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International audience; The study of the new forms of magnetic states in magnetic cylinders has recently attracted much attention [1]. However, multi-layered structures in cylindrical geometry, which are basic blocks for spin torque nano-oscillators for example, have been poorly studied up to now. Among others, one of the main challenge for such studies is the experimental observation of magnetic configurations below 100 nm. In this work, we used off-axis electron holography to observe the remnant magnetic states of Co/Cu multi-layered nano-cylinders with a spatial resolution down to 2 nm. Nanocylinders are grown by electrodeposition in commercial polycarbonate membranes. Their diameters range between 70 and 90 nm. In order to study the effect of the aspect ratio and dipolar coupling on the magnetic states, four series of samples with different nominal Co and Cu thicknesses have been realized, namely Co25 nm/Cu15 nm, Co25 nm/Cu45 nm , Co50 nm/Cu50 nm and Co100 nm/Cu100 nm. The magnetic configurations are recovered from direct qualitative and quantitative comparison between the experimental magnetic phase shift image obtained by holography and the one calculated from micromagnetic simulations (OOMMF). These ones are performed including the geometrical properties of each individual layers deduced from EFTEM experiments. With our method, we have observed in the different wires either uniform magnetic states with antiparallel coupling or vortex states with different orientations of the core with respect to the wire axis [2,3]. In addition, different magnetic states can coexist within the same nanowire. Such a wide variety of magnetic configuration arises from the low values of the Co magnetic constants with respect to bulk, typical of electrodeposition process in single bath. To explain our results, we have calculated the phase diagram of the remnant states in a single disc for different orientations of the crystal anisotropy and saturation field. We show that the occurrence of each configuration depends on the aspect ratio of the layers, the direction of magneto crystalline anisotropy, and, in some cases, the interlayer dipolar coupling. In particular case, we will show that information on the preferential orientation of the crystalline anisotropy can be recovered from the statistics of occurrence of each magnetic configurations in the multilayer. Finally, we discuss the interest of 3D holographic vector field electron tomography for nanomagnetism studies. Preliminary results performed on the Co25 nm/Cu15 nm cylinders demonstrates that it allows getting the exact shape of each layer and the 3D components of the magnetic induction in each layer. This avoids geometrical uncertainties in micromagnetic simulations and solves the problem of 2D projection in off-axis electron holography experiments, leading to a much better determination of the magnetic constant of the layers.

The reduced dimensionality in two-dimensional materials leads to a wealth of unusual properties, which are currently explored for both fundamental and applied sciences. In order to study the crystal structure, edge states, the formation of defects and grain boundaries, or the impact of adsorbates, high-resolution microscopy techniques are indispensable. Here we report on the development of an electron holography (EH) transmission electron microscopy (TEM) technique, which facilitates high spatial resolution by an automatic correction of geometric aberrations. Distinguished features of EH beyond conventional TEM imaging are gap-free spatial information signal transfer and higher dose efficiency for certain spatial frequency bands as well as direct access to the projected electrostatic potential of the two-dimensional material. We demonstrate these features with the example of h-BN, for which we measure the electrostatic potential as a function of layer number down to the monolayer limit and obtain evidence for a systematic increase of the potential at the zig-zag edges.

Electron holographic tomography was used to obtain three-dimensional reconstructions of the morphology and electrostatic potential gradient of axial GaInP/InP nanowire tunnel diodes. Crystal growth was carried out in two opposite directions: GaInP-Zn/InP-S and InP-Sn/GaInP-Zn, using Zn as the p-type dopant in the GaInP but with changes to the n-type dopant (S or Sn) in the InP. Secondary electron and electron beam-induced current images obtained using scanning electron microscopy indicated the presence of p-n junctions in both cases and current-voltage characteristics measured via lithographic contacts showed the negative differential resistance, characteristic of band-to-band tunneling, for both diodes. Electron holographic tomography measurements confirmed a short depletion width in both cases (21 ± 3 nm) but different built-in potentials, Vbi, of 1.0 V for the p-type (Zn) to n-type (S) transition, and 0.4 V for both were lower than the expected 1.5 V for these junctions if degenerately doped. Charging induced by the electron beam was evident in phase images which showed nonlinearity in the surrounding vacuum, most severe in the case of the nanowire grounded at the p-type Au contact. We attribute their lower Vbi to asymmetric secondary electron emission, beam-induced current biasing, and poor grounding contacts.

Off-axis electron holography is a well-established transmission electron microscopy technique, typically employed to investigate electric and magnetic fields in and around nanoscale materials, which modify the phase of the reconstructed electron wave function. Here, we elaborate on a detailed analysis of the two characteristic intensity terms that are completing the electron hologram, the conventional image intensity and the interference fringe intensity. We show how both are related to elastic and inelastic scattering absorption at the sample and how they may be separated to analyze the chemical composition of the sample. Since scattering absorption is aperture dependent, a quantitative determination of the corresponding attenuation coefficients (reciprocal mean free path lengths) requires the use of holographic image modi with well-defined objective aperture stops in the back-focal plane of the objective lens. The proposed method extends quantitative electron holography to a correlated three-in-one characterization of electric and magnetic fields, Z-contrast and dielectric losses in materials.

Inspired by chains of ferrimagnetic nanocrystals (NCs) in magnetotactic bacteria (MTB), the synthesis and detailed characterization of ferrimagnetic magnetite NC chain-like assemblies is reported. An easy green synthesis route in a thermoreversible gelatin hydrogel matrix is used. The structure of these magnetite chains prepared with and without gelatin is characterized by means of transmission electron microscopy, including electron tomography (ET). These structures indeed bear resemblance to the magnetite assemblies found in MTB, known for their mechanical flexibility and outstanding magnetic properties and known to crystallographically align their magnetite NCs along the strongest magnetization easy axis. Using electron holography (EH) and angular dependent magnetic measurements, the magnetic interaction between the NCs and the generation of a magnetically anisotropic material can be shown. The electro- and magnetostatic modeling demonstrates that in order to precisely determine the magnetization (by means of EH) inside chain-like NCs assemblies, their exact shape, arrangement and stray-fields have to be considered (ideally obtained using ET). �� 2019 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Envisaged applications of Skyrmions in magnetic memory and logic devices crucially depend on the stability and mobility of these topologically nontrivial magnetic textures in thin films. We present for the first time quantitative maps of the magnetic induction that provide evidence for a 3D modulation of the Skyrmionic spin texture. The projected in-plane magnetic induction maps as determined from in-line and off-axis electron holography carry the clear signature of Bloch Skyrmions. However, the magnitude of this induction is much smaller than the values expected for homogeneous Bloch Skyrmions that extend throughout the thickness of the film. This finding can only be understood if the underlying spin textures are modulated along the out-of-plane $z$ direction. The projection of (the in-plane magnetic induction of) helices is further found to exhibit thickness-dependent lateral shifts, which show that this $z$ modulation is accompanied by an (in-plane) modulation along the $x$ and $y$ directions.

Thin TEM specimen are regarded as weak objects (WPO), if the amplitude variation of the electron wave by the specimen can be neglected and the phase modulation is very small (≪π). Large classes of topical materials can be described in this approximation, such as most 2D materials, organic semiconductor materials or biological specimen. Due to the lack of amplitude (and hence intensity) contrast, conventional TEM (CTEM) investigations on WPOs are commonly performed under a certain defocus, which transfers part of the phase information to the recorded intensity. This intermixing contrast transfer from amplitude to phase and vice versa is commonly described by the phase contrast transfer function (PCTF), while the non-mixing contrast transfer for amplitude and phase is referred to as amplitude contrast transfer function (ACTF). Due to the transfer gap in the PCTF, the CTEM contrast transfer at low spatial frequencies is degraded in defocused images of WPOs (Fig. 1). By employing electron holography, however, both amplitude and phase of the electron wave can be reconstructed without a transfer gap. Having the whole wave information also enables the a-posteriori correction of geometric aberrations as it was already proposed in D. Gabor’s seminal paper from 1948 [1]. The realization of his idea, however, remains challenging in the absence of additional knowledge about the sample, due to the lack of a criterion for a successful aberration correction.

The recently derived general transfer theory for off-axis electron holography provides a new approach for reconstructing the electron wave beyond the conventional sideband information limit. Limited ensemble coherence of the electron beam between object and reference area leads to an attenuation of spatial frequencies of the object exit wave in the presence of aberrations of the objective lens. Concerted tilts of the reference wave under the condition of an invariant object exit wave are proposed to diminish the aberration impact on spatial frequencies even beyond the sideband information limit allowing its transfer with maximum possible contrast. In addition to the theoretical considerations outlined in detail, an experimental proof-of-principle is presented. A fully controlled tilt of the reference wave, however, remains as a promising task for the future. The use of a hologram series with varying reference wave tilt is considered for linearly synthesizing an effective aperture for the transfer into the sideband with broader bandwidth compared to conventional off-axis electron holography allowing us to correct the incoherent aberrations in transmission electron microscopy. Furthermore, tilting a reference wave with respect to a plane wave is expected to be an alternative way for measuring the coherent and incoherent aberrations of a transmission electron microscope. The capability of tilting the reference wave is expected to be beneficial for improving the signal-to-noise ratio in dark-field off-axis electron holography as well.

In this chapter, we will separately consider the holographic reconstruction of mixed (quantum) states and pure states (wave), employing a variety of holographic setups in TEM, namely Off-Axis Holography, Transport of Intensity Reconstruction, Focal Series Inline Holography, Differential Phase Contrast, and Ptychography. Each holographic technique is in the first place considered as a general mixed quantum state reconstruction scheme, and the conventional wave (pure state) reconstruction is treated as a special case of the former. This practice permits a comprehensive discussion of the ramifications of partial coherence on conventional wave reconstructions as well as a generalization toward partially coherent or incoherent signals such as resulting from inelastic scattering.

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.

Electron holography initially was invented by Dennis Gabor for solving the problems raised by the aberrations of electron lenses in Transmission Electron Microscopy. Nowadays, after hardware correction of aberrations allows true atomic resolution of the structure, for comprehensive understanding of solids, determination of electric and magnetic nanofields is the most challenging task. Since fields are phase objects in the TEM, electron holography is the unrivaled method of choice. After more than 40 years of experimental realization and steady improvement, holography is increasingly contributing to these highly sophisticated and essential questions in materials science, as well to the understanding of electron waves and their interaction with matter.

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.

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 system In 2 O 3 ( ZnO ) 7 exhibits a strained ZnO-like domain structure intersected by indium containing, parallely arranged defect planes with a regular spacing of about 2.4 nm. We propose that the strain within the domains originates from long-range electric fields due to charge localization at the defects inducing ionic displacements. The origin of the electric fields has been investigated theoretically by means of density functional theory (DFT). Calculated electric fields were incorporated as scattering potentials in holographic imaging simulations. Since the exact structure of the system is unknown, a novel structure model was derived for In 2 O 3 ( ZnO ) 7 from known members of the homologous series of In 2 O 3 ( ZnO ) m with m = 3 , 5 and refined by structure optimization at DFT level. The theoretical results are compared to experimental findings in high-resolution phase images obtained by means of electron holography, which suggest residual intrinsic electric fields. A careful consideration of noise levels and the influence of the microscope, however, show that the electric field signal is at the detection limit of state-of-the-art high-resolution electron holography.

Capable of quantitatively imaging static magnetic and electric potentials and even strain electron holography is a very versatile and powerful TEM technique. In this paper we compare off-axis electron holography with a recently developed focal series reconstruction algorithm and phase retrieval based on the transport of intensity equation. Based on theoretical considerations and simulations we compare the different techniques with respect to parameters such as the coherence requirements, field of view, resolution, noise properties, and other required experimental conditions.

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.

Tomography commonly requires a linear relation between the measured signal and the underlying specimen property; for Electron Holographic Tomography this is given by the Phase Grating Approximation (PGA). While largely valid at medium resolution, discrepancies arise at high resolution imaging conditions. We set out to investigate the artefacts that are produced if the reconstruction still assumes the PGA even with an atomic resolution tilt series. To forego experimental difficulties the holographic tilt series was simulated. The reconstructed electric potential clearly shows peaks at the positions of the atoms. These peaks have characterisitic deformations, which can be traced back to the defocus a particular atom has in the holograms of the tilt series. Exchanging an atom for one of a different atomic number results in a significant change in the reconstructed potential that is well contained within the atom's peak.

Off-axis electron holography provides access to the phase of the elastically scattered wave in a transmission electron microscope at scales ranging from several hundreds of nanometres down to 0.1nm. In many cases the reconstructed phase shift is directly proportional to projected electric and magnetic potentials rendering electron holography a useful and established characterisation method for materials science. However, quantitative interpretation of experimental phase shifts requires quantitative knowledge about the noise, which has been previously established for some limiting cases only. Here, we present a general noise transfer formalism for off-axis electron holography allowing to compute the covariance (noise) of reconstructed amplitude and phase from characteristic detector functions and general properties of the reconstruction process. Experimentally, we verify the presented noise transfer formulas for two different cameras with and without objects within the errors given by the experimental noise determination.

cited By 0; International audience; We present the state of the art in strain mapping at the nanoscale using aberration - corrected high - resolution transmission electron microscopy, HRTEM and HAADF - STEM, and dark - field electron holography (DFEH) [1]. In particular, we will focus on the examination of localized strains around defects. A broader comparison of TEM strain mapping techniques can be found i n a recent review [2]. High - resolution images can be analysed by geometric phase analysis (GPA) [3] or applying peak - finding routines to determine the positions of individual atomic columns. GPA is best adapted to measuring the deformation of the crystall ine lattice, as the example concerning a five - fold twinned Pt nanoparticle will show (Figure 1). These star - shaped particles [4] have a disclination - like strain fields around their centres, as found for Au nanoparticles [5]. In multiferroic materials, peak - finding can be used to determine the relative displacements of atom columns within a unit cell [6]. The local polarization and strain can be mapped around dislocations and in the vicinity of domain walls (Figure 2). DFEH was developed to measure strain over wide fields of view to high precision and nanometre spatial resolution. We have nevertheless been applying the technique to the study of quantum dots to relatively high resolution [7]. As with any TEM technique the samples are necessarily thin which allows some of the strain to be relaxed: the well - known thin film effect. In addition, dynamical scattering effects the strain information [8]. These issues will be addressed using a combination of finite - element modelin g (FEM) and dynamical - scattering simulations. This overview will, in addition, show results from the recently installed I2TEM microscope (Hitachi), an instrument specifically designed for DFEH experiments and aberration - corrected HRTEM over wide fields of view and for in - situ experiments (Figure 3).

Here, we study the effect of dynamic scattering on the projected geometric phase and strain maps reconstructed using dark-field electron holography (DFEH) for non-uniformly strained crystals. The investigated structure consists of a {SiGe/Si} superlattice grown on a (001)-Si substrate. The three dimensional strain held within the thin TEM lamella is modelled by the finite element method. The observed projected strain is simulated in two ways by multiplying the strain at each depth in the crystal by a weighting function determined from a recently developed analytical two-beam dynamical theory, and by simply taking the average value. We demonstrate that the experimental results need to be understood in terms of the dynamical theory and good agreement is found between the experimental and simulated results. Discrepancies do remain for certain cases and are likely to be from an imprecision in the actual two-beam diffraction conditions, notably the deviation parameter, and points to limitations in the 2-beam approximation. Finally, a route towards a 3D reconstruction of strain fields is proposed. (C) 2014 Elsevier B.V. All rights reserved.

Dark-held electron holography maps strain in crystal lattices into reconstructed phases over large fields of view. Here we investigate the details of the lattice strain-reconstructed phase relationship by applying dynamic scattering theory both analytically and numerically. We develop efficient analytic linear projection rules for 3D strain fields, facilitating a straight-forward calculation of reconstructed phases from 3D strained materials. They are used in the following to quantify the influence of various experimental parameters like strain magnitude, specimen thickness, excitation error and surface relaxation. (C) 2013 Elsevier B.V. All rights reserved.

The distribution and movement of charge is fundamental to many physical phenomena, particularly for applications involving nanoparticles, nanostructures, and electronic devices. However, there are very few ways of quantifying charge at the necessary length scale. Here, we show that aberration-corrected electron holography is capable of counting the charge on individual nanoparticles to a precision of one elementary unit of charge. We present a method that measures charges within predefined contours by directly applying Gauss's law at the nanoscale. We perform a statistical analysis to reveal the relationship between the size of the contours and the precision of the charge measurement and present strategies to optimize the spatial and signal resolution for the presented method.

International audience; The microstructure of ion-implanted crystals is profoundly dictated by mechanical strain developing in interplay with structural defects. Understanding the origin of strain during the early stages of development is challenging and requires accurate measurements and modeling. Here, we investigate the mechanical strain in H-implanted Si. X-ray diffraction analysis is performed to measure the mesoscopic out-of-plane strain and dark-field electron holography to map strain in two-dimensions (2D) with nanometer spatial resolution. Supported by finite element method modeling, we propose that the mean strain field is explained by overlapping and averaging discrete strain fields generated by sub-nanoscopic defects that are intimately related to the H depth concentration.

Electron holography at medium resolution simultaneously probes projected electrostatic and magnetostatic potentials as well as elastic and inelastic attenuation coefficients with a spatial resolution of a few nanometers. In this work, we derive how the elastic and inelastic attenuation can be disentangled. Using that result, we perform the first three dimensional tomographic reconstruction of potential and (in) elastic attenuation in parallel. The technique can be applied to distinguish between functional potentials and composition changes in nanostructures, as demonstrated using the example of a GaAs-Al0.33Ga0.67As core-shell nanowire. (C) 2014 AIP Publishing LLC.

BaTiO${}_{3}$ (BTO) nanocubes of about 50 nm in size were investigated by means of off-axis electron holography combined with in situ heating above and below the Curie temperature. It is shown that reconstructed electron phase maps of the BTO nanocubes are associated with the ferroelectric polarization pattern through a mechanism that could either be direct imaging of the internal potential or lattice variations that are common in ferroelectric domain patterns.

The phase loss encountered in conventional (S)TEM means a substantial loss of object information, because essential structure components, e.g. electric and magnetic fields, mainly modulate the image phase hence are virtually invisible in a conventional micrograph. This presents a huge obstacle for a thorough understanding of modern functional materials e.g. in semiconductors and nano-magnetism. Phases can only be determined by interference of the image wave with a reference wave. Gabor’s bright idea of holography was to use the interference pattern (hologram) as a diffraction grating, where one of the diffracted waves turns out a replica of the image wave. This replica wave is reconstructed from the hologram allowing subsequent quantitative evaluation of both amplitude and phase separately.

Electron holography is a very powerful technique for mapping static electric and magnetic potentials down to atomic resolution. While electron holography is commonly considered synonymous with its off-axis variant in the high energy electron microscopy community, inline electron holography is widely applied in low-energy electron microscopy, where the realization of the off-axis setup is still an experimental challenge. This paper demonstrates that both inline and off-axis holography may be used to recover amplitude and phase shift of the very same object, in our example latex spheres of 90 and 200 nm in diameter, producing very similar results, provided the object does not charge under the electron beam.

Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.

Extended abstract of a paper presented at Microscopy and Microanalysis 2010 in Portland, Oregon, USA, August 1 – August 5, 2010.

Electron holography in the transmission electron microscope (TEM) offers the spatial and signal resolution for studying effects like Fermi level pinning or dopant concentration variations important for the design of modern electronic devices. To overcome the loss of information along the projection direction, surface effects, and surface damage due to TEM specimen preparation, we apply electron holographic tomography to analyze the 3D potential distribution of semiconductor samples prepared by focused-ion-beam. We observe mid-band gap pinning of the Fermi level at Si surfaces but valence band pinning at Ge surfaces. The pinning extends over tens of nanometers into the bulk.