Designer Entropy Enables High Thermoelectric Power and Efficiency

Abstract

Thermoelectric (TE) materials promise sustainable energy conversion from waste heat, but their practical utility is often governed by a fundamental trade-off between conversion efficiency (η) and output power (P). High-entropy engineering has emerged as a powerful strategy to boost efficiency by maximizing phonon scattering, yet this compositional complexity can inadvertently degrade electronic properties and thus suppress output power. Here, we introduce “Designer Entropy”—a chemically guided paradigm that moves beyond maximizing disorder to achieve targeted transport properties by consciously selecting alloying elements. We demonstrate this principle by systematically contrasting two distinct pathways in a SnTe(GeSe)_0.25 matrix: doping with Sb (near-matched atomic radius) versus Bi (large radius/mass mismatch). While both pathways yield nearly identical high conversion efficiencies of ~5.7% at a temperature difference of 500 K, their power generation capabilities diverge significantly. The Sb-doped device, designed to preserve electronic transport, delivers a maximum output power of 23.1 mW, an ~20% enhancement over its Bi-doped counterpart. This non-equivalent optimization stems from a mechanistic dichotomy: Sb doping preserves high carrier mobility and suppresses bipolar effects, leading to a superior power factor, whereas Bi doping, despite inducing ultralow lattice thermal conductivity by creating strong local distortions, suffers from severe carrier scattering and a premature bipolar onset. Our work establishes a rational design framework that decouples the optimization of efficiency and power, providing a blueprint for developing next-generation TE materials that shift the focus from compositional complexity to compositional intelligence for high-power applications.

Keywords

entropy / output power / power factor / SnTe / thermoelectric

References

[1] D. Yang, Y. Xing, J. Wang, et al., “Multifactor Roadmap for Designing Low-Power-Consumed Micro Thermoelectric Thermostats in a Closed-Loop Integrated 5G Optical Module,” Interdisciplinary Materials 3, no. 2 (2024): 326–337.

[2] G. Peng, L. Hu, W. Qu, et al., “Structural–Functional Unit Ordering for High-Performance Electron-Correlated Materials,” Interdisciplinary Materials 2, no. 1 (2023): 30–52.

[3] J. Mao, H. Zhu, Z. Ding, et al., “High Thermoelectric Cooling Performance of n-Type Mg₃Bi₂-Based Materials,” Science 365, no. 6452 (2019): 495–498.

[4] J. He and T. M. Tritt, “Advances in Thermoelectric Materials Research: Looking Back and Moving Forward,” Science 357, no. 6358 (2017): eaak9997.

[5] Y. Xing, R. Liu, J. Liao, et al., “A Device-to-Material Strategy Guiding the ‘Double-High’ Thermoelectric Module,” Joule 4, no. 11 (2020): 2475–2483.

[6] L. Yin, F. Yang, X. Bao, et al., “Low-Temperature Sintering of Ag Nanoparticles for High-Performance Thermoelectric Module Design,” Nature Energy 8, no. 7 (2023): 665–674.

[7] X. L. Shi, N. H. Li, M. Li, and Z. G. Chen, “Toward Efficient Thermoelectric Materials and Devices: Advances, Challenges, and Opportunities,” Chemical Reviews 125, no. 16 (2025): 7525–7724.

[8] L. Xie, L. Yin, Y. Yu, et al., “Screening Strategy for Developing Thermoelectric Interface Materials,” Science 382, no. 6673 (2023): 921–928.

[9] S. Xu, S. Horta, A. Lawal, K. Maji, M. Lorion, and M. Ibáñez, “Interfacial Bonding Enhances Thermoelectric Cooling in 3D-Printed Materials,” Science 387, no. 6736 (2025): 845–850.

[10] X. Sun, Y. Hou, Z. Zhu, et al., “Modular Assembly of Self-Healing Flexible Thermoelectric Devices With Integrated Cooling and Heating Capabilities,” Nature Communications 16, no. 1 (2025): 4220.

[11] Y. Zhang, G. Peng, S. Li, et al., “Phase Interface Engineering Enables State-of-the-Art Half-Heusler Thermoelectrics,” Nature Communications 15, no. 1 (2024): 5978.

[12] X. Qian, J. Zhou, and G. Chen, “Phonon-Engineered Extreme Thermal Conductivity Materials,” Nature Materials 20, no. 9 (2021): 1188–1202.

[13] Y. Zhang, S. Li, F. Liu, et al., “Zr Vacancy Interfaces: An Effective Strategy for Collaborative Optimization of ZrNiSn-Based Thermoelectric Performance,” Journal of Materials Chemistry A 7, no. 45 (2019): 26053–26061.

[14] Y. Wu, Z. Chen, P. Nan, et al., “Lattice Strain Advances Thermoelectrics,” Joule 3, no. 5 (2019): 1276–1288.

[15] M. Liu, Y. Sun, J. Zhu, et al., “High Performance GeTe Thermoelectrics Enabled by Lattice Strain Construction,” Acta Materialia 244 (2023): 118565.

[16] J. Zhong, X. Yang, T. Lyu, et al., “Nuanced Dilute Doping Strategy Enables High-Performance GeTe Thermoelectrics,” Science Bulletin 69, no. 8 (2024): 1037–1049.

[17] R. Hanus, M. T. Agne, A. J. E. Rettie, et al., “Lattice Softening Significantly Reduces Thermal Conductivity and Leads to High Thermoelectric Efficiency,” Advanced Materials 31, no. 21 (2019): 1900108.

[18] W. Yao, Y. Zhang, T. Lyu, et al., “Two-Step Phase Manipulation by Tailoring Chemical Bonds Results in High-Performance GeSe Thermoelectrics,” Innovation 4, no. 6 (2023): 100522.

[19] Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, and G. J. Snyder, “Convergence of Electronic Bands for High Performance Bulk Thermoelectrics,” Nature 473, no. 7345 (2011): 66–69.

[20] Z. Zhang, K. Zhao, T. R. Wei, P. Qiu, L. Chen, and X. Shi, “Cu₂Se-Based Liquid-Like Thermoelectric Materials: Looking Back and Stepping Forward,” Energy & Environmental Science 13, no. 10 (2020): 3307–3329.

[21] G. Tan, F. Shi, J. W. Doak, et al., “Extraordinary Role of Hg in Enhancing the Thermoelectric Performance of p-Type SnTe,” Energy & Environmental Science 8, no. 1 (2015): 267–277.

[22] F. Guo, B. Cui, Y. Liu, et al., “Thermoelectric SnTe With Band Convergence, Dense Dislocations, and Interstitials Through Sn Self-Compensation and Mn Alloying,” Small 14, no. 37 (2018): 1802615.

[23] H. Hu, Y. Ju, J. Yu, et al., “Highly Stabilized and Efficient Thermoelectric Copper Selenide,” Nature Materials 23, no. 4 (2024): 527–534.

[24] B. Qin, M. G. Kanatzidis, and L. D. Zhao, “The Development and Impact of Tin Selenide on Thermoelectrics,” Science 386, no. 6719 (2024): eadp2444.

[25] S. Roychowdhury, T. Ghosh, R. Arora, et al., “Enhanced Atomic Ordering Leads to High Thermoelectric Performance in AgSbTe₂,” Science 371, no. 6530 (2021): 722–727.

[26] C. Fu, S. Bai, Y. Liu, et al., “Realizing High Figure of Merit in Heavy-Band p-Type Half-Heusler Thermoelectric Materials,” Nature Communications 6, no. 1 (2015): 8144.

[27] Y. Huang, T. Lyu, M. Zeng, et al., “Manipulation of Metavalent Bonding to Stabilize Metastable Phase: A Strategy for Enhancing zT in GeSe,” Interdisciplinary Materials 3, no. 4 (2024): 607–620.

[28] L. Wang, R. Moshwan, N. Yuan, Z. G. Chen, and X. L. Shi, “Advances and Challenges in SnTe-Based Thermoelectrics,” Advanced Materials 37, no. 10 (2025): 2418280.

[29] B. Qin, D. Wang, X. Liu, et al., “Power Generation and Thermoelectric Cooling Enabled by Momentum and Energy Multiband Alignments,” Science 373, no. 6554 (2021): 556–561.

[30] Y. Liu, C. Fu, K. Xia, et al., “Lanthanide Contraction as a Design Factor for High-Performance Half-Heusler Thermoelectric Materials,” Advanced Materials 30, no. 32 (2018): 1800881.

[31] Y. Qin, B. Qin, T. Hong, et al., “Grid-Plainification Enables Medium-Temperature PbSe Thermoelectrics to Cool Better Than Bi₂Te₃,” Science 383, no. 6688 (2024): 1204–1209.

[32] D. Liu, D. Wang, T. Hong, et al., “Lattice Plainification Advances Highly Effective SnSe Crystalline Thermoelectrics,” Science 380, no. 6647 (2023): 841–846.

[33] P. Ying, Q. Jian, Y. Gong, et al., “Matrix Plainification Leads to High Thermoelectric Performance in Plastic Cu₂Se/SnSe Composites,” Nature Communications 16, no. 1 (2025): 3305.

[34] H. Zhu, W. Li, A. Nozariasbmarz, et al., “Half-Heusler Alloys as Emerging High Power Density Thermoelectric Cooling Materials,” Nature Communications 14, no. 1 (2023): 3300.

[35] L. Hu, Y. Zhang, H. Wu, et al., “Entropy Engineering of SnTe: Multi-Principal-Element Alloying Leading to Ultralow Lattice Thermal Conductivity and State-of-the-Art Thermoelectric Performance,” Advanced Energy Materials 8, no. 29 (2018): 1802116.

[36] Q. Tang, B. Jiang, K. Wang, et al., “High-Entropy Thermoelectric Materials,” Joule 8, no. 6 (2024): 1641–1666.

[37] C. Liu, S. Li, Y. Zheng, et al., “Advances in High Entropy Oxides: Synthesis, Structure, Properties and Beyond,” Progress in Materials Science 148 (2025): 101385.

[38] Y. Zhang, T. T. Zuo, Z. Tang, et al., “Microstructures and Properties of High-Entropy Alloys,” Progress in Materials Science 61 (2014): 1–93.

[39] B. Jiang, Y. Yu, J. Cui, et al., “High-Entropy-Stabilized Chalcogenides With High Thermoelectric Performance,” Science 371, no. 6531 (2021): 830–834.

[40] G. Liang, T. Lyu, L. Hu, et al., “(GeTe)_1–x(AgSnSe₂)_x: Strong Atomic Disorder-Induced High Thermoelectric Performance Near the Ioffe–Regel Limit,” ACS Applied Materials & Interfaces 13, no. 39 (2021): 47081–47089.

[41] Z. Fan, H. Wang, Y. Wu, X. Liu, and Z. Lu, “Thermoelectric Performance of PbSnTeSe High-Entropy Alloys,” Materials Research Letters 5, no. 3 (2017): 187–194.

[42] Z. Rao, P. Y. Tung, R. Xie, et al., “Machine Learning-Enabled High-Entropy Alloy Discovery,” Science 378, no. 6615 (2022): 78–85.

[43] Q. Zhang, Z. Guo, R. Wang, et al., “High-Performance Thermoelectric Material and Module Driven by Medium-Entropy Engineering in SnTe,” Advanced Functional Materials 32, no. 35 (2022): 2205458.

[44] Z. Chen, Z. Jian, W. Li, et al., “Lattice Dislocations Enhancing Thermoelectric PbTe in Addition to Band Convergence,” Advanced Materials 29, no. 23 (2017): 1606768.

[45] S. Roychowdhury, T. Ghosh, R. Arora, U. V. Waghmare, and K. Biswas, “Stabilizing n-Type Cubic GeSe by Entropy-Driven Alloying of AgBiSe₂: Ultralow Thermal Conductivity and Promising Thermoelectric Performance,” Angewandte Chemie 130, no. 46 (2018): 15387–15391.

[46] H. Shang, Z. Liang, C. Xu, et al., “N-Type Mg₃Sb_2−xBi_x Alloys as Promising Thermoelectric Materials,” Research: A Journal of Science and its Applications 2020 (2020): 1219461.

[47] Z. M. Gibbs, H. S. Kim, H. Wang, and G. J. Snyder, “Band Gap Estimation From Temperature Dependent Seebeck Measurement—Deviations From the 2e|S|_maxT_max Relation,” Applied Physics Letters 106, no. 2 (2015): 022112.

[48] M. Hong, Y. Wang, S. Xu, et al., “Nanoscale Pores Plus Precipitates Rendering High-Performance Thermoelectric SnTe_1−xSe_x With Refined Band Structures,” Nano Energy 60 (2019): 1–7.

[49] Y. Liu, X. Zhang, P. Nan, et al., “Improved Solubility in Metavalently Bonded Solid Leads to Band Alignment, Ultralow Thermal Conductivity, and High Thermoelectric Performance in SnTe,” Advanced Functional Materials 32, no. 47 (2022): 2209980.

[50] W. Li, L. Zheng, B. Ge, et al., “Promoting SnTe as an Eco-Friendly Solution for p-PbTe Thermoelectric via Band Convergence and Interstitial Defects,” Advanced Materials 29, no. 17 (2017): 1605887.

[51] G. J. Snyder, A. H. Snyder, M. Wood, R. Gurunathan, B. H. Snyder, and C. Niu, “Weighted Mobility,” Advanced Materials 32, no. 25 (2020): 2001537.

[52] A. R. Muchtar, B. Srinivasan, S. L. Tonquesse, et al., “Physical Insights on the Lattice Softening Driven Mid-Temperature Range Thermoelectrics of Ti/Zr-Inserted SnTe—An Outlook Beyond the Horizons of Conventional Phonon Scattering and Excavation of Heikes' Equation for Estimating Carrier Properties,” Advanced Energy Materials 11, no. 28 (2021): 2101122.

[53] X. Zhang, Z. Bu, X. Shi, et al., “Electronic Quality Factor for Thermoelectrics,” Science Advances 6, no. 46 (2020): eabc0726.

[54] X. Qian, H. Wu, D. Wang, et al., “Synergistically Optimizing Interdependent Thermoelectric Parameters of n-type PbSe Through Alloying CdSe,” Energy & Environmental Science 12, no. 6 (2019): 1969–1978.

[55] Y. Wu, P. Nan, Z. Chen, et al., “Thermoelectric Enhancements in PbTe Alloys Due to Dislocation-Induced Strains and Converged Bands,” Advanced Science 7, no. 12 (2020): 1902628.

[56] Q. Xie, L. Xu, C. Hu, et al., “Phonon Anharmonicity of Thermoelectric Material HfTe₅ Studied by Raman Spectroscopy,” Journal of Raman Spectroscopy 52, no. 5 (2021): 988–994.

[57] K. Monikapani, V. Vijay, S. Harish, J. Archana, C. Muthamizhchelvan, and M. Navaneethan, “Ultra-Low Thermal Conductivity Through the Reduced Phonon Lifetime by Microstructural and Umklapp Scattering in Sn_1−xMn_xSe Nanostructures,” Journal of Alloys and Compounds 917 (2022): 165152.

[58] A. Banik, T. Ghosh, R. Arora, et al., “Engineering Ferroelectric Instability to Achieve Ultralow Thermal Conductivity and High Thermoelectric Performance in Sn_1−xGe_xTe,” Energy & Environmental Science 12, no. 2 (2019): 589–595.

[59] Y. Gong, W. Dou, B. Lu, et al., “Divacancy and Resonance Level Enables High Thermoelectric Performance in n-Type SnSe Polycrystals,” Nature Communications 15, no. 1 (2024): 4231.

[60] B. Jiang, W. Wang, S. Liu, et al., “High Figure-of-Merit and Power Generation in High-Entropy GeTe-Based Thermoelectrics,” Science 377, no. 6602 (2022): 208–213.

[61] S. J. Pennycook and L. A. Boatner, “Chemically Sensitive Structure-Imaging With a Scanning Transmission Electron Microscope,” Nature 336, no. 6199 (1988): 565–567.

[62] S. Pennycook and D. Jesson, “High-Resolution Incoherent Imaging of Crystals,” Physical Review Letters 64, no. 8 (1990): 938–941.

RIGHTS & PERMISSIONS

2026 The Author(s). Interdisciplinary Materials published by Wuhan University of Technology and John Wiley & Sons Australia, Ltd.