Full-landscape selection rules of electrons and phonons and temperature-induced effects in 2D silicon and germanium allotropes 

Le Shu, Yujie Xia, Ben Li, Lei Peng, Hezhu Shao, Zengxu Wang, Yan Ce, Heyuan Zhu & Hao Zhang

npj Computational Materials 10: 2 (2024); Published online: 02 January 2024

Editorial Summary

Electrons and phonons scattering: Importance of selection rules

The search for materials with a high thermoelectric figure of merit (zT) has attracted lots of attention for centuries. Silicon is the cornerstone of the semiconductor industry, with a high power factor, but its high lattice thermal conductivity limits its application in the thermoelectric field. However, the emergence of two-dimensional materials has broken this limitation and sparked strong interest in the potential thermoelectric properties of two-dimensional layered silicon and germanium. A team led by Professor Hao Zhang from Fudan University used first principles and group theory to investigate the temperature induced effect and the lattice thermal conductivity and thermoelectric merit corrected by the full electroacoustic coupling effect in two-dimensional silicon germanium allotropes.  This paper uses group theory to construct the full-landscape selection rules for intravalley and intervalley scattering for carriers in 2D Si and Ge allotropes, and finds that it is completely consistent with the results of first-principles numerical calculations. The selection rules for the three-phonon scattering channels for phonon-phonon interactions indicate that in 2D Si/Ge allotropes, the phase space P3 of the three-phonon interaction is mainly dominated by the emission process of optical phonon modes. The larger optical phonon bandwidth and optical flat band in LB and LHD Si/Ge respectively lead to significant aoo and ooo scattering phase spaces. In addition, temperature-induced effects significantly increase the ratio between mode-resolved four-phonon interactions and three-phonon interactions in most phonon frequency regions, and even lead to the disappearance of quasi acoustic-optical phonon band gaps. On this basis, this work accurately evaluated the thermoelectric properties of these materials by considering full electron-phonon coupling and high-order anharmonic phonon-phonon interaction. It was found that the maximum ZT values of LHD Si and LB Ge at 700 K reached 1.06 and 0.66, respectively, significantly exceeding their corresponding bulk materials. This work is poised to stimulate wide-ranging exploration into phonon transport across diverse materials, and benefits both fundamental knowledge and advanced technologies of 2D Si/Ge allotropes.

编辑概述 

二维材料电声子散射：选择定则的重要性

由于热电材料在废热发电和固态制冷等领域有着广泛的应用前景，人们一直在努力提高热电材料的性能。硅材料是半导体工业的基石，具有很高的功率因子，但其高晶格热导率限制了它在热电领域的应用。然而，二维材料的出现打破了这一局限，激发了人们对于二维层状硅和锗潜在热电特性的浓厚兴趣。该研究提出了一种对硅烯和锗烯热电性能的准确预测，揭示了谷间散射和温度诱导效应在确定热电优值的电子输运部分中的关键作用，并且展示了热电材料的计算框架以及选择定则在电声散射和声声散射中的应用。来自复旦大学的张浩副教授、温州大学邵和助副研究员与南京邮电大学王增旭研究团队，利用第一性原理和群论探究了二维硅锗同素异形体中温度诱导效应以及全电声耦合作用修正的晶格热导率和热电优值。该研究利用群论构建了二维硅/锗同素异形体中载流子谷内和谷间散射的全景选择定则，发现与第一性原理数值计算的结果完全一致。对于声子-声子相互作用，三声子散射通道的选择定则表明，在二维硅/锗同素异形体中，三声子相互作用的相空间P3主要由光学声子模式的发射过程所主导，LB和LHD Si/Ge中较大的光学声子带宽和光学平带分别导致了显著的声学-光学-光学（aoo）和光学-光学-光学（ooo）散射相空间。此外，温度诱导效应引起的非谐性变化随温度升高而加剧，特别是在LHD Ge中，声光声子带隙的消失导致群速度和格林艾森常数显著增加。研究比较了三声子与四声子散射率，发现温度效应在大部分声子频率区域中显著增加了模式分辨的四声子相互作用与三声子相互作用之间的比率，这一发现有助于解释LB和LHD Si/Ge中低热导率的原因。在这一基础上，本文通过考虑全电声耦合及高阶非谐声子-声子相互作用，对这些材料的热电性能进行了精确评估，发现LHD Si和LB Ge在700 K下的最大ZT值分别达到1.06和0.66，显著超过了它们相应的体相材料。研究成果不仅为二维硅/锗同素异形体的物理性质和应用潜力提供了更全面的理解，也可能激发对其他材料中声子输运机制的广泛研究。