Higher-order anharmonicity leads to ultra-low thermal conductivity and high output power density of SnTe-based thermoelectric materials and modules
Graphical abstract
Introduction
Thermoelectric (TE) materials could convert heat into electricity via Seebeck effect or use electricity for cooling via Peltier effect [1]. Figure of merit zT quantifies conversion efficiency of TE materials, and high zT means more effective energy conversion [2]. Due to the complicated relation between Seebeck coefficient S, electrical resistivity ρ and electrical thermal conductivity κe, dilemma appears when one tries to increase zT without comprehensive considerations [3]. On the other hand, decreasing the lattice thermal conductivity κL is an effective way to increase zT due to its independent nature.
Tin Telluride (SnTe) alloys have been studied intensively in recent years as an alternative candidate of Lead Telluride (PbTe) from eco-friendly point of view [4]. But the TE performance of SnTe cannot match with that of PbTe, mainly due to low S and high κ of pristine SnTe [5]. For boosting the electrical properties of SnTe, band convergence was proposed, and Mn is one of the most effective elements due to its high solubility limit in SnTe [[6], [7], [8]]. For optimizing thermal properties, reduction of κL is crucial. To this end, in-situ defects introduced by copper (Cu) doping was reported lowering κL without influencing electric transport properties [9,10]. Apart from microstructure modification applicable for room temperature range, enhancing ionic-potential anharmonicity shows strong relevance with low κL via Umklapp scattering at high temperature range [11]. Novel phenomena and deeper understandings are constantly being reported in this research direction especially for state-of-art TE materials. O. Delaire et al. identified strong anharmonic coupling between transverse optical (TO, soft optical phonons) and longitudinal acoustic (LA) phonons in PbTe single crystals [12]. They believe the anharmonic coupling plays a key role for explaining unusual low κL in such a simple rock-salt crystal structure. Using the same research strategy, C.W. Li et al. showed that giant phonon anharmonicity associated with the unstable electronic structure and orbital interactions are responsible for the unique low κL of tin selenium (SnSe) single crystals [13]. SnTe exists strong anharmonicity as well according to theoretical prediction. Sangyeop Lee et al. revealed that the resonant bond induced long-ranged interaction causes optical phonon softening, strong an-harmonic scattering and large phase space for three-phonon scattering processes, which further confirmed SnTe is one of the most promising TE materials with respect to foreseeable low κL [14]. As anharmonicity is an intrinsic character of lattice vibration, doping is thus a powerful way to manipulate it. Using germanium (Ge) doping, Banik et al. created cationic off-centering in SnTe lattice, and consequently soft optical phonon got maintained [15]. They think the soft optical phonon could cause effective scattering of acoustic phonons, which leads to κL as low as 0.7 Wm−1K−1. However, rare evidences such as thermal expansion measurement were reported to present anharmonicity directly. Moreover, how the anharmonicity influences κL is still not clear considering relaxation time and speed of phonons are all suspicious.
In this work, we will show direct evidences of the enlarged ionic-potential anharmonicity of Cu/Mn co-doped SnTe alloys via thermal expansion measurement and analyzation. We found that not only the cubic anharmonic term, but also the quartic anharmonic term contributes to the enlarged anharmonicity. Meanwhile, changes of acoustic and optical phonons are fully analyzed rely on the Brillouin and Raman scattering spectrometers to reveal the influences of anharmonicity on decreasing κL. Additionally, the variation of ρ and S will be discussed in details. Combined with the synergistic optimized electrical and thermal transport properties via Cu/Mn co-doping, an increased zT of SnTe and high output power densities of the corresponding modules are achieved.
Section snippets
Crystal structure
The XRD patterns for (SnTe)1-x-(MnTe)0.5x-(Cu2Te)0.5x shown in Fig. 1(a) indicate all samples are rock-salt crystal structure [9,16,17]. Notably, the XRD patterns for x = 0.02 and 0.16 samples show unusual trend. When x = 0.02, the entire doping concentration for SnTe is 0.03 (0.01 Mn and 0.02 Cu) which is a critical point for SnTe as Sn vacancies will be fully occupied [18,19]. Substitution of Sn atoms occurs with further doping, and the lattice parameter changes regularly based on the
Conclusions
An ultra-low κL 0.5 Wm−1K−1 is achieved in (SnTe)0.86-(MnTe)0.07-(Cu2Te)0.07 samples. Combining with the enhanced S due to band convergence, the thermoelectric properties of SnTe alloys promote 225%. Quartic anharmonic term has been observed in Cu/Mn co-doped SnTe from thermal expansion measurement. Diffused peak of acoustic phonons found in the Brillouin scattering spectrometers indicate that enlarged anharmonic ionic-potential could decrease the phonon lifetime rather than phonon speed, which
Author statement
Teng Wang: Methodology, Data curation, Writing-Original draft preparation, Formal analysis, Investigation. Kunpeng Dou: Software, Data Curation. Hongchao Wang: Conceptualization, Supervision, Project administration, Funding acquisition, Writing-Review & Editing. Jiyong Kim: Software. Xue Wang: Software. Wenbin Su: Supervision. Tingting Chen: Investigation. Woochul Kim: Supervision, Project administration, Funding acquisition, Writing-Review & Editing. Chunlei Wang: Supervision, Writing-Review &
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The work is financially supported by National Key R&D Program of China of 2017YFE0195200, the Natural Science Fund of China under grant Nos. 51871134, 52171216 and 5201101703, the Science Fund of Shandong Province under grant No. ZR2019MEM007, Qilu Young Scholar Program of Shandong University and a National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIP) (NRF-2018K1A3A1A20026439, 2021R1A4A1032129). The authors also thank Prof. Shishou Kang and Wenjun Zhang from
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These authors contributed equally.