journal article·2021-07-22Open access

Restructured single parabolic band model for quick analysis in thermoelectricity

Jianbo Zhu, Xuemei Zhang, Muchun Guo, Jingyu Li, Jinsuo Hu, Songting Cai, Wei Cai, Yongsheng Zhang, Jiehe Sui

npj Computational Materials· Volume 7· Issue 1

Abstract

Abstract The single parabolic band (SPB) model has been widely used to preliminarily elucidate inherent transport behaviors of thermoelectric (TE) materials, such as their band structure and electronic thermal conductivity, etc. However, in the SPB calculation, it is necessary to determine some intermediate variables, such as Fermi level or the complex Fermi-Dirac integrals. In this work, we establish a direct carrier-concentration-dependent restructured SPB model, which eliminates Fermi-Dirac integrals and Fermi level calculation and emerges stronger visibility and usability in experiments. We have verified the reliability of such restructured model with 490 groups of experimental data from state-of-the-art TE materials and the relative error is less than 2%. Moreover, carrier effective mass, intrinsic carrier mobility and optimal carrier concentration of these materials are systematically investigated. We believe that our work can provide more convenience and accuracy for thermoelectric data analysis as well as instructive understanding on future optimization design.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Advanced Thermoelectric Materials and Devices · Thermal properties of materials · Heusler alloys: electronic and magnetic properties

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (55)

Show source-provided references
1. Liu, W., Jie, Q., Kim, H. S. & Ren, Z. Current progress and future challenges in thermoelectric power generation: from materials to devices. Acta Mater. 87, 357–376 (2015).10.1016/j.actamat.2014.12.042 ↗
2. Poudel, B. et al. High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys. Science 320, 634–638 (2008).10.1126/science.1156446 ↗
3. Snyder, G. J. & Toberer, E. S. Complex thermoelectric materials. Nat. Mater. 7, 105–114 (2008).10.1038/nmat2090 ↗
4. Kim, H. S., Liu, W., Chen, G., Chu, C. & Ren, Z. Relationship between thermoelectric figure of merit and energy conversion efficiency. Proc. Natl Acad. Sci. USA 112, 8205–8210 (2015).10.1073/pnas.1510231112 ↗
5. Kim, H. S., Liu, W. & Ren, Z. Efficiency and output power of thermoelectric module by taking into account corrected Joule and Thomson heat. J. Appl. Phys. 118, 115103 (2015).10.1063/1.4930869 ↗
6. Mehdizadeh Dehkordi, A., Zebarjadi, M., He, J. & Tritt, T. M. Thermoelectric power factor: enhancement mechanisms and strategies for higher performance thermoelectric materials. Mater. Sci. Eng. R. 97, 1–22 (2015).10.1016/j.mser.2015.08.001 ↗
7. Zhu, H. et al. Discovery of TaFeSb-based half-Heuslers with high thermoelectric performance. Nat. Commun. 10, 1–8 (2019).10.1038/s41467-018-07882-8 ↗
8. Fu, C., Zhu, T., Liu, Y., Xie, H. & Zhao, X. Band engineering of high performance p-type FeNbSb based half-Heusler thermoelectric materials for figure of merit zT > 1. Energy Environ. Sci. 8, 216–220 (2015).10.1039/C4EE03042G ↗
9. Perumal, S., Roychowdhury, S., Negi, D. S., Datta, R. & Biswas, K. High thermoelectric performance and enhanced mechanical stability of p-type Ge1-xSbxTe. Chem. Mater. 27, 7171–7178 (2015).10.1021/acs.chemmater.5b03434 ↗
10. Cai, S. et al. Discordant nature of Cd in PbSe: off-centering and core-shell nanoscale CdSe precipitates lead to high thermoelectric performance. Energy Environ. Sci. 13, 200–211 (2020).10.1039/C9EE03087E ↗
11. Zhang, X. & Zhao, L. Thermoelectric materials: energy conversion between heat and electricity. J. Materiomics 1, 92–105 (2015).10.1016/j.jmat.2015.01.001 ↗
12. Park, J., Xia, Y., Ozolins, V. & Jain, A. Optimal band structure for thermoelectrics with realistic scattering and bands. npj Comput. Mater. 7, 1–9 (2021).10.1038/s41524-021-00512-w ↗
13. Hao, S., Dravid, V. P., Kanatzidis, M. G. & Wolverton, C. Computational strategies for design and discovery of nanostructured thermoelectrics. npj Comput. Mater. 5, 1–10 (2019).10.1038/s41524-019-0197-9 ↗
14. Luo, Z. et al. Ultralow thermal conductivity and high-temperature thermoelectric performance in n-type K2.5Bi8.5Se14. Chem. Mater. 31, 5943–5952 (2019).10.1021/acs.chemmater.9b02327 ↗
15. Cai, S. et al. Ultralow thermal conductivity and thermoelectric properties of Rb2Bi8Se13. Chem. Mater. 32, 3561–3569 (2020).10.1021/acs.chemmater.0c00703 ↗
16. Madsen, G. K. H., Carrete, J. & Verstraete, M. J. BoltzTraP2, a program for interpolating band structures and calculating semi-classical transport coefficients. Comput. Phys. Commun. 231, 140–145 (2018).10.1016/j.cpc.2018.05.010 ↗
17. Li, X. et al. TransOpt. A code to solve electrical transport properties of semiconductors in constant electron–phonon coupling approximation. Comput. Mater. Sci. 186, 110074 (2021).10.1016/j.commatsci.2020.110074 ↗
18. Zhou, Z., Cao, G., Liu, J. & Liu, H. High-throughput prediction of the carrier relaxation time via data-driven descriptor. npj Comput. Mater. 6, 1–6 (2020).10.1038/s41524-020-00417-0 ↗
19. Hughes, A. C. & Buchan, A. G. A discontinuous and adaptive reduced order model for the angular discretization of the Boltzmann transport equation. Int. J. Numer. Methods Eng. 121, 5647–5666 (2020).10.1002/nme.6516 ↗
20. Hong, M., Chen, Z. & Zou, J. Fundamental and progress of Bi2Te3-based thermoelectric materials. Chin. Phys. B 27, 48403 (2018).10.1088/1674-1056/27/4/048403 ↗
21. Naithani, H. & Dasgupta, T. Critical analysis of single band modeling of thermoelectric materials. ACS Appl. Energy Mater. 3, 2200–2213 (2020).10.1021/acsaem.9b02015 ↗
22. Deng, T. et al. EPIC STAR: a reliable and efficient approach for phonon- and impurity-limited charge transport calculations. npj Comput. Mater. 6, 1–11 (2020).10.1038/s41524-020-0316-7 ↗
23. Zhou, T. et al. Thermoelectric properties of Zintl phase YbMg2Sb2. Chem. Mater. 32, 776–784 (2020).10.1021/acs.chemmater.9b04131 ↗
24. Fu, C. et al. Realizing high figure of merit in heavy-band p-type half-Heusler thermoelectric materials. Nat. Commun. 6, 1–7 (2015).10.1038/ncomms9144 ↗
25. Goldsmid, H. J. in Introduction to Thermoelectricity (ed. Goldsmid, H. J.) 25–44 (Springer, 2016).10.1007/978-3-662-49256-7_3 ↗
26. Liu, Y. et al. Synergistically optimizing electrical and thermal transport properties of BiCuSeO via a dual-doping approach. Adv. Energy Mater. 6, 1502423 (2016).10.1002/aenm.201502423 ↗
27. Liu, Z. et al. Lithium doping to enhance thermoelectric performance of MgAgSb with weak electron-phonon coupling. Adv. Energy Mater. 6, 1502269 (2016).10.1002/aenm.201502269 ↗
28. Mao, J. et al. Manipulation of ionized impurity scattering for achieving high thermoelectric performance in n-type Mg3Sb2-based materials. Proc. Natl Acad. Sci. USA 114, 10548–10553 (2017).10.1073/pnas.1711725114 ↗
29. Zhang, J., Song, L. & Iversen, B. B. Insights into the design of thermoelectric Mg3Sb2 and its analogs by combining theory and experiment. npj Comput. Mater. 5, 1–17 (2019).10.1038/s41524-019-0215-y ↗
30. Yan, J. et al. Material descriptors for predicting thermoelectric performance. Energy Environ. Sci. 8, 983–994 (2015).10.1039/C4EE03157A ↗
31. Malyi, O. I. & Zunger, A. False metals, real insulators, and degenerate gapped metals. Appl. Phys. Rev. 7, 41310 (2020).10.1063/5.0015322 ↗
32. Recatala-Gomez, J., Suwardi, A., Nandhakumar, I., Abutaha, A. & Hippalgaonkar, K. Toward accelerated thermoelectric materials and process discovery. ACS Appl. Energy Mater. 3, 2240–2257 (2020).10.1021/acsaem.9b02222 ↗
33. Bassman, L. et al. Active learning for accelerated design of layered materials. npj Comput. Mater. 4, 1–9 (2018).10.1038/s41524-017-0060-9 ↗
34. Kim, H., Gibbs, Z. M., Tang, Y., Wang, H. & Snyder, G. J. Characterization of Lorenz number with Seebeck coefficient measurement. APL Mater. 3, 41506 (2015).10.1063/1.4908244 ↗
35. Fukushima, T. Precise and fast computation of generalized Fermi-Dirac integral by parameter polynomial approximation. Appl. Math. Comput. 270, 802–807 (2015).10.1016/j.amc.2015.08.094 ↗
36. Chang, K. & Liu, C. An algorithm of calculating transport parameters of thermoelectric materials using single band model with optimized integration methods. Comput. Phys. Commun. 247, 106875 (2020).10.1016/j.cpc.2019.106875 ↗
37. He, R. et al. Achieving high power factor and output power density in p-type half-Heuslers Nb1-xTixFeSb. Proc. Natl Acad. Sci. USA 113, 13576–13581 (2016).10.1073/pnas.1617663113 ↗
38. Bhardwaj, R. et al. Collective effect of Fe and Se to improve the thermoelectric performance of unfilled p-type CoSb3 skutterudites. ACS Appl. Energy Mater. 2, 1067–1076 (2019).10.1021/acsaem.8b01609 ↗
39. Zhu, T. et al. Compromise and synergy in high-efficiency thermoelectric materials. Adv. Mater. 29, 1605884 (2017).10.1002/adma.201605884 ↗
40. Tang, Y. et al. Convergence of multi-valley bands as the electronic origin of high thermoelectric performance in CoSb3 skutterudites. Nat. Mater. 14, 1223–1228 (2015).10.1038/nmat4430 ↗
41. Imasato, K., Kang, S. D., Ohno, S. & Snyder, G. J. Band engineering in Mg3Sb2 by alloying with Mg3Bi2for enhanced thermoelectric performance. Mater. Horiz. 5, 59–64 (2018).10.1039/C7MH00865A ↗
42. Qin, B., He, W. & Zhao, L. Estimation of the potential performance in p-type SnSe crystals through evaluating weighted mobility and effective mass. J. Materiomics 6, 671–676 (2020).10.1016/j.jmat.2020.06.003 ↗
43. Liu, W. et al. New insight into the material parameter B to understand the enhanced thermoelectric performance of Mg2Sn1-x-yGexSby. Energy Environ. Sci. 9, 530–539 (2016).10.1039/C5EE02600H ↗
44. Snyder, G. J. et al. Weighted mobility. Adv. Mater. 32, 2001537 (2020).10.1002/adma.202001537 ↗
45. Ovchinnikov, A. & Bobev, S. Zintl phases with group 15 elements and the transition metals: a brief overview of pnictides with diverse and complex structures. J. Solid State Chem. 270, 346–359 (2019).10.1016/j.jssc.2018.11.029 ↗
46. Zheng, L. et al. Ternary thermoelectric AB2C2 Zintls. J. Alloy. Compd. 821, 153497 (2020).10.1016/j.jallcom.2019.153497 ↗
47. Zhang, J. et al. Designing high-performance layered thermoelectric materials through orbital engineering. Nat. Commun. 7, 1–7 (2016).
48. Wang, X. et al. Experimental revelation of multiband transport in heavily doped BaCd2Sb2 with promising thermoelectric performance. Mater. Today Phys. 8, 123–127 (2019).10.1016/j.mtphys.2019.03.002 ↗
49. Zheng, L., Li, W., Wang, X. & Pei, Y. Alloying for orbital alignment enables thermoelectric enhancement of EuCd2Sb2. J. Mater. Chem. A 7, 12773–12778 (2019).10.1039/C9TA03502H ↗
50. Brebrick, R. F. & Strauss, A. J. Anomalous thermoelectric power as evidence for two-valence bands in SnTe. Phys. Rev. 131, 104–110 (1963).10.1103/PhysRev.131.104 ↗
51. Chen, Z. et al. Routes for advancing SnTe thermoelectrics. J. Mater. Chem. A 8, 16790–16813 (2020).10.1039/D0TA05458E ↗
52. Zhang, Q. et al. High thermoelectric performance by resonant dopant indium in nanostructured SnTe. Proc. Natl Acad. Sci. USA 110, 13261–13266 (2013).10.1073/pnas.1305735110 ↗
53. Guo, F. et al. Simultaneous boost of power factor and figure‐of‐merit in In-Cu codoped SnTe. Small 15, 1902493 (2019).10.1002/smll.201902493 ↗
54. Bardeen, J. & Shockley, W. Deformation potentials and mobilities in non-polar crystals. Phys. Rev. 80, 72–80 (1950).10.1103/PhysRev.80.72 ↗
55. Zhang, X. et al. Electronic quality factor for thermoelectrics. Sci. Adv. 6, c726 (2020).10.1126/sciadv.abc0726 ↗