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


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.

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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.

Data availability

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


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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.

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Authors and Affiliations



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.

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The authors declare no competing interests.

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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.

ac, 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. bd, 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.

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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).

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