title: Quantitative measurement of mean inner potential and specimen thickness from high-resolution off-axis electron holograms of ultra-thin layered WSe2.
abstract: The phase and amplitude of the electron wavefunction that has passed through ultra-thin flakes of WSe2is measured from high-resolution off-axis electron holograms. Both the experimental measurements and corresponding computer simulations are used to show that, as a result of dynamical diffraction, the spatially averaged phase does not increase linearly with specimen thickness close to an [001] zone axis orientation even when the specimen has a thickness of only a few layers. It is then not possible to infer the local specimen thickness of the WSe2from either the phase or the amplitude alone. Instead, we show that the combined analysis of phase and amplitude from experimental measurements and simulations allows an accurate determination of the local specimen thickness. The relationship between phase and projected potential is shown to be approximately linear for extremely thin specimens that are tilted by several degrees in certain directions from the [001] zone axis. A knowledge of the specimen thickness then allows the electrostatic potential to be determined from the measured phase. By using this combined approach, we determine a value for the mean inner potential of WSe2of 18.9±0.8V, which is 12% lower than the value calculated from neutral atom scattering factors.
authors.affiliation: Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons (ER-C), Forschungszentrum Jülich, D-52425 Jülich, Germany; Peter Grünberg Institute 5 (PGI-5), Forschungszentrum Jülich, D-52425 Jülich, Germany. Electronic address: f.winkler@fz-juelich.de.
authors.forename: Florian
authors.initials: F
authors.lastname: Winkler
authors.affiliation: Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons (ER-C), Forschungszentrum Jülich, D-52425 Jülich, Germany; Peter Grünberg Institute 5 (PGI-5), Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors.forename: Amir H
authors.initials: AH
authors.lastname: Tavabi
authors.affiliation: Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons (ER-C), Forschungszentrum Jülich, D-52425 Jülich, Germany; Gemeinschaftslabor für Elektronenmikroskopie (GFE), RWTH Aachen University, D-52074 Aachen, Germany.
authors.forename: Juri
authors.initials: J
authors.lastname: Barthel
authors.affiliation: Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons (ER-C), Forschungszentrum Jülich, D-52425 Jülich, Germany; Peter Grünberg Institute 5 (PGI-5), Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors.forename: Martial
authors.initials: M
authors.lastname: Duchamp
authors.affiliation: FEI Company, Achtseweg Noord 5, Eindhoven 5600 KA, The Netherlands.
authors.forename: Emrah
authors.initials: E
authors.lastname: Yucelen
authors.affiliation: Peter Grünberg Institute 9 (PGI-9), Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors.forename: Sven
authors.initials: S
authors.lastname: Borghardt
authors.affiliation: Peter Grünberg Institute 9 (PGI-9), Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors.forename: Beata E
authors.initials: BE
authors.lastname: Kardynal
authors.affiliation: Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons (ER-C), Forschungszentrum Jülich, D-52425 Jülich, Germany; Peter Grünberg Institute 5 (PGI-5), Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors.forename: Rafal E
authors.initials: RE
authors.lastname: Dunin-Borkowski
keywords: Mean inner potential; Off-axis electron holography; Specimen thickness; Transition metal dichalcogenide; Transmission electron microscopy; WSe(2)