title: Measurement of atomic electric fields and charge densities from average momentum transfers using scanning transmission electron microscopy.
abstract: This study sheds light on the prerequisites, possibilities, limitations and interpretation of high-resolution differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). We draw particular attention to the well-established DPC technique based on segmented annular detectors and its relation to recent developments based on pixelated detectors. These employ the expectation value of the momentum transfer as a reliable measure of the angular deflection of the STEM beam induced by an electric field in the specimen. The influence of scattering and propagation of electrons within the specimen is initially discussed separately and then treated in terms of a two-state channeling theory. A detailed simulation study of GaN is presented as a function of specimen thickness and bonding. It is found that bonding effects are rather detectable implicitly, e.g., by characteristics of the momentum flux in areas between the atoms than by directly mapping electric fields and charge densities. For strontium titanate, experimental charge densities are compared with simulations and discussed with respect to experimental artifacts such as scan noise. Finally, we consider practical issues such as figures of merit for spatial and momentum resolution, minimum electron dose, and the mapping of larger-scale, built-in electric fields by virtue of data averaged over a crystal unit cell. We find that the latter is possible for crystals with an inversion center. Concerning the optimal detector design, this study indicates that a sampling of 5mrad per pixel is sufficient in typical applications, corresponding to approximately 10×10 available pixels.
authors.affiliation: Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany. Electronic address: mueller@ifp.uni-bremen.de.
authors.forename: Knut
authors.initials: K
authors.lastname: Müller-Caspary
authors.affiliation: Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany. Electronic address: f.krause@ifp.uni-bremen.de.
authors.forename: Florian F
authors.initials: FF
authors.lastname: Krause
authors.affiliation: Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany.
authors.forename: Tim
authors.initials: T
authors.lastname: Grieb
authors.affiliation: Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10/E138, A-1040 Vienna, Austria; University Service Centre for Transmission Electron Microscopy, Wiedner Hauptstraße 8-10/E052, A-1040 Vienna, Austria.
authors.forename: Stefan
authors.initials: S
authors.lastname: Löffler
authors.affiliation: Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany.
authors.forename: Marco
authors.initials: M
authors.lastname: Schowalter
authors.affiliation: EMAT, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium.
authors.forename: Armand
authors.initials: A
authors.lastname: Béché
authors.affiliation: Institut für Experimentelle und Angewandte Physik, Universität Regensburg, Universitätsstraße 31, 93040 Regensburg, Germany.
authors.forename: Vincent
authors.initials: V
authors.lastname: Galioit
authors.affiliation: Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany.
authors.forename: Dennis
authors.initials: D
authors.lastname: Marquardt
authors.affiliation: Institut für Experimentelle und Angewandte Physik, Universität Regensburg, Universitätsstraße 31, 93040 Regensburg, Germany.
authors.forename: Josef
authors.initials: J
authors.lastname: Zweck
authors.affiliation: Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10/E138, A-1040 Vienna, Austria; University Service Centre for Transmission Electron Microscopy, Wiedner Hauptstraße 8-10/E052, A-1040 Vienna, Austria.
authors.forename: Peter
authors.initials: P
authors.lastname: Schattschneider
authors.affiliation: EMAT, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium.
authors.forename: Johan
authors.initials: J
authors.lastname: Verbeeck
authors.affiliation: Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany.
authors.forename: Andreas
authors.initials: A
authors.lastname: Rosenauer
keywords: Charge density measurement; DPC; Field measurement; Momentum transfer; STEM; TEM