期刊
ULTRAMICROSCOPY
卷 219, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.ultramic.2020.113020
关键词
Graphene; Twisted bilayer graphene; Multilayer graphene; van der Waals structures; Interlayer distance; Transmission electron microscopy; TEM; Convergent beam electron diffraction; CBED
类别
资金
- European Union Graphene Flagship Program
- European Research Council Synergy [319277]
- European Research Council [715502]
- Royal Society, UK
- Engineering and Physical Sciences Research Council (UK)
- US Army Research Office [W911NF-161-0279]
- Defense Threat Reduction Agency, USA [HDTRA1-12-1-0013]
- Engineering and Physical Sciences Research Council (UK) [EP/K016946/1, EP/L01548X/1, EP/M010619/1, EP/P009050/1]
- European Research Council (ERC) [715502, 319277] Funding Source: European Research Council (ERC)
- EPSRC [EP/K005014/1, EP/P009050/1, EP/M010619/1, EP/K016946/1] Funding Source: UKRI
The convergent beam electron diffraction (CBED) patterns of twisted bilayer samples exhibit interference patterns in their CBED spots. Such interference patterns can be treated as off-axis holograms and the phase of the scattered waves, meaning the interlayer distance can be reconstructed. A detailed protocol of the reconstruction procedure is provided in this study. In addition, we derive an exact formula for reconstructing the interlayer distance from the recovered phase distribution, which takes into account the different chemical compositions of the individual monolayers. It is shown that one interference fringe in a CBED spot is sufficient to reconstruct the distance between the layers, which can be practical for imaging samples with a relatively small twist angle or when probing small sample regions. The quality of the reconstructed interlayer distance is studied as a function of the twist angle. At smaller twist angles, the reconstructed interlayer distance distribution is more precise and artefact free. At larger twist angles, artefacts due to the moire structure appear in the reconstruction. A method for the reconstruction of the average interlayer distance is presented. As for resolution, the interlayer distance can be reconstructed by the holographic approach at an accuracy of +/- 0.5 angstrom, which is a few hundred times better than the intrinsic z-resolution of diffraction limited resolution, as expressed through the spread of the measured k-values. Moreover, we show that holographic CBED imaging can detect variations as small as 0.1 angstrom in the interlayer distance, though the quantitative reconstruction of such variations suffers from large errors.
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