Convergent and divergent beam electron holography and reconstruction of adsorbates on free-standing two-dimensional crystals

Abstract

Van der Waals heterostructures have been lately intensively studied because they offer a large variety of properties that can be controlled by selecting 2D materials and their sequence in the stack. The exact arrangement of the layers as well as the exact arrangement of the atoms within the layers, both are important for the properties of the resulting device. However, it is very difficult to control and characterize the exact position of the atoms and the layers in such heterostructures, in particular, along the vertical (z) dimension. Recently it has been demonstrated that convergent beam electron diffraction (CBED) allows quantitative three-dimensional mapping of atomic positions in three-dimensional materials from a single CBED pattern. In this study we investigate CBED in more detail by simulating and performing various CBED regimes, with convergent and divergent wavefronts, on a somewhat simplified system: a two-dimensional (2D) monolayer crystal. In CBED, each CBED spot is in fact an in-line hologram of the sample, where in-line holography is known to exhibit high intensity contrast in detection of weak phase objects that are not detectable in conventional in-focus imaging mode. Adsorbates exhibit strong intensity contrast in the zero and higher order CBED spots, whereas lattice deformation such as strain or rippling cause noticeable intensity contrast only in the first and higher order CBED spots. The individual CBED spots can thus be reconstructed as typical in-line holograms, and a resolution of 2.13 Å can in principle be achieved in the reconstructions. We provide simulated and experimental examples of CBED of a 2D monolayer crystal. The simulations show that individual CBED spots can be treated as in-line holograms and sample distributions such as adsorbates, can be reconstructed. Individual atoms can be reconstructed from a single CBED pattern provided the later exhibits high-order CBED spots. The experimental results were obtained in a transmission electron microscope (TEM) at 80 keV on free-standing monolayer hBN containing adsorbates. Examples of reconstructions obtained from experimental CBED patterns at a resolution of 2.7 Å are shown. CBED technique can be potentially useful for imaging individual biological macromolecules, because it provides a relatively high resolution and does not require additional scanning procedure or multiple image acquisitions and therefore allows minimizing the radiation damage.

Keywords

graphene / two-dimensional materials / van der Waals structures / electron holography / convergent beam electron diffraction

References

[1] W. Kossel and G. Möllenstedt, Elektroneninterferenzen im konvergenten Bündel, Ann. Phys. 428(2), 113 (1939)

[2] J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, D. Obergfell, S. Roth, C. Girit, and A. Zettl, On the roughness of single- and bi-layer graphene membranes, Solid State Commun. 143(1–2), 101 (2007)

[3] T. Latychevskaia, W. H. Hsu, W. T. Chang, C. Y. Lin, and I. S. Hwang, Three-dimensional surface topography of graphene by divergent beam electron diffraction, Nat. Commun. 8, 14440 (2017)

[4] T. Latychevskaia, C. R. Woods, Y. B. Wang, M. Holwill, E. Prestat, S. J. Haigh, and K. S. Novoselov, Convergent beam electron holography for analysis of van der Waals heterostructures, Proc. Natl. Acad. Sci. USA 115(29), 7473 (2018)

[5] P. M. Kelly, A. Jostsons, R. G. Blake, and J. G. Napier, The determination of foil thickness by scanning transmission electron microscopy, Phys. Status Solidi A Appl. Res. 31(2), 771 (1975)

[6] P. Goodman, A practical method of three-dimensional space-group analysis using convergent-beam electron diffraction, Acta Crystallogr. A 31(6), 804 (1975)

[7] B. F. Buxton, J. A. Eades, J. W. Steeds, and G. M. Rackham, The symmetry of electron diffraction zone axis patterns, Philos. Trans. Royal Soc. A 281(1301), 171 (1976)

[8] P. M. Jones, G. M. Rackham, and J. W. Steeds, Higher order Laue zone effects in electron diffraction and their use in lattice parameter determination, Proc. R. Soc. London Ser. A 354 (1677), 197 (1977)

[9] J. C. H. Spence and J. M. Zuo, Electron Microdiffraction, Plenum Press, 1992

[10] J. M. Zuo and J. C. H. Spence, Advanced Transmission Electron Microscopy, Springer, 2017

[11] L. J. Wu, Y. M. Zhu, and J. Tafto, Picometer accuracy in measuring lattice displacements across planar faults by interferometry in coherent electron diffraction, Phys. Rev. Lett. 85(24), 5126 (2000)

[12] L. J. Wu, Y. M. Zhu, J. Tafto, D. O. Welch, and M. Suenaga, Quantitative analysis of twist boundaries and stacking faults in Bi-based superconductors by parallel recording of dark-field images with a coherent electron source, Phys. Rev. B 66(10), 104517 (2002)

[13] T. Latychevskaia, J. N. Longchamp, and H. W. Fink, When holography meets coherent diffraction imaging, Opt. Express 20(27), 28871 (2012)

[14] D. Gabor, A new microscopic principle, Nature 161(4098), 777 (1948)

[15] D. Gabor, Microscopy by reconstructed wave-fronts, Proc. R. Soc. Lond. A 197(1051), 454 (1949)

[16] E. J. Kirkland, Advanced Computing in Electron Microscopy, Springer, 2010

[17] J. J. Barton, Photoelectron holography, Phys. Rev. Lett. 61(12), 1356 (1988)

[18] T. Latychevskaia and H. W. Fink, Practical algorithms for simulation and reconstruction of digital in-line holograms, Appl. Opt. 54(9), 2424 (2015)

[19] T. Latychevskaia and H. W. Fink, Simultaneous reconstruction of phase and amplitude contrast from a single holographic record, Opt. Express 17(13), 10697 (2009)

[20] T. Latychevskaia, P. Formanek, C. T. Koch, and A. Lubk, Off-axis and inline electron holography: Experimental comparison, Ultramicroscopy 110(5), 472 (2010)

[21] T. Latychevskaia and H. W. Fink, Reconstruction of purely absorbing, absorbing and phase-shifting, and strong phase-shifting objects from their single-shot in-line holograms, Appl. Opt. 54(13), 3925 (2015)

[22] T. Matsumoto, T. Tanji, and A. Tonomura, Visualization of DNA in solution by Fraunhofer in-line electron holography (II): Experiments, Optik 100(2), 71 (1995)

[23] R. R. Nair, P. Blake, J. R. Blake, R. Zan, S. Anissimova, U. Bangert, A. P. Golovanov, S. V. Morozov, A. K. Geim, K. S. Novoselov, and T. Latychevskaia, Graphene as a transparent conductive support for studying biological molecules by transmission electron microscopy, Appl. Phys. Lett. 97(15), 153102 (2010)

[24] H. Adaniya, M. Cheung, C. Cassidy, M. Yamashita, and T. Shintake, Development of a SEM-based low-energy inline electron holography microscope for individual particle imaging, Ultramicroscopy 188, 31 (2018)

[25] R. S. Pantelic, J. C. Meyer, U. Kaiser, W. Baumeister, and J. M. Plitzko, Graphene oxide: A substrate for optimizing preparations of frozen-hydrated samples, J. Struct. Biol. 170(1), 152 (2010)

[26] A. Thust, W. M. J. Coene, M. Op de Beeck, and D. Van Dyck, Focal-series reconstruction in HRTEM: Simulation studies on non-periodic objects, Ultramicroscopy 64(1–4), 211 (1996)

[27] M. A. Dyson, A. M. Sanchez, J. P. Patterson, R. K. O’Reilly, J. Sloan, and N. R. Wilson, A new approach to high resolution, high contrast electron microscopy of macromolecular block copolymer assemblies, Soft Matter 9(14), 3741 (2013)

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