Measurement of atomic electric fields and charge densities from average momentum transfers using scanning transmission electron microscopy

• Published in: Ultramicroscopy Vol. 178; pp. 62 - 80
• Main Authors: Müller-Caspary, Knut, Krause, Florian F., Grieb, Tim, Löffler, Stefan, Schowalter, Marco, Béché, Armand, Galioit, Vincent, Marquardt, Dennis, Zweck, Josef, Schattschneider, Peter, Verbeeck, Johan, Rosenauer, Andreas
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.07.2017
• Subjects: Charge density measurement; DPC; Field measurement; Momentum transfer; STEM; TEM; Field measurement; Momentum transfer; Charge density measurement; TEM; DPC; STEM
• ISSN: 0304-3991; 1879-2723
• DOI: 10.1016/j.ultramic.2016.05.004

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. •STEM methods to measure electric fields on nano and subatomic scale are analysed.•Limitations of conventional differential phase contrast are worked out.•Measuring momentum transfer by from diffraction patterns was related to fields.•Electric field can be derived via Ehrenfest theorem or in phase object approximation.•Interaction with the specimen is studied via s-state and multislice simulations.