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.

  • Article
  • Published:

Real-space charge-density imaging with sub-ångström resolution by four-dimensional electron microscopy

Nature volume 575, pages 480–484 (2019)Cite this article

Subjects

Abstract

The distribution of charge density in materials dictates their chemical bonding, electronic transport, and optical and mechanical properties. Indirectly measuring the charge density of bulk materials is possible through X-ray or electron diffraction techniques by fitting their structure factors1,2,3, but only if the sample is perfectly homogeneous within the area illuminated by the beam. Meanwhile, scanning tunnelling microscopy and atomic force microscopy enable us to see chemical bonds, but only on the surface4,5,6. It remains a challenge to resolve charge density in nanostructures and functional materials with imperfect crystalline structures—such as those with defects, interfaces or boundaries at which new physics emerges. Here we describe the development of a real-space imaging technique that can directly map the local charge density of crystalline materials with sub-ångström resolution, using scanning transmission electron microscopy alongside an angle-resolved pixellated fast-electron detector. Using this technique, we image the interfacial charge distribution and ferroelectric polarization in a SrTiO3/BiFeO3 heterojunction in four dimensions, and discover charge accumulation at the interface that is induced by the penetration of the polarization field of BiFeO3. We validate this finding through side-by-side comparison with density functional theory calculations. Our charge-density imaging method advances electron microscopy from detecting atoms to imaging electron distributions, providing a new way of studying local bonding in crystalline solids.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Fig. 1: Experimental setup and the electric field in SrTiO3.
Fig. 2: Atomic structure and electric-field dipole of BiFeO3.
Fig. 3: Real-space charge-density mapping in SrTiO3 and BiFeO3.
Fig. 4: Charge-density map, O octahedron rotation and valence charge state at the interface between SrTiO3 and BiFeO3.

Similar content being viewed by others

Data availability

The datasets generated or analysed here are available from the corresponding authors on reasonable request.

References

  1. Midgley, P. A. Electronic bonding revealed by electron diffraction. Science 331, 1528–1529 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  2. Zuo, J. M., Kim, M., O’Keeffe, M. & Spence, J. C. H. Direct observation of d-orbital holes and Cu–Cu bonding in Cu2O. Nature 401, 49–52 (1999).

    Article  ADS  CAS  Google Scholar 

  3. Nakashima, P. N. H., Smith, A. E., Etheridge, J. & Muddle, B. C. The bonding electron density in aluminum. Science 331, 1583–1586 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  4. Han, Z. et al. Imaging the halogen bond in self-assembled halogenbenzenes on silver. Science 358, 206–210 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  5. Altman, E. I., Baykara, M. Z. & Schwarz, U. D. Noncontact atomic force microscopy: an emerging tool for fundamental catalysis research. Acc. Chem. Res. 48, 2640–2648 (2015).

    Article  CAS  PubMed  Google Scholar 

  6. Mohn, F., Gross, L., Moll, N. & Meyer, G. Imaging the charge distribution within a single molecule. Nat. Nanotechnol. 7, 227–231 (2012).

    Article  ADS  CAS  PubMed  Google Scholar 

  7. Shibata, N. et al. Differential phase-contrast microscopy at atomic resolution. Nat. Phys. 8, 611–615 (2012).

    Article  CAS  Google Scholar 

  8. Shibata, N. et al. Direct visualization of local electromagnetic field structures by scanning transmission electron microscopy. Acc. Chem. Res. 50, 1502–1512 (2017).

    Article  CAS  PubMed  Google Scholar 

  9. Müller-Caspary, K. et al. Measurement of atomic electric fields and charge densities from average momentum transfers using scanning transmission electron microscopy. Ultramicroscopy 178, 62–80 (2017).

    Article  PubMed  CAS  Google Scholar 

  10. Müller, K. et al. Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction. Nat. Commun. 5, 5653 (2014).

    Article  ADS  PubMed  CAS  Google Scholar 

  11. LeBeau, J. M., Findlay, S. D., Allen, L. J. & Stemmer, S. Position averaged convergent beam electron diffraction: theory and applications. Ultramicroscopy 110, 118–125 (2010).

    Article  CAS  PubMed  Google Scholar 

  12. Wang, J. et al. Epitaxial BiFeO3 multiferroic thin film heterostructures. Science 299, 1719–1722 (2003).

    Article  ADS  CAS  PubMed  Google Scholar 

  13. Seshadri, R. & Hill, N. A. Visualizing the role of Bi 6s “lone pairs” in the off-center distortion in ferromagnetic BiMnO3. Chem. Mater. 13, 2892–2899 (2001).

    Article  CAS  Google Scholar 

  14. Kim, Y.-M. et al. Direct observation of ferroelectric field effect and vacancy-controlled screening at the BiFeO3/LaxSr1−xMnO3 interface. Nat. Mater. 13, 1019–1025 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  15. Nelson, C. T. et al. Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces. Nano Lett. 11, 828–834 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  16. Gauss, C. F. in Werke: Fünfter Band 3–22 (Springer, 1877).

  17. Moon, E. J. et al. Spatial control of functional properties via octahedral modulations in complex oxide superlattices. Nat. Commun. 5, 5710 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Thomas, S. et al. Localized control of Curie temperature in perovskite oxide film by capping-layer-induced octahedral distortion. Phys. Rev. Lett. 119, 177203 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  19. Li, J. et al. Dramatically enhanced polarization in (001), (101), and (111) BiFeO3 thin films due to epitiaxial-induced transitions. Appl. Phys. Lett. 84, 5261–5263 (2004).

    Article  ADS  CAS  Google Scholar 

  20. Yu, P., Chu, Y.-H. & Ramesh, R. Oxide interfaces: pathways to novel phenomena. Mater. Today 15, 320–327 (2012).

    Article  CAS  Google Scholar 

  21. Spaldin, N. A., Cheong, S.-W. & Ramesh, R. Multiferroics: past, present, and future. Phys. Today 63, 38–43 (2010).

    Article  Google Scholar 

  22. Bert, J. A. et al. Direct imaging of the coexistence of ferromagnetism and superconductivity at the LaAlO3/SrTiO3 interface. Nat. Phys. 7, 767–771 (2011).

    Article  CAS  Google Scholar 

  23. Li, L., Richter, C., Mannhart, J. & Ashoori, R. C. Coexistence of magnetic order and two-dimensional superconductivity at LaAlO3/SrTiO3 interfaces. Nat. Phys. 7, 762–766 (2011).

    Article  CAS  Google Scholar 

  24. Reyren, N. et al. Superconducting interfaces between insulating oxides. Science 317, 1196–1199 (2007).

    Article  ADS  CAS  PubMed  Google Scholar 

  25. Tsukazaki, A. et al. Quantum hall effect in polar oxide heterostructures. Science 315, 1388–1391 (2007).

    Article  ADS  CAS  PubMed  Google Scholar 

  26. Zhang, Y. et al. Discovery of a magnetic conductive interface in PbZr0.2Ti0.8O3/SrTiO3 heterostructures. Nat. Commun. 9, 685 (2018).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  27. Guo, R. et al. Non-volatile memory based on the ferroelectric photovoltaic effect. Nat. Commun. 4, 1990 (2013).

    Article  ADS  PubMed  CAS  Google Scholar 

  28. Ohtomo, A., Muller, D. A., Grazul, J. L. & Hwang, H. Y. Artificial charge-modulation in atomic-scale perovskite titanate superlattices. Nature 419, 378–380 (2002).

    Article  ADS  CAS  PubMed  Google Scholar 

  29. Tan, H., Verbeeck, J., Abakumov, A. & Van Tendeloo, G. Oxidation state and chemical shift investigation in transition metal oxides by EELS. Ultramicroscopy 116, 24–33 (2012).

    Article  CAS  Google Scholar 

  30. Rojac, T. et al. Domain-wall conduction in ferroelectric BiFeO3 controlled by accumulation of charged defects. Nat. Mater. 16, 322–327 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  31. Jang, H. W. et al. Metallic and insulating oxide interfaces controlled by electronic correlations. Science 331, 886–889 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  32. Ohtomo, A. & Hwang, H. Y. A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface. Nature 427, 423–426 (2004); corrigendum 441, 120 (2006).

    Article  ADS  CAS  PubMed  Google Scholar 

  33. Lee, H. et al. Direct observation of a two-dimensional hole gas at oxide interfaces. Nat. Mater. 17, 231–236 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Zuo, J. M. & Spence, J. C. H. Electron Microdiffraction (Plenum, 1991).

  35. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    Article  ADS  CAS  Google Scholar 

  36. Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251–14269 (1994).

    Article  ADS  CAS  Google Scholar 

  37. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  CAS  PubMed  Google Scholar 

  38. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

    Article  ADS  CAS  Google Scholar 

  39. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    ADS  Google Scholar 

  40. Dudarev, S. L., Botton, G. A., Savrasov, S. Y., Humphreys, C. J. & Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998).

    Article  ADS  CAS  Google Scholar 

  41. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  42. Elsässer, C., Fähnle, M., Chan, C. T. & Ho, K. M. Density-functional energies and forces with Gaussian-broadened fractional occupations. Phys. Rev. B 49, 13975–13978 (1994).

    Article  ADS  Google Scholar 

  43. Wang, Z., Wang, H., Yu, C. C. & Wu, R. Q. Hydrogen as a source of flux noise in SQUIDs. Phys. Rev. B 98, 020403 (2018).

    Article  ADS  Google Scholar 

  44. Wang, H. et al. Candidate source of flux noise in SQUIDs: adsorbed oxygen molecules. Phys. Rev. Lett. 115, 077002 (2015).

    Article  ADS  PubMed  CAS  Google Scholar 

  45. Wang, H. et al. Possibility of realizing quantum spin Hall effect at room temperature in stanene / Al2O3 (0001). Phys. Rev. B 94, 035112 (2016).

    Article  ADS  CAS  Google Scholar 

  46. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  47. Shannon, R. D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. A 32, 751–767 (1976).

    Article  ADS  Google Scholar 

  48. Henkelman, G., Arnaldsson, A. & Jónsson, H. A fast and robust algorithm for Bader decomposition of charge density. Comput. Mater. Sci. 36, 354–360 (2006).

    Article  Google Scholar 

  49. Bader, R. F. W. Atoms in Molecules—A Quantum Theory (Oxford Univ. Press, 1990).

Download references

Acknowledgements

Our experimental work was supported by the US Department of Energy (DOE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under grant DE-SC0014430. TEM specimen preparation and sample thickness fitting were partially supported by the US National Science Foundation (NSF) under grant number DMR-1506535. DFT studies were supported by the US DOE (grant number DE-FG02-05ER46237) and the National Energy Research Scientific Computing Center (NERSC). Growth of BiFeO3 films at Cornell University was supported by the National Science Foundation (Nanosystems Engineering Research Center for Translational Applications of Nanoscale Multiferroic Systems) under grant number EEC-1160504, and film growth at Nanjing University was supported by the National Basic Research Program of China (grant number 2015CB654901). TEM experiments were conducted using the facilities in the Irvine Materials Research Institute (IMRI) at the University of California at Irvine. We thank H. Sawada from Jeol Ltd. for help with experiments.

Author information

Author notes

  1. Hui Wang

    Present address: Hunan Key Laboratory of Super Microstructure and Ultrafast Process, School of Physics and Electronics, Central South University, Changsha, China

  2. These authors contributed equally: Wenpei Gao, Christopher Addiego, Hui Wang

Authors and Affiliations

  1. Department of Materials Science and Engineering, University of California at Irvine, Irvine, CA, USA

    Wenpei Gao, Xingxu Yan, Yi Zhang, Linze Li, Huaixun Huyan & Xiaoqing Pan

  2. Department of Physics and Astronomy, University of California at Irvine, Irvine, CA, USA

    Christopher Addiego, Hui Wang, Yusheng Hou, Thomas Blum, Ruqian Wu & Xiaoqing Pan

  3. National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China

    Dianxiang Ji & Yuefeng Nie

  4. Department of Materials Science and Engineering, Cornell University, Ithaca, NY, USA

    Colin Heikes & Darrell G. Schlom

  5. Irvine Materials Research Institute, University of California at Irvine, Irvine, CA, USA

    Toshihiro Aoki & Xiaoqing Pan

  6. Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, NY, USA

    Darrell G. Schlom

Authors
  1. Wenpei Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christopher Addiego
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xingxu Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yusheng Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Dianxiang Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Colin Heikes
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Yi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Linze Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Huaixun Huyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Thomas Blum
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Toshihiro Aoki
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Yuefeng Nie
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. Darrell G. Schlom
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. Ruqian Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. Xiaoqing Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

W.G., R.W. and X.Q.P. conceived this project and designed the studies; W.G. and C.A. performed electron microscopy experiments and data analysis with the help of T.A.; H.W. and Y.H. carried out DFT calculations; X.Y. performed EELS experiments and analysis; Y.Z., L.L., H.H., T.B., W.G. and C.A. prepared TEM samples; D.J., C.H., Y.N. and D.S. made thin films; W.G., C.A., H.W., R.W. and X.Q.P. wrote the paper with the contributions from all authors.

Corresponding authors

Correspondence to Ruqian Wu or Xiaoqing Pan.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Measured electric-field strength in SrTiO3 films of different thicknesses.

The electric-field strength at locations close to Sr atoms (black), farther away (red) and farthest away, in between the Sr and O atomic columns (blue), was calculated from simulated diffraction data with different sample thicknesses up to 6 nm. The measured electric-field strength is shown as points, and the dashed lines denote linear fitting. The inset shows the sampling locations for each line on a map of the simulated electric field. Diffraction data were generated using multi-slice simulations in which conditions were matched to experimental conditions.

Extended Data Fig. 2 Measuring SrTiO3 thickness using PACBED.

a, HAADF-STEM image of SrTiO3. b, Least-squares fitting of the experimental PACBED results with the simulated PACBEDs (red line). The inset shows the PACBED acquired from the boxed region in the STEM image, and simulated PACBEDs of SrTiO3 with thicknesses from 0.8 nm to 10.4 nm.

Extended Data Fig. 3 Measuring BiFeO3 thickness using PACBED.

Shown are the PACBED acquired in experiment and simulated PACBEDs for BiFeO3 with thicknesses of 2–10 nm.

Extended Data Fig. 4 Separation of positive and negative charge in a BiFeO3 unit cell.

a–c, Negative charge (a); positive charge (b); and overlapping of positive and negative charge (c) in the pseudo-cubic unit cell of BiFeO3. d, Positions of positive (blue) and negative (red) charge centres.

Extended Data Fig. 5 Atomic-resolution EDS maps across the BiFeO3/SrTiO3 interface.

The EDS map was acquired using a JEM300CF AC-STEM system with EDS dual silicon-drift detectors (SDDs). Thirty scans (each with a 0.4-ms dwell time) in the same area across the interface were aligned and summed. The HAADF-STEM image and atomic-resolution EDS maps of Bi, Fe, Sr and Ti reveal an atomically sharp interface.

Extended Data Fig. 6 Measurement of O octahedron rotation.

a, Atomic model of the BiFeO3/SrTiO3 interface, which is relaxed and then calculated by DFT. The rotation of O octahedra is readily visible from the splitting of the O atoms in this projection. b, Charge-density image calculated using DFT. The images of O charge become elongated and weak with higher O octahedron rotation. c, Intensity of O column charge (blue) and width of O intensity (red) plotted against O octahedron rotation measured using the atomic model from DFT calculations.

Extended Data Fig. 7 Determination of the region for measuring the total charge of atomic columns.

a, 2D charge-density image of SrTiO3. b, Charge-intensity profile drawn along the horizontal (red) and vertical (blue) directions as shown in a. Local minima in the charge-intensity profile are defined as the boundary of the area included for integrating the charge.

Extended Data Fig. 8 Measurement of the total charge of each atomic site.

Histograms showing the integrated intensity of Bi columns, Fe + O columns, O columns, Sr columns and Ti + O columns from charge-density images of BiFeO3 and SrTiO3.

Extended Data Fig. 9 Charge-intensity change as a function of valence.

a, Integrated intensity in each atomic column in the charge-density image, plotted as a function of valence derived through DFT to show their correlation. The red line is the linear fit. b, Partial charge and valence states of all atoms derived through Bader charge analysis in DFT.

Extended Data Fig. 10 High-resolution core-loss EELS measurement of Ti, O and Fe at the SrTiO3/BiFeO3 interface.

a, HAADF-STEM image used for acquiring EELS data on the SrTiO3/BiFeO3 interface. Scale bar, 1 nm. b–d, Stacking EEL spectra of the Ti L2,3-edge (b); O K-edge (c); and Fe L2,3-edge (d) across the interface. The location of each coloured spectrum is marked by the colour bar in a. Each spectrum is averaged in the direction parallel with the SrTiO3/BiFeO3 interface. The purple, yellow and maroon arrows indicate respectively the top edge, interface and bottom edge of the mapping region in a.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gao, W., Addiego, C., Wang, H. et al. Real-space charge-density imaging with sub-ångström resolution by four-dimensional electron microscopy. Nature 575, 480–484 (2019). https://doi.org/10.1038/s41586-019-1649-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-019-1649-6

This article is cited by

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