Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals

Journal name:
Nature
Volume:
508,
Pages:
373–377
Date published:
DOI:
doi:10.1038/nature13184
Received
Accepted
Published online

The thermoelectric effect enables direct and reversible conversion between thermal and electrical energy, and provides a viable route for power generation from waste heat. The efficiency of thermoelectric materials is dictated by the dimensionless figure of merit, ZT (where Z is the figure of merit and T is absolute temperature), which governs the Carnot efficiency for heat conversion. Enhancements above the generally high threshold value of 2.5 have important implications for commercial deployment1, 2, especially for compounds free of Pb and Te. Here we report an unprecedented ZT of 2.6±0.3 at 923K, realized in SnSe single crystals measured along the b axis of the room-temperature orthorhombic unit cell. This material also shows a high ZT of 2.3±0.3 along the c axis but a significantly reduced ZT of 0.8±0.2 along the a axis. We attribute the remarkably high ZT along the b axis to the intrinsically ultralow lattice thermal conductivity in SnSe. The layered structure of SnSe derives from a distorted rock-salt structure, and features anomalously high Grüneisen parameters, which reflect the anharmonic and anisotropic bonding. We attribute the exceptionally low lattice thermal conductivity (0.23±0.03Wm−1K−1 at 973K) in SnSe to the anharmonicity. These findings highlight alternative strategies to nanostructuring for achieving high thermoelectric performance.

At a glance

Figures

  1. SnSe crystal structure Pnma and ZT values.
    Figure 1: SnSe crystal structure Pnma and ZT values.

    a, Crystal structure along the a axis: grey, Sn atoms; red, Se atoms. b, Highly distorted SnSe7 coordination polyhedron with three short and four long Sn–Se bonds. c, Structure along the b axis. d, Structure along the c axis. e, Main panel, ZT values along different axial directions; the ZT measurement uncertainty is about 15% (error bars). Inset images: left, a typical crystal; right, a crystal cleaved along the (l00) plane, and specimens cut along the three axes and corresponding measurement directions. Inset diagram, how crystals were cut for directional measurements; ZT values are shown on the blue, red and grey arrows; colours represent specimens oriented in different directions.

  2. Thermoelectric properties as a function of temperature for SnSe crystals.
    Figure 2: Thermoelectric properties as a function of temperature for SnSe crystals.

    a, Electrical conductivity. b, Seebeck coefficient. c, Power factor, PF. d, Total thermal conductivity, κtot. Inset, lattice thermal conductivity, κlat (same units as κtot), versus temperature (same units as main panel).

  3. High-temperature in situ TEM observations.
    Figure 3: High-temperature in situ TEM observations.

    a, Main panel, high-resolution TEM image of single-crystal SnSe (scale bar, 2nm). Bottom inset, corresponding diffraction pattern along the [011] zone axis; top inset, the line profile (distance is plotted in Å, y axis) along the dotted line AB in the main panel showing the d spacing of (100). b, Simulated crystal structures of the phase at room temperature (RT; Pnma) and at high temperature (HT; Cmcm), viewing along the [211] and [121] directions; planes (1−1−1), (−101) and (0−11) are marked by blue lines. c, Diffraction patterns obtained at different temperatures. B, zone axis. There is a difference in measured angle between (1−1−1) and (0−11) of about 2.6° between room and elevated temperatures.

  4. Theoretically calculated phonon and Gruneisen dispersions, and measured lattice thermal conductivity.
    Figure 4: Theoretically calculated phonon and Grüneisen dispersions, and measured lattice thermal conductivity.

    a, Phonon dispersion. TA, TA′, transverse acoustic phonon scattering branches; LA, longitudinal acoustic phonon scattering branch. b, Grüneisen dispersion; inset, the average Grüneisen parameters along a, b and c axes. TA, red colour; TA′, green colour; LA, blue colour. The high symmetry points in the first Brillouin zone can be found in Extended Data Fig. 4. c, The lattice thermal conductivity comparison of SnSe along the b axis (ZTmax = 2.62) and hierarchical architectured PbTe-4SrTe-2Na (ZTmax = 2.2)11.

  5. XRD measurement of SnSe on the cleavage plane, and the simulated diffraction pattern.
    Extended Data Fig. 1: XRD measurement of SnSe on the cleavage plane, and the simulated diffraction pattern.

    The (400) reflection plane indicates that the SnSe crystal is cleaved at the plane that is perpendicular to the a axis.

  6. EBSD analysis on a 1[thinsp]mm2 surface.
    Extended Data Fig. 2: EBSD analysis on a 1mm2 surface.

    a, The all-Euler map showing a large area of sample surface with homogeneous orientation. b, The inverse pole figures of samples cut along the ab, ca and bc planes, respectively. The view down the c-axis (left figure) indicates a slight deviation (~11°) from it. Scale bar, 200μm.

  7. Hall transport properties of crystalline SnSe.
    Extended Data Fig. 3: Hall transport properties of crystalline SnSe.

    a, Inverse RH (RH, Hall coefficient), and b, RH/ρ (ρ, electrical resistivity) of SnSe crystals along different axial directions. Inverse RH gives an indication of the carrier concentration; RH/ρ is related to the carrier mobility.

  8. Electronic band structures of low-temperature (Pnma) and high-temperature (Cmcm) phases of SnSe.
    Extended Data Fig. 4: Electronic band structures of low-temperature (Pnma) and high-temperature (Cmcm) phases of SnSe.

    a, SnSe at low temperature (Low-T) with the Pnma space group. b, SnSe at high temperature (High-T) with the Cmcm space group. The dashed lines indicate the position of the Fermi level (EF). Inset figures are the first Brillouin zones (BZ) of SnSe with high-symmetry points (red points) that we considered in our band structure calculations. Both phases are indirect-bandgap (Eg) compounds. For the low-temperature phase, the indirect bandgap is along ΓY in its BZ; for the high-temperature phase, the indirect bandgap is from a point within the ΓP direction to the Z point in its BZ.

  9. Bandgap of SnSe at room temperature.
    Extended Data Fig. 5: Bandgap of SnSe at room temperature.

    Optical absorption spectrum (black trace) and energy bandgap (x-axis intercept) indicate a bandgap of 0.86eV (red) of SnSe at room temperature. See Methods for details of α and S.

  10. Thermoelectric properties as a function of temperature for crystalline SnSe along different directions.
    Extended Data Fig. 6: Thermoelectric properties as a function of temperature for crystalline SnSe along different directions.

    a, Thermal diffusivity. b, Heat capacity. c, Electronic thermal conductivity. d, The ratio of lattice thermal conductivity (κlat) to total thermal conductivity (κtot). The Lorenz number (L) used for obtaining κlat (κlat = κtotσLT, where σ is the electrical conductivity and T is absolute temperature) was approximately equal to 1.5×10−8V2K−2 since the undoped SnSe is a non-degenerate semiconductor; the ratio of κlat to κtot indicates that κtot is dominated by phonon transport.

  11. High-resolution TEM images of single-crystal SnSe along four zone axes, and SAD along a low-order zone axis (in insets).
    Extended Data Fig. 7: High-resolution TEM images of single-crystal SnSe along four zone axes, and SAD along a low-order zone axis (in insets).

    a, Along the [100] direction. b, Along the [201] direction. c, Along the [211] direction. d, Along the [021] direction. e, Electron diffraction pattern along the [001] direction. f, Electron diffraction pattern along the [010] direction. The combination of all six figures provides strong evidence of the single-crystal orthorhombic layered structure of SnSe.

  12. Simulated SADs for SnSe.
    Extended Data Fig. 8: Simulated SADs for SnSe.

    a, Room-temperature (RT; Pnma) phase; b, high-temperature (HT; Cmcm) phase. B, zone axis. Note is used here to indicate −1.

  13. Differential thermal analysis of SnSe.
    Extended Data Fig. 9: Differential thermal analysis of SnSe.

    DTA measurements showing two heating and cooling cycles. DTA results indicate that SnSe appears to melt congruently; one endothermic peak is observed at 881°C on the heating curve and one exothermic peak is observed at 868°C on the cooling curve. Two heating–cooling cycles indicate the same melting and crystallization point for a given sample, consistent with high purity. Heat flow is represented as a μV signal, plotted on the y axis.

  14. Reproducibility, and thermoelectric properties as a function of temperature, for seven samples of SnSe crystals along the b axis.
    Extended Data Fig. 10: Reproducibility, and thermoelectric properties as a function of temperature, for seven samples of SnSe crystals along the b axis.

    a, Electrical conductivity. b, Seebeck coefficient. c, Power factor. d, Total thermal conductivity. e, ZT; error bars are ±15%.

Tables

  1. Transverse (TA/TA/') and longitudinal (LA) Debye temperatures ([Theta]), phonon velocities (v) and Gruneisen parameters ([ggr]) along a, b and c axes in the low-temperature SnSe phase.
    Extended Data Table 1: Transverse (TA/TA’) and longitudinal (LA) Debye temperatures (Θ), phonon velocities (v) and Grüneisen parameters (γ) along a, b and c axes in the low-temperature SnSe phase.

References

  1. Heremans, J. P., Dresselhaus, M. S., Bell, L. E. & Morelli, D. T. When thermoelectrics reached the nanoscale. Nature Nanotechnol. 8, 471473 (2013)
  2. Zhao, L. D., Dravid, V. P. & Kanatzidis, M. G. The panoscopic approach to high performance thermoelectrics. Energ. Environ. Sci. 7, 251268 (2014)
  3. Snyder, G. J. & Toberer, E. S. Complex thermoelectric materials. Nature Mater. 7, 105114 (2008)
  4. Dresselhaus, M. S. et al. New directions for low-dimensional thermoelectric materials. Adv. Mater. 19, 10431053 (2007)
  5. Heremans, J. P. et al. Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states. Science 321, 554557 (2008)
  6. Pei, Y. et al. Convergence of electronic bands for high performance bulk thermoelectrics. Nature 473, 6669 (2011)
  7. Liu, W. et al. Convergence of conduction bands as a means of enhancing thermoelectric performance of n-type Mg2Si1-xSnx solid solutions. Phys. Rev. Lett. 108, 166601 (2012)
  8. Hicks, L. D. & Dresselhaus, M. S. Effect of quantum-well structures on the thermoelectric figure of merit. Phys. Rev. B 47, 1272712731 (1993)
  9. Heremans, J. P., Thrush, C. M. & Morelli, D. T. Thermopower enhancement in lead telluride nanostructures. Phys. Rev. B 70, 115334 (2004)
  10. Hsu, K. F. et al. Cubic AgPbmSbTe2+m: bulk thermoelectric materials with high figure of merit. Science 303, 818821 (2004)
  11. Biswas, K. et al. High-performance bulk thermoelectrics with all-scale hierarchical architectures. Nature 489, 414418 (2012)
  12. Biswas, K. et al. Strained endotaxial nanostructures with high thermoelectric figure of merit. Nature Chem. 3, 160166 (2011)
  13. Zhao, L. D. et al. High thermoelectric performance via hierarchical compositionally alloyed nanostructures. J. Am. Chem. Soc. 135, 73647370 (2013)
  14. Zhao, L. D. et al. Raising the thermoelectric performance of p-type PbS with endotaxial nanostructuring and valence-band offset engineering using CdS and ZnS. J. Am. Chem. Soc. 134, 1632716336 (2012)
  15. Brown, S. R., Kauzlarich, S. M., Gascoin, F. & Snyder, G. J. Yb14MnSb11: new high efficiency thermoelectric material for power generation. Chem. Mater. 18, 18731877 (2006)
  16. Kurosaki, K., Kosuga, A., Muta, H., Uno, M. & Yamanaka, S. Ag9TITe5: a high-performance thermoelectric bulk material with extremely low thermal conductivity. Appl. Phys. Lett. 87, 061919 (2005)
  17. Rhyee, J.-S. et al. Peierls distortion as a route to high thermoelectric performance in In4Se3-δ crystals. Nature 459, 965968 (2009)
  18. Yu, J. G., Yue, A. S. & Stafsudd, O. M. Growth and electronic properties of the SnSe semiconductor. J. Cryst. Growth 54, 248252 (1981)
  19. Wasscher, J. D., Albers, W. & Haas, C. Simple evaluation of the maximum thermoelectric figure of merit, with application to mixed crystals SnS1-xSex. Solid-State Electron. 6, 261264 (1963)
  20. Peters, M. J. & McNeil, L. E. High-pressure Mossbauer study of SnSe. Phys. Rev. B 41, 58935897 (1990)
  21. Chattopadhyay, T., Pannetier, J. & Vonschnering, H. G. Neutron-diffraction study of the structural phase-transition in SnS and SnSe. J. Phys. Chem. Solids 47, 879885 (1986)
  22. Baumgardner, W. J., Choi, J. J., Lim, Y.-F. & Hanrath, T. SnSe nanocrystals: synthesis, structure, optical properties, and surface chemistry. J. Am. Chem. Soc. 132, 95199521 (2010)
  23. Morelli, D. T., Jovovic, V. & Heremans, J. P. Intrinsically minimal thermal conductivity in cubic I-V-VI2 semiconductors. Phys. Rev. Lett. 101, 035901 (2008)
  24. Fultz, B. & Howe, J. M. Transmission Electron Microscopy and Diffractometry of Materials (Springer, 2012)
  25. Nielsen, M. D., Ozolins, V. & Heremans, J. P. Lone pair electrons minimize lattice thermal conductivity. Energ. Environ. Sci. 6, 570578 (2013)
  26. Zhang, Y. S. et al. First-principles description of anomalously low lattice thermal conductivity in thermoelectric Cu-Sb-Se ternary semiconductors. Phys. Rev. B 85, 054306 (2012)
  27. Slack, G. A. in Solid State Physics (ed. Seitz, F. et al.) 171 (Academic, 1979)
  28. Clarke, D. T. Materials selection guidelines for low thermal conductivity thermal barrier coatings. Surf. Coat. Technol. 163–164, 6774 (2003)
  29. Cahill, D. G., Watson, S. K. & Pohl, R. O. Lower limit to the thermal conductivity of disordered crystals. Phys. Rev. B 46, 61316140 (1992)
  30. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 17581775 (1999)
  31. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 38653868 (1996)
  32. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-Zone integrations. Phys. Rev. B 13, 51885192 (1976)
  33. van de Walle, A., Asta, M. & Ceder, G. The alloy theoretical automated toolkit: a user guide. Calphad 26, 539553 (2002)
  34. Cahill, D. G., Watson, S. K. & Pohl, R. O. Lower limit to the thermal conductivity of disordered crystals. Phys. Rev. B 46, 61316140 (1992)
  35. Chattopadhyay, T., Pannetier, J. & Vonschnering, H. G. Neutron-diffraction study of the structural phase-transition in SnS and SnSe. J. Phys. Chem. Solids 47, 879885 (1986)
  36. Baumgardner, W. J., Choi, J. J., Lim, Y.-F. & Hanrath, T. SnSe nanocrystals: synthesis, structure, optical properties, and surface chemistry. J. Am. Chem. Soc. 132, 95199521 (2010)

Download references

Author information

Affiliations

  1. Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA

    • Li-Dong Zhao,
    • Gangjian Tan &
    • Mercouri G. Kanatzidis
  2. Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA

    • Shih-Han Lo,
    • Yongsheng Zhang,
    • C. Wolverton &
    • Vinayak P. Dravid
  3. Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

    • Hui Sun &
    • Ctirad Uher

Contributions

L.-D.Z. synthesized the samples, designed and carried out thermoelectric experiments, and wrote the paper. S.-H.L. and V.P.D. performed the TEM characterizations. Y.Z. carried out the calculations. H.S. and C.U. carried out the Hall measurements. G.T. helped with sample synthesis. L.-D.Z., S.-H.L., Y.Z., H.S., G.T., C.U., C.W., V.P.D. and M.G.K. conceived the experiments, analysed the results and co-edited the manuscript. S.-H.L. and Y.Z. contributed equally.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Extended data figures and tables

Extended Data Figures

  1. Extended Data Figure 1: XRD measurement of SnSe on the cleavage plane, and the simulated diffraction pattern. (146 KB)

    The (400) reflection plane indicates that the SnSe crystal is cleaved at the plane that is perpendicular to the a axis.

  2. Extended Data Figure 2: EBSD analysis on a 1mm2 surface. (341 KB)

    a, The all-Euler map showing a large area of sample surface with homogeneous orientation. b, The inverse pole figures of samples cut along the ab, ca and bc planes, respectively. The view down the c-axis (left figure) indicates a slight deviation (~11°) from it. Scale bar, 200μm.

  3. Extended Data Figure 3: Hall transport properties of crystalline SnSe. (137 KB)

    a, Inverse RH (RH, Hall coefficient), and b, RH/ρ (ρ, electrical resistivity) of SnSe crystals along different axial directions. Inverse RH gives an indication of the carrier concentration; RH/ρ is related to the carrier mobility.

  4. Extended Data Figure 4: Electronic band structures of low-temperature (Pnma) and high-temperature (Cmcm) phases of SnSe. (322 KB)

    a, SnSe at low temperature (Low-T) with the Pnma space group. b, SnSe at high temperature (High-T) with the Cmcm space group. The dashed lines indicate the position of the Fermi level (EF). Inset figures are the first Brillouin zones (BZ) of SnSe with high-symmetry points (red points) that we considered in our band structure calculations. Both phases are indirect-bandgap (Eg) compounds. For the low-temperature phase, the indirect bandgap is along ΓY in its BZ; for the high-temperature phase, the indirect bandgap is from a point within the ΓP direction to the Z point in its BZ.

  5. Extended Data Figure 5: Bandgap of SnSe at room temperature. (85 KB)

    Optical absorption spectrum (black trace) and energy bandgap (x-axis intercept) indicate a bandgap of 0.86eV (red) of SnSe at room temperature. See Methods for details of α and S.

  6. Extended Data Figure 6: Thermoelectric properties as a function of temperature for crystalline SnSe along different directions. (258 KB)

    a, Thermal diffusivity. b, Heat capacity. c, Electronic thermal conductivity. d, The ratio of lattice thermal conductivity (κlat) to total thermal conductivity (κtot). The Lorenz number (L) used for obtaining κlat (κlat = κtotσLT, where σ is the electrical conductivity and T is absolute temperature) was approximately equal to 1.5×10−8V2K−2 since the undoped SnSe is a non-degenerate semiconductor; the ratio of κlat to κtot indicates that κtot is dominated by phonon transport.

  7. Extended Data Figure 7: High-resolution TEM images of single-crystal SnSe along four zone axes, and SAD along a low-order zone axis (in insets). (692 KB)

    a, Along the [100] direction. b, Along the [201] direction. c, Along the [211] direction. d, Along the [021] direction. e, Electron diffraction pattern along the [001] direction. f, Electron diffraction pattern along the [010] direction. The combination of all six figures provides strong evidence of the single-crystal orthorhombic layered structure of SnSe.

  8. Extended Data Figure 8: Simulated SADs for SnSe. (109 KB)

    a, Room-temperature (RT; Pnma) phase; b, high-temperature (HT; Cmcm) phase. B, zone axis. Note is used here to indicate −1.

  9. Extended Data Figure 9: Differential thermal analysis of SnSe. (166 KB)

    DTA measurements showing two heating and cooling cycles. DTA results indicate that SnSe appears to melt congruently; one endothermic peak is observed at 881°C on the heating curve and one exothermic peak is observed at 868°C on the cooling curve. Two heating–cooling cycles indicate the same melting and crystallization point for a given sample, consistent with high purity. Heat flow is represented as a μV signal, plotted on the y axis.

  10. Extended Data Figure 10: Reproducibility, and thermoelectric properties as a function of temperature, for seven samples of SnSe crystals along the b axis. (598 KB)

    a, Electrical conductivity. b, Seebeck coefficient. c, Power factor. d, Total thermal conductivity. e, ZT; error bars are ±15%.

Extended Data Tables

  1. Extended Data Table 1: Transverse (TA/TA’) and longitudinal (LA) Debye temperatures (Θ), phonon velocities (v) and Grüneisen parameters (γ) along a, b and c axes in the low-temperature SnSe phase. (118 KB)

Additional data