3D charge and 2D phonon transports leading to high out-of-plane ZT in n-type SnSe crystals

See allHide authors and affiliations

Science  18 May 2018:
Vol. 360, Issue 6390, pp. 778-783
DOI: 10.1126/science.aaq1479

SnSe doped a different way

Heat can be converted into electricity by thermoelectric materials. Such materials are promising for use in solid-state cooling devices. A challenge for developing efficient thermoelectric materials is to ensure high electrical but low thermal conductivity. Chang et al. found that bromine doping of tin selenide (SnSe) does just this by maintaining low thermal conductivity in the out-of-plane direction of this layered material. The result is a promising n-type thermoelectric material with electrons as the charge carriers—an important step for developing thermoelectric devices from SnSe.

Science, this issue p. 778


Thermoelectric technology enables the harvest of waste heat and its direct conversion into electricity. The conversion efficiency is determined by the materials figure of merit ZT. Here we show a maximum ZT of ~2.8 ± 0.5 at 773 kelvin in n-type tin selenide (SnSe) crystals out of plane. The thermal conductivity in layered SnSe crystals is the lowest in the out-of-plane direction [two-dimensional (2D) phonon transport]. We doped SnSe with bromine to make n-type SnSe crystals with the overlapping interlayer charge density (3D charge transport). A continuous phase transition increases the symmetry and diverges two converged conduction bands. These two factors improve carrier mobility, while preserving a large Seebeck coefficient. Our findings can be applied in 2D layered materials and provide a new strategy to enhance out-of-plane electrical transport properties without degrading thermal properties.

Thermoelectric technology, which converts heat into electricity, provides a promising route to environmentally friendly power generation through the harvest of industrial waste heat (1, 2). The conversion efficiency of thermoelectric materials is determined by the dimensionless figure of merit ZT = [(S2σ)/к]T, where S, σ, к, and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively. However, the complex interrelationships among thermoelectric parameters prevent us from maximizing the ZT value and conversion efficiency (3, 4). To date, various approaches have been adopted to optimize these critical thermoelectric parameters, such as enhancing the electrical transport properties (power factor, S2σ) through engineering band structures (57), lowering the thermal conductivity through scattering all-scale length phonons (8), and seeking potential materials with low thermal conductivity (9, 10). Impressive achievements have been made in various thermoelectric systems on the basis of these strategies, including bismuth (11), lead (8, 12), tin (13) and copper (14) chalcogenides; germanium silicides (15); Zintl phase (16); skutterudite (17); half-Heusler (18); and magnesium-based systems (1921).

Over the past decade, bulk crystals with two-dimensional (2D) layered structures have been studied because of their strongly anisotropic transport features. High thermoelectric performance along the in-plane direction was primarily achieved by improving charge-carrier mobility (2224). However, the out-of-plane properties have garnered less attention because electrical transport is always impeded by the 2D interlayers. Out-of-plane thermal conductivities in 2D layered materials are sufficiently low enough that they approach the amorphous limit (25, 26). Enhancing the out-of-plane electrical properties may result in excellent thermoelectric performance in this direction.

Very low thermal conductivity due to strong anharmonic and anisotropic bonding was found along the in-plane direction of p-type SnSe crystals with a 2D layered structure (2729). After hole doping, SnSe shows an exceptionally high power factor enabled by its multiple valence bands (28, 30). These results reveal that p-type SnSe is a remarkable compound with promising thermoelectric performance. However, the discrepancy of in-plane thermal conductivity observed in fully dense SnSe crystals seems to conclude that the thermal conductivity was underestimated owing to low sample density (31). On the contrary, the ultralow thermal conductivity observed in the fully dense SnSe crystals revealed the story to be more complicated (32). The continued reports elucidate the thermal conductivity discrepancy, clarifying that the low thermal conductivity in SnSe is sensitive to the vast off-stoichiometric defects (33), much softer van der Waals–like Se–Sn bonding (34), polycrystalline oxidations (35), crystal cracks (36), and so on. These investigations on in-plane thermal conductivity are enriching the physical and chemical stories behind SnSe.

Compared to its in-plane thermal conductivity, SnSe exhibits a more steady and even lower thermal conductivity along the out-of-plane direction (27, 28, 32), which motivated us to investigate its power factor. We synthesized n-type SnSe crystals through the temperature gradient method and bromine doping (figs. S1 and S2). We found that the conduction bands of n-type SnSe have much more complex behavior owing to a temperature-dependent continuous phase transition from Pnma to Cmcm, which leads to an outstanding temperature-independent power factor and a maximum ZT (ZTmax) of ∼2.8 at 773 K along the out-of-plane direction. We obtained independent tests from third-party inspection institutions to verify the high performance and reproducibility [Fig. 1A, green line (37)].

Fig. 1 ZT values as a function of temperature and a schematic of phonon and charge transport in n- and p-type SnSe crystals along the out-of-plane direction.

(A) ZT values for p- and n-type SnSe with and without phase transition; the high performance of n-type SnSe is well reproduced by third parties (green line, test reports are provided in the supplementary materials). Inset images show the SnSe crystal structure (blue, Sn atoms; red, Se atoms) with the investigated out-of-plane direction. The typical sample cleaved along the (100) plane and the diagram show how the crystals are cut for measurements (inset images, from left to right). 1.2E19, carrier concentration of ~1.2 × 1019 cm–3. (B) Schematic out-of-plane charge and phonon transports in n- and p-type SnSe. The colored dots represent the charge densities. The gray blocks represent the two-atom-thick SnSe slabs along the out-of-plane direction (a axis) of SnSe.

The high performance we achieved for n-type SnSe is explained by two cumulative features. First, density functional theory (DFT) calculations and scanning tunneling microscopy (STM) observations indicate that delocalized Sn and Se p electrons near the conduction band minimum (CBM) contribute to more orbital overlap along the out-of-plane direction. When the carrier concentration is fixed at ~1.2 × 1019 cm–3, in contrast to p-type SnSe, the charge density of n-type SnSe overlaps to fill the crystal-structure interlayers. The overlapped charge density can facilitate electron transport through the interlayers, resulting in an expected ZTmax of ∼2.1 at 773 K for n-type SnSe. By contrast, the ZTmax is ∼0.5 at 773 K for p-type SnSe (Fig. 1A). Second, high-temperature synchrotron radiation x-ray diffraction (SR-XRD) indicates a continuous phase transition from Pnma to Cmcm starting at ~600 K before the critical temperature (800 K) in SnSe. This apparently continuous phase transition in n-type SnSe leads to an increased symmetry in the crystal structure, which is further confirmed by in situ spherical aberration–corrected transmission electron microscopy (Cs-corrected TEM). This phase transition also results in the divergence of two converged conduction bands at ~600 K. In contrast to the band convergence, the band divergence decreases the average inertial band mass and thus leads to higher carrier mobility. The changes in the band structure due to the continuous phase transition further increase ZTmax from 2.1 to 2.8 at 773 K (Fig. 1A). Collectively, our findings show that the out-of-plane electrical transport properties in n-type SnSe are comparable to those along the in-plane direction (3D charge transport) (Fig. 1B), which has rarely been observed in bulk materials with a 2D structure (38, 39). For comparison, we measured thermoelectric properties as a function of temperature along the in-plane and out-of-plane directions for both p- and n-type SnSe crystals (fig. S3).

To clarify the origin of the huge difference in the out-of-plane thermoelectric performance between the n- and p-type SnSe crystals, we compared the transport properties of the n- and p-type SnSe crystals with the same carrier concentration of ~1.2 × 1019 cm–3 (abbreviated 1.21E19, Fig. 2). The electrical conductivity of n-type SnSe is twofold higher than that of p-type SnSe (Fig. 2A), indicating a twofold-higher carrier mobility. At room temperature, the Seebeck coefficient of approximately –180 μV K–1 for n-type SnSe is lower than that of p-type SnSe, which is +210 μV K–1 (Fig. 2B), indicating a lower effective mass for the n-type crystal. Interestingly, with an increasing temperature, the magnitude of the n-type Seebeck coefficient increases faster and higher than the p-type Seebeck coefficients above ∼600 K. This indicates that the conduction band structure is much more complex than that of the valence bands as the temperature increases (28). The power factor for p-type SnSe declines monotonically with rising temperature. By contrast, the power factor for n-type SnSe preserves a high value of ~9.0 μW cm–1 K–2 over the entire temperature range. Finally, the power factor at 773 K for n-type SnSe is five times that of p-type SnSe (Fig. 2C). The carrier concentrations for n-type SnSe show a decreasing trend with increasing temperature (Fig. 2D) and a more pronounced decline than those of p-type SnSe (Fig. 2D, inset), which is consistent with the higher carrier mobility in n-type SnSe (Fig. 2E, inset). Particularly, a distinct rise in the carrier mobility above ∼600 K is observed in all n-type SnSe with different carrier concentrations (Fig. 2E), which contributes to higher electrical transport properties above 600 K. The strong anharmonic and anisotropic bonding of SnSe leads to very low thermal conductivity (27, 28, 32, 40), which is expected to be even lower along the out-of-plane direction of SnSe owing to strong interlayer phonon scattering. Indeed, both the total and lattice thermal conductivities (κtot and κlat) along the out-of-plane direction for both the n- and p-type SnSe crystals are extremely low (Fig. 2F and fig. S4), which even reach a minimum lattice thermal conductivity (κlatmin) as low as 0.18 W m–1 K–1 at 773 K. These thermoelectric transport properties show good reproducibility by varying the carrier concentration (figs. S5 and S6). Moreover, the highest performance also shows good thermal stability upon temperature changes (fig. S7) and excellent reproducibility through cross-checking in independent inspections [Fig. 2, A to C and F (37)].

Fig. 2 Thermoelectric properties as a function of temperature for the out-of-plane n- and p-type SnSe crystals.

(A) Electrical conductivity. (B) Seebeck coefficient. (C) Power factor (PF). (D) Hall carrier concentrations and (E) carrier mobilities, where both insets compare n- and p-type SnSe. (F) Total and lattice thermal conductivities. The dashed black line is the out-of-plane minimum lattice thermal conductivity. The reproduced data provided by third parties (green lines) for the high-performance n-type SnSe are also plotted for comparison.

The twofold-higher n-type out-of-plane electrical conductivity originates from the higher carrier mobility, which indicates that electron transport is facilitated through the interlayers. We investigated the charge density for both types of SnSe along both the out-of-plane (ab plane) and in-plane (bc plane) directions to determine the origins of the high carrier mobility (Fig. 3A). We investigated the density of states (DOS) near the band edges through DFT calculations [Fig. 3B, (37)]. Our calculations reveal that the anisotropies of the charge density in n- and p-type SnSe are dominated by the partial DOS of Sn (p) and Se (p), respectively. Specifically, in the valence band maximum (VBM), Se (pz) largely contributes to the total DOS, whereas Sn (px) predominately contributes to the total DOS in the CBM. These contributions indicate that the charge density tends to distribute within the in-plane direction in p-type SnSe and along the out-of-plane direction in n-type SnSe. Our DFT calculations further indicate the distinct overlaps of the electron orbitals in the out-of-plane direction of n-type SnSe, which form electrical conduction pathways (Fig. 3C). However, the charge densities mainly distribute along the in-plane direction in p-type SnSe (Fig. 3D). The features in n-type SnSe become more pronounced with increasing temperature (figs. S8 and S9). We further verify the charge-density differences between n- and p-type SnSe through scanning tunneling spectroscopy (STS) and STM images. The dI/dV curves describe the partial DOS distributed along the kx direction (41), where I is current and V is voltage, which corresponds to the out-of-plane direction in SnSe (Fig. 3E). The sharp slope near the CBM and gradual slope near the VBM are in good accordance with the DOS calculations (Fig. 3B). We visualized the charge density distribution in the bc plane using the contrast STM image and dI/dV mapping, where a large difference in charge density results in strong contrast. The low contrast in the images of n-type SnSe (Fig. 3, F and G) indicates an extended charge density distribution, whereas the stronger contrast in p-type SnSe (Fig. 3, H and I) shows a localized preference in the charge density distribution. This is consistent with the DFT calculations in the bc plane (Fig. 3, C and D). In summary, overlapping charge density fills the interlayers in n-type SnSe, explaining the high carrier mobility out of plane. By contrast, the charge density for p-type SnSe prefers to fill the in-plane intralayers (42, 43).

Fig. 3 Crystal structures, DOS, and charge density of n- and p-type SnSe.

(A) Crystal structures of SnSe in the ab and bc planes. (B) Projected DOS of SnSe near the CBM and VBM ~0.4 eV. The Fermi level is shifted to zero. The inset diagram shows the Brillouin zone of SnSe. Calculated charge densities of (C) n- and (D) p-type SnSe in the ab and bc planes, given by wave functions around ~0.2 eV for the CBM and VBM, respectively. The color scale indicates the normalized charge density. (E) STS of the undoped, n-type, and p-type SnSe crystals. The spectra are vertically shifted for clarity. STM images and corresponding dI/dV mapping for the (F and G) n- and (H and I) p-type SnSe crystals in the bc plane. Image sizes are 3 nm by 3 nm. STM and dI/dV mapping are taken at sample biases of 0.4 and –0.2 V for the n- and p-type SnSe crystals, respectively.

The dynamic structural behavior of SnSe at 800 K involves a reversible phase transition from Pnma to Cmcm, and the highly symmetric Cmcm phase can enhance carrier mobility and preserve the high power factor of SnSe (44). To directly capture the structural evolution of SnSe as a function of temperature, we conducted in situ Cs-corrected TEM heating experiments for both n- and p-type SnSe. We tilted both samples along the [010] direction (Fig. 4A). The Sn and Se columns are displayed as brighter and dimmer dots, clearly resolved from the [010] direction. At room temperature, the SnSe unit cell consists of two SnSe bilayers with Se atoms in a different planes from the Sn atoms. This lowers the symmetry of the crystal structure. With an increasing temperature, the Se atoms gradually move closer to the nearest Sn layers in n-type SnSe. We quantitatively identified the atomic column positions with a peak-finding program (37) and used the d/D ratio to determine symmetry (Fig. 4B), where d and D are the Se intralayer and Se interlayer distances, respectively (an intralayer corresponds to a two-atom-thick SnSe slab along the a axis). Initially, the Se-Se layer distance follows a d-D-d-D sequence along the out-of-plane direction, where d and D are approximately 0.25 and 0.34 nm, respectively (figs. S10 to S12). After heating, in n-type SnSe, the d/D ratio increases with increasing temperature, which indicates an increase in the symmetry (Fig. 4C). This behavior is particularly obvious above ∼600 K for n-type SnSe. We observed the same phenomenon through high-temperature SR-XRD (fig. S13). We obtained lattice parameters (fig. S14) and atomic positions (tables S1 and S2) for a range of temperatures (37). The d/D ratio we calculated from SR-XRD agrees with that from the in situ TEM, indicating the larger movement of Se atoms and thus higher symmetry in n-type SnSe. Collectively, the SR-XRD results indicate a continuous phase transition initializing at ~600 K, and the experimental Cs-corrected TEM observations confirmed that this continuous phase transition is much more pronounced in n-type SnSe. We believe enhanced carrier mobility is related to the high symmetry in the crystal structure of n-type SnSe.

Fig. 4 In situ Cs-corrected TEM, the Se displacements detected by Cs-corrected TEM, and SR-XRD of n- and p-type SnSe.

(A) High-angle annular dark-field scanning transmission electron microscopy images of n- and p-type SnSe at increasing temperatures as viewed along the b axis. Owing to the Z contrast of the Cs-corrected TEM image, brighter dots are Sn columns and dimmer dots are Se columns. (B) Atomic model of SnSe viewed along the b axis; blue atoms are Sn, and green atoms are Se. (C) The d/D ratio of the n- and p-type SnSe crystals with rising temperature. The markedly increasing d/D ratio after ∼600 K derived from both Cs-corrected TEM (dotted lines) and SR-XRD (solid lines) indicates that n-type SnSe tends to easily undergo a continuous phase transition from Pnma to Cmcm.

We performed DFT calculations based on the temperature-dependent crystal structures (figs. S15 and S16) to clarify the Seebeck coefficient enhancements above ~600 K in n-type SnSe. Our DFT calculations indicate that the lowest CBM lies in the Γ-Y direction (Fig. 5A, CBM1), whereas the second CBM is located at point Γ (Fig. 5A, CBM2). The energy offset for these two conduction bands is ~0.10 eV at room temperature, and as the temperature increases, the energy offset narrows and reaches a minimum value of ~0.04 eV at about 600 K. Above this temperature, the energy gap sharply rises and then returns to ~0.10 eV again at 773 K (Fig. 5B). Converging band structures can enhance thermoelectric performance by enhancing the effective mass through introduction of additional band degeneracy (Nv) from heavy band contributions (6, 7). However, increasing the effective mass usually deteriorates the carrier mobility (45). Distinct band structures are desirable if they can balance the effective mass and carrier mobility. We found that the conduction bands of n-type SnSe experience energy convergence and divergence within 0.10 eV as the temperature increases. We expect the conduction band divergence to improve the carrier mobility by reducing Nv. Indeed, the distinct conduction band structures in n-type SnSe lead to optimization of both the Seebeck coefficient and carrier mobility, which are critical to preserving a higher power factor (Fig. 2F).

Fig. 5 DFT-calculated band structures, Seebeck coefficients, and carrier mobilities of n-type SnSe with rising temperature.

(A) Electronic band structures at 323, 473, 623, and 773 K. (B) The changing energy gap (ΔE) between CBM1 and CBM2 at elevated temperature. Inset diagram indicates that the two conduction bands experience convergence and then divergence with rising temperature. Comparisons of the experimental and calculated (C) Seebeck coefficients and (D) carrier mobilities as a function of carrier concentration with rising temperature. The triangles are the experimental values, which are compared to the calculated values (string of purple squares) with the same carrier concentrations. Both the Seebeck coefficient and carrier mobility can be optimized through band convergence and divergence. The insets show the deviations of experimental and calculated Seebeck coefficient and carrier mobility as a function of temperature, with the blue regions indicating the temperature range before the conduction band divergence.

To investigate the Seebeck coefficient enhancements, we conducted Seebeck coefficient calculations as a function of carrier concentration at different temperatures on the basis of the single-band model (Fig. 5C). At room temperature, the experimentally observed Seebeck coefficients with different carrier concentrations are consistent with the Pisarenko relation (fig. S17), which indicates that the single-band characteristics dominate carrier transport at low temperature. However, with rising temperature, the experimental Seebeck coefficients gradually deviate to higher values compared to the calculated Seebeck coefficients (Fig. 5C, inset). The deviation maximizes at ~600 K, indicative of the greatest amount of band convergence. Above ~600 K, the contribution of CBM2 declined owing to band divergence, leading to a smaller deviation between the experimental and calculated values, which agrees with the observed considerable rise in carrier mobility at about 600 K (Fig. 5D). Considering the band convergence, the experimentally observed Seebeck coefficients in the middle temperature range agree with the calculated results. Meanwhile, the notable carrier mobility rise is attributed to the band divergence, which occurs above 600 K. Interestingly, our results indicate that the continuous phase transition that starts at 600 K can enhance the power factor and the final ZT value (fig. S18).

Utilizing the ultralow thermal conductivity of out-of-plane SnSe along with an outstanding power factor, we realized a ZTmax ∼ 2.8 at 773 K in out-of-plane n-type SnSe crystals. We initially selected the very low lattice thermal conductivity in the out-of-plane direction of SnSe crystals. Then, we optimized the carrier mobility and Seebeck coefficient by modifying the temperature-dependent crystal and band structures deriving from the continuous phase transition. Our results open prospects for new strategies to improve the out-of-plane electrical transport properties in 2D layered materials, while maintaining low thermal conductivity.

Supplementary Materials

Materials and Methods

Figs. S1 to S18

Tables S1 to S6

References (4656)

References and Notes

  1. Materials, methods, and test reports are available as supplementary materials.
Acknowledgments: The authors thank BL14B1 (Shanghai Synchrotron Radiation Facility) for the SR-XRD experiments. Funding: This work was supported by the National Natural Science Foundation of China (51571007, 51772012, 11474176, 51602143, 11574128, and 51788104), the Beijing Municipal Science and Technology Commission (Z171100002017002), the Shenzhen Peacock Plan team (KQTD2016022619565991), and the 111 Project (B17002). J.H. is grateful for the Pico Center at SUSTech, supported by the Presidential fund and Development and Reform Commission of Shenzhen Municipality, and also for support from the Natural Science Foundation of Guangdong Province (grant no. 2015A030308001), the leading talents of Guangdong Province Program (grant no. 00201517). H.Y. and Y.C. are grateful for financial support from the Early Career Scheme of the Research Grants Council (27202516). Author contributions: C.C. and L.-D.Z. synthesized the samples, designed and carried out the experiments, analyzed the results, and wrote the paper. M.W., H.Y., Y.C., and L.H. carried out the DFT calculations. C.-F.W. and J.-F.L. carried out the Hall measurements. J.-F.L. provided helpful discussion. X.W. and K.W. carried out STM and STS measurements. D.H. and J.H. conducted microscopy experiments and confirmed the thermoelectric transport properties. Y.P. confirmed the thermal transport properties. F.Z. and C.C. carried out the high-temperature SR-XRDs and Rietveld refinements. All authors conceived the experiments, analyzed the results, and coedited the manuscript. Competing interests: The authors declare no competing interests. Data and materials availability: All data are available in the manuscript or the supplementary materials. Test reports are also available in the supplementary materials.
View Abstract

Stay Connected to Science

Navigate This Article