Higher-order anharmonicity leads to ultra-low thermal conductivity and high output power density of SnTe-based thermoelectric materials and modules

Highlights

• Quartic an-harmonic term plays an important role for Cu/Mn doped SnTe samples.

• Enhanced anharmonicity results in short phonon lifetime and ultra-low κ_L.

• A maximum figure of merit 1.3 is achieved.

• Maximum hot side temperature difference and output power density are increased.

Abstract

Higher-order anharmonicity is found in copper and manganese doped tin telluride (SnTe) alloys, and its effect on thermoelectric performance is systematically studied. Analyzation of thermal expansion shows that the ionic potential not only consists of cubic term, but also quartic term. Short phonon lifetime derived from more diffused peak of Brillouin spectrometer results from the higher-order anharmonicity. As a result, an ultra-low lattice thermal conductivity of 0.5 Wm⁻¹K⁻¹ is achieved. Soft optical phonon mode was observed from Raman spectrometer, the transverse optical - longitudinal acoustic phonon interaction may be the reason for the enhanced anharmonicity. Combining with the enlarged power factor caused by band convergence, the highest figure of merit reaches 1.3 at 873 K for doped samples. Additionally, the large temperature difference of 600 K and high output power densities of 291 mWmm⁻³ of simulated SnTe uni-leg module are achieved. This work supplies way for revealing the anharmonicity experimentally, and proves modification of intrinsic anharmonicity is an avenue for enhancing the thermoelectric performance of SnTe alloys.

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 κ_e, dilemma appears when one tries to increase zT without comprehensive considerations [3]. On the other hand, decreasing the lattice thermal conductivity κ_L 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 κ_L is crucial. To this end, in-situ defects introduced by copper (Cu) doping was reported lowering κ_L 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 κ_L 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 κ_L 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 κ_L 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 κ_L [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 κ_L 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 κ_L 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 κ_L. 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.