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Stray electric fields in free space generated by two biased gold needles have been quantified in comprehensive finite-element (FE) simulations, accompanied by first moment (FM) scanning TEM (STEM) and electron holography (EH) experiments. The projected electrostatic potential and electric field have been derived numerically under geometrical variations of the needle setup. In contrast to the FE simulation, application of an analytical model based on line charges yields a qualitative understanding. By experimentally probing the electric field employing FM STEM and EH under alike conditions, a discrepancy of about 60% became apparent initially. However, the EH setup suggests the reconstructed phase to be significantly affected by the perturbed reference wave effect, opposite to STEM where the field-free reference was recorded subsequently with unbiased needles in which possibly remaining electrostatic influences are regarded as being minor. In that respect, the observed discrepancy between FM imaging and EH is resolved after including the long-range potential landscape from FE simulations into the phase of the reference wave in EH. • Electric field of biased needles mapped by first-moment STEM and electron holography • Quantitative understanding of both signals obtained by finite element (FE) simulations • Referencing to field-free cases is fundamentally different for both methods • Perturbed reference wave in electron holography reproducible by extensive FE simulations • Electrode stray fields in electrically biased specimens contribute significantly to signal [ABSTRACT FROM AUTHOR]

Highlights • Off-axis electron holography enables quantification of electrostatic fields. • Outline of theoretical basis and experimental aspects for electron holography. • Applications to many different types of materials problems briefly reviewed. • Challenges and opportunities for off-axis electron holography. Abstract Off-axis electron holography has evolved into a powerful electron-microscopy-based technique for characterizing electromagnetic fields with nanometer-scale resolution. In this paper, we present a review of the application of off-axis electron holography to the quantitative measurement of electrostatic potentials and charge density distributions. We begin with a short overview of the theoretical and experimental basis of the technique. Practical aspects of phase imaging, sample preparation and microscope operation are outlined briefly. Applications of off-axis electron holography to a wide range of materials are then described in more detail. Finally, challenges and future opportunities for electron holography investigations of electrostatic fields and charge density distributions are presented. [ABSTRACT FROM AUTHOR]

Highlights • Mean-inner-potential of single crystal α-Al 2 O 3 sapphire measured at 16.90 ± 0.36 V using off-axis electron holography. • Measurement method, based on mechanically polished wedge sample, is discussed. • Density-Functional-Theory calculations of the mean-inner-potential based on VASP. • The plasmon mean free path for inelastic scattering of sapphire is measured. Abstract The mean inner potential (MIP) of a single crystal α-Al 2 O 3 sapphire was measured using off-axis electron holography. To measure the MIP, we use mechanically polished wedge specimens for transmission electron microscopy (TEM). This approach also enabled us to measure the plasmon mean free path for inelastic scattering (IMFP). The wedge specimen, chosen here at an angle of approximately 45°, allows to determine the MIP by measuring the gradient of phase variations of the reconstructed electron wave over extended regions across the sample. The angle of the wedge was measured to an accuracy of better than 1° by two methods: first, perpendicular sectioning in a focused ion beam for direct measurement by TEM and second, by a non-destructive approach of confocal optical microscopy. The validity of this methodology was examined on a single crystal Si(001) sample showing that the mechanically polished wedge approach can be applied to a wide range of materials. Our measurements concluded that the MIP of sapphire is V 0 = 16.90 ± 0.36 V. Furthermore, the IMFP of sapphire was measured at 136 ± 2 nm for 197 keV electrons with a collection angle of 18mrad. The measured MIP of sapphire reflects its degree of ionicity, which lies between theoretical calculations based on electron scattering factors of charged and neutral isolated atoms obtained by Dirac–Fock calculations. Our MIP measurements tend to the expected value for this predominantly ionic material. To account for chemical bonding and the role of the crystallographic plane at the surface of the sample, we compared the experimental measurements to density-functional-theory calculations of the MIP. Calculations of α-Al 2 O 3 slabs cut along (0001) and (1–100) planes obtained MIP values of 15.7 V and 16.7 V, respectively. [ABSTRACT FROM AUTHOR]

The technique of double exposure electron holography, which is based on the superposition of two off-axis electron holograms, was originally introduced before the availability of digital image processing to allow differences between electron-optical phases encoded in two electron holograms to be visualised directly without the need for holographic reconstruction. Here, we review the original method and show how it can now be extended to permit quantitative studies of phase shifts that oscillate in time. We begin with a description of the theory of off-axis electron hologram formation for a time-dependent electron wave that results from the excitation of a specimen using an external stimulus with a square, sinusoidal, triangular or other temporal dependence. We refer to the more general method as continuous exposure electron holography, present preliminary experimental measurements and discuss how the technique can be used to image electrostatic potentials and magnetic fields during high frequency switching experiments. [ABSTRACT FROM AUTHOR]

The phase and amplitude of the electron wavefunction that has passed through ultra-thin flakes of WSe 2 is 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 WSe 2 from 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 WSe 2 of 18.9±0.8 V, which is 12% lower than the value calculated from neutral atom scattering factors. [ABSTRACT FROM AUTHOR]

The phase shift of the electron wave is a useful measure for the projected magnetic flux density of magnetic objects at the nanometer scale. More important for materials science, however, is the knowledge about the magnetization in a magnetic nano-structure. As demonstrated here, a dominating presence of stray fields prohibits a direct interpretation of the phase in terms of magnetization modulus and direction. We therefore present a model-based approach for retrieving the magnetization by considering the projected shape of the nano-structure and assuming a homogeneous magnetization therein. We apply this method to FePt nano-islands epitaxially grown on a SrTiO 3 substrate, which indicates an inclination of their magnetization direction relative to the structural easy magnetic [001] axis. By means of this real-world example, we discuss prospects and limits of this approach. [ABSTRACT FROM AUTHOR]

Electrostatic charging of specimens during electron, photon or ion irradiation is a complicated and poorly understood phenomenon, which can affect the acquisition and interpretation of experimental data and alter the functional properties of the constituent materials. It is usually linked to secondary electron emission, but also depends on the geometry and electrical properties of the specimen. Here, we use off-axis electron holography in the transmission electron microscope to study electron-beam-induced charging of an insulating Al 2 O 3 nanotip on a conducting support. The measurements are performed under parallel electron illumination conditions as a function of specimen temperature, electron dose, primary electron energy and surface cleanliness. We observe a lack of reproducibility of charge density measurements after cycling the specimen temperature. Surprisingly, we find both positively and negatively charged regions in closely adjacent parts of the specimen. • Study electrostatic charging of specimens in the TEM by off-axis electron holography. • Varying parameters, including specimen temperature, electron dose, primary electron energy and surface cleanliness. • Understanding charging requires improved control and knowledge of the specimen geometry, surface state, electrical contact and surrounding environment. [ABSTRACT FROM AUTHOR]

Electron holography is a powerful technique for characterizing electrostatic potentials, charge distributions, electric and magnetic fields, strain distributions and semiconductor dopant distributions with sub-nm spatial resolution. Mapping internal electrostatic and magnetic fields within nanoparticles and other low-dimensional materials by TEM requires both high spatial resolution and high phase sensitivity. Carrying out such an analysis fully quantitatively is even more challenging, since artefacts such as dynamical electron scattering may strongly affect the measurement. In-line electron holography, one of the variants of electron holography, features high phase sensitivity at high spatial frequencies, but suffers from inefficient phase recovery at low spatial frequencies. Off-axis electron holography, in contrast, can recover low spatial frequency phase information much more reliably, but is less effective in retrieving phase information at high spatial frequencies when compared to in-line holography. We investigate gold nanoparticles using hybrid electron holography at both atomic-resolution and intermediate magnification. Hybrid electron holography is a novel technique that synergistically combines off-axis and in-line electron holography, allowing the measurement of the complex wave function describing the scattered electrons with excellent signal-to-noise properties at both high and low spatial frequencies. The effect of dynamical electron scattering is minimized by beam tilt averaging. [ABSTRACT FROM AUTHOR]

As proposed recently, a tilted reference wave in off-axis electron holography is expected to be useful for aberration measurement and correction. Furthermore, in dark-field electron holography, it is considered to replace the reference wave, which is conventionally diffracted in an unstrained object area, by a well-defined object-independent reference wave. Here, we first realize a tilted reference wave by employing a biprism placed in the condenser system above three condenser lenses producing a relative tilt magnitude up to 20/nm at the object plane (300 kV). Paraxial ray-tracing predicts condenser settings for a parallel illumination at the object plane, where only one half of the round illumination disc is tilted relative to the optical axis without displacement. Holographic measurements verify the kink-like phase modulation of the incident beam and return the interference fringe contrast as a function of the relative tilt between both parts of the illumination. Contrast transfer theory including condenser aberrations and biprism instabilities was applied to explain the fringe contrast measurement. A first dark-field hologram with a tilted – object-free – reference wave was acquired and reconstructed. A new application for bright/dark-field imaging is presented. [ABSTRACT FROM AUTHOR]

Pronounced improvements in the understanding of semiconductor device performance are expected if electrostatic potential distributions can be measured quantitatively and reliably under working conditions with sufficient sensitivity and spatial resolution. Here, we employ off-axis electron holography to characterize an electrically-biased Si p – n junction by measuring its electrostatic potential, electric field and charge density distributions under working conditions. A comparison between experimental electron holographic phase images and images obtained using three-dimensional electrostatic potential simulations highlights several remaining challenges to quantitative analysis. Our results illustrate how the determination of reliable potential distributions from phase images of electrically biased devices requires electrostatic fringing fields, surface charges, specimen preparation damage and the effects of limited spatial resolution to be taken into account. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The reduced density matrix completely describes the quantum state of an electron scattered by an object in transmission electron microscopy. However, the detection process restricts access to the diagonal elements only. The off-diagonal elements, determining the coherence of the scattered electron, may be obtained from electron holography. In order to extract the influence of the object from the off-diagonals, however, a rigorous consideration of the electron microscope influences like aberrations of the objective lens and the Möllenstedt biprism in the presence of partial coherence is required. Here, we derive a holographic transfer theory based on the generalization of the transmission cross-coefficient including all known holographic phenomena. We furthermore apply a particular simplification of the theory to the experimental analysis of aloof beam electrons scattered by plane silicon surfaces. [ABSTRACT FROM AUTHOR]

Abstract: Off-axis electron holography is a method for the transmission electron microscope (TEM) that measures the electric and magnetic properties of a specimen. The electrostatic and magnetic potentials modulate the electron wavefront phase. The error in measurement of the phase therefore determines the smallest observable changes in electric and magnetic properties. Here we explore the summation of a hologram series to reduce the phase error and thereby improve the sensitivity of electron holography. Summation of hologram series requires independent registration and correction of image drift and phase wavefront drift, the consequences of which are discussed. Optimization of the electro-optical configuration of the TEM for the double biprism configuration is examined. An analytical model of image and phase drift, composed of a combination of linear drift and Brownian random-walk, is derived and experimentally verified. The accuracy of image registration via cross-correlation and phase registration is characterized by simulated hologram series. The model of series summation errors allows the optimization of phase error as a function of exposure time and fringe carrier frequency for a target spatial resolution. An experimental example of hologram series summation is provided on WS2 fullerenes. A metric is provided to measure the object phase error from experimental results and compared to analytical predictions. The ultimate experimental object root-mean-square phase error is 0.006rad (2π/1050) at a spatial resolution less than 0.615nm and a total exposure time of 900s. The ultimate phase error in vacuum adjacent to the specimen is 0.0037rad (2π/1700). The analytical prediction of phase error differs with the experimental metrics by +7% inside the object and −5% in the vacuum, indicating that the model can provide reliable quantitative predictions. [Copyright &y& Elsevier]

Abstract: Modern semiconductor devices function due to accurate dopant distribution. Off-Axis Electron Holography (OAEH) in the transmission electron microscope (TEM) can map quantitatively the electrostatic potential in semiconductors with high spatial resolution. For the microelectronics industry, ongoing reduction of device dimensions, 3D device geometry, and failure analysis of specific devices require preparation of thin TEM samples, under 70nm thick, by focused ion beam (FIB). Such thicknesses, which are considerably thinner than the values reported to date in the literature, are challenging due to FIB induced damage and surface depletion effects. Here, we report on preparation of TEM samples of silicon PN junctions in the FIB completed by low-energy (5keV) ion milling, which reduced amorphization of the silicon to 10nm thick. Additional perpendicular FIB sectioning enabled a direct measurement of the TEM sample thickness in order to determine accurately the crystalline thickness of the sample. Consequently, we find that the low-energy milling also resulted in a negligible thickness of electrically inactive regions, approximately 4nm thick. The influence of TEM sample thickness, FIB induced damage and doping concentrations on the accuracy of the OAEH measurements were examined by comparison to secondary ion mass spectrometry measurements as well as to 1D and 3D simulations of the electrostatic potentials. We conclude that for TEM samples down to 100nm thick, OAEH measurements of Si-based PN junctions, for the doping levels examined here, resulted in quantitative mapping of potential variations, within ~0.1V. For thinner TEM samples, down to 20nm thick, mapping of potential variations is qualitative, due to a reduced accuracy of ~0.3V. This article is dedicated to the memory of Zohar Eliyahou. [Copyright &y& Elsevier]

Abstract: Two-dimensional finite element simulations of electrostatic dopant potentials in parallel-sided semiconductor specimens that contain p–n junctions are used to assess the effect of the electrical state of the surface of a thin specimen on projected potentials measured using off-axis electron holography in the transmission electron microscope. For a specimen that is constrained to have an equipotential surface, the simulations show that the step in the projected potential across a p–n junction is always lower than would be predicted from the properties of the bulk device, but is relatively insensitive to the value of the surface state energy, especially for thicker specimens and higher dopant concentrations. The depletion width measured from the projected potential, however, has a complicated dependence on specimen thickness. The results of the simulations are of broader interest for understanding the influence of surfaces and interfaces on electrostatic potentials in nanoscale semiconductor devices. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Focused ion beam (FIB) milling is one of the few specimen preparation techniques that can be used to prepare parallel-sided specimens with nm-scale site specificity for examination using off-axis electron holography in the transmission electron microscope (TEM). However, FIB milling results in the implantation of Ga, the formation of amorphous surface layers and the introduction of defects deep into the specimens. Here we show that these effects can be reduced by lowering the operating voltage of the FIB and by annealing the specimens at low temperature. We also show that the electrically inactive thickness is dependent on both the operating voltage and type of ion used during FIB milling. [Copyright &y& Elsevier]

Abstract: Off-axis electron holography in the transmission electron microscope is a powerful interferometric technique that enables electrostatic and magnetic fields to be imaged and quantified with spatial resolution often approaching the nanometer scale. Here, we demonstrate the capabilities of the technique for phase quantification at the nanoscale by briefly reviewing some of our recent studies of nanostructured materials. Examples that are described include determination of the electrostatic potential profiles associated with doped Si- and GaAs-based semiconductor devices, measurement of hole accumulation in Ge quantum dots, mapping of polarization fields in III-nitride heterostructures, and observation of the remanent states and reversal mechanisms of lithographically patterned magnetic nanorings. Some issues associated with sample preparation for doped semiconductor heterostructures are also briefly discussed. [Copyright &y& Elsevier]

Abstract: GaAs specimens containing p–n junctions have been prepared using focused ion beam (FIB) milling for examination using off-axis electron holography. By lowering the FIB operating voltage from 30 to 8kV, we have shown a systematic reduction of the electrically ‘inactive’ thickness from 220 to 100nm, resulting in a significant increase in the step in phase measured across the junctions as well as an improvement in the signal-to-noise ratio. We also show that the step in phase measured across the junctions can be influenced by the intensity of the electron beam. [Copyright &y& Elsevier]

Abstract: Off-axis electron holography is used to characterize a linear array of transistors, which was prepared for examination in cross-sectional geometry in the transmission electron microscope (TEM) using focused ion beam (FIB) milling from the substrate side of the semiconductor device. The measured electrostatic potential is compared with results obtained from TEM specimens prepared using the more conventional ‘trench’ FIB geometry. The use of carbon coating to remove specimen charging effects, which result in electrostatic fringing fields outside ‘trench’ specimens, is demonstrated. Such fringing fields are not observed after milling from the substrate side of the device. Analysis of the measured holographic phase images suggests that the electrically inactive layer on the surface of each FIB-milled specimen typically has a thickness of 100nm. [Copyright &y& Elsevier]

• Performed off-axis electron holography in a gas environment. • Quantified the change in beam coherency due to inelastic scattering. • Identified gas parameters affecting the coherency: species, pressure, temperature. • Highlighted the difference between Environmental TEM and a closed cell holder. Using the combination of off-axis electron holography and environmental Transmission Electron Microscopy (TEM), an experimental setup termed 'gas electron holography', we investigate how the presence of gas in the microscope affects the spatial and phase resolution of electron holograms. The gas is introduced either by using an Environmental TEM (ETEM) or a closed-cell holder. The ETEM data on gas electron holography shows that the number of electrons reaching the detector decreases exponentially as a function of gas pressure. From this evidence, we construct a phenomenological model that describes how coherency changes as a function of gas pressure. By linking the model with the concept of inelastic scattering cross section we find that the change in the coherency of the electron beam due to the presence of gas is related to the number of gas molecules present, their atomic weight and the average energy lost due to inelastic scattering. Regarding gas electron holography with a closed cell holder, we conclude that the membranes surrounding the gas are the primary factor in determining the quality of the electron hologram, while the gas pressure inside the cell has a small impact on the spatial and phase resolution of the electron holograms. [ABSTRACT FROM AUTHOR]

Magnetic skyrmions are complex swirling spin structures that are of interest for applications in energy-efficient memories and logic technologies. Multilayers of heavy metals and ferromagnets have been shown to host magnetic skyrmions at room temperature. Lorentz transmission electron microscopy is often used to study magnetic domain structures in multilayer samples using mainly Fresnel defocus imaging. Here, off-axis electron holography is used to obtain in-focus electron optical phase images of Néel-type domains and skyrmions in an Ir/Fe/Co/Pt multilayer sample. The preparation of the sample, reconstruction of the holograms and influence of sample tilt angle on the signal-to-noise ratio in the phase images are discussed. A good agreement is found between images of individual skyrmions that are stabilized using an external magnetic field and simulated images based on theoretical models of Néel-type skyrmions. • An Ir/Fe/Co/Pt multilayer was studied using off-axis electron holography. • The sample hosts Néel-type magnetic skyrmions at room temperature. • Electron optical phase images of magnetic domains and skyrmions were recorded. • Good agreement was found with simulated phase images. • Sample preparation, observation and reconstruction parameters are discussed. [ABSTRACT FROM AUTHOR]

• Development of a cartridge based turning holder. • Increase the reliability of magnetic induction mapping in TEM. • Cartridge system for wide range of samples. • Measurements of materials with low and high magnetic coercivity. • Precise holder tilt measurement using an inclinometer. Magnetic induction mapping in the transmission electron microscope using phase contrast techniques such as off-axis electron holography and differential phase contrast imaging often requires the separation of the magnetic contribution to the recorded signal from the electrostatic contribution. When using off-axis electron holography, one of the experimental approaches that can be used to achieve this separation is to evaluate half of the difference between phase shift images that have been recorded before and after turning the sample over. Here, we introduce a cartridge-based sample mounting system, which is based on an existing on-axis tomography specimen holder and can be used to turn a sample over inside the electron microscope, thereby avoiding the need to remove the holder from the microscope to turn the sample over manually. We present three cartridge designs, which are compatible with all pole piece designs and can be used to support conventional 3-mm-diameter sample grids, Si 3 N 4 -based membrane chips and needle-shaped specimens. We make use of a wireless inclinometer that has a precision of 0.1° to monitor the sample holder tilt angle independently of the microscope goniometer readout. We also highlight the need to remove geometrical image distortions when aligning pairs of phase shift images that have been recorded before and after turning the sample over. The capabilities of the cartridge-based specimen holder and the turning approach are demonstrated by using off-axis electron holography to record magnetic induction maps of lithographically-patterned soft magnetic Co elements, a focused ion beam milled hard magnetic Nd-Fe-B lamella and an array of four Fe 3 O 4 nanocrystals. [ABSTRACT FROM AUTHOR]

• Conceptual difference between holography and STEM due to aperture. • Strong defocus dependency in first moment STEM imaging. • STEM more kinematic at optimum focus compared to electron holography. • Negligible effect of TDS on momentum transfer (for thin samples). Off-axis electron holography and first moment STEM are sensitive to electromagnetic potentials or fields, respectively. In this work, we investigate in what sense the results obtained from both techniques are equivalent and work out the major differences. The analysis is focused on electrostatic (Coulomb) potentials at atomic spatial resolution. It is shown that the probe-forming/objective aperture strongly affects the reconstructed electrostatic potentials and that, as a result of the different illumination setups, dynamical diffraction effects show a specific response with increasing specimen thickness. It is shown that thermal diffuse scattering is negligible for a wide range of specimen thicknesses, when evaluating the first moment of diffraction patterns. [ABSTRACT FROM AUTHOR]