Two-Step Phase Transition in SnSe and the Origins of its High Power Factor from First Principles

Antoine Dewandre, Olle Hellman, Sandip Bhattacharya, Aldo H. Romero, Georg K. H. Madsen, and Matthieu J. Verstraete

Phys. Rev. Lett. 117, 276601 – Published 30 December 2016

Abstract

The interest in improving the thermoelectric response of bulk materials has received a boost after it has been recognized that layered materials, in particular SnSe, show a very large thermoelectric figure of merit. This result has received great attention while it is now possible to conceive other similar materials or experimental methods to improve this value. Before we can now think of engineering this material it is important we understand the basic mechanism that explains this unusual behavior, where very low thermal conductivity and a high thermopower result from a delicate balance between the crystal and electronic structure. In this Letter, we present a complete temperature evolution of the Seebeck coefficient as the material undergoes a soft crystal transformation and its consequences on other properties within SnSe by means of first-principles calculations. Our results are able to explain the full range of considered experimental temperatures.

Received 5 January 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.276601

Physics Subject Headings (PhySH)

Phase transitions Thermoelectric effects

Chalcogenides

Pseudopotentials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Antoine Dewandre¹, Olle Hellman^2,3, Sandip Bhattacharya⁴, Aldo H. Romero^5,6, Georg K. H. Madsen⁷, and Matthieu J. Verstraete¹

¹CESAM, QMAT, European Theoretical Spectroscopy Facility, Université de Liège, allée du 6 août, 19, B-4000 Liège, Belgium
²Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
³Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden
⁴ICAMS, Ruhr-Universität Bochum, 44780 Bochum, Germany
⁵Department of Physics, West Virginia University, 207 White Hall, 26506 West Virginia, USA
⁶Facultad de Ingenieria, Benemerita Universidad Autonoma de Puebla, 72570 Puebla, Pue., Mexico
⁷Institute of Materials Chemistry, TU Wien, A-1060 Vienna, Austria

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Vol. 117, Iss. 27 — 30 December 2016

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Images

Figure 1
Ball and stick model for both orthorhombic phases of SnSe. (a) Modified high- $T$ Cmcm phase; (b) distortion of the modified Cmcm structure by the unstable phonon mode at $Y$ , which leads to the stable Pnma phase; (c) low- $T$ Pnma phase.
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Figure 2
The defect formation energies versus the electronic chemical potential $μ_{e}$ are shown here for (a) the Pmna phase and for the (b) Cmcm phase in the Se rich limit. In both phases the most stable defects are the Sn vacancy, $V_{Sn}^{(2 -)}$ (intrinsic defect) which will produce holes. The slopes of $E_{d}$ versus $μ_{e}$ plots are the charges of the corresponding defects.
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Figure 3
Temperature dependence of the carrier concentration. In black, the average inverse Hall coefficient measured by Zhao et al. [1]. In green, the extrapolation determined as the carrier concentration which maximizes the Seebeck coefficient of the Cmcm phase (details in the Supplemental Material [17]). In blue, the carrier concentrations due to $V_{Sn}^{(2 -)}$ for the Pnma and Cmcm phases. In magenta, the simple thermally activated behavior, with a defect energy of 0.67 eV.
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Figure 4
Seebeck coefficients calculated with temperature-dependent carrier concentrations for three different regions of temperature. For the low-temperature region, we use the experimental structure of the Pnma phase at 298 K [50]. For the intermediate region, we used the Pnma experimental structure at 790 K [50]. For the last region, we used the Cmcm experimental structure at 825 K [50]. These calculations are compared with Ref. [1].
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Figure 5
Phonon band structure for SnSe in the Cmcm phase at different temperatures. (a) Harmonic 0 K phonons of the modified Cmcm structure where the $a$ and $b$ cell parameters are exchanged. A strong harmonic instability at the $Y$ point returns the structure to the 0 K Pnma ground state. (b) Phonons of Cmcm calculated within TDEP at 807 K and for a pressure of 4 GPa—the structure is fully stabilized.
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Figure 6
Top left panel: full phase diagram of SnSe, from the TDEP method. The experimental $T_{c}$ is recovered under a small volume contraction. Magenta and blue dots in the phase diagram: position in phase space for the metadynamics calculations. Top right panel: Gibbs free energy as a function of the metadynamics step, for 0.1 GPa at 300 and 700 K. Bottom left panel: $b / a$ ratio of the crystal as a function of the metadynamics step. Bottom right panel: scalar product of the metadynamics and DFT generalized forces, indicating whether one is being pushed in to ( $> 1$ ) or out of ( $< 1$ ) a well in the PES.
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