Interferometric methods for mapping static electric and magnetic fields

Giulio Pozzi; Marco Beleggia; Takeshi Kasama; Rafal E. Dunin-Borkowski

doi:10.1016/j.crhy.2014.01.005

Electron microscopy / Microscopie électronique

Interferometric methods for mapping static electric and magnetic fields

Giulio Pozzi ¹ ; Marco Beleggia ²; Takeshi Kasama ²; Rafal E. Dunin-Borkowski ³

¹ University of Bologna, Department of Physics and Astronomy, viale B. Pichat 6/2, 40127 Bologna, Italy
² Center for Electron Nanoscopy, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
³ Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungzentrum Jülich, 52425 Jülich, Germany

Comptes Rendus. Physique, Volume 15 (2014) no. 2-3, pp. 126-139.

Abstract
Résumé

The mapping of static electric and magnetic fields using electron probes with a resolution and sensitivity that are sufficient to reveal nanoscale features in materials requires the use of phase-sensitive methods such as the shadow technique, coherent Foucault imaging and the Transport of Intensity Equation. Among these approaches, image-plane off-axis electron holography in the transmission electron microscope has acquired a prominent role thanks to its quantitative capabilities and broad range of applicability. After a brief overview of the main ideas and methods behind field mapping, we focus on theoretical models that form the basis of the quantitative interpretation of electron holographic data. We review the application of electron holography to a variety of samples (including electric fields associated with p–n junctions in semiconductors, quantized magnetic flux in superconductors and magnetization topographies in nanoparticles and other magnetic materials) and electron-optical geometries (including multiple biprism, amplitude and mixed-type set-ups). We conclude by highlighting the emerging perspectives of (i) three-dimensional field mapping using electron holographic tomography and (ii) the model-independent determination of the locations and magnitudes of field sources (electric charges and magnetic dipoles) directly from electron holographic data.

La cartographie de champs électriques et magnétiques statiques avec une sonde d'électrons à un niveau de résolution et de sensibilité suffisant pour révéler des variations à l'échelle nanométrique requiert l'utilisation de méthodes sensibles à la phase, telles que la technique de l'ombrage, l'imagerie cohérente en mode de Foucault ou l'équation de transport de l'intensité (TIE). Parmi ces différentes approches, l'holographie électronique « hors axe » en microscopie électronique à transmission joue un rôle prépondérant, en raison de son caractère quantitatif et de son vaste domaine d'utilisation. Après une brève revue des principales idées et méthodes sous-jacentes, nous nous attacherons à décrire les modèles théoriques qui constituent le fondement de l'interprétation quantitative des données holographiques. Nous passerons rapidement en revue l'utilisation de l'holographie électronique pour étudier un grand nombre d'échantillons avec leurs champs électriques et magnétiques associés : jonctions $p – n$ dans les semi-conducteurs, lignes de flux magnétique quantifié dans les supraconducteurs, topographies du champ magnétique dans et autour de nanoparticules et autres… Les aspects relatifs aux géométries utilisées en optique électronique (doubles biprismes et dispositifs mixtes pour jouer sur la phase et l'amplitude) sont aussi mentionnés. Enfin, nous identifions plusieurs perspectives émergentes de grand intérêt : (i) la cartographie tridimensionnelle de champs en associant tomographie et holographie, (ii) la détermination de la position et de l'intensité de sources de champ (charges électriques et dipôles magnétiques) directement à partir des données holographiques.

Published online: 2014-02-01

DOI: 10.1016/j.crhy.2014.01.005

Keywords: Transmission electron microscopy, Electron holography, Field mapping, Electric fields, Magnetic fields
Mot clés : Microscopie électronique en transmission, Holographie électronique, Cartographie de champs, Champs électriques, Champs magnétiques

Author's affiliations:

Giulio Pozzi ¹; Marco Beleggia ²; Takeshi Kasama ²; Rafal E. Dunin-Borkowski ³

¹ University of Bologna, Department of Physics and Astronomy, viale B. Pichat 6/2, 40127 Bologna, Italy
² Center for Electron Nanoscopy, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
³ Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungzentrum Jülich, 52425 Jülich, Germany

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Giulio Pozzi; Marco Beleggia; Takeshi Kasama; Rafal E. Dunin-Borkowski. Interferometric methods for mapping static electric and magnetic fields. Comptes Rendus. Physique, Volume 15 (2014) no. 2-3, pp. 126-139. doi : 10.1016/j.crhy.2014.01.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2014.01.005/

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