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Plasmonic nanostructures and -devices are rapidly transforming light manipulation technology by allowing to modify and enhance optical fields on sub-wavelength scales. Advances in this field rely heavily on the development of new characterization methods for the fundamental nanoscale interactions. However, the direct and quantitative mapping of transient electric and magnetic fields characterizing the plasmonic coupling has been proven elusive to date. Here we demonstrate how to directly measure the inelastic momentum transfer of surface plasmon modes via the energy-loss filtered deflection of a focused electron beam in a transmission electron microscope. By scanning the beam over the sample we obtain a spatially and spectrally resolved deflection map and we further show how this deflection is related quantitatively to the spectral component of the induced electric and magnetic fields pertaining to the mode. In some regards this technique is an extension to the established differential phase contrast into the dynamic regime., Characterizing plasmonic coupling has proven elusive. Here, the authors obtain a spectrally resolved deflection map related to a focused electron beam, which has excited a surface plasmon resonance, and relate this deflection to the spectral component of the induced electric and magnetic fields pertaining to the mode.

Semiconductors with native ferromagnetism barely exist and defined nanostructures are almost unknown. This lack impedes the exploration of a new class of materials characterized by a direct combination of effects on the electronic system caused by quantum confinement effects with magnetism. A good example is EuO for which currently no reliable routes for nanoparticle synthesis can be established. Bottom-up approaches applicable to other oxides fail because of the labile oxidation state +II. Instead of targeting a direct synthesis, the two steps—“structure control” and “chemical transformation”—are separated. The generation of a transitional, hybrid nanophase is followed by its conversion into EuO under full conservation of all morphological features. Hierarchical EuO materials are now accessible in the shape of oriented nanodisks stacked to tubular particles. Magnetically, the coupling of either vortex or onion states has been found. An unexpected temperature dependence is governed by thermally activated transitions between these states. published

In this work we introduce the Rytov approximation in the scope of high-energy electron scattering with the motivation of developing better linear models for electron scattering. Such linear models play an important role in tomography and similar reconstruction techniques. Conventional linear models, such as the Phase Grating Approximation, have reached their limits in current and forsee- able applications, most importantly in achieving three-dimensional atomic resolution using electron holographic tomography. The Rytov approximation incorporates propagation effects which are the most pressing limitation of conventional models. While predominately used in the weak-scattering regime of light microscopy we show that the Rytov approximation can give reasonable results in the inherently strong-scattering regime of transmission electron microscopy.

Off-axis electron holography (EH) is a powerful method for mapping projected electric potentials, such as built-in potentials in semiconductor devices, in two dimensions (2D) at nanometer resolution. However, not well-defined thickness profiles, surface effects, and composition changes of the sample under investigation complicate the interpretation of the projected potentials. Here, we demonstrate how these problems can be overcome by combining EH with tomographic techniques, that is, electron holographic tomography (EHT), reconstructing electric potentials in 3D. We present EHT reconstructions of an n-type MOSFET including its dopant-related built-in potentials inside the device, as well as of a GaAs/AlGaAs core-multishell nanowire containing a 5 nm thick quantum well tube.

Off-axis electron holographic tomography (EHT) has been successfully applied to reveal the 3D structure of III-V semiconductor core-shell nanowires (NWs) [1,2]. The technique probes the phase shift of an electron wave transmitted through such a NW that is proportional to the NWs projected electrostatic potential. Thus, a tilt series of phase images (projected potentials) can be used as input to compute a 3D tomogram of the electrostatic potential by tomographic reconstruction algorithms. Typically, the recovered 3D potential is dominated by the mean inner potential (MIP), which is related to the materials composition. Consequently, space charge potentials determining for example the electric properties, e.g., at interfaces or pn-junctions in semiconductors [2] may be superimposed by MIP variations caused by compositional changes within the heterostructures. Here, we show on the example of a GaAs/AlGaAs core-multishell NW, how the space charge potentials can be uncovered from materials contrast (MIP) by determining the latter independently: To this end, high-angle annular dark-field (HAADF) STEM tomography was applied in addition to EHT on the same NW. STEM tomograms provide solely materials contrast that depends exponentially on the atomic number. Fig. 1 compares both methods in terms of the relation between reconstructed signal and projected property, exemplary for three different tomogram regions identified as pure Au, GaAs and AlGaAs: In case of EHT between the reconstructed potential and the MIP, and in case of STEM tomography between the reconstructed intensity and the atomic number. The latter relation enables converting the STEM tomogram in units of (mean) atomic numbers. Tilt series were acquired from -70° to +71° with 3° tilt steps in holography mode, and from -68° to +68° with 2° tilt steps in STEM mode. Since phase images of axially scattered electrons are used for EHT, it suffers much more from diffraction contrast than STEM tomography (high-angle scattering). Consequently, only 39 projections could be used for tomographic reconstruction in the case of EHT compared to 68 in the case of STEM tomography. For this reason, resolution and contrast in the 3D potential are slightly lower than in the STEM tomogram, which can be seen on the cross-section of the NW in Fig. 2. Nevertheless, the core-shell structure, the ca. (5-10) nm thick GaAs shell acting as quantum well tube (QWT), and unintended Al segregations are clearly resolved in both cases. Last but not least, longitudinal slices (Fig.3) exhibit clear differences of both tomograms that strongly suggest additional local space-charge related potentials to be investigated in greater detail in a next step. References: [1] A Lubk, D Wolf, P Prete, N Lovergine, T Niermann, S Sturm and H Lichte, Phys. Rev. B 90 (2014) p. 125404. [2] D Wolf, A Lubk, P Prete, N Lovergine and H Lichte, J. Phys. D: Appl. Phys. 49 (2016) p. 364004 [3] We thank N Lovergine of University of Salento, Lecce for provision of the samples. [4] We thank the group of Michael Lehmann at TU Berlin for access to the TEM FEI Titan 80-300 Berlin Holography Special. [5] DW acknowledges financial support within the European Union"s Horizon 2020 research and innovation program under Grant Agreement No 688072 (Project IONS4SET). AL has received funding from the European Research Council (ERC) under the European Union"s Horizon 2020 research and innovation programme (grant agreement No 715620).

We report on the development of electron holographic tomography towards a versatile potential measurement technique, overcoming several limitations, such as a limited tilt range, previously hampering a reproducible and accurate electrostatic potential reconstruction in three dimensions. Most notably, tomographic reconstruction is performed on optimally sampled polar grids taking into account symmetry and other spatial constraints of the nanostructure. Furthermore, holographic tilt series acquisition and alignment have been automated and adapted to three dimensions. We demonstrate 6 nm spatial and 0.2 V signal resolution by reconstructing various, previously hidden, potential details of a GaAs/AlGaAs core-shell nanowire. The improved tomographic reconstruction opens pathways towards the detection of minute potentials in nanostructures and an increase in speed and accuracy in related techniques such as x-ray tomography.

Off-Axis Electron Holography permits the direct reconstruction of amplitude and phase of electron waves elastically scattered by an object (see, e.g., [1]). The technique employs the Möllenstedt biprism to mutually incline an object modulated wave and a plane reference wave to form an interference pattern at the detector plane. Limited coherence of the electron beam in presence of aberrations attenuates high spatial frequencies of the object exit wave spectrum, which is illustrated by the sideband envelope function for a non-corrected TEM in Fig. 1a. In this work, we explore an extension of the conventional setup given by deliberately tilting the reference wave independent from the object wave. This allows the transfer of spatial frequencies beyond the conventional sideband information limit in Fig. 1a as predicted by a generalized transfer theory for Off-Axis Electron Holography [2]. This is because a reference wave tilted by q0 compensates the berration impact on the spatial frequency q0 of the object wave spectrum. The resulting transfer envelope for a tilt of q0x = -10/nm perpendicular to the post-specimen biprism is shown in Fig. 1b, where the contrast maximum of the total envelope (TCC) is located at q0x. Thus, an off-axis hologram series with varying reference wave tilt allows in principle a linear synthesis of an effective coherent aperture with a radius reaching out beyond the conventional information limit. Furthermore, an object-independent measurement of aberrations as well as dark-field electron holography can be realized using this setup. The experimental realization of an arbitrarily tilted reference wave is challenging and could be realized for the first time at the Hitachi HF3300C I2TEM at CEMES Toulouse for one direction [3]. We used an additional biprism placed in the illumination system. Three condenser lenses were adjusted to provide a demagnified image of the condenser biprism at the sample plane under parallel illumination (Fig. 2). The pre-specimen deflectors were adapted to maintain the incident wave vector of the object wave and to realize a tilt of the reference wave as a function of the condenser biprism voltage. Optimal condenser lens settings were found by means of paraxial ray tracing (Fig. 3) finally producing a mutual tilt of up to 20/nm at the object plane. We verified the kink-like phase modulation of the incident beam by means of holographic measurements. Contrast transfer theory including condenser aberrations and biprism instabilities was applied to explain detailed fringe contrast measurements. Finally, we have experimentally shown that dark-field holography [4] can be conducted with an object-independent reference. [1] H Lichte et al, Rep. Prog. Phys. 71 (2008) 016102 [2] F Röder et al, Ultramic. 152 (2015) 63-74 [3] F Röder et al, Ultramic. 161 (2016) 23–40 [4] MJ Hÿtch et al, Nature 453 (2008), 1086–1089 Acknowledgments We thank the Graduate Academy of the TU Dresden for the financial support. The research leading to these results has received funding from the European Union Seventh Framework Programme under Grant Agreement 312483-ESTEEM2 (Integrated Infrastructure Initiative-I3).

Focal series wave reconstruction in the Transmission Electron Microscope (TEM) is a well established holographic technique employed in both the medium and atomic resolution regime to study electric, magnetic and strain fields in solids as well as atomic configurations at crystal defects or grain boundaries. Focal series reconstruction does not require an undisturbed reference wave as off-axis holography and may be conducted under relaxed partial coherence provided that the latter is well-behaved and well-known in advance [1]. Moreover, focal series holography may be considered as an instance of the more general quantum state tomography (see Fig. 1) that is successfully employed to study mixed (i.e., incoherent) quantum states of matter (e.g., atoms) and light [2]. These advantages are opposed by ambiguities in the reconstructed wave function, e.g., due to inconsistent and incomplete focal series data. In reality every focal series is inconsistent, e.g., due to the presence of partial coherence, shot and detector noise, as well as geometric and chromatic aberrations depending on the defocus. Similarly, every focal series is incomplete because of a limited number of foci, typically limited to the near field regime, and the restriction to isotropic foci, where astigmatic foci are necessary to provide a dataset allowing for an unabiguous reconstruction of an underlying wave function [3]. For instance, the problematic reconstruction of low spatial frequencies can be traced back to missing focal series data in the far field. Here, we elaborate on focal series reconstruction from the perspective of quantum state tomography and use the obtained results to increase the scope of the technique in terms of convergence and uniqueness in particular for low spatial frequencies. Moreover, we explain a number of previous results by exploiting the above analogy, and open pathways to further improvements. We particularly report on the recording, preprocessing, calibration and reconstruction of a long range focal series ranging from the near to the far field in a TEM. We calibrate the focal series, including the effective defocus and magnification, by a careful calibration of the proportionality between squared current and reziprocal focal length in a magnetic lens. We derive non-linear focal sampling schemes from the phase space analogy. Subsequently, we adapt a modified Gerchberg-Saxton algorithm to the long range focal series by exploiting the link to randomized Kaczmarz (ART) algorithm used in tomography [4]. We use different numerical propagation regimes in the near and far field to take into account the scaling of the wave function and overcome convergence problems by replacing the Kaczmarz iteration with the Landweber (SIRT) iteration as proposed by Allen et al.. [5]. To overcome remaining ambiguities in the reconstruction (e.g, pertaining to a different starting guess in the Gerchberg-Saxton algorithm) resulting from inconsistencies in combination with the non-convex nature of the set of wave functions possessing the same modulus, we discuss several additional constraints such imposed by the topology of the starting guess [6]. To illustrate the above reconstruction principles, we perform a case study on a higher-order vortex beam with topological charge (winding number) 3 truncated by a square aperture (Fig. 2). The beam possesses a non-trivial topology by design, which is nicely suited to discuss the impact of (implicit) topology constraints, rotation alignment as well as other issues. [1] Koch, C. T., Micron, 2014, 63, 69-75 [2] Schleich, W. P., Quantum Optics in Phase Space, Wiley VCH, 2001 [3] Lubk, A. & Röder, F., Phys. Rev. A, 2015, 92, 033844 [4] Natterer, F., Wübbeling, F., Mathematical Methods in Image Reconstruction,SIAM, 2001 [5] Allen, L. J.; McBride, W.; O’Leary, N. L.,Oxley, M. P., Ultramicroscopy, 2004, 100, 91-104 [6] Martin, A. & Allen, L., Optics Communications, 2007, 277, 288-294 [7] Financial support by the DIP programme of the DFG is greatly acknowledged.

As has been shown in subsection 2.2, sustainability is widely acknowledged as overarching goal; and sustainable development is a generally accepted principle und guideline for political action. The degree of familiarity with the concept has increased considerably in the last decade; and sustainable development has been institutionalized and mainstreamed into many areas of politics and everyday life. But the simple fact that the concept is known and has been introduced into rules for decision-making on many levels and in many countries does not necessarily mean that the world is closer to realizing sustainability than before. It is common knowledge that knowing is not the same as doing; and added to this, the many facets of sustainability and sustainable development may not be as well understood as surveys asking about the familiarity with the concept imply. In Germany, for example, sustainability is translated as “Nachhaltigkeit”, but the word “nachhaltig”, sustainable, is often used to simply describe something as long-term.

The theories and discussions in the preceding chapters were aimed at developing an understanding of sustainability and its application to the labor market. To pursue a sustainability strategy that comprises policies to further sustainable labor, tools for the evaluation of said policies with regard to their contribution to a sustainable development must be provided.

The sustainability strategy of the German government demands the implementation of sustainability as guiding principle for all political actions. This includes the obligation to assess every new regulation and law regarding their impact on the indicators for sustainable development (Bundesregierung 2008). As labor market policy (LMP) is a substantial dimension of political actions, it must follow the guiding principle and consider it in the decisions and measures.

Based on a recent claim [Phys. Rev. Lett. 116, 127203 (2016)] that electron vortex can be used to image magnetism at the nanoscale in elastic scattering experiments, using transmission electron microscopy, a comprehensive computational study is performed to study magnetic effects in the paraxial regime of elastic electron scattering in magnetic solids. Magnetic interactions from electron vortex beams, spin polarized electron beams and beams with phase aberrations are considered, as they pass through ferromagnetic FePt or antiferromagnetic LaMnAsO. The magnetic signals are obtained by comparing the intensity over a disk in the diffraction plane for beams with opposite angular momentum or aberrations. The strongest magnetic signals are obtained from vortex beams with large orbital angular momentum, where relative magnetic signals above $10^{-3}$ are indicated for $10\hbar$ orbital angular momentum, meaning that relative signals of one percent could be expected with the even larger orbital angular momenta, which have been produced in experimental setups. All results indicate that beams with low acceleration voltage and small convergence angles yield stronger magnetic signals, which is unfortunately problematic for the possibility of high spatial resolution imaging. Nevertheless, under atomic resolution conditions, relative magnetic signals in the order of $10^{-4}$ are demonstrated, corresponding to an increase with one order of magnitude compared to previous work.

For the characterization of light materials using transmission electron microscopy, a low electron acceleration voltage of 80 kV or even 60 kV is attractive due to reduced beam damage to the specimen. The concomitant reduction in resolving power of the microscope can be restored when using spherical aberration (C(s) ) correctors, which for the most part are only available in the latest and most expensive microscopes. Here, we show that upgrading of existing TEMs is an attractive and cost-effective alternative. We report on the low-voltage performance on graphitic material of a JEOL JEM-2010F built in the early 1990s and retro-fitted with a conventional imaging C(s) corrector and a probe C(s) corrector. The performance data show C(s) retro-fitted instruments can compete very favourably against more modern state-of-the-art instruments in both conventional imaging (TEM) and scanning (STEM) modes.

Strain engineering enables modification of the properties of thin films using the stress from the substrates on which they are grown. Strain may be relaxed, however, and this can also modify the properties thanks to the coupling between strain gradient and polarization known as flexoelectricity. Here we have studied the strain distribution inside epitaxial films of the archetypal ferroelectric PbTiO3, where the mismatch with the substrate is relaxed through the formation of domains (twins). Synchrotron X-ray diffraction and high-resolution scanning transmission electron microscopy reveal an intricate strain distribution, with gradients in both the vertical and, unexpectedly, the horizontal direction. These gradients generate a horizontal flexoelectricity that forces the spontaneous polarization to rotate away from the normal. Polar rotations are a characteristic of compositionally engineered morphotropic phase boundary ferroelectrics with high piezoelectricity; flexoelectricity provides an alternative route for generating such rotations in standard ferroelectrics using purely physical means.

The standard treatment for the different plane wave components of incoming electrons in transmission electron microscope imaging is an incoherent superposition. However, projectile electrons in transmission electron microscopes are localized in space, and therefore have to be described as coherent wave-packets. Moreover, recent developments towards ultrafast electron microscopy and dynamic transmission electron microscopy require a description using highly localized wave-packets. Here we will extend the standard stationary modeling of the elastic scattering processes in high-resolution microscopy to a fully time-dependent approach, by using the direct solution of the time-dependent Schrödinger equation. We will draw the connection to the detection of coherent wave-packets, giving explicit implications for the reconstructed waves in off-axis electron holography. Additionally the description of incoherent aberrations is extended to incorporate the influence of the biprism accurately, leading to a modified form of the damping of spatial frequencies.

The perovskite BaBiO3 (BBO) is a versatile oxide parent material which displays superconductivity upon p-doping, while n-doping has been predicted to establish a wide-bandgap topological insulator phase. Here, we report on a mechanism that allows for epitaxial deposition of high-quality crystalline BBO thin films on SrTiO3 substrates despite a significant lattice mismatch of as large as 12%. It is revealed that the growth takes place through domain matching epitaxy, resulting in domains with alternating lateral sizes of 8 and 9 BBO unit cells. In particular, a structurally modified interface layer is identified which serves as a nucleation layer for the BBO films and gradually relieves the strain by decoupling the film lattice from the substrate. The BBO growth mechanism identified here may be prototypical for prospective thin film deposition of other perovskites with large lattice constants.

Electron-holographic tomography (EHT), that is, the combination of off-axis electron holography with electron tomography, was successfully applied for the quantitative 3D mapping of electrostatic potentials at the nanoscale. Here we present the first software package (THOMAS) for semi-automated acquisition of holographic tilt series, a prerequisite for efficient data collection. Using THOMAS, the acquisition time for a holographic tilt series, consisting of object and reference holograms, is reduced by a factor of five on average, compared to the previous, completely manual approaches. Moreover, the existing software packages for retrieving amplitude and phase information from electron holograms have been extended, now including a one-step procedure for holographic tilt series reconstruction. Furthermore, a modified SIRT algorithm (WSIRT) was implemented for the quantitative 3D reconstruction of the electrostatic potential from the aligned phase tilt series. Finally, the application of EHT to a polystyrene latex sphere test-specimen and a pn-doped Ge 'needle'-shaped specimen are presented, illustrating the quantitative character of EHT. For both specimens the mean inner potential (MIP) values were accurately determined from the reconstructed 3D potential. For the Ge specimen, additionally the 'built-in' voltage across the pn junction of 0.5. V was obtained.

The loss of the quantum phase information in the measurement process constitutes a fundamental limitation to transmission electron microscopy as the electron wave's phase often contains valuable information about the studied specimen. Phase retrieval from focal series is a holographic technique that seeks to recover the lost information from a set of images recorded at different defoci. In spite of its widespread use, especially for wave reconstruction at atomic resolution, a number of fundamental properties (e.g., regarding the conditions for a unique wave function reconstruction) the magnitude of the reconstruction error and the influence of inconsistencies or incomplete data are not well understood. Here, we elaborate on the fundamentals of the technique, making extensive use of the tomographic representation of a focal series as tilt series in phase space. Using this perspective, we discuss, among others, requirements for the focal series for a unique reconstruction, such as the focus interval ranging from the far field at underfocus to the far field at overfocus or the focus step size. We reveal that the prominent Gerchberg–Saxton iterative projection algorithm corresponds to a numerical integration of the quantum Hamilton–Jacobi equation in the small focus step limit. Moreover, we show that the topology of the starting guess divides the solution space of the Gerchberg–Saxton algorithm into equivalence classes, which mitigates the impact of the incompleteness of typical focal series data. To facilitate a focal series reconstruction meeting these theoretical requirements, such as the long range focus interval, we develop a dedicated calibration procedure facilitating the determination of unknown electron optical parameters such as the focal length of the principal imaging lens or the position of object and image planes. The findings are demonstrated with an example of a focal series reconstruction of an electron vortex beam.

The use of phase plates in the back focal plane of a microscope is a well established technique in optical microscopy to increase the contrast of weakly interacting samples and is gaining interest in electron microscopy as well. In this paper we study the spiral phase plate (SPP), also called helical, vortex, or two-dimensional Hilbert phase plate, that adds an angularly dependent phase of the form $e^{i\ell\phi}$ to the exit wave in Fourier space. In the limit of large collection angles, we analytically calculate that the average of a pair of $\ell=\pm1$ SPP images is directly proportional to the gradient squared of the exit wave, explaining the edge contrast previously seen in optical SPP work. The difference between a clockwise-anticlockwise pair of SPP images and conditions where this difference vanishes and the gradient of the exit wave can be seen from one single SPP image, are discussed. Finally, we demonstrate how with three images, one without and one with each of an $\ell=\pm1$ SPP, may give enough information to reconstruct both the amplitude and the phase of the exit wave. This work provides the theoretical background to interpret images obtained with a SPP and can help enable new experiments to study for example magnetic materials in an electron microscope., Comment: 7 pages, 4 figures

The use of phase plates in the back focal plane of a microscope is a well-established technique in optical microscopy to increase the contrast of weakly interacting samples and is gaining interest in electron microscopy as well. In this paper we study the spiral phase plate (SPP), also called helical, vortex, or two-dimensional Hilbert phase plate, which adds an angularly dependent phase of the form ${e}^{i\ensuremath{\ell}{\ensuremath{\phi}}_{k}}$ to the exit wave in Fourier space. In the limit of large collection angles, we analytically calculate that the average of a pair of $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ SPP filtered images is directly proportional to the gradient squared of the exit wave, explaining the edge contrast previously seen in optical SPP work. We discuss the difference between a clockwise-anticlockwise pair of SPP filtered images and derive conditions under which the modulus of the wave's gradient can be seen directly from one SPP filtered image. This work provides the theoretical background to interpret images obtained with a SPP, thereby opening new perspectives for new experiments to study, for example, magnetic materials in an electron microscope.

Electron vortex beams hold great promise for development in transmission electron microscopy, but have yet to be widely adopted. This is partly due to the complex set of interactions that occur between a beam carrying orbital angular momentum (OAM) and a sample. Herein, the system is simplified to focus on the interaction between geometrical symmetries, OAM and topology. We present multiple simulations, alongside experimental data to study the behaviour of a variety of electron vortex beams after interacting with apertures of different symmetries, and investigate the effect on their OAM and vortex structure, both in the far-field and under free-space propagation., Comment: 11 pages

We present the synthesis of Co2FeGa Heusler nanowires and the results of our investigations on their three-dimensional (3D) electric and magnetic internal and external fields mapped by electron holographic tomography (EHT). These fields will be of great importance in next-generation nanomagnets integrated in spintronics and memory devices. The Co2FeGa nanowires with a L21 ordered structure are prepared by a SBA-15 silica-assisted method. The magnetic dipole-like stray fields of several Co2FeGa nanowires are revealed by holographically reconstructed phase images. Based on the measured magnetic phase shifts of an individual nanowire and its 3D reconstruction using EHT, we obtain an internal magnetic induction with a magnitude of 1.15 T and a nonmagnetic surface layer of 10 nm thickness. Furthermore, we also reconstruct the 3D distribution of the electrostatic potential of the same nanowire.