Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction
10.1038/ncomms6653
Crossref journal-article
Springer Science and Business Media LLC
Nature Communications (297)
Abstract

AbstractBy focusing electrons on probes with a diameter of 50 pm, aberration-corrected scanning transmission electron microscopy (STEM) is currently crossing the border to probing subatomic details. A major challenge is the measurement of atomic electric fields using differential phase contrast (DPC) microscopy, traditionally exploiting the concept of a field-induced shift of diffraction patterns. Here we present a simplified quantum theoretical interpretation of DPC. This enables us to calculate the momentum transferred to the STEM probe from diffracted intensities recorded on a pixel array instead of conventional segmented bright-field detectors. The methodical development yielding atomic electric field, charge and electron density is performed using simulations for binary GaN as an ideal model system. We then present a detailed experimental study of SrTiO3 yielding atomic electric fields, validated by comprehensive simulations. With this interpretation and upgraded instrumentation, STEM is capable of quantifying atomic electric fields and high-contrast imaging of light atoms.

Bibliography

Müller, K., Krause, F. F., Béché, A., Schowalter, M., Galioit, V., Löffler, S., Verbeeck, J., Zweck, J., Schattschneider, P., & Rosenauer, A. (2014). Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction. Nature Communications, 5(1).

Authors 10
  1. Knut Müller (first)
  2. Florian F. Krause (additional)
  3. Armand Béché (additional)
  4. Marco Schowalter (additional)
  5. Vincent Galioit (additional)
  6. Stefan Löffler (additional)
  7. Johan Verbeeck (additional)
  8. Josef Zweck (additional)
  9. Peter Schattschneider (additional)
  10. Andreas Rosenauer (additional)
References 35 Referenced 270
  1. Wen, Z., Li, C., Wu, D., Li, A. & Ming, N. Ferroelectric-field-effect-enhanced electroresistance in metal/ferroelectric/semiconductor tunnel junctions. Nat. Mater. 12, 617–621 (2013). (10.1038/nmat3649) / Nat. Mater. by Z Wen (2013)
  2. Tsymbal, E. Y. & Kohlstedt, H. Tunneling across a ferroelectric. Science 313, 181–183 (2006). (10.1126/science.1126230) / Science by EY Tsymbal (2006)
  3. Nakamura, S., Mukai, T. & Senoh, M. Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes. Appl. Phys. Lett. 64, 1687–1689 (1994). (10.1063/1.111832) / Appl. Phys. Lett. by S Nakamura (1994)
  4. Iso, K. et al. High brightness blue InGaN/GaN light emitting diode on nonpolar m-plane bulk GaN substrate. Jpn. J. Appl. Phys. 46, L960–L962 (2007). (10.1143/JJAP.46.L960) / Jpn. J. Appl. Phys. by K Iso (2007)
  5. Masui, H. et al. Effects of piezoelectric fields on optoelectronic properties of InGaN/GaN quantum-well light-emitting diodes prepared on nonpolar and semipolar orientations. J. Phys. D. Appl. Phys. 42, 135106 (2009). (10.1088/0022-3727/42/13/135106) / J. Phys. D. Appl. Phys. by H Masui (2009)
  6. Nellist, P. D. Electron microscopy: atomic resolution comes into phase. Nat. Phys. 8, 586–587 (2012). (10.1038/nphys2357) / Nat. Phys. by PD Nellist (2012)
  7. Lohr, M. et al. Differential phase contrast 2.0—opening new ‘‘fields'' for an established technique. Ultramicroscopy 117, 7–14 (2012). (10.1016/j.ultramic.2012.03.020) / Ultramicroscopy by M Lohr (2012)
  8. Shibata, N. et al. Differential phase-contrast microscopy at atomic resolution. Nat. Phys. 8, 611–615 (2012). (10.1038/nphys2337) / Nat. Phys. by N Shibata (2012)
  9. Tsymbal, E. Y. & Gruverman, A. Ferroelectric tunnel junctions: beyond the barrier. Nat. Mater. 12, 602–604 (2013). (10.1038/nmat3669) / Nat. Mater. by EY Tsymbal (2013)
  10. Takeuchi, T. et al. Quantum-confined stark effect due to piezoelectric fields in GaInN strained quantum wells. Jpn. J. Appl. Phys. 36, L382–L385 (1997). (10.1143/JJAP.36.L382) / Jpn. J. Appl. Phys. by T Takeuchi (1997)
  11. Ploessl, R., Chapman, J. N., Thompson, A. M., Zweck, J. & Hoffmann, H. Investigation of the micromagnetic structure of cross-tie walls in permalloy. J. Appl. Phys. 73, 2447–2452 (1993). (10.1063/1.353102) / J. Appl. Phys. by R Ploessl (1993)
  12. Zweck, J., Zimmermann, T. & Schuhrke, T. TEM imaging and evalution of magnetic structures in Co/Cu multilayers. Ultramicroscopy 67, 153–162 (1997). (10.1016/S0304-3991(96)00107-6) / Ultramicroscopy by J Zweck (1997)
  13. Sandweg, C. W. et al. Direct observation of domain wall structures in curved permalloy wires containing an antinotch. J. Appl. Phys. 103, 093906 (2008). (10.1063/1.2913318) / J. Appl. Phys. by CW Sandweg (2008)
  14. Rose, H. Nonstandard imaging methods in electron microscopy. Ultramicroscopy 2, 251–267 (1977). (10.1016/S0304-3991(76)91538-2) / Ultramicroscopy by H Rose (1977)
  15. Chapman, J., Batson, P., Waddell, E. & Ferrier, R. The direct determination of magnetic domain wall profiles by differential phase contrast electron microscopy. Ultramicroscopy 3, 203–214 (1978). (10.1016/S0304-3991(78)80027-8) / Ultramicroscopy by J Chapman (1978)
  16. Shibata, N. et al. New area detector for atomic-resolution scanning transmission electron microscopy. J. Electron Microsc. (Tokyo) 59, 473–479 (2010). (10.1093/jmicro/dfq014) / J. Electron Microsc. (Tokyo) by N Shibata (2010)
  17. 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). (10.1107/S0365110X57002194) / Acta Crystallogr. by JM Cowley (1957)
  18. Bethe, H. Theorie der Beugung von Elektronen an Kristallen. Ann. Phys. 87, 55–129 (1928). (10.1002/andp.19283921704) / Ann. Phys. by H Bethe (1928)
  19. Ehrenfest, P. Bemerkung über die angenäherte Gültigkeit der klassischen Mechanik innerhalb der Quantenmechanik. Z. Phys. A 45, 455–457 (1927). (10.1007/BF01329203) / Z. Phys. A by P Ehrenfest (1927)
  20. Rosenauer, A. & Schowalter, M. InSpringer Proceedings in Physics vol. 120, (eds Cullis A. G., Midgley P. A. 169–172Springer (2007). / Springer Proceedings in Physics by A Rosenauer (2007)
  21. Blaha, P., Schwarz, K., Madsen, G., Kvasnicka, D. & Luitz, J. Wien2k, An Augmented Plane Wave+Local Orbitals Program for Calculating Crystal Properties Technische Universität Wien: Austria, (2001).
  22. Meyer, J. C. et al. Experimental analysis of charge redistribution due to chemical bonding by high-resolution transmission electron microscopy. Nat. Mater. 10, 209–215 (2011). (10.1038/nmat2941) / Nat. Mater. by JC Meyer (2011)
  23. Van Aert, S., Batenburg, K. J., Rossell, M. D., Erni, R. & Van Tendeloo, G. Three-dimensional atomic imaging of crystalline nanoparticles. Nature 470, 374–377 (2011). (10.1038/nature09741) / Nature by S Van Aert (2011)
  24. Jones, L. & Nellist, P. D. Identifying and correcting scan noise and drift in the scanning transmission electron microscope. Microsc. Microanal. 19, 1050–1060 (2013). (10.1017/S1431927613001402) / Microsc. Microanal. by L Jones (2013)
  25. Jia, C. L. & Urban, K. Atomic-resolution measurement of oxygen concentration in oxide materials. Science 303, 2001–2004 (2004). (10.1126/science.1093617) / Science by CL Jia (2004)
  26. Findlay, S. D. et al. Dynamics of annular bright field imaging in scanning transmission electron microscopy. Ultramicroscopy 110, 903–923 (2010). (10.1016/j.ultramic.2010.04.004) / Ultramicroscopy by SD Findlay (2010)
  27. Müller, K. et al. Scanning transmission electron microscopy strain measurement from millisecond frames of a direct electron charge coupled device. Appl. Phys. Lett. 101, 212110 (2012). (10.1063/1.4767655) / Appl. Phys. Lett. by K Müller (2012)
  28. 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 (2011). (10.1038/ncomms1733) / Nat. Commun. by MJ Humphry (2011)
  29. Rodenburg, J. M. & Bates, R. H. T. The theory of super-resolution electron microscopy via Wigner-distribution deconvolution. Phil. Trans. R Soc. A 339, 521–553 (1992). / Phil. Trans. R Soc. A by JM Rodenburg (1992)
  30. Rodenburg, J. M., McCallum, B. C. & Nellist, P. D. Experimental tests on double-resolution coherent imaging via STEM. Ultramicroscopy 48, 304–314 (1993). (10.1016/0304-3991(93)90105-7) / Ultramicroscopy by JM Rodenburg (1993)
  31. Maiden, A. M. & Rodenburg, J. M. An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy 109, 1256–1262 (2009). (10.1016/j.ultramic.2009.05.012) / Ultramicroscopy by AM Maiden (2009)
  32. Mott, N. F. The scattering of electrons by atoms. Proc. R. Soc. Lond. A 127, 658–665 (1930). (10.1098/rspa.1930.0082) / Proc. R. Soc. Lond. A by NF Mott (1930)
  33. Rosenauer, A., Schowalter, M., Glas, F. & Lamoen, D. First-principles calculations of 002 structure factors for electron scattering in strained InxGa1−xAs. Phys. Rev. B 72, 085326 (2005). (10.1103/PhysRevB.72.085326) / Phys. Rev. B by A Rosenauer (2005)
  34. Schowalter, M., Rosenauer, A., Titantah, J. & Lamoen, D. Temperature-dependent Debye-Waller factors for semiconductors with the wurtzite-type structure. Acta Crystallogr. A 65, 227–231 (2009). (10.1107/S0108767309004966) / Acta Crystallogr. A by M Schowalter (2009)
  35. Weickenmeier, A. & Kohl, H. Computation of absorptive form factors for high-energy electron diffraction. Acta Crystallogr. A 47, 590–597 (1991). (10.1107/S0108767391004804) / Acta Crystallogr. A by A Weickenmeier (1991)
Dates
Type When
Created 10 years, 8 months ago (Dec. 15, 2014, 9:15 a.m.)
Deposited 2 years, 7 months ago (Jan. 5, 2023, 9:31 p.m.)
Indexed 2 days ago (Aug. 19, 2025, 6:13 a.m.)
Issued 10 years, 8 months ago (Dec. 15, 2014)
Published 10 years, 8 months ago (Dec. 15, 2014)
Published Online 10 years, 8 months ago (Dec. 15, 2014)
Funders 0

None

@article{M_ller_2014, title={Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction}, volume={5}, ISSN={2041-1723}, url={http://dx.doi.org/10.1038/ncomms6653}, DOI={10.1038/ncomms6653}, number={1}, journal={Nature Communications}, publisher={Springer Science and Business Media LLC}, author={Müller, Knut and Krause, Florian F. and Béché, Armand and Schowalter, Marco and Galioit, Vincent and Löffler, Stefan and Verbeeck, Johan and Zweck, Josef and Schattschneider, Peter and Rosenauer, Andreas}, year={2014}, month=dec }