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  • Wang, Heng*; and Pan, Zhenyu "Performance Optimization of Thermoelectric Devices and its Dependence on Materials Properties", Materials Lab 1, 220053 (2022).


In this perspective, we provided in depth discussion on a few issues regarding the design and performance of thermoelectric cooling devices. We pointed out a few notions that were often mistaken: 1) only the coefficient of performance (COP) is the key index that fundamental device design should focus on. others including the cooling power are device specific adjustments for particular applications. 2) the shapes of legs have can't make COP better. 3) given the same temperatures on each side of device, COP only depends on z (zT) and the seebeck coefficient. In many but not all cases, higher z means higher COP. 4) because COP can also be affected by the seebeck coefficient, it is possible to design segmented legs to achieve higher COP without having higher z (zT), even though the gain is not as big as previously advocated.

  • Wang, Heng*; Gurunathan, Ramya; Fu, Chenguang; Cui, Runzi; Zhu, Tiejun; and Snyder, G. Jeffrey, "Thermoelectric transport effects beyond single parabolic band and acoustic phonon scattering", Materials Advances 3, 734 (2022).


In thermoelectric materials research, single parabolic band with acoustic phonon scattering is often used in modeling to fit experimental data and gain insights about different material systems.  However, this has become increasingly insufficient to understand high-performance thermoelectrics where the charge transport is more complex. In this invited review, we discussed three cases where modeling can be done more accurately, providing rational strategies for research design. These include: 1) point defects, 2) systems with multiple sets of conduction or valence bands, which are not necessarily aligned (converged), 3) resonant dopants. 

  • Pan, Zhenyu; Cui, Runzi; Xiao, Xudong and Wang, Heng*, "Material pairing and selection considerations for thermoelectric cooling devices with components dissimilar to Bi2Te3 based alloys", Materials Today Physics 20, 100457 (2021).

Bi2Te3 based alloys are the materials used in essentially all commercial thermoelectric coolers (TECs) today. Even though they offer the best performance available, these devices are likely not the best candidate when factors such as impact resistance, system size and weight, or materials cost, are critical. New TECs made of deformable materials, given some moderate performance, would be promising alternatives. In this work, we used a numerical method based on the concept of relative current to illustrate the pairing principles when choosing candidate for new TECs, for example: 1) device performance is only determined by zT when the two legs have similar zTs. 2) when the two legs have different zTs, the better leg should have higher Seebeck coefficient for best performance, the other leg, might opt for lower Seebeck coefficient, instead of best zT. 3) even a low zT of 0.2 (n-type) is meaningful for pairing, delivering better performance than a uni-couple design. 4) On the fundamental level, the coefficient of performance COP is the only metric for performance, even when efficiency is not the primary concern for certain applications, and large cooling power is more critical.  


  • Pan, Zhenyu; Zhu, Zheng; Yang, Fan; Sahu, Ayaskanta; Urban, Jeffrey J. and Wang, Heng*, "Evaluating the ratio of electron and hole mobilities from a single bulk sample using Photo-Seebeck effect", Materials Today Physics 17, 100331 (2021).


We are all used to thermoelectric effects when a material is under thermal equilibrium, but what about when extra carriers are excited by photons? Just as the electrical conductivity would change in many semiconductors when illuminated, which is the photo-conductivity, the Seebeck coefficient of the same material would change as well. Unfortunately, very few studies have been devoted to this effect, even less is a systematic interpretation of results observed. We believe a better understanding could lead to new doping scheme, new materials characterization method, as well as complimentary light-sensing principles. In this work we reported our effort on how to properly measure and analyze the photo-Seebeck effect, with an initial demonstration of its value in evaluating mobilities of both types of charge carriers from the same sample. Different from the reported photo-thermoelectric effect, where the "photo-" only comes as a heating source and the "thermoelectric" is still near-equilibrium transport, the photo-Seebeck effect here is the transport phenomenon from photo-excited carriers. 

  • ​Pan, Zhenyu; Zhu, Zheng; Wilcox, Jonathon; Urban, Jeffrey; Yang, Fan and Wang, Heng*, "Tackling Challenges in Seebeck Coefficient Measurement of Ultra-High Resistance Samples with an AC Technique", Advanced Electronic Materials, 6, 1901340 (2020).

Seebeck coefficient is a fundamental transport property for semiconductors, yet for many semiconductors that are intrinsic and resistive, accurate measurement of Seebeck coefficient had been extremely challenging. We have developed a method based on AC phase sensitive technique, which allowed us to extract Seebeck signal out of overwhelming large voltage readings associated with high resistance samples. This paper offered very thorough description of what to considered and how to construct a measurement system that is capable to measure Seebeck coefficient from samples with resistances over Gohms. No other report had offered measurement with comparable quality on samples of this kind. With this capacity we reported the Seebeck coefficient of a CH3NH3PbI3 film at dark condition, which is +500 to +550 uV/K, with the sample resistance exceeding 100Gohm. No one else has been able to perform such measurement. 

  • ​Long, Xiang; Pan, Zhenyu; Zhang, Zhuolei; Urban, Jeffrey and Wang, Heng*, "Solvent-free synthesis of organometallic halides CH3NH3PbI3 and (CH3NH3)3Bi2I9 and their thermoelectric transport properties", Applied Physics Letters 115, 072104 (2019).


Hybrid Perovskites are interesting semiconductors. Many researchers including us, had thought they might make promising thermoelectric materials, as their thermal conductivities are low and their mobilities were believed high. In our previous research on the iconic hybrid perovskite of CH3NH3PbI3, we realized two problems, one is the macroscopic charge mobilities are not that impressive, the other is the lack of dopability. This work is an effort to address these two problems. We believed solvent-free synthesis would provide needed stoichiometry control that is missing in solvent synthesis routes, meanwhile hot pressing would lead to better-fused grain boundaries thus true bulk transport behavior. What we had found however, is that the two compounds are not yet dopable even with better stoichiometry design and the compounds are highly resistive even in hot pressed forms. The most notable result we offered, is the Seebeck coefficient values measured off two bulk samples with resistances over Gohms. With solvent free synthesis, CH3NH3PbI3 showed n type behavior, suggesting different defect composition. We also suggested that there is no big changes in thermal conductivity over the reported phase transition.

  • ​Pan, Zhenyu, and Wang, Heng*, "A Descriptive Model of Thermoelectric Transport in the Resonant System of PbSe doped with Tl", Journal of Materials Chemistry A 7, 12859 (2019).


In thermoelectrics research, resonant doping is one of the few proven strategies that reshape the fundamental relationships between transport properties of a semiconductor. Until recently, how to utilize this strategy is largely a hit-or-miss process. no model is available for experimentalists to understand their results, or to guide rational alloy design. In this article we tried to change this: we presented a model that describes observed thermoelectric properties in a resonant system. We discussed general guidelines on how to optimize energy levels and doping for best thermoelectric performance.  

  • Ma, Hao; Ma, Yunwei; Wang, Heng; Slebodnick, Carla; Alatas, Ahmet; Urban, Jeffrey; Tian, Zhiting, "Experimental Phonon Dispersion and Lifetimes of Tetragonal CH3NH3PbI3 Perovskite Crystals", The Journal of Physical Chemistry Letters 10,1 (2019)


In this collaboration with scientists at LBL, Cornell and Argonne, we provided single crystal samples that enabled high quality measurement of phonon dispersion in the iconic hybrid perovskite known for its great photovoltaic performance.


  • Wu, Chao-Feng; Wang, Heng*, Yan, Qimin; Wei, Tianran and Li, Jing-Feng*, "Doping of thermoelectric PbSe with chemically inert secondary phase nanoparticles", Journal of Materials Chemistry C 5, 10881-10887 (2017). link

Chemically inert particles such as SiC, SiO2, or Si could "dope" the thermoelectric compound of PbSe. The free carrier density exceeds the upper bound for PbSe without other foreign atoms. This happened, at different extent, regardless of the particles'  composition, conductivity, or hardness. Although the compounds need to be made under non-equilibrium conditions, we believe these samples are doped by intrinsic point defects stablized at the PbSe - particle interface. Similar strategy might help dope other compounds that can not be doped otherwise.

  • Zhoug, Min; Gibbs, Zachary M.; Wang, Heng*; Han, Yemao; Li, Laifeng*; and Snyder, G. Jeffrey, , "Thermoelectric performance of co-doped SnTe with resonant levels", Applied Physics Letters 109, 042102 (2016). link

SnTe doped with In is arguably the first example where resonant dopant made better performing thermoelectric material that is otherwise not achievable. This work is Heng's first published effort to elucidate the influence of resonant dopants on charge transport, using co-doping of another regular dopant. There is not yet a complete theory on how resonant dopants affects either charge density of states, or charge scattering, or both. It is Heng's continued interest to find a way so these resonant dopants can be modeled in Boltzmann transport equations.   

  • Bajaj, Saurabh; Wang, Heng; Doak, Jeff W; Wolverton, Chris; and Snyder, G Jeffrey, "Calculation of dopant solubilities and phase diagrams of X–Pb–Se (X = Br, Na) limited to defects with localized charge", Journal of Materials Chemistry C 4, 1769 (2016). link

Phase diagrams are the "maps" for material synthesis. However conventional method of obtaining phase diagrams from experiments is hard to implement when doping is the concern, especially as we push the limit on how many impurities can be introduced. This work is the first part of an effort to combine DFT defect formation energy calculation with CALPHAD (calculation of phase diagram) to get detailed information on phase boundaries with typical impurity of a few percent.    

  • Wang, Heng; Cao, Xianlong; Takagiwa, Yoshiki; and Snyder, G. Jeffrey, "Higher mobility in bulk semiconductors by separating the dopants from the charge- conducting band – a case study of thermoelectric PbSe", Materials Horizons 2, 323 – 329 (2015). link

On the first order, what a (regular) dopant do to a semiconductor is shifting the chemical potential of its carriers, other than that all dopants are pretty much the same. Choice of dopant is based on convenience for processing. This notion is incorrect for heavily doped semiconductors. This work demonstrated that in polar semiconductors, dopants on cation lattice are different from those on anion lattice. One group lead to higher mobilities than the other. The difference can be explained by different scattering potentials.


  • Borup, Kasper A; De Boor, Johannes; Wang, Heng; Drymiotis, Fivos; Gascoin, Franck; Shi, Xun; Chen, Lidong; Fedorov, Mikhail I; Muller, Eckhard; Iversen, Bo B; and Snyder, G. Jeffrey, "Measuring thermoelectric transport properties of materials", Energy&Environmental Science 8, 423 (2015). link

A collaborative article with many experts that discusses better practices for thermoelectric properties measurement at high temperatures.

  • Wang, Heng; Gibbs, Zachary M.; Takagiwa, Yoshiki; and Snyder, G. Jeffrey,  "Tuning bands of PbSe for better thermoelectric efficiency", Energy&Environmental Science 7, 804 (2014). link

Rare-earth elements are "magic" additives to IV-VI thermoelectrics. Many successful studies have used them and achieved higher zTs. There are different explanations as of why. Some suggested they causes more phonon scattering than carrier scattering due to band energy alignment. This work, with careful experimental design, wide composition range under survey, and multiple-band transport modeling, put forward an argument that the benefit comes from favorable band structure change, whereas rare-earths indeed scatter carriers more than phonons. 

  • Chen, Cheng-Lung*; Wang, Heng*; Chen, Yang-Yuan; Day, Tristan; and Snyder, G. Jeffrey,  "Thermoelectric properties of p-type polycrystalline SnSe doped with Ag", Journal of Materials Chemistry A 2, 11171 (2014). link

We published our own study on p type SnSe in polycrystalline form about the same time a record zT of 2.6 was reported on this compound. Our conclusion was much more conservative. we found before phase transition around 800 K, the compound of SnSe does not have the "quality" to be a outstanding thermoelectric material. We also believe polycrystalline SnSe suffer from hysteresis issue through temperature cycles, which must be overcome before any discussion on zT could be meaningful.


  • Wang, Heng; Wang, Jianli; Cao, xianlong; and Snyder, G. Jeffrey,  "Thermoelectric alloys between PbSe and PbS with effective thermal conductivity reduction and high figure of merit", Journal of Materials Chemistry A 2, 3169 (2014). link

We quantitatively explained how alloying affects both effective masses and electron scattering in the solid solution of PbSe-PbS, with the use of only one constant fitting parameter. 

  • Wei, Tian-Ran*; Wang, Heng*; Gibbs, Zachary M; Wu, Chao-Feng; Snyder, G. Jeffrey; and Li, Jing-Feng,  "Thermoelectric properties of Sn-doped p-type Cu3SbSe4: a compound with large effective mass and small band gap", Journal of Materials Chemistry A 2, 13527 (2014). link


  • Xie, Hanhui; Wang, Heng; Fu, Chengguang; Liu, Yintu; Snyder, G. Jeffrey; Zhao, Xinbing; Zhu, Tiejun, The intrinsic disorder related alloy scattering in ZrNiSn Half-Heusler thermoelectric materials, Scientific Reports 4, 6888 (2014). link

The formula of half-Heusler compound ZrNiSn doesn't suggest any disorder, yet we found it contains a large number of intrinsic disorder such that its transport behavior has the signature of a disordered alloy. This contribute to its good thermoelectric performance.


  • Zhou, Min; Gibbs, Zachary M.; Wang Heng; Han, Yemao; Xin, Caini; Li, Laifeng; and Snyder, G. Jeffrey, "Optimization of thermoelectric efficiency in SnTe: the case for the light band" , Physical Chemistry Chemical Physics 16, 20741, (2014). link

  • Wang, H., Pei, Y., LaLonde, A. D. and Snyder, G. J., "Material Design Considerations Based on Thermoelectric Quality Factor", in Thermoelectric Nanomaterials, Springer Series in Materials Science Vol 182, 2013, pp

In this lead chapter of a Springer series in materials science, we discussed the different factors that influence the quality factor, which describes a compound's "quality" as thermoelectrics, given it can be optimized.

  • Wang, H., Schechtel, E., Pei, Y. and Snyder, G. J., "High Thermoelectric Efficiency of n-type PbS", Advanced Energy Materials 3, 488 (2013). link


  • Wang, H., LaLonde, A. D., Pei, Y. and Snyder, G. J., "The Criteria for Beneficial Disorder in Thermoelectric Solid Solutions", Advanced Functional Materials 23, 1586 (2013). link

We found the proper way to treat iso-valent atomic substitution in thermoelectric transport equations. once a constant scattering potential is known, the transport of any composition, with any doping level, at any temperature, can be predicted.

  • Xie, Hanhui; Wang, Heng; Pei, Yanzhong; Fu, Chenguang; Liu, Xiaohua; Snyder, G. Jeffrey; Zhao, Xinbing; and Zhu, Tiejun, Beneficial Contribution of Alloy Disorder to Electron and Phonon Transport in Half-Heusler Thermoelectric Materials, Advanced Functional Materials 23, 5123, (2013). link


  • Wang, H., Pei, Y., LaLonde, A. D. and Snyder, G. J., "Weak electron-phonon coupling contributing to high thermoelectric performance in n-type PbSe", Proceedings of the National Academy of Sciences of the United States of America 109, 9705, (2012). link 

​We explained why n type Pb chalcogenides are great thermoelectrics even though they don't have high band degeneracy as their p type counterparts. 

Selected Publications

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