Thermoelectricity

# The ugly duckling

### Subjects

Single crystals of tin selenide have been shown to display, along one crystallographic direction of their high-temperature state, the highest thermoelectric efficiency of any bulk material. See Letter p.373

More than 90% of the energy we use comes from thermal processes1, which produce the bulk of the electricity generated by power plants, as well as powering aeroplanes and most cars. Heat engines have existed since the early eighteenth century, drove the Industrial Revolution and gave rise to the science of thermodynamics. Thermoelectricity was discovered about a century later2 and is based on the same thermodynamic principles that heat engines depend on, except for the fact that thermoelectric power generators use electrons, rather than steam or air, as the working fluid. A testament to the importance of these fields is the fact that progress in the thermal sciences has been unrelenting: this includes work by Zhao et al.3 on page 373 of this issue.

The second law of thermodynamics dictates that, to deliver work, heat engines must operate between a source of heat at a hot temperature (Thot) and a heat sink at a cooler temperature (Tcold). The Carnot efficiency, ηmax = 1 − (Tcold/Thot), is the upper bound for the efficiency (η) of a heat engine, where η is the ratio between the amount of work an engine does and the amount of heat it uses. A thermoelectric generator works as follows. A temperature gradient, T, across two thermoelectric materials — a semiconductor in which most of the charge carriers are electrons (n-type semiconductor) and a semiconductor that has mostly notional holes created by the absence of electrons (p-type) — creates an electric field, E, between the cold side and the hot side of each material (Fig. 1). The Seebeck coefficient, S, which is given by the ratio E/T and is negative for the n-type material and positive for the p-type, corresponds4 to the entropy of the electron divided by its charge. The two materials complete a cycle that converts the heat supplied at the hot side into electrical power. Assuming that S does not vary along the length of each thermoelectric material even though the temperature does, if this cycle were reversible it would have the Carnot efficiency.

Thermodynamically irreversible processes limit the efficiency of the cycle to a value much lower than that of the Carnot efficiency. Examples of such processes are heat conduction through the crystal lattice of atoms that constitute the semiconductors and the Joule heating that arises inside the semiconductors when the voltage produced by the electric field is used to deliver a current to an external electrical load (Fig. 1). The fraction of the Carnot efficiency of a thermoelectric cycle is quantified by the thermoelectric figure of merit ZT of the system as a whole, which is the average of the zT of the n- and p-type semiconductors, where zT = S2T/ρϰ, with ρ representing each semiconductor's electrical resistivity, ϰ its thermal conductivity and T the absolute temperature of the device. The thermal conductivity has two components: electrons carry some heat (electronic conductivity, ϰe), but most of the heat is carried by phonons, vibrations of the atoms in the crystal lattice that also transport sound (lattice conductivity, ϰlat). The goal of thermoelectric research is to discover new materials with maximum zT, by maximizing the ratio S2/ρ and minimizing ϰlat without increasing ρ.

The maximum achievable value of zT has doubled in the past 15 years5 from 1 to 2, thanks to the application of nanotechnology and quantum theory to this problem. Engineering the energy-band structure of the materials5 — for example, through the effect of quantum confinement or by enhancing interactions between the wavefunctions of impurities and of free electrons — is used to boost S2/ρ. Decreases in ϰlat can be achieved by phonon engineering5 of the semiconductors — by, for instance, nanostructuring them, generating specific localized lattice vibrations (rattling phonon modes) in them, or selecting atoms that induce chemical bonds that vibrate highly anharmonically6. For decades before Zhao and colleagues' study, which examined the thermoelectric efficiency of single crystals of tin selenide (SnSe), the record for zT was held by alloys created using several of these techniques in lead telluride7 (PbTe), a semiconductor that has a simple rock-salt crystal structure and a long history in thermoelectric technology, infrared diode lasers and radiation detectors.

In comparison to PbTe, SnSe is the ugly duckling. Chemically and structurally akin to PbTe, SnSe is lighter, has stiffer bonds and a distorted lattice. This made it seem a poor choice for thermoelectrics; indeed, SnSe has a low zT at room temperature. It was a surprise to learn that Zhao and colleagues had investigated SnSe at all, let alone to see it achieve the highest zT (2.6 along one crystallographic direction of its high-temperature phase) of any bulk material in an as-grown sample; that is, one without any addition of impurities or other optimization. SnSe has good prospects for practical use: it is not subject to the legislation that limits the use of Pb, contains only Earth-abundant elements (unlike Te), and can be prepared with good reproducibility3.

Finally, the physics of SnSe is fascinating. The authors attribute the material's low ϰlat to the high anharmonicity of its chemical bonds. A solid with purely harmonic bonds would look like a three-dimensional array of balls and springs. If an atom is pulled from its equilibrium position during the passage of a phonon, the force that the atom is subjected to is proportional to its displacement, and the proportionality constant of this relationship is called the spring constant. In an anharmonic solid, the spring constant does not remain constant with atom displacements, which has important consequences when two phonons run into each other. The presence of the first phonon then changes the value of the spring constant seen by the second phonon. The second phonon thus runs into a medium with modified elastic properties, which is more likely to reflect it. Anharmonicity results in enhanced phonon–phonon scattering, which reduces ϰlat without affecting the solid's electronic properties5,6. Therefore, this effect may well be behind the high zT of SnSe, an idea that will stimulate further experimental and theoretical work.

## References

1. 1
2. 2

Seebeck, T. J. Magnetische Polarisation der Metalle und Erze durch Temperatur-Differenz (Abhandlungen der Preussischen Akad. Wissenschaften) 265–373 (1822–23; reprinted W. Engelmann, 1895).

3. 3

Zhao, L.-D. et al. Nature 508, 373–377 (2014).

4. 4

Callen, H. B. Thermodynamics: An Introduction to the Physical Theories of Equilibrium Thermostatics and Irreversible Thermodynamics (Wiley, 1960).

5. 5

Heremans, J. P., Dresselhaus, M. S., Bell, L. E. & Morelli, D. T. Nature Nanotechnol. 8, 471–473 (2013).

6. 6

Nielsen, M. D., Ozolins, V. & Heremans, J. P. Energy Environ. Sci. 6, 570–578 (2013).

7. 7

Biswas, K. et al. Nature 489, 414–418 (2012).

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Correspondence to Joseph P. Heremans.

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Heremans, J. The ugly duckling. Nature 508, 327–328 (2014). https://doi.org/10.1038/508327a

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