High thermoelectric performance of environmentally friendly sodium-doped Cu 2 ZnSnS 4 single crystal: Evidence of valleytronics based strategy.

Thermoelectrics (TEs) are an important class of technologies for harvesting electric power directly from heat sources. To design high performace TE materials, valleytronics has great theoretical potential to maximize a dimensionless figure of merit ZT but has not yet been demonstrated experimentally. Pseudocubic structure approach based on valleytronics paves a new path to manipulate valley degeneracy and anisotoropy with low thermal conductivity caused by short-range lattice distortion. Here, we report a record high ZT = 1.6 around 800 K, realized in totally enviromentally benign Na-doped Cu 2 ZnSnS 4 (CZTS) single crystal. The exceptional performance comes from a high power factor while maintaining intrinsically low thermal conductivity. The results demonstrate that valleytronics is a new strategy and direction in the TE field, which takes advantage of simple material nature tuning without complex techniques.


Electronic band structure of CZTS
shows the kesterite structure of CZTS, wherein the cation layers of Cu-Sn, Cu-Zn, Cu-Sn and Cu-Zn are alternated along the c-axis. In the Cu-Zn layer, the two atoms are easily disorderd leading to short-range distortion for low thermal conductivity. The experimental crystal structure parameter η value of CZTS is 0.997 ( a = 5.455 Ǻ and c = 10.880 Ǻ), which minimizes the energy splitting parameter ΔCF. The utilization of a rational pseudo-cubic structure supports cubic-like degenerate electronic bands to be high power factor (PF) in Fig. 1b. The electronic band structure of CZTS was computed by density functional theory (DFT) and is shown in Fig. 1c. The spin-orbit interaction is included. Cubic-like valence band edges are observed as a result of the symmetry framework, which is highly degenerate at Γ point indicating an ideal character of pseudo-cubic structure. The band structure with direct bandgap can be observed. As is often the case, the DFT band gap is slighty smaller than the experimental value which we measured to be 1.6 eV for CZTS single crystal by using transient reflectivity measurements 28 . The top of the valence band is split by the crystal field in Fig. 1d. Kesterite CZTS have Γ7+8 symmetry for the topmost (v1) and second (v2) valence bands and Γ5+6 symmetry for the third band (v3) where the single state is above the twofold degenerate state with ΔCF = 0.06 eV in the vicinity of Γ point. This theoretical result is in good agreement with a pseudo-cubic approach 26 . Table 1 shows the anisotoropic effective hole masses obtained directly from the band energy dispersion.

TE properties
In this study, we fabricated samples with different compositions including a stoichiometric Cu2ZnSnS4 (sample 1), Cu-poor Cu1.9ZnSnS4 (sample 2), Cu-poor Cu1.9ZnSnS4 with Na: 0.1 mol% doped (sample 3), and 0.04 mol% doped (sample 4) by Sn-solvent traveling heater method (THM) 26 . Sodium is known to benefit CZTS PV devices as an effective dopant for enhancement of electrical properties 29 . Single crystals were cut in the transverse (⊥; perpendicular to the c-acis) and the longitudinal (∥; parallel to the c-axis) directions for thermoelectric measurements. The structural and compositional properties were investigated by powder X-ray diffraction (XRD), Raman spectroscopy, energy dispersive X-ray spectroscopy (EDX), and inductively coupled plasma atomic emission spectroscopy (ICP-AES) in Supplementary Fig. 1
The temperature dependent electrical and TE properties of CZTS single crystals from 300 K to 800 K are shown in Fig. 2 with the accuracy of TE measurements discussed in Supplementary Figs. 2-4. Consistent with our previous work on CZTS in PV devices, the electrical conductivity with a Cu-poor composition and Na-doping increased by approximately two orders of magnitude greater than the stoichiometric sample (Fig. 2a). We have reported that the carrier transport mechanism can be expressed by band conduction from valence band to defect level near room temperature 29 . The conductivity data can be described quantitatively as typical thermal activation where is pre-factor, A is the relevant activation energy associated with band conduction, and b is the Boltzmann constant. The conduction parameters are shown in Supplementary The temperature dependence of thermal conductivity, , is shown in Fig. 2d, which was calculated by the thermal diffusivity, , specific heat capacity, p , and density . The thermal diffusivity and specific heat capacity dependence on temperature are shown in Supplementary Figs. 3b-3c. Weak anisotoropy of thermal conductivity was observed which ⊥ indicates ~3% larger than ∥ . The lattice thermal concudctivity along a-axis is ~5% larger than that of c-axis in the kesterite structure from theoretical calculation based on the phonon Boltzmann transport 35 . Weak anisotropy of thermal conductivity in this study is in good agreement with theoretical study 35 37,38 . In this work, we see evidence that lattice scattering is impacted by the intrinsic complexity of the crystallographic structure. For example, consider the disorder between Cu and Zn by off-stoichiometric compositions and Na-doping. Even though these are single crystals which do not benefit from lattice thermal conductivity reduction due to grain boundary scattering, the values of at 800 K are only between 0.94 to 1.7 W/mK.
Such low values are only moderately higher than the other reported values of related polycrystalline quaternary compounds such as CZTSe and Cu2CdSnSe4 39,40 . The ability to achieve such low thermal conductivity due to the intrinsic defects in this material while maintaining good electrical transport is an unexpected improvement which can be attributed to the single crystal nature of these samples. Grain boundaries are typically known to present energy barriers of order 50-150 meV in polycrystalline chalcogenide semiconductors like CZTS 41 . Recent literature points out that continued ZT enhancement due to lattice thermal conductivity reduction is fundamentally limited without a means whereby the PF is also enhanced 42 . In light of this, the single crystal approach with a site-disordered material is promising.
Taken together, the outstanding electrical properties with relatively low thermal conductivity of sample 3 resulted an totally environmentally friendly TE material with TE figure of merit of up to ZT = 1.6 at 800 K (Fig. 3). This value is comparable to the highest ZT reported for other relating quaternary materials in Supplementary Table 5. The combined uncertainty of all measurements involved in the calculation of ZT leads to an estimated uncertainty near 30%. Our approach reveals that TE valleytronics concept is comparable with phonon-liquid electron-crystal concept discovering non-toxic earth-aboundant Cu2-xS with ZT =1.7 at 1000 K 43 .

Intrinsic cation fluctuation for low thermal conductivity
Intrinsically disordered structures, such as CZTS where the Cu and Zn cations can exchange site occupancy with little energy cost, lead to low thermal conductivity. Single crystals provide an exceptional opportunity to control and quantify the degree of this fluctuation by simply controlling single crystal cooling rates. The cation fluctuation in CZTS was studied by scanning transmission microscopy (STEM) and EDX relating to structure and chemical composition. Fig. 4a shows a STEM-based image that was subsequently chemically mapped using EDX with the point-resolved

Enhancement of electrical and TE properties
Admittance spectroscopy (AS) measurements were used to characterize the defect levels and concentrations in samples. Figure 5a shows an Arrhenius plot to verify the defect levels, which were extracted from inflection points from the AS curves in Figs. 5b-d. All parameters for AS measurement are shown in Supplementary Table 3 The Seebeck coefficient of CZTS single crystal along a-axis is large, for example as Na: 0.1 mol% sample 3, 290 μV/K at 300 K and 347 μV/K at 800 K. As mentioned above, we suggested that it is possible to tune DOS by the formation of VCu in Cu-deficient samples and Nadoping. The energetic defect DOS is obtained by converting frequency into energy by using equations (1) and (2) 45 .
Where Nt is integrated defect density, is pre-exponential factor comprising all temperature independent terms, Vbi is built-in potential, Wd is depletion width. for the ease of analyzing anisotropic effective masses along the a and c directions. The band unfolding for the Na-doped supercell were performed using Band UP code 50 .
Characterization. The structural properties were analyzed by powder X-ray diffraction (XRD; Panalytical X′Pert PRO) and Raman spectroscopy (HORIBA T64000). XRD measurement was operated under 40 kV and 40 mA using a Cu-Kα radiation source. A 514 nm Ar + laser was used in the Raman measurements and focused on the sample by an objective lens with a numerical aperture of 0.55. The laser power on the sample was 100 mW. The spectra were calibrated based on 520 cm −1 of Si peak.
The disorder structure in stoichiometric CZTS single crystal was performed by STEM (JEOL 2800) operated at 200 kV using two simultaneous solid-state EDX detectors. The spectral image acquisition was performed over a series of consecutive sub-second frames with drift correction between frames with a total acquisition time of less than 20 min. The EDX data were processed using Thermo-Scientific Image Analysis software. The X-ray emission spectra captured were quantified after subtracting the background and each of elements. The analytical certainty associated with EDX profiling is within 0.5 at.%.
The electrical conductivity and Seebeck coefficient were measured simultaneously in a helium atmosphere at 300-800 K using

Data availability
The data that support the findings of this study are available from the authors on reasonable request.