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Anharmonic Convergence: Tuning Two Dials on Phonons for High zT in p-type PbTe
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Anharmonic Convergence: Tuning Two Dials on Phonons for High zT in p-type PbTe Jeffrey J. Urban1,* Thermoelectric materials development is a complex balancing act between electronic and thermal transport properties, which often have opposing optimization strategies. Researchers are always seeking new options for tailoring thermoelectric materials. In this issue of Joule, Pei, Ge, and colleagues unveil a new twopronged attack for reducing thermal conductivity without perturbing electrical conductivity. This approach, yielding high zT values exceeding 2.5 at 900 K, should inspire similar approaches in other common thermoelectric materials. In this issue of Joule, the groups of Yanzhong Pei and Binghui Ge describe a two-pronged strategy for enhancing thermoelectric performance by decreasing thermal conductivity through strain engineering1 without degrading electronic transport. Traditionally, lattice thermal conductivity suppression has been realized via one of two predominant strategies: (1) reduction of grain size below a median phonon mean free path or (2) introduction of heteroatoms of contrasting mass as point scatterers.2 However, these approaches often detract substantially from the electronic characteristics of the thermoelectrics as well. Here, the authors are able to install thermodynamically stable in-grain dislocations into PbTe alloys, thereby disrupting lattice thermal conductivity without harming electrical transport. This achievement has enabled remarkable zT values exceeding 2.5 at 900 K that remain stable over >1 month.3 Thermoelectric conversion of temperature gradients directly into electricity is often benchmarked by a unitless figure of merit, ZT, which encompasses the balance of electrical transport (S2s, where S is the Seebeck coefficient or thermovoltage, and s is the electrical
conductivity; this product is to be maximized) and thermal transport (k, the thermal conductivity; to be minimized) characteristics needed for high performance.4 Historically, commercially successful thermoelectrics have been realized by taking bulk narrow-band-gap semiconductors like PbTe or Bi2Te3 and doping them to optimize the electrical characteristics, while simultaneously nanostructuring them to minimize lattice thermal conductivity. However, most thermoelectric development along these lines is a teetertotter of tradeoffs, where researchers aim to degrade electrical transport properties only a bit while making larger gains in minimization of lattice thermal conductivity. Rarely can a material be engineered to make performance gains in one set of transport phenomena without making sizable sacrifices in a competing set of transport values; thus emerges an engineering tension between S, s, and k that has playfully been called the ‘‘Bermuda triangle’’ of thermoelectrics. In this issue of Joule, however, Pei, Ge, and co-workers have apparently navigated the Bermuda triangle and successfully optimized both electrical and thermal transport in one material. They
1180 Joule 3, 1180–1189, May 15, 2019 ª 2019 Elsevier Inc.
have taken a multifaceted approach to optimizing zT in p-type PbTe alloys, specifically Na0.03Eu0.03Sn0.02Pb0.92Te. To maximize the electronic power factor (S2s), they have used band convergence, which is a well-known phenomenon in PbTe to increase the density-of-states effective mass (and, consequently, the Seebeck coefficient). This has previously been reported to increase the zT of p-type PbTe1-xSex alloys up to 1.8.5 The new innovation in this report is the ability to perform this band convergence to boost electronic characteristics while also incorporating a ‘‘two-knob’’ strategy to diminish lattice thermal conductivity (Kl) at the same time. Heat in semiconductor thermoelectrics is largely carried by quantized lattice vibrational excitations called phonons. These quantized lattice waves, at the atomistic scale, represent periodic oscillations of neighboring atoms toward and away from each other. The basic set of lattice vibrations present in a solid (often depicted in phonon frequency versus wavevector plots) can be approximated by a simple harmonic oscillator picture, given the location and mass of each of the atoms and strength of their springs (force constant). However, this perfect crystal never exists in reality (and is a perfect thermal conductor, besides), so researchers in thermoelectrics are continually aiming to introduce mechanisms to lower the lattice contribution to thermal conductivity as far as possible. In essence, there are two physical mechanisms that researchers rely on heavily to reduce Kl: bond anharmonicity (acting on the force constant term) and point scattering (acting on the mass term). Here, as highlighted in Figure 1, the authors have cleverly
1The
Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA *Correspondence: [email protected] https://doi.org/10.1016/j.joule.2019.04.014
Figure 1. Influence of Anharmonicity and Strain Effects on Phonons in PbTe Fluctuations in both bonding and mass promote phonon-phonon scattering and low lattice thermal conductivity. Reproduced from Wu et al. 1
designed a system to allow dopants to increase phonon scattering via both mechanisms simultaneously. In the simple mass-spring picture, lattice anharmonicity promotes phonon-phonon scattering by changing the force constant dynamically6 while periodic lattice strains increase phonon-phonon scattering by introducing fluctuations in the mass term. Thus, this combination of anharmonicity and strain engineering in one material has a profound impact on thermal conductivity. Indeed, the authors measure their lattice thermal conductivity to be below 1 W/mK, which approaches the theoretical amorphous limit for the minimum thermal conductivity in this material. One of the most compelling aspects of this approach is that all of this substitution, strain, and compositional and microstructural variation appears to
have so little impact on the electronic carriers. The authors report electronic mobilities that apparently vary little with temperature and are not massively diminished by these morphological changes, hovering 25 cm2/Vs. In sum, this yields an impressive p-type zT of >2.5 at 900 K. This is on par with many of the best-in-class lab-scale thermoelectrics around now, which are around 2.8 or so and rely on other physics to achieve this.
law bounding ZT (an infinite ZT simply recaptures the efficiency of a standard thermal Carnot engine), and thus our shortcoming as a community to find these optimizations has stood as a scientific challenge to the field. Over the past 15 years, however, there have been many breakthroughs on this front, and it is now routine to report lab-scale material values of zT > 1, which used to be a holy grail of sorts. These are very optimistic times for thermoelectrics.
While an impressive feat, it remains to be seen how generalizable and stable this phenomenon is. The authors report results over 1,000 h, which is commendable, but this amounts to roughly a week of performance. Thermoelectrics operate under conditions of large temperature fluctuations and must be reliable on the order of decades to be cost-sensible. Moreover, the authors report this effect for p-type PbTe alloys. However, PbTe has a rather tame crystal structure (cubic) among thermoelectrics (although its band structure is notably non-parabolic), many of which are very low symmetry and/or intrinsically low dimensional (e.g., Bi2Te3, SnTe). It is unclear how well these strategies for PbTe will translate to other materials, although this set of results is so promising that it should inspire other researchers to pursue this concept.
ACKNOWLEDGMENTS
More broadly, it is encouraging to see an expanding community of researchers realizing thermoelectric materials with zT values that exceed 2, and even 2.5. While challenging, there is no physical
5. Pei, Y., Shi, X., LaLonde, A., Wang, H., Chen, L., and Snyder, G.J. (2011). Convergence of electronic bands for high performance bulk thermoelectrics. Nature 473, 66–69.
This work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. 1. Wu, Y., Chen, Z., Nan, P., Xiong, F., Lin, S., Zhang, X., Chen, Y., Chen, L., Ge, B., and Pei, Y. (2019). Lattice Strain Advances Thermoelectrics. Joule 3, 1–13. 2. Urban, J.J. (2015). Prospects for thermoelectricity in quantum dot hybrid arrays. Nat. Nanotechnol. 10, 997–1001. 3. Thermoelectric devices require both p-type and n-type thermoelectric materials to be wired up, electrically in series and thermally in parallel. Individual materials cannot act as thermoelectric devices. To make this distinction explicit in research, often lowercase zT is used to describe developments in singleleg (i.e., p-type or n-type) materials, and uppercase ZT is used to discuss the performance of thermoelectric devices. We follow this convention in the article. 4. Shakouri, A. (2011). Recent developments in semiconductor thermoelectric physics and materials. Annu. Rev. Mater. Res. 41, 399–431.
6. Heremans, J.P. (2015). The anharmonicity blacksmith. Nat. Phys. 11, 990–991.
Joule 3, 1180–1189, May 15, 2019 1181
Anharmonic Convergence: Tuning Two Dials on Phonons for High zT in p-type PbTe Jeffrey J. Urban1,* Thermoelectric materials development is a complex balancing act between electronic and thermal transport properties, which often have opposing optimization strategies. Researchers are always seeking new options for tailoring thermoelectric materials. In this issue of Joule, Pei, Ge, and colleagues unveil a new twopronged attack for reducing thermal conductivity without perturbing electrical conductivity. This approach, yielding high zT values exceeding 2.5 at 900 K, should inspire similar approaches in other common thermoelectric materials. In this issue of Joule, the groups of Yanzhong Pei and Binghui Ge describe a two-pronged strategy for enhancing thermoelectric performance by decreasing thermal conductivity through strain engineering1 without degrading electronic transport. Traditionally, lattice thermal conductivity suppression has been realized via one of two predominant strategies: (1) reduction of grain size below a median phonon mean free path or (2) introduction of heteroatoms of contrasting mass as point scatterers.2 However, these approaches often detract substantially from the electronic characteristics of the thermoelectrics as well. Here, the authors are able to install thermodynamically stable in-grain dislocations into PbTe alloys, thereby disrupting lattice thermal conductivity without harming electrical transport. This achievement has enabled remarkable zT values exceeding 2.5 at 900 K that remain stable over >1 month.3 Thermoelectric conversion of temperature gradients directly into electricity is often benchmarked by a unitless figure of merit, ZT, which encompasses the balance of electrical transport (S2s, where S is the Seebeck coefficient or thermovoltage, and s is the electrical
conductivity; this product is to be maximized) and thermal transport (k, the thermal conductivity; to be minimized) characteristics needed for high performance.4 Historically, commercially successful thermoelectrics have been realized by taking bulk narrow-band-gap semiconductors like PbTe or Bi2Te3 and doping them to optimize the electrical characteristics, while simultaneously nanostructuring them to minimize lattice thermal conductivity. However, most thermoelectric development along these lines is a teetertotter of tradeoffs, where researchers aim to degrade electrical transport properties only a bit while making larger gains in minimization of lattice thermal conductivity. Rarely can a material be engineered to make performance gains in one set of transport phenomena without making sizable sacrifices in a competing set of transport values; thus emerges an engineering tension between S, s, and k that has playfully been called the ‘‘Bermuda triangle’’ of thermoelectrics. In this issue of Joule, however, Pei, Ge, and co-workers have apparently navigated the Bermuda triangle and successfully optimized both electrical and thermal transport in one material. They
1180 Joule 3, 1180–1189, May 15, 2019 ª 2019 Elsevier Inc.
have taken a multifaceted approach to optimizing zT in p-type PbTe alloys, specifically Na0.03Eu0.03Sn0.02Pb0.92Te. To maximize the electronic power factor (S2s), they have used band convergence, which is a well-known phenomenon in PbTe to increase the density-of-states effective mass (and, consequently, the Seebeck coefficient). This has previously been reported to increase the zT of p-type PbTe1-xSex alloys up to 1.8.5 The new innovation in this report is the ability to perform this band convergence to boost electronic characteristics while also incorporating a ‘‘two-knob’’ strategy to diminish lattice thermal conductivity (Kl) at the same time. Heat in semiconductor thermoelectrics is largely carried by quantized lattice vibrational excitations called phonons. These quantized lattice waves, at the atomistic scale, represent periodic oscillations of neighboring atoms toward and away from each other. The basic set of lattice vibrations present in a solid (often depicted in phonon frequency versus wavevector plots) can be approximated by a simple harmonic oscillator picture, given the location and mass of each of the atoms and strength of their springs (force constant). However, this perfect crystal never exists in reality (and is a perfect thermal conductor, besides), so researchers in thermoelectrics are continually aiming to introduce mechanisms to lower the lattice contribution to thermal conductivity as far as possible. In essence, there are two physical mechanisms that researchers rely on heavily to reduce Kl: bond anharmonicity (acting on the force constant term) and point scattering (acting on the mass term). Here, as highlighted in Figure 1, the authors have cleverly
1The
Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA *Correspondence: [email protected] https://doi.org/10.1016/j.joule.2019.04.014
Figure 1. Influence of Anharmonicity and Strain Effects on Phonons in PbTe Fluctuations in both bonding and mass promote phonon-phonon scattering and low lattice thermal conductivity. Reproduced from Wu et al. 1
designed a system to allow dopants to increase phonon scattering via both mechanisms simultaneously. In the simple mass-spring picture, lattice anharmonicity promotes phonon-phonon scattering by changing the force constant dynamically6 while periodic lattice strains increase phonon-phonon scattering by introducing fluctuations in the mass term. Thus, this combination of anharmonicity and strain engineering in one material has a profound impact on thermal conductivity. Indeed, the authors measure their lattice thermal conductivity to be below 1 W/mK, which approaches the theoretical amorphous limit for the minimum thermal conductivity in this material. One of the most compelling aspects of this approach is that all of this substitution, strain, and compositional and microstructural variation appears to
have so little impact on the electronic carriers. The authors report electronic mobilities that apparently vary little with temperature and are not massively diminished by these morphological changes, hovering 25 cm2/Vs. In sum, this yields an impressive p-type zT of >2.5 at 900 K. This is on par with many of the best-in-class lab-scale thermoelectrics around now, which are around 2.8 or so and rely on other physics to achieve this.
law bounding ZT (an infinite ZT simply recaptures the efficiency of a standard thermal Carnot engine), and thus our shortcoming as a community to find these optimizations has stood as a scientific challenge to the field. Over the past 15 years, however, there have been many breakthroughs on this front, and it is now routine to report lab-scale material values of zT > 1, which used to be a holy grail of sorts. These are very optimistic times for thermoelectrics.
While an impressive feat, it remains to be seen how generalizable and stable this phenomenon is. The authors report results over 1,000 h, which is commendable, but this amounts to roughly a week of performance. Thermoelectrics operate under conditions of large temperature fluctuations and must be reliable on the order of decades to be cost-sensible. Moreover, the authors report this effect for p-type PbTe alloys. However, PbTe has a rather tame crystal structure (cubic) among thermoelectrics (although its band structure is notably non-parabolic), many of which are very low symmetry and/or intrinsically low dimensional (e.g., Bi2Te3, SnTe). It is unclear how well these strategies for PbTe will translate to other materials, although this set of results is so promising that it should inspire other researchers to pursue this concept.
ACKNOWLEDGMENTS
More broadly, it is encouraging to see an expanding community of researchers realizing thermoelectric materials with zT values that exceed 2, and even 2.5. While challenging, there is no physical
5. Pei, Y., Shi, X., LaLonde, A., Wang, H., Chen, L., and Snyder, G.J. (2011). Convergence of electronic bands for high performance bulk thermoelectrics. Nature 473, 66–69.
This work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. 1. Wu, Y., Chen, Z., Nan, P., Xiong, F., Lin, S., Zhang, X., Chen, Y., Chen, L., Ge, B., and Pei, Y. (2019). Lattice Strain Advances Thermoelectrics. Joule 3, 1–13. 2. Urban, J.J. (2015). Prospects for thermoelectricity in quantum dot hybrid arrays. Nat. Nanotechnol. 10, 997–1001. 3. Thermoelectric devices require both p-type and n-type thermoelectric materials to be wired up, electrically in series and thermally in parallel. Individual materials cannot act as thermoelectric devices. To make this distinction explicit in research, often lowercase zT is used to describe developments in singleleg (i.e., p-type or n-type) materials, and uppercase ZT is used to discuss the performance of thermoelectric devices. We follow this convention in the article. 4. Shakouri, A. (2011). Recent developments in semiconductor thermoelectric physics and materials. Annu. Rev. Mater. Res. 41, 399–431.
6. Heremans, J.P. (2015). The anharmonicity blacksmith. Nat. Phys. 11, 990–991.
Joule 3, 1180–1189, May 15, 2019 1181