Abstract
The charge distribution in materials at the nanoscale can often explain the origin of macroscopic properties such as localized conductivity or the plasmonic response and illuminate more fundamental changes in the microscopic structure such as changes in chemical bonding characteristics. Previously, direct visualization of the charge density with high spatial resolution was often a missing link in the formation of structure–property relationships, especially in heterogeneous materials systems. However, recent advancements in microscopy technology have enabled researchers to visualize the charge distribution in materials down to subatomic length scales. In this Technical Review, we discuss the developments in high-resolution real-space charge distribution imaging using diffraction techniques and electron microscopy, with a focus on the recent advancement of four-dimensional scanning transmission electron microscopy, electron holography, and applications to materials interfaces.
Key points
-
Real-space charge density imaging can provide key insights into the electronic properties of a material that are unavailable with other methods.
-
Transmission electron microscopy can provide high spatial resolution charge images through various methods.
-
Quantum crystallography and quantitative convergent beam electron diffraction can reveal the charge distribution in uniform structures with unparalleled accuracy and spatial resolution.
-
Phase-retrieval methods provide more direct ways to reveal the charge distribution in heterogeneous materials at atomic resolution in real space.
-
Continued development of both microscopy hardware and data analysis techniques will further enhance charge density imaging methods and expand our understanding of materials.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$99.00 per year
only $8.25 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Genoni, A. et al. Quantum crystallography: current developments and future perspectives. Chem. A Eur. J. 24, 10881–10905 (2018).
Nakashima Philip, N. H., Smith Andrew, E., Etheridge, J. & Muddle Barrington, C. The bonding electron density in aluminum. Science 331, 1583–1586 (2011).
Peng, D. & Nakashima, P. N. H. Measuring density functional parameters from electron diffraction patterns. Phys. Rev. Lett. 126, 176402 (2021).
Shibata, N. et al. Differential phase-contrast microscopy at atomic resolution. Nat. Phys. 8, 611–615 (2012).
Sánchez-Santolino, G. et al. Probing the internal atomic charge density distributions in real space. ACS Nano 12, 8875–8881 (2018).
Müller, K. et al. Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction. Nat. Commun. 5, 5653 (2014).
Gao, W. et al. Real-space charge-density imaging with sub-ångström resolution by four-dimensional electron microscopy. Nature 575, 480–484 (2019).
Beyer, A. et al. Quantitative characterization of nanometer-scale electric fields via momentum-resolved STEM. Nano Lett. 21, 2018–2025 (2021).
Zheng, Q. et al. Direct visualization of anionic electrons in an electride reveals inhomogeneities. Sci. Adv. 7, eabe6819 (2021).
Song, K. et al. Direct imaging of the electron liquid at oxide interfaces. Nat. Nanotechnol. 13, 198–203 (2018).
Boureau, V. et al. Quantitative mapping of the charge density in a monolayer of MoS2 at atomic resolution by off-axis electron holography. ACS Nano 14, 524–530 (2020).
Winkler, F. et al. Absolute scale quantitative off-axis electron holography at atomic resolution. Phys. Rev. Lett. 120, 156101 (2018).
Massa, L., Huang, L. & Karle, J. Quantum crystallography and the use of kernel projector matrices. Int. J. Quantum Chem. 56, 371–384 (1995).
Piela, L. Ideas of Quantum Chemistry (Elsevier, 2014).
Johnson, K. H. Quantum chemistry. Annu. Rev. Phys. Chem. 26, 39–57 (1975).
Helgaker, T., Klopper, W. & Tew, D. P. Quantitative quantum chemistry. Mol. Phys. 106, 2107–2143 (2008).
Hansen, N. K. & Coppens, P. Testing aspherical atom refinements on small-molecule data sets. Acta Crystallogr. A 34, 909–921 (1978).
Stewart, R. Electron population analysis with rigid pseudoatoms. Acta Crystallogr. A 32, 565–574 (1976).
Fischer, A. et al. Experimental and theoretical charge density studies at subatomic resolution. J. Phys. Chem. A 115, 13061–13071 (2011).
Makal, A. M., Plażuk, D., Zakrzewski, J., Misterkiewicz, B. & Woźniak, K. Experimental charge density analysis of symmetrically substituted ferrocene derivatives. Inorg. Chem. 49, 4046–4059 (2010).
Dittrich, B., Sze, E., Holstein, J. J., Hubschle, C. B. & Jayatilaka, D. Crystal-field effects in l-homoserine: multipoles versus quantum chemistry. Acta Crystallogr. A 68, 435–442 (2012).
Metherell, J. F. in Electron Microscopy in Materials Science, Part 2 Vol. 397 (eds Valdre, U. & Ruedl, E.) 401–550 (1976).
Midgley Paul, A. Electronic bonding revealed by electron diffraction. Science 331, 1528–1529 (2011).
Zuo, J. M. & Spence, J. C. H. Electron Microdiffraction (Springer, 1991).
Tsuda, K. & Tanaka, M. Refinement of crystal structure parameters using convergent-beam electron diffraction: the low-temperature phase of SrTiO3. Acta Crystallogr. A 51, 7–19 (1995).
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).
Koshima, H. Photomechanical motion of molecular crystals. Acta Crystallogr. A 67, C176 (2011).
Sang, X. H., Kulovits, A. & Wiezorek, J. M. K. Simultaneous determination of highly precise Debye–Waller factors and structure factors for chemically ordered NiAl. Acta Crystallogr. A 66, 694–702 (2010).
Jiang, B., Zuo, J. M., Jiang, N., O’Keeffe, M. & Spence, J. C. Charge density and chemical bonding in rutile, TiO2. Acta Crystallogr. A 59, 341–350 (2003).
Pennington, R. S., Wang, F. & Koch, C. T. Stacked-Bloch-wave electron diffraction simulations using GPU acceleration. Ultramicroscopy 141, 32–37 (2014).
Cowley, J. M. & Moodie, A. F. The scattering of electrons by atoms and crystals. I. A new theoretical approach. Acta Crystallogr. 10, 609–619 (1957).
Saunders, M. et al. Measurement of low-order structure factors for silicon from zone-axis CBED patterns. Ultramicroscopy 60, 311–323 (1995).
Müller, K. et al. Refinement of the 200 structure factor for GaAs using parallel and convergent beam electron nanodiffraction data. Ultramicroscopy 109, 802–814 (2009).
Ogata, Y., Tsuda, K., Akishige, Y. & Tanaka, M. Refinement of the crystal structural parameters of the intermediate phase of h-BaTiO3 using convergent-beam electron diffraction. Acta Crystallogr. A 60, 525–531 (2004).
Ogata, Y., Tsuda, K. & Tanaka, M. Determination of the electrostatic potential and electron density of silicon using convergent-beam electron diffraction. Acta Crystallogr. A 64, 587–597 (2008).
Nakashima, P. N. H. Quantitative convergent-beam electron diffraction and quantum crystallography — the metallic bond in aluminium. Struct. Chem. 28, 1319–1332 (2017).
Zuo, J. M. Measurements of electron densities in solids: a real-space view of electronic structure and bonding in inorganic crystals. Rep. Prog. Phys. 67, 2053–2103 (2004).
Tanaka, M. & Tsuda, K. Convergent-beam electron diffraction. J. Electron. Microsc. 60, S245–S267 (2011).
Vulović, M., Voortman, L. M., van Vliet, L. J. & Rieger, B. When to use the projection assumption and the weak-phase object approximation in phase contrast cryo-EM. Ultramicroscopy 136, 61–66 (2014).
Kirkland, E. J. Advanced Computing in Electron Microscopy 3rd edn (Springer, 2020).
Knut, M. in Transmissionelektronenmikroskopie von InGaNAs Nanostrukturen mittels ab-initio Strukturfaktoren für verspannungsrelaxierte Superzellen (Universität Bremen FB1 Physik/Elektrotechnik, 2011).
Brown, H. G. Advances in Atomic Resolution Imaging Using Scanning Transmission Electron Microscopy (2017).
Winkler, F., Barthel, J., Dunin-Borkowski, R. E. & Müller-Caspary, K. Direct measurement of electrostatic potentials at the atomic scale: a conceptual comparison between electron holography and scanning transmission electron microscopy. Ultramicroscopy 210, 112926 (2020).
Hachtel, J. A., Idrobo, J. C. & Chi, M. Sub-ångstrom electric field measurements on a universal detector in a scanning transmission electron microscope. Adv. Struct. Chem. Imaging 4, 10 (2018).
Shukla, A. K. et al. Effect of composition on the structure of lithium- and manganese-rich transition metal oxides. Energy Environ. Sci. 11, 830–840 (2018).
Nalin Mehta, A. et al. Unravelling stacking order in epitaxial bilayer MX2 using 4D-STEM with unsupervised learning. Nanotechnology 31, 445702 (2020).
Ozdol, V. B. et al. Strain mapping at nanometer resolution using advanced nano-beam electron diffraction. Appl. Phys. Lett. 106, 253107 (2015).
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).
Tsuda, K., Yasuhara, A. & Tanaka, M. Two-dimensional mapping of polarizations of rhombohedral nanostructures in the tetragonal phase of BaTiO3 by the combined use of the scanning transmission electron microscopy and convergent-beam electron diffraction methods. Appl. Phys. Lett. 103, 082908 (2013).
Yadav, A. K. et al. Spatially resolved steady-state negative capacitance. Nature 565, 468–471 (2019).
Han, L. et al. High-density switchable skyrmion-like polar nanodomains integrated on silicon. Nature 603, 63–67 (2022).
Panova, O. et al. Diffraction imaging of nanocrystalline structures in organic semiconductor molecular thin films. Nat. Mater. 18, 860–865 (2019).
Cao, M. C. et al. Theory and practice of electron diffraction from single atoms and extended objects using an EMPAD. Microscopy 67, i150–i161 (2018).
Levin, B. D. A. Direct detectors and their applications in electron microscopy for materials science. J. Phys. Mater. 4, 042005 (2021).
Plotkin-Swing, B. et al. 100,000 Diffraction patterns per second with live processing for 4D-STEM. Microsc. Microanal. 28, 422–424 (2022).
Ciston, J. et al. The 4D camera: very high speed electron counting for 4D-STEM. Microsc. Microanal. 25, 1930–1931 (2019).
Ercius, P. et al. The 4D camera — an 87 kHz frame-rate detector for counted 4D-STEM experiments. Microsc. Microanal. 26, 1896–1897 (2020).
Philipp, H. et al. Wide dynamic range, 10 kHz framing detector for 4D-STEM. Microsc. Microanal. 27, 992–993 (2021).
Ophus, C. Four-dimensional scanning transmission electron microscopy (4D-STEM): from scanning nanodiffraction to ptychography and beyond. Microsc. Microanal. 25, 563–582 (2019).
MacLaren, I., Macgregor, T. A., Allen, C. S. & Kirkland, A. I. Detectors — the ongoing revolution in scanning transmission electron microscopy and why this important to material characterization. APL Mater. 8, 110901 (2020).
Rose, H. Phase contrast in scanning transmission electron microscopy. Optik 39, 416–436 (1974).
De Christoph, H. Differential phase constrast in a STEM. Optik 41, 452–456 (1974).
Rose, H. Nonstandard imaging methods in electron microscopy. Ultramicroscopy 2, 251–267 (1976).
Lazić, I., Bosch, E. G. T. & Lazar, S. Phase contrast STEM for thin samples: integrated differential phase contrast. Ultramicroscopy 160, 265–280 (2016).
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).
Brown, H. G. et al. Measuring nanometre-scale electric fields in scanning transmission electron microscopy using segmented detectors. Ultramicroscopy 182, 169–178 (2017).
Gabor, D. A new microscopic principle. Nature 161, 777–778 (1948).
Gabor, D. & Bragg, W. L. Microscopy by reconstructed wave-fronts. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 197, 454–487 (1949).
Lichte, H. & Lehmann, M. Electron holography — basics and applications. Rep. Prog. Phys. 71, 016102 (2007).
Linck, M., Freitag, B., Kujawa, S., Lehmann, M. & Niermann, T. State of the art in atomic resolution off-axis electron holography. Ultramicroscopy 116, 13–23 (2012).
Bürger, J., Riedl, T. & Lindner, J. K. N. Influence of lens aberrations, specimen thickness and tilt on differential phase contrast STEM images. Ultramicroscopy 219, 113118 (2020).
Lichte, H. Performance limits of electron holography. Ultramicroscopy 108, 256–262 (2008).
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).
Addiego, C., Gao, W. & Pan, X. Thickness and defocus dependence of inter-atomic electric fields measured by scanning diffraction. Ultramicroscopy 208, 112850 (2020).
Robert, H. L. et al. Dynamical diffraction of high-energy electrons investigated by focal series momentum-resolved scanning transmission electron microscopy at atomic resolution. Ultramicroscopy 233, 113425 (2022).
Lehmann, M. Determination and correction of the coherent wave aberration from a single off-axis electron hologram by means of a genetic algorithm. Ultramicroscopy 85, 165–182 (2000).
Rodenburg, J. M. in Advances in Imaging and Electron Physics Vol. 150 (ed. Hawkes, P.) 87–184 (Elsevier, 2008).
Rodenburg, J. M. & Faulkner, H. M. L. A phase retrieval algorithm for shifting illumination. Appl. Phys. Lett. 85, 4795–4797 (2004).
Maiden, A. M. & Rodenburg, J. M. An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy 109, 1256–1262 (2009).
Rodenburg, J. M. & Bates, R. H. T. The theory of super-resolution electron microscopy via Wigner-distribution deconvolution. Philos. Trans. R. Soc. Lond. Ser. A Phys. Eng. Sci. 339, 521–553 (1992).
Nellist, P. D., McCallum, B. C. & Rodenburg, J. M. Resolution beyond the ‘information limit’ in transmission electron microscopy. Nature 374, 630–632 (1995).
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).
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).
Zhou, L. et al. Low-dose phase retrieval of biological specimens using cryo-electron ptychography. Nat. Commun. 11, 2773 (2020).
Yang, H. et al. Electron ptychographic phase imaging of light elements in crystalline materials using Wigner distribution deconvolution. Ultramicroscopy 180, 173–179 (2017).
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).
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).
Lozano, J. G., Martinez, G. T., Jin, L., Nellist, P. D. & Bruce, P. G. Low-dose aberration-free imaging of Li-rich cathode materials at various states of charge using electron ptychography. Nano Lett. 18, 6850–6855 (2018).
Chen, Z. et al. Mixed-state electron ptychography enables sub-ångström resolution imaging with picometer precision at low dose. Nat. Commun. 11, 2994 (2020).
Gao, S. et al. Electron ptychographic microscopy for three-dimensional imaging. Nat. Commun. 8, 163 (2017).
Jiang, Y. et al. Electron ptychography of 2D materials to deep sub-ångström resolution. Nature 559, 343–349 (2018).
Chen, Z. et al. Electron ptychography achieves atomic-resolution limits set by lattice vibrations. Science 372, 826–831 (2021).
Martinez, G. T. et al. Direct imaging of charge redistribution due to bonding at atomic resolution via electron ptychography. Preprint at https://doi.org/10.48550/arXiv.1907.12974 (2019).
Lupini, A. R., Oxley, M. P. & Kalinin, S. V. Pushing the limits of electron ptychography. Science 362, 399–400 (2018).
Rodenburg, J. & Maiden, A. in Springer Handbook of Microscopy (eds Hawkes, P. W. & Spence, J. C. H.) 819–904 (Springer, 2019).
Ge, R. et al. Atomristor: nonvolatile resistance switching in atomic sheets of transition metal dichalcogenides. Nano Lett. 18, 434–441 (2018).
Kim, M. et al. Zero-static power radio-frequency switches based on MoS2 atomristors. Nat. Commun. 9, 2524 (2018).
Akinwande, D., Petrone, N. & Hone, J. Two-dimensional flexible nanoelectronics. Nat. Commun. 5, 5678 (2014).
Siao, M. D. et al. Two-dimensional electronic transport and surface electron accumulation in MoS2. Nat. Commun. 9, 1442 (2018).
Geim, A. K. Graphene: status and prospects. Science 324, 1530–1534 (2009).
Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).
Banhart, F., Kotakoski, J. & Krasheninnikov, A. V. Structural defects in graphene. ACS Nano 5, 26–41 (2011).
Wang, L. et al. Fundamental transport mechanisms, fabrication and potential applications of nanoporous atomically thin membranes. Nat. Nanotechnol. 12, 509–522 (2017).
Fang, S. et al. Atomic electrostatic maps of 1D channels in 2D semiconductors using 4D scanning transmission electron microscopy. Nat. Commun. 10, 1127 (2019).
Han, Y. et al. Sub-nanometre channels embedded in two-dimensional materials. Nat. Mater. 17, 129–133 (2018).
Huang, L. et al. Anomalous fracture in two-dimensional rhenium disulfide. Sci. Adv. 6, eabc2282 (2020).
O’Leary, C. M. et al. Phase reconstruction using fast binary 4D STEM data. Appl. Phys. Lett. 116, 124101 (2020).
Chang, S. L. Y., Dwyer, C., Barthel, J., Boothroyd, C. B. & Dunin-Borkowski, R. E. Performance of a direct detection camera for off-axis electron holography. Ultramicroscopy 161, 90–97 (2016).
Müller-Caspary, K. et al. Atomic-scale quantification of charge densities in two-dimensional materials. Phys. Rev. B 98, 121408 (2018).
Ishikawa, R. et al. Direct electric field imaging of graphene defects. Nat. Commun. 9, 3878 (2018).
O’Leary, C. M., Haas, B., Koch, C. T., Nellist, P. D. & Jones, L. Increasing spatial fidelity and SNR of 4D-STEM using multi-frame data fusion. Microsc. Microanal. 28, 1417–1427 (2022).
Shibata, N. et al. Imaging of built-in electric field at a p–n junction by scanning transmission electron microscopy. Sci. Rep. 5, 10040 (2015).
Rau, W. D., Schwander, P., Baumann, F. H., Höppner, W. & Ourmazd, A. Two-dimensional mapping of the electrostatic potential in transistors by electron holography. Phys. Rev. Lett. 82, 2614–2617 (1999).
McCartney, M. R. & Smith, D. J. Electron holography: phase imaging with nanometer resolution. Annu. Rev. Mater. Res. 37, 729–767 (2007).
McCartney, M. R., Dunin-Borkowski, R. E. & Smith, D. J. Quantitative measurement of nanoscale electrostatic potentials and charges using off-axis electron holography: developments and opportunities. Ultramicroscopy 203, 105–118 (2019).
Han, M.-G. et al. Sample preparation for precise and quantitative electron holographic analysis of semiconductor devices. Microsc. Microanal. 12, 295–301 (2006).
Ikarashi, N., Takeda, H., Yako, K. & Hane, M. In-situ electron holography of surface potential response to gate voltage application in a sub-30-nm gate-length metal-oxide-semiconductor field-effect transistor. Appl. Phys. Lett. 100, 143508 (2012).
Haas, B., Rouvière, J.-L., Boureau, V., Berthier, R. & Cooper, D. Direct comparison of off-axis holography and differential phase contrast for the mapping of electric fields in semiconductors by transmission electron microscopy. Ultramicroscopy 198, 58–72 (2019).
Bruas, L. et al. Improved measurement of electric fields by nanobeam precession electron diffraction. J. Appl. Phys. 127, 205703 (2020).
Koch, C. T. Towards full-resolution inline electron holography. Micron 63, 69–75 (2014).
Schlom, D. G. et al. Elastic strain engineering of ferroic oxides. MRS Bull. 39, 118–130 (2014).
Huyan, H., Li, L., Addiego, C., Gao, W. & Pan, X. Structures and electronic properties of domain walls in BiFeO3 thin films. Natl Sci. Rev. 6, 669–683 (2019).
Ye, F. et al. Emergent properties at oxide interfaces controlled by ferroelectric polarization. npj Comput. Mater. 7, 130 (2021).
Ramesh, R. & Schlom, D. G. Creating emergent phenomena in oxide superlattices. Nat. Rev. Mater. 4, 257–268 (2019).
Ohtomo, A. & Hwang, H. Y. A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface. Nature 427, 423–426 (2004).
Niranjan, M. K., Wang, Y., Jaswal, S. S. & Tsymbal, E. Y. Prediction of a switchable two-dimensional electron gas at ferroelectric oxide interfaces. Phys. Rev. Lett. 103, 016804 (2009).
Zhang, Z., Wu, P., Chen, L. & Wang, J. First-principles prediction of a two dimensional electron gas at the BiFeO3/SrTiO3 interface. Appl. Phys. Lett. 99, 062902 (2011).
Fredrickson, K. D. & Demkov, A. A. Switchable conductivity at the ferroelectric interface: nonpolar oxides. Phys. Rev. B 91, 115126 (2015).
Yin, B., Aguado-Puente, P., Qu, S. & Artacho, E. Two-dimensional electron gas at the PbTiO3/SrTiO3 interface: an ab initio study. Phys. Rev. B 92, 115406 (2015).
Zhang, Y. et al. Anisotropic polarization-induced conductance at a ferroelectric–insulator interface. Nat. Nanotechnol. 13, 1132–1136 (2018).
Li, L. et al. Giant resistive switching via control of ferroelectric charged domain walls. Adv. Mater. 28, 6574–6580 (2016).
Ma, J. et al. Controllable conductive readout in self-assembled, topologically confined ferroelectric domain walls. Nat. Nanotechnol. 13, 947–952 (2018).
Campanini, M., Erni, R., Yang, C. H., Ramesh, R. & Rossell, M. D. Periodic giant polarization gradients in doped BiFeO3 thin films. Nano Lett. 18, 717–724 (2018).
Campanini, M. et al. Atomic-resolution differential phase contrast STEM on ferroelectric materials: a mean-field approach. Phys. Rev. B 101, 184116 (2020).
Bader, R. F. W. & Nguyen-Dang, T. T. in Advances in Quantum Chemistry Vol. 14 (ed. Löwdin, P.-O.) 63–124 (Academic Press, 1981).
Henkelman, G., Arnaldsson, A. & Jónsson, H. A fast and robust algorithm for Bader decomposition of charge density. Comput. Mater. Sci. 36, 354–360 (2006).
Huyan, H. et al. Direct observation of polarization-induced two-dimensional electron/hole gases at ferroelectric-insulator interface. npj Quantum Mater. 6, 88 (2021).
Campanini, M. et al. Imaging and quantification of charged domain walls in BiFeO3. Nanoscale 12, 9186–9193 (2020).
Zachman, M. J. et al. Measuring and directing charge transfer in heterogenous catalysts. Nat. Commun. 13, 3253 (2022).
Yadav, A. K. et al. Observation of polar vortices in oxide superlattices. Nature 530, 198–201 (2016).
Das, S. et al. Observation of room-temperature polar skyrmions. Nature 568, 368–372 (2019).
Das, S. et al. Local negative permittivity and topological phase transition in polar skyrmions. Nat. Mater. 20, 194–201 (2021).
Deb, P. et al. Imaging polarity in two dimensional materials by breaking Friedel’s Law. Ultramicroscopy 215, 113019 (2020).
Seo, J., Koch, C. T., Ryu, S., Eom, C.-B. & Oh, S. H. Analysis of local charges at hetero-interfaces by electron holography—a comparative study of different techniques. Ultramicroscopy 231, 113236 (2021).
Ozsoy-Keskinbora, C., Boothroyd, C. B., Dunin-Borkowski, R. E., van Aken, P. A. & Koch, C. T. Hybridization approach to in-line and off-axis (electron) holography for superior resolution and phase sensitivity. Sci. Rep. 4, 7020 (2014).
Ozsoy-Keskinbora, C., Boothroyd, C. B., Dunin-Borkowski, R. E., van Aken, P. A. & Koch, C. T. Mapping the electrostatic potential of Au nanoparticles using hybrid electron holography. Ultramicroscopy 165, 8–14 (2016).
Nakajima, H. et al. Electrostatic potential measurement at the Pt/TiO2 interface using electron holography. J. Appl. Phys. 129, 174304 (2021).
Wu, L., Meng, Q. & Zhu, Y. Mapping valence electron distributions with multipole density formalism using 4D-STEM. Ultramicroscopy 219, 113095 (2020).
Zhang, C., Han, R., Zhang, A. R. & Voyles, P. M. Denoising atomic resolution 4D scanning transmission electron microscopy data with tensor singular value decomposition. Ultramicroscopy 219, 113123 (2020).
Kohno, Y., Seki, T., Findlay, S. D., Ikuhara, Y. & Shibata, N. Real-space visualization of intrinsic magnetic fields of an antiferromagnet. Nature 602, 234–239 (2022).
Addiego, C., Gao, W. & Pan, X. Multiscale electric field imaging of vortices in PbTiO3-SrTiO3 superlattice. Microsc. Microanal. 26, 466–468 (2020).
Eldred, T. B., Smith, J. G. & Gao, W. Polarization fluctuation of BaTiO3 at unit cell level mapped by four-dimensional scanning transmission electron microscopy. J. Vac. Sci. Technol. A 40, 013205 (2021).
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).
Zhang, Z., Sigle, W. & Rühle, M. Atomic and electronic characterization of the a[100] dislocation core in SrTiO3. Phys. Rev. B 66, 094108 (2002).
Egerton, R. Electron Energy-Loss Spectroscopy in the Electron Microscope 3rd edn (Springer, 2011).
Muller, D. A. Simple model for relating EELS and XAS spectra of metals to changes in cohesive energy. Phys. Rev. B 58, 5989–5995 (1998).
Hitchcock, A. P. Near edge electron energy loss spectroscopy: comparison to X-ray absorption. Jpn J. Appl. Phys. 32, 176 (1993).
Mory, C., Kohl, H., Tencé, M. & Colliex, C. Experimental investigation of the ultimate EELS spatial resolution. Ultramicroscopy 37, 191–201 (1991).
Hitchcock, A. P., Dynes, J. J., Johansson, G., Wang, J. & Botton, G. Comparison of NEXAFS microscopy and TEM-EELS for studies of soft matter. Micron 39, 741–748 (2008).
Wang, Z. L., Yin, J. S. & Jiang, Y. D. EELS analysis of cation valence states and oxygen vacancies in magnetic oxides. Micron 31, 571–580 (2000).
Rez, P. & Muller, D. A. The theory and interpretation of electron energy loss near-edge fine structure. Annu. Rev. Mater. Res. 38, 535–558 (2008).
Colella, M., Lumpkin, G. R., Zhang, Z., Buck, E. C. & Smith, K. L. Determination of the uranium valence state in the brannerite structure using EELS, XPS, and EDX. Phys. Chem. Miner. 32, 52–64 (2005).
Yoshiya, M., Tanaka, I., Kaneko, K. & Adachi, H. First principles calculation of chemical shifts in ELNES/NEXAFS of titanium oxides. J. Phys. Condens. Matter 11, 3217–3228 (1999).
Lee, J. S. et al. Titanium dxy ferromagnetism at the LaAlO3/SrTiO3 interface. Nat. Mater. 12, 703–706 (2013).
Ma, C. et al. Atomic-scale origin of the large grain-boundary resistance in perovskite Li-ion-conducting solid electrolytes. Energy Environ. Sci. 7, 1638–1642 (2014).
Yu, L., Li, M., Wen, J., Amine, K. & Lu, J. (S)TEM-EELS as an advanced characterization technique for lithium-ion batteries. Mater. Chem. Front. 5, 5186–5193 (2021).
Su, L. et al. Direct observation of elemental fluctuation and oxygen octahedral distortion-dependent charge distribution in high entropy oxides. Nat. Commun. 13, 2358 (2022).
Gadre, C. A. et al. Nanoscale imaging of phonon dynamics by electron microscopy. Nature 606, 292–297 (2022).
Li, L. et al. Observation of strong polarization enhancement in ferroelectric tunnel junctions. Nano Lett. 19, 6812–6818 (2019).
Repp, J., Meyer, G., Stojković, S. M., Gourdon, A. & Joachim, C. Molecules on insulating films: scanning-tunneling microscopy imaging of individual molecular orbitals. Phys. Rev. Lett. 94, 026803 (2005).
Gross, L. et al. High-resolution molecular orbital imaging using a p-wave STM tip. Phys. Rev. Lett. 107, 086101 (2011).
Han, Z. et al. Imaging the halogen bond in self-assembled halogenbenzenes on silver. Science 358, 206–210 (2017).
Acknowledgements
This work was supported primarily by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under grant number DE-SC0014430, and partially by the National Science Foundation under grant number DMR-2034738.
Author information
Authors and Affiliations
Contributions
The authors contributed equally to all aspects of the article.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Reviews Physics thanks the anonymous reviewers for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Addiego, C., Gao, W., Huyan, H. et al. Probing charge density in materials with atomic resolution in real space. Nat Rev Phys 5, 117–132 (2023). https://doi.org/10.1038/s42254-022-00541-4
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s42254-022-00541-4