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

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.

On detector linearity and precision of beam shift detection for quantitative differential phase contrast applications.

Differential phase contrast is a STEM imaging mode where minute sideways deflections of the electron probe are monitored, usually by using a position sensitive device (Chapman, 1984 [1]; Lohr et al., 2012 [2]) or, alternatively in some cases, a fast camera (Müller et al., 2012 [3,4]; Yang et al., 2015 [5]; Pennycook et al., 2015 [6]) as a pixelated detector. While traditionally differential phase contrast electron microscopy was mainly focused on investigations of micro-magnetic domain structures and their specific features, such as domain wall widths, etc. (Chapman, 1984 [1]; Chapman et al., 1978, 1981, 1985 [7-9]; Sannomiya et al., 2004 [10]), its usage has recently been extended to mesoscopic (Lohr et al., 2012, 2016 [2,12]; Bauer et al., 2014 [11]; Shibata et al., 2015 [13]) and nano-scale electric fields (Shibata et al., 2012 [14]; Mueller et al., 2014 [15]). In this paper, the various interactions which can cause a beam deflection are reviewed and expanded by two so far undiscussed mechanisms which may be important for biological applications. As differential phase contrast microscopy strongly depends on the ability to detect minute beam deflections we first treat the linearity problem for an annular four quadrant detector and then determine the factors which limit the minimum measurable deflection angle, such as S/N ratio, current density, dwell time and detector geometry. Knowing these factors enables the experimenter to optimize the set-up for optimum performance of the microscope and to get a clear figure for the achievable field resolution error margins.

Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction.

By 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.