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Electron ptychography of 2D materials to deep sub-ångström resolution

Abstract

Aberration-corrected optics have made electron microscopy at atomic resolution a widespread and often essential tool for characterizing nanoscale structures. Image resolution has traditionally been improved by increasing the numerical aperture of the lens (α) and the beam energy, with the state-of-the-art at 300 kiloelectronvolts just entering the deep sub-ångström (that is, less than 0.5 ångström) regime. Two-dimensional (2D) materials are imaged at lower beam energies to avoid displacement damage from large momenta transfers, limiting spatial resolution to about 1 ångström. Here, by combining an electron microscope pixel-array detector with the dynamic range necessary to record the complete distribution of transmitted electrons and full-field ptychography to recover phase information from the full phase space, we increase the spatial resolution well beyond the traditional numerical-aperture-limited resolution. At a beam energy of 80 kiloelectronvolts, our ptychographic reconstruction improves the image contrast of single-atom defects in MoS2 substantially, reaching an information limit close to 5α, which corresponds to an Abbe diffraction-limited resolution of 0.39 ångström, at the electron dose and imaging conditions for which conventional imaging methods reach only 0.98 ångström.

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Fig. 1: STEM imaging using the EMPAD.
Fig. 2: Comparison of different imaging techniques using 4D EMPAD dataset measured from monolayer MoS2.
Fig. 3: Real-space resolution test of full-field ptychography using twisted bilayer MoS2.
Fig. 4: Ptychographic reconstructions using data with different cutoff angles.
Fig. 5: Simulation study of full-field ptychography as a function of cutoff angle and beam current.
Fig. 6: Comparison between ptychographic techniques and low-angle ADF imaging at low electron doses.

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References

  1. Meyer, J. C., Girit, C. O., Crommie, M. F. & Zettl, A. Imaging and dynamics of light atoms and molecules on graphene. Nature 454, 319–322 (2008).

    Article  ADS  PubMed  CAS  Google Scholar 

  2. Krivanek, O. L. et al. Atom-by-atom structural and chemical analysis by annular dark-field electron microscopy. Nature 464, 571–574 (2010).

    Article  ADS  PubMed  CAS  Google Scholar 

  3. Huang, P. Y. et al. Grains and grain boundaries in single-layer graphene atomic patchwork quilts. Nature 469, 389–392 (2011).

    Article  ADS  PubMed  CAS  Google Scholar 

  4. Sparrow, C. M. On spectroscopic resolving power. Astrophys. J. 44, 76–86 (1916).

    Article  ADS  Google Scholar 

  5. Black, G. & Linfoot, E. H. Spherical aberration and the information content of optical images. Proc. R. Soc. Lond. A 239, 522–540 (1957).

    Article  ADS  MATH  CAS  Google Scholar 

  6. Haider, M. et al. Electron microscopy image enhanced. Nature 392, 768–769 (1998).

    Article  ADS  CAS  Google Scholar 

  7. Batson, P. E., Dellby, N. & Krivanek, O. L. Sub-ångström resolution using aberration corrected electron optics. Nature 418, 617–620 (2002).

    Article  ADS  PubMed  CAS  Google Scholar 

  8. Erni, R., Rossell, M. D., Kisielowski, C. & Dahmen, U. Atomic-resolution imaging with a sub-50-pm electron probe. Phys. Rev. Lett. 102, 096101 (2009).

    Article  ADS  PubMed  CAS  Google Scholar 

  9. Sawada, H. et al. STEM imaging of 47-pm-separated atomic columns by a spherical aberration-corrected electron microscope with a 300-kV cold field emission gun. J. Electron Microsc. 58, 357–361 (2009).

    Article  CAS  Google Scholar 

  10. Kaiser, U. et al. Transmission electron microscopy at 20kV for imaging and spectroscopy. Ultramicroscopy 111, 1239–1246 (2011).

    Article  PubMed  CAS  Google Scholar 

  11. Meyer, J. C. et al. Accurate measurement of electron beam induced displacement cross sections for single-layer graphene. Phys. Rev. Lett. 108, 196102 (2012).

    Article  ADS  PubMed  CAS  Google Scholar 

  12. Sawada, H., Sasaki, T., Hosokawa, F. & Suenaga, K. Atomic-resolution STEM imaging of graphene at low voltage of 30 kV with resolution enhancement by using large convergence angle. Phys. Rev. Lett. 114, 166102 (2015).

    Article  ADS  PubMed  CAS  Google Scholar 

  13. Linck, M. et al. Chromatic aberration correction for atomic resolution TEM imaging from 20 to 80 kV. Phys. Rev. Lett. 117, 076101 (2016).

    Article  ADS  PubMed  CAS  Google Scholar 

  14. Henderson, R. The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of unstained biological molecules. Q. Rev. Biophys. 28, 171–193 (1995).

    Article  PubMed  CAS  Google Scholar 

  15. Gabor, D. A new microscopic principle. Nature 161, 777–778 (1948).

    Article  ADS  PubMed  CAS  Google Scholar 

  16. Hoppe, W. Beugung im inhomogenen Primärstrahlwellenfeld. I. Prinzip einer Phasenmessung von Elektronenbeungungsinterferenzen. Acta Crystallogr. A 25, 495–501 (1969).

    Article  ADS  Google Scholar 

  17. Nellist, P. D., McCallum, B. C. & Rodenburg, J. M. Resolution beyond the ‘information limit’ in transmission electron microscopy. Nature 374, 630–632 (1995).

    Article  ADS  CAS  Google Scholar 

  18. Nellist, P. D. & Rodenburg, J. M. Electron ptychography. I. Experimental demonstration beyond the conventional resolution limits. Acta Crystallogr. A 54, 49–60 (1998).

    Article  Google Scholar 

  19. Thibault, P. et al. High-resolution scanning X-ray diffraction microscopy. Science 321, 379–382 (2008).

    Article  ADS  PubMed  CAS  Google Scholar 

  20. Maiden, A. M. & Rodenburg, J. M. An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy 109, 1256–1262 (2009).

    Article  PubMed  CAS  Google Scholar 

  21. Thibault, P. & Menzel, A. Reconstructing state mixtures from diffraction measurements. Nature 494, 68–71 (2013).

    Article  ADS  PubMed  CAS  Google Scholar 

  22. Li, P., Edo, T. B. & Rodenburg, J. M. Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design. Ultramicroscopy 147, 106–113 (2014).

    Article  PubMed  CAS  Google Scholar 

  23. Yang, H. et al. Simultaneous atomic-resolution electron ptychography and Z-contrast imaging of light and heavy elements in complex nanostructures. Nat. Commun. 7, 12532 (2016).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  24. Pelz, P. M., Qiu, W. X., Bücker, R., Kassier, G. & Miller, R. J. D. Low-dose cryo electron ptychography via non-convex Bayesian optimization. Sci. Rep. 7, 9883 (2017).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  25. Maiden, A. M., Humphry, M. J. & Rodenburg, J. M. Ptychographic transmission microscopy in three dimensions using a multi-slice approach. J. Opt. Soc. Am. A 29, 1606–1614 (2012).

    Article  ADS  CAS  Google Scholar 

  26. Gao, S. et al. Electron ptychographic microscopy for three-dimensional imaging. Nat. Commun. 8, 163 (2017).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  27. Rodenburg, J. M., Hurst, A. C. & Cullis, A. G. Transmission microscopy without lenses for objects of unlimited size. Ultramicroscopy 107, 227–231 (2007).

    Article  PubMed  CAS  Google Scholar 

  28. Rodenburg, J. M. et al. Hard-X-ray lensless imaging of extended objects. Phys. Rev. Lett. 98, 034801 (2007).

    Article  ADS  PubMed  CAS  Google Scholar 

  29. Hüe, F., Rodenburg, J. M., Maiden, A. M., Sweeney, F. & Midgley, P. A. Wave-front phase retrieval in transmission electron microscopy via ptychography. Phys. Rev. B 82, 121415 (2010).

    Article  ADS  CAS  Google Scholar 

  30. Hüe, F., Rodenburg, J. M., Maiden, A. M. & Midgley, P. A. Extended ptychography in the transmission electron microscope: possibilities and limitations. Ultramicroscopy 111, 1117–1123 (2011).

    Article  PubMed  CAS  Google Scholar 

  31. Putkunz, C. T. et al. Atom-scale ptychographic electron diffractive imaging of boron nitride cones. Phys. Rev. Lett. 108, 073901 (2012).

    Article  ADS  PubMed  CAS  Google Scholar 

  32. D’Alfonso, A. J. et al. Deterministic electron ptychography at atomic resolution. Phys. Rev. B 89, 064101 (2014).

    Article  ADS  CAS  Google Scholar 

  33. Pennycook, T. J. et al. Efficient phase contrast imaging in STEM using a pixelated detector. Part 1: experimental demonstration at atomic resolution. Ultramicroscopy 151, 160–167 (2015).

    Article  PubMed  CAS  Google Scholar 

  34. Yang, H. et al. Electron ptychographic phase imaging of light elements in crystalline materials using Wigner distribution deconvolution. Ultramicroscopy 180, 173–179 (2017).

    Article  PubMed  CAS  Google Scholar 

  35. Wang, P., Zhang, F., Gao, S., Zhang, M. & Kirkland, A. I. Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals. Sci. Rep. 7, 2857 (2017).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  36. Humphry, M. J., Kraus, B., Hurst, A. C., Maiden, A. M. & Rodenburg, J. M. Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging. Nat. Commun. 3, 730 (2012).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  37. Frojdh, E. et al. Count rate linearity and spectral response of the Medipix3RX chip coupled to a 300μm silicon sensor under high flux conditions. J. Instrum. 9, C04028 (2014).

    Article  Google Scholar 

  38. Rose, A. Vision Human and Electronic Ch. 1 (Plenum Press, New York, 1949).

    Google Scholar 

  39. Tate, M. W. et al. High dynamic range pixel array detector for scanning transmission electron microscopy. Microsc. Microanal. 22, 237–249 (2016).

    Article  ADS  PubMed  CAS  Google Scholar 

  40. Close, R., Chen, Z., Shibata, N. & Findlay, S. D. Towards quantitative, atomic-resolution reconstruction of the electrostatic potential via differential phase contrast using electrons. Ultramicroscopy 159, 124–137 (2015).

    Article  PubMed  CAS  Google Scholar 

  41. Lazić, I., Bosch, E. G. T. & Lazar, S. Phase contrast STEM for thin samples: integrated differential phase contrast. Ultramicroscopy 160, 265–280 (2016).

    Article  PubMed  CAS  Google Scholar 

  42. Maiden, A. M., Humphry, M. J., Zhang, F. & Rodenburg, J. M. Superresolution imaging via ptychography. J. Opt. Soc. Am. A 28, 604–612 (2011).

    Article  ADS  Google Scholar 

  43. Rodenburg, J. M. & Bates, R. H. T. The theory of super-resolution electron microscopy via Wigner-distribution deconvolution. Philos. Trans. R. Soc. Lond. A 339, 521–553 (1992).

    Article  ADS  Google Scholar 

  44. Lee, J. & Barbastathis, G. Denoised Wigner distribution deconvolution via low-rank matrix completion. Opt. Express 24, 20069–20079 (2016).

    Article  ADS  PubMed  Google Scholar 

  45. Abbe, E. The relation of aperture and power in the microscope. J. R. Microsc. Soc. 2, 300–309 (1882).

    Article  Google Scholar 

  46. van der Zande, A. M. et al. Tailoring the electronic structure in bilayer molybdenum disulfide via interlayer twist. Nano Lett. 14, 3869–3875 (2014).

    Article  ADS  PubMed  CAS  Google Scholar 

  47. Hovden, R. & Muller, D. A. Efficient elastic imaging of single atoms on ultrathin supports in a scanning transmission electron microscope. Ultramicroscopy 123, 59–65 (2012).

    Article  PubMed  CAS  Google Scholar 

  48. Zuo, C., Sun, J. & Chen, Q. Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy. Opt. Express 24, 20724–20744 (2016).

    Article  ADS  PubMed  Google Scholar 

  49. Maiden, A., Johnson, D. & Li, P. Further improvements to the ptychographical iterative engine. Optica 4, 736–745 (2017).

    Article  Google Scholar 

  50. Suzuki, A. et al. High-resolution multislice X-ray ptychography of extended thick objects. Phys. Rev. Lett. 112, 053903 (2014).

    Article  ADS  PubMed  CAS  Google Scholar 

  51. Hovden, R., Jiang, Y., Xin, H. L. & Kourkoutis, L. F. Periodic artifact reduction in Fourier transforms of full field atomic resolution images. Microsc. Microanal. 21, 436–441 (2015).

    Article  ADS  PubMed  CAS  Google Scholar 

  52. Allen, L. J., D’Alfonso, A. J. & Findlay, S. D. Modelling the inelastic scattering of fast electrons. Ultramicroscopy 151, 11–22 (2015).

    Article  PubMed  CAS  Google Scholar 

  53. Waasmaier, D. & Kirfel, A. New analytical scattering-factor functions for free atoms and ions. Acta Crystallogr. A 51, 416–431 (1995).

    Article  Google Scholar 

  54. Nellist, P. D. & Rodenburg, J. M. Beyond the conventional information limit: the relevant coherence function. Ultramicroscopy 54, 61–74 (1994).

    Article  Google Scholar 

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Acknowledgements

Y.J. and V.E. acknowledge support from DOE grant DE-SC0005827. Z.C. and D.A.M. are supported by the PARADIM Materials Innovation Platform in-house programme by NSF grant DMR-1539918. We acknowledge the electron microscopy facility and support for Y.H. from the NSF MRSEC programme (DMR 1719875) and NSF MRI grant DMR-1429155. H.G., S.X. and J.P. acknowledge additional support from AFOSR MURI (FA9550-16-1-003) and UChicago NSF MRSEC programme (DMR 1420709). Detector development at Cornell was supported by the Kavli Institute at Cornell for Nanoscale Science and DOE grant DE-SC0017631 to S.M.G. We thank K. Nguyen, P. Huang, M. Humphry and P. Nellist for discussions and B. Jiang from Thermo Scientific for help during the initial experiments.

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Nature thanks J. Rodenburg and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Authors and Affiliations

Authors

Contributions

Experiments were performed and designed by Z.C., Y.H. and D.A.M. Y.J. contributed to data analysis and ptychographic reconstruction, with support from V.E. Sample preparation was done by P.D. and Y.H., from MoS2 thin films synthesized by H.G., S.X. and J.P. EMPAD was optimized by P.P., M.W.T. and S.M.G. All authors discussed the results and implications throughout the investigation. All authors have approved the final version of the manuscript.

Corresponding author

Correspondence to David A. Muller.

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Cornell University has licensed the EMPAD hardware to Thermo Scientific.

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Extended data figures and tables

Extended Data Fig. 1 Position-averaged diffraction pattern of the 4D dataset from monolayer MoS2.

a, Position-averaged convergent beam electron diffraction (CBED) pattern from the 4D dataset from monolayer MoS2. b, Radially averaged intensity distribution (on a logarithmic scale) of the CBED pattern, showing the dynamic range spanned by the scattering distribution.

Extended Data Fig. 2 Line profiles through atom pairs in the twisted bilayer MoS2.

Line profiles are from atom pairs in Fig. 3, with the respective subregions shown on the left. ac, The measured peak–peak separations between two atoms are 0.42 ± 0.02 Å (a), 0.61 ± 0.02 Å (b) and 0.85 ± 0.02 Å (c).

Extended Data Fig. 3 ADF image and line profiles through atom pairs in the twisted bilayer MoS2.

a, ADF image synthesized from the 4D diffraction dataset. b, Phase of the transmission function reconstructed by ptychography. The yellow marker indicates a pair of atoms that is predicted to have a separation of 0.2 Å on the basis of the structural model, but cannot be resolved explicitly in our reconstruction. For a more detailed comparison, a red box is placed over corresponding regions in a and b. c, Enlarged image of the red boxed region in b, with the false colour scale of Fig. 3. d, Line profiles across the atom pairs labelled with dashed lines in c. The peak–peak separations are overlaid near the line profiles.

Extended Data Fig. 4 Reconstructed amplitude and phase of monolayer MoS2 at different cutoff angles.

Both the amplitude (left panels) and phase (right panels) of the reconstructed transmission function show the atomic structure of monolayer MoS2. Image resolution improves as the cutoff angle increases. Amplitude modulations are relatively weak, deviating by only a few per cent from a pure phase object (that is, an object function with unit amplitude).

Extended Data Fig. 5 Comparison between ptychography techniques and low-angle ADF imaging of graphene.

a, b, Ptychographic reconstructions of simulated data with an in-focused probe, using the WDD (a) and ePIE (b) methods. c, Low-angle ADF (integrating from 1α to 4α) reconstruction using the same simulated datasets. Both ptychographic methods show similar reconstructions and are about 10 times more dose-efficient than the low-angle ADF technique. Beam energy, 80 keV; aperture size (α), 21.4 mrad.

Extended Data Fig. 6 Influence of scanning drift and contamination.

ac, ADF image (a), iCoM image (b) and phase of transmission reconstructed by full-field ptychography (c) using 128 × 128 diffraction patterns, covering a field of view of 2.7 nm × 2.7 nm. The ADF and iCoM reconstructions both suffer from stripe artefacts and large contrast variations. In the ptychographic reconstruction, scanning drift distorts and blurs reconstructed atoms in the vicinity of the scan distortion, but the overall resolution away from the distortion remains higher than the other imaging modes.

Extended Data Fig. 7 Effect of dose and cutoff angles on ptychographic reconstructions of monolayer MoS2 using simulated diffraction patterns.

At high beam current, the resolution of the ptychography reconstruction is fundamentally determined by the collection angle of the detector. As the beam current decreases, the resolution becomes dose-limited and noise artefacts start to appear in the ePIE reconstruction. Beam energy, 80 keV; aperture size (α), 21.4 mrad.

Extended Data Fig. 8 Effect of chromatic aberrations at different electron doses for ptychographic reconstructions of monolayer MoS2 using simulated datasets at 80 keV.

Two convergence semi-angles are shown, 21.4 mrad (left two columns) and 35 mrad (right two columns), representing conditions under which chromatic aberrations have moderate and large effects on the incident probe shape, respectively (Cc = 1.72 mm, ΔE = 1.1 eV). 21.4 mrad is also the experimental convergence angle. The incident electron dose levels are an infinite dose (top row), the experimental dose of 1.16 × 105 electrons per Å2 (middle row) and a low dose of 104 electrons per Å2 (bottom row). In the presence of noise, chromatic aberrations degrade the phase range of the reconstruction compared with the achromatic data. The data for the larger convergence semi-angle are more strongly affected. At infinite and experimental doses, ptychographic reconstructions with and without chromatic aberration are visually similar for both convergence angles. At low dose and with chromatic aberration, the reconstructed atoms are broadened, and distinct artefacts appear for a convergence angle of 35 mrad.

Supplementary information

Video 1: Evolution of unit-cell averaged diffraction patterns at various scan positions.

The left panel shows a synthesized ADF image from a unit-cell averaged 4D dataset, and the right panels show the averaged diffraction patterns from the scan positions marked with the red circle on the left ADF image. The intensity of the diffraction patterns are displayed on a linear scale to show variations in the centre disk (upper right panel) and a logarithmic scale to show variations in the weaker the dark field disks (lower right panel), respectively.

Video 2: Evolution of raw diffraction patterns at various scan positions.

The left panel shows a synthesized ADF image from a raw 4D dataset, and the right panels show the diffraction patterns from the scan positions marked with the circle on the left ADF image. The intensity of the diffraction patterns are displayed on a linear scale to show variations in the centre disk (upper right panel) and a logarithmic scale to show variations in the weaker the dark field disks (lower right panel), respectively.

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Jiang, Y., Chen, Z., Han, Y. et al. Electron ptychography of 2D materials to deep sub-ångström resolution. Nature 559, 343–349 (2018). https://doi.org/10.1038/s41586-018-0298-5

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