二维材料堆叠方式的电子衍射研究

二维材料堆叠方式的电子衍射研究

王春雯，王照清，姚 湲*，周 武*

（1. 中国科学院大学，物理科学学院，北京100049；2. 中国科学院物理研究所，先进材料与结构分析实验室，北京 100090）

摘 要 二维材料的电子衍射花样与晶体结构密切相关。此前已有不少工作利用电子衍射花样从实验上识别二维材料的层数、堆叠方式、层间转角等，但此前的工作尚未给出二维材料的电子衍射花样与晶体结构之间的定量解析表达式。本文通过理论推导，得到电子衍射强度随二维材料样品倾转角度的变化公式，并利用石墨烯与MoSe2样品对公式的有效性进行定量的实验验证。在此基础上，通过选定特定电子衍射斑点进行透射电镜暗场成像，实现对不同堆垛方式的双层石墨烯的区分以及晶畴分布的实空间成像，展示了电子衍射在二维材料结构分析方面的应用潜力。该研究给出的电子衍射强度公式可用于包括石墨烯/氮化硼异质结、过渡金属硫族化合物等在内的各种二维材料的堆叠方式、组成成分的研究。

关键词 透射电子显微学；电子衍射；二维材料；堆叠方式

中图分类号：O722；TG115.21+5.3 文献识别码：A Doi:10.3969/j.issn.1000-6281.2025.02.007

Electron diffraction intensity study of stacking orders of two-dimensional materials

WANG Chunwen，WANG Zhaoqing，YAO Yuan*，ZHOU Wu*

(1. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049；2. Institute of Physics, Chinese Academy of Sciences, Laboratory of Advanced Materials and Structural Analysis, Beijing 100090，China)

Abstract Electron diffraction provides valuable insights into the crystal structures of two-dimensional (2D) materials. Previous studies have utilized electron diffraction patterns to identify layer numbers, stacking orders, interlayer twist angles, and other properties of 2D materials. However, quantitative analytical expressions that relate the intensity of electron diffraction patterns of 2D materials to their crystal structures have not been reported. In this paper, we derive a formula that describes the variation of electron diffraction intensity as a function of tilt angle of 2D materials relative to the electron beam direction. The formula is quantitatively verified by experiments using few-layered graphene and MoSe2. Using this formula, we obtained real-space images of the spatial distribution of crystal domains with AB and BA stacking orders within twisted bilayer graphene by selecting specific electron diffraction spots for transmission electron microscopy dark-field imaging. This work demonstrates the important application of the formula in the structural analysis of 2D materials. The formula can be extended to investigate the stacking orders and components of various 2D materials and their heterostructures, including graphene/boron nitride heterostructures and transition metal dichalcogenides.

Keywords transmission electron microscopy; electron diffraction; 2D materials; stacking order

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