute to the phonon scattering.
The conduction bands of CsCu 2 I 3 is relatively dispersive and has multiple valleys, which is the reason for its high σ and S, respectively, characteristics of a novel ntype thermoelectric material.POP is the dominant scattering mechanism for both Cmcm and Amm2, and PIE scattering is also considered in Amm2 because of its lack of inversion symmetry.Similar to κ latt , the electronic properties are also anisotropic (superior along the a-and b-axes).
The predicted ZT of CsCu 2 I 3 reaches 2.2 at 600 K along the b-axis (n e = 6 × 10 18 cm −3 ), comparable to the ZT of state-of-the-art thermoelectric materials.The origin of high ZT is a combination of ultra-low κ latt and high P F .η of 13.1 % is achievable when CsCu 2 I 3 is used in a thermoelectric generator (T H = 600 K, T C = 200 K).
For structure optimization, the Perdew-Burke-Ernzerhof exchange-correlation (xc) functional revised for solids (PBEsol) [54] was used with a 6 × 6 × 8 Γ-centered k-mesh, a plane-wave kinetic energy cutoff of 700 eV, and the convergence criteria set to 10 −8 eV and 10 −4 eV/ Å for the total energy and atomic forces, respectively.The elastic and dielectric constant was calculated using the finite-displacement (FD) method and density functional perturbation theory (DFPT), respectively.The bulk modulus was calculated using the Phonopy [55] code by fitting the energy-volume to the third-order Birch-Murnaghan equation of state [56].
Calculations of the electronic band structure and electron transport were done using the hybrid DFT functional of Heyd, Scuseria, and Ernzerhof (HSE06) [57].Compared to the structure optimization, a denser k-mesh of 12 × 12 × 16 was used, while the kinetic energy cutoff was lowered to 400 eV.The hole and electron effective mass, m * , was calculated using the sumo [58] code, which uses parabolic fitting by the following equation: where E(k) is the band energy as a function of the electron wavevector k, and is the reduced Plank's constant.The electronic band structure calculated above was used as the input.

B. Structure distortion
Harmonic level phonon calculations were performed using the Phonopy [55] code with VASP as the force calculator.The second-order interatomic force constants (IFCs) were computed using the supercell FD approach with a 3 × 3 × 3 k-mesh, step size of 0.01 Å.A total of 11 displacements for Cmcm and 22 displacements for Amm2 were calculated.A 2 × 2 × 3 supercell of the 12 -atom unit cell (144 atoms), was employed for both structures.The ModeMap [36] code was used to compute the displacement of the atoms, u j,l (jth atom in the lth unit cell), along an imaginary-mode eigenvector, W λ,j (λ is the phonon mode), at the Γ-point: where m j is the atomic mass, n a is the number of atoms in the supercell used to model the displacement, Q λ is the distortion amplitude, q is the phonon wavevector, and r j,l is the atomic position.Post processing was also performed using the code to map the energy, ∆U (Q), as a function of Q λ along the given W λ,j (c.f.Fig. 4).The ground-state structure, Amm2, was then obtained using the structure at the energy minimum.
C. Phonon and electron transport κ latt calculations were carried out using the Phono3py [59] code, solving the linearized Boltzmann transport equation (BTE) using the single-mode relaxation-time approximation (RTA) (Eq.( 2)).The third-order IFCs were calculated with a FD step size of 0.03 Å, and a total of 5568 displacements were considered in a 48 -atom unit cell.A q-mesh of 12 × 12 × 16 was employed to compute the lattice thermal conductivity.Graphical analysis of the modal properties were performed using the Phonopy-power-tool [42] code.Convergence tests for the lattice thermal conductivity over q-mesh, and distribution of force norms for the force sets can be found in Fig. S6.
Unlike the BoltzTraP [60] code, the AMSET [61] package uses DFT band structures to solve the BTE without the constant RTA.The characteristic scattering rate, τ e , is calculated using the Matthiessen's rule: The mode dependent scattering rates, from state |nk to state |mk + q , is calculated using Fermi's golden rule: where ε is the electron energy, δ is the Dirac delta function and g is the coupling matrix element.The electron transport properties were computed by the generalized transport coefficients: where α and β denotes Cartesian coordinates, Σ αβ (ε) is the spectral conductivity, ε F is the fermi level at a certain doping concentration and temperature, and f 0 is the Fermi-Dirac distribution.The properties are obtained as As mentioned above, the required material parameters such as the dielectric, elastic, and piezoelectric constants, phonon frequencies, and deformation potential were determined by DFT calculations (Table S1).As the valence bands are relatively flat, calculations were only conducted under n-type doping conditions, in the doping range from 10 16 to 10 21 , and the temperature range from 200 K to 600 K.The interpolation factor was set to 10 for all AMSET calculations.Convergence tests for the electron transport calculations over k-mesh and the interpolation factor can be found in Fig. S5.

FIG. 1 .
FIG. 1. Diagram for a first-principles thermoelectrics assessment workflow (total 9 steps).Steps which are optional or only required in certain cases are shown by gray boxes and arrows.
(a).The eigenvector components for the imaginary mode at the Γ-point of Cmcm are shown by arrows in Fig. 2(a), (c).Using

FIG. 3 .
FIG. 3. Phonon dispersion of CsCu 2 I 3 , (a) Cmcm and (b) Amm2 structure.The atom-projected phonon density of states is plotted on the right side of the phonon dispersion.

FIG. 4 .
FIG. 4. Potential energy surface along the eigenvector components (arrows in Fig. 2(a), (c)) for the imaginary mode at the Γ-point of CsCu 2 I 3 , Cmcm structure.Filled circles represent calculated data points, and the solid line is a fit to a polynomial function.

FIG. 10
FIG. 10.(a) Calculated figure of merit (ZT ) as a function of electron concentration and temperature.Isotropically averaged ZT are given by solid lines, and ZT along the b-axis (at 600 K) by the gray dotted line.(b) Thermodynamic efficiency (η, red), average ZT (ZT , blue), and ZT (gray) as a function of the hot side temperature, TH, of CsCu 2 I 3 , Amm2 structure.

TABLE I .
Representative works on metal halides studies for thermoelectric devices with their κ latt and ZT values.The mentioned values are for room temperature unless indicated otherwise.