Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

‘Big Bang’ tomography as a new route to atomic-resolution electron tomography

Nature volume 486, pages 243–246 (2012)Cite this article

Subjects

A Corrigendum to this article was published on 15 August 2012

Abstract

Until now it has not been possible to image at atomic resolution using classical electron tomographic methods1, except when the target is a perfectly crystalline nano-object imaged along a few zone axes2. The main reasons are that mechanical tilting in an electron microscope with sub-ångström precision over a very large angular range is difficult, that many real-life objects such as dielectric layers in microelectronic devices impose geometrical constraints and that many radiation-sensitive objects such as proteins limit the total electron dose. Hence, there is a need for a new tomographic scheme that is able to deduce three-dimensional information from only one or a few projections. Here we present an electron tomographic method that can be used to determine, from only one viewing direction and with sub-ångström precision, both the position of individual atoms in the plane of observation and their vertical position. The concept is based on the fact that an experimentally reconstructed exit wave3,4 consists of the superposition of the spherical waves that have been scattered by the individual atoms of the object. Furthermore, the phase of a Fourier component of a spherical wave increases with the distance of propagation at a known ‘phase speed’. If we assume that an atom is a point-like object, the relationship between the phase and the phase speed of each Fourier component is linear, and the distance between the atom and the plane of observation can therefore be determined by linear fitting. This picture has similarities with Big Bang cosmology, in which the Universe expands from a point-like origin such that the distance of any galaxy from the origin is linearly proportional to the speed at which it moves away from the origin (Hubble expansion). The proof of concept of the method has been demonstrated experimentally for graphene with a two-layer structure and it will work optimally for similar layered materials, such as boron nitride and molybdenum disulphide.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Big Bang analogy.
Figure 2: Phase of the exit wave of a two-layer graphene object.
Figure 3: Steps in the Hubble analysis.
Figure 4: Hubble plots and histogram of the focal distance.

References

  1. Midgley, P. A. & Dunin-Borkowski, R. E. Electron tomography and holography in materials science. Nature Mater. 8, 271–280 (2009)

    Article  ADS  CAS  Google Scholar 

  2. Van Aert, S. Batenburg, K. J., Rossell, M. D., Erni, R. & Van Tendeloo, R. Three- dimensional atomic imaging of crystalline nanoparticles. Nature 470, 374–377 (2011)

    Article  ADS  CAS  Google Scholar 

  3. Coene, W., Thust, A., Van Dyck, D. & Op de Beeck, M. Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy. Ultramicroscopy 64, 109–135 (1996)

    Article  CAS  Google Scholar 

  4. Hsieh, W. K., Chen, F. R., Kai, J. J. & Kirkland, A. I. Resolution extension and exit wave reconstruction in complex HREM. Ultramicroscopy 98, 99–114 (2004)

    Article  CAS  Google Scholar 

  5. Lehmann, M. & Lichte, H. Tutorial on off-axis electron holography. Microsc. Microanal. 8, 447–466 (2002)

    Article  ADS  CAS  Google Scholar 

  6. Van Dyck, D. Wave reconstruction in TEM using a variable phase plate. Ultramicroscopy 110, 571–572 (2010)

    Article  CAS  Google Scholar 

  7. Hubble, E. Effects of red shifts on the distribution of nebulae. Astrophys. J. 84, 517–554 (1936)

    Article  ADS  Google Scholar 

  8. Hubble, E. A relation between distance and radial velocity among extra-galactic nebulae. Proc. Natl Acad. Sci. USA 15, 168–173 (1929)

    Article  ADS  CAS  Google Scholar 

  9. Spence, J. C. H. High Resolution Electron Microscopy 3rd edn 61, 62 (Oxford Sci. Publ., 2003)

    Google Scholar 

  10. Bals, S., Van Aert, S., Van Tendeloo, G. & Avila-Brande, D. Statistical estimation of atomic positions from exit wave reconstruction with a precision in the picometer range. Phys. Rev. Lett. 96, 096106 (2006)

    Article  ADS  Google Scholar 

  11. Jinschek, J. R., Yucelen, E., Calderon, H. A. & Freitag, B. Quantitative atomic 3-D imaging of single/double sheet graphene structure. Carbon 49, 556–562 (2011)

    Article  CAS  Google Scholar 

  12. Reich, S., Maultzsch, J. & Thomsen, C. Tight-binding description of graphene. Phys. Rev. B 66, 035412 (2002)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge discussions with A. Wang, S. Van Aert and I. Lobato. D.V.D. acknowledges financial support from the “Research foundation - Flanders (FWO)” under project nos G.0220.05 and G.0188.08. F.-R.C. would like to acknowledge the support from NSC-100-2120-M-007-005 and NSC-99-2120-M-007-008. J.R.J. thanks E. Yucelen, R. Dunin-Borkowski and Ch. Kisielowski for support, and N. Alem and A. Zettl for the gift of the graphene sample.’’.

Author information

Authors and Affiliations

  1. University of Antwerp, Groenenborgerlaan 171, B2020 Antwerp, Belgium,

    Dirk Van Dyck

  2. FEI Europe, Europe NanoPort, Achtseweg Noord 5, 5651 CG Eindhoven, The Netherlands.,

    Joerg R. Jinschek

  3. National Tsing Hua University, Number 101, Section 2, Kuang-Fu Road, Hsin Chu, Taiwan 300, China,

    Fu-Rong Chen

Authors
  1. Dirk Van Dyck
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joerg R. Jinschek
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fu-Rong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

D.V.D. and F.-R.C. read and commented on the paper, and contributed equally to the work. J.R.J. provided the experimental images of graphene.

Corresponding authors

Correspondence to Dirk Van Dyck or Fu-Rong Chen.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text 1-2 and Supplementary Figures 1-2. (PDF 758 kb)

Supplementary Movie 1

This movie file shows the reconstructed tomography from Hubble analysis. It is a movie version for figure (b) and (c) of Supplementary Figures 1-2. (MOV 24837 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Van Dyck, D., Jinschek, J. & Chen, FR. ‘Big Bang’ tomography as a new route to atomic-resolution electron tomography. Nature 486, 243–246 (2012). https://doi.org/10.1038/nature11074

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature11074

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing