Microscopy Conference 2023

Prof. Dr.

Session chairs

This session focusses on methods associated with different aspects of phase in electron microscopy. A first topic concerns mapping of the Coulomb potential, electric or magnetic fields, for instance using methods that retrieve the phase of the electron wave such as electron holography or focus variation reconstruction. The session also covers differential phase contrast (DPC) microscopy, which is based on the acquisition of a Ronchigram per scan position (4D-STEM) with a segmented, pixelated or other dedicated detector, using the first moment of the intensity distribution or a ptychographic reconstruction of the object phase. Another topic is related to the shaping of the phase of the electron wave using different kinds of phase plates, vortex beams, and beam shaping in general. Contributions may also tackle related theoretical topics, image simulation, influence of inelastic contributions and similar aspects.

Prof.

Nanoscale 3D imaging of magnetic spin textures with holographic vector-field electron tomography

Abstract text (incl. figure legends and references) Lorentz transmission electron microscopy (LTEM) and off-axis electron holography (EH) are the methods of choice to image magnetism at the nanometer scale. Both techniques exploit the electro-magnetic Aharonov-Bohm effect imprinting a phase shift on the wave function of highly-energetic electrons after transmitting a thin sample. However, for investigation of three-dimensional (3D) nanomagnetism [1], which involves complex 3D magnetic configurations such as exotic domain walls (e.g. of Bloch point type) or magnetic textures (e.g. (braided) Skyrmion tubes, chiral bobbers, Hopfions), these 2D techniques are insufficient for a unique mapping of the underlying magnetic structure. To overcome this problem EH is combined with electron tomography to holographic vector-field electron tomography (VFET). After recording and reconstructing holographic tilt series, the resulting phase image tilt series are input in tomographic reconstruction algorithms to obtain both the mean inner potential (MIP) and the magnetic induction B in 3D. Here, at least three tilt series are required to reconstruct two linearly-independent B-field components, and the MIP contribution to the phase. The latter is sensitive to the 3D morphology and chemical composition of the sample. The third B-field component can be computed by solving div.B=0. We discuss state-of-the-art VFET including comparison to x-ray-based magnetic vector-field reconstruction and methodological challenges, e.g., imperfect and incomplete projection data, alignment errors, as well as regularization schemes in the tomographic reconstruction algorithms. Moreover, we present examples how VFET has been applied to obtain 3D magnetic vector fields with a few nanometer resolution: (I) We reconstructed in 3D two remanent magnetic states including their peculiar domain walls in CoNi nanowires with large transversal magnetocrystalline anisotropy [2]. (II) We revealed with holographic VFET Bloch-type Skyrmion tubes (SkTs) in an FeGe needle-shaped specimen [3]. This experiment is challenging because it has to be performed under cryogenic conditions (provided by an LN-cooled sample holder) in the presence of an out-of-plane applied B-field (provided by a ring magnet of Sm2Co17 underneath the specimen), stabilizing the Skyrmion lattice in the FeGe needle. Fig. 1 shows a 3D reconstruction obtained from three holographic tilt series recorded over a tilt range of ±66° in 3° steps. The 3D MIP distribution was determined from a tilt series recorded at room temperature, at which FeGe is paramagnetic. The resulting tomogram was then subtracted from tomograms reconstructed from two tilt series recorded at 95 K to determine the 3D B-field of the FeGe sample in its Skyrmion phase. These results give direct insights into 3D Skyrmion spin texture. An analysis of, e.g., planar energy density maps across the SkTs reflecting the interplay between symmetric exchange and antisymmetric Dzyaloshinskii–Moriya interaction, as well as a comparison with micromagnetic simulations is presented. Figure 1. 3D magnetic induction of the skyrmions in an FeGe sample. Left: Color-coded components Bx and By with arrow plots show the direction and magnitude of the magnetic field. Right: Extracted single SkT with arrow plots at a top, middle and bottom plane. [1] A. Fernandez-Pacheco et al., Nat Commun 8, 15756 (2017) [2] I. M. Andersen et al., Phys. Rev. Res. 3, 033085 (2021) [3] D. Wolf et al., Nat. Nanotechnol. 17, 250 (2022)

IM 6: Phase-related techniques & 4D STEM

Invited talk

4D STEM – characterisation of materials and contrast enhancement in light matter

Abstract text (incl. figure legends and references) The simultaneous availability of densely sampled real- and diffraction space data in momentum-resolved (MR) STEM increases the versatility of established imaging modes and enables the development of a multitude of new techniques. Prominent ones are first moment (FM) STEM imaging and ptychography, which will be outlined as to basic concepts, limitations and paradigm applications. Then, first results in the field of imaging weakly scattering organic specimens will be shown. The flexibility provided by MR STEM as to the generation of FM, bright field (BF), dark field (DF) and annular BF (ABF) signals implies it being termed a universal imaging mode. However, it is found that many signals obey their own focus dependence already at moderate specimen thicknesses [1], as demonstrated in a 4D STEM focal series experiment in Fig. 1a, yielding the contrast dependencies in Fig. 1b. A simultaneous recording of, e.g., Z-contrast and FM STEM data at their optimum foci is thus usually not possible. Moreover, we discuss the second moment of the diffracted intensity as to its capability to recover the locations of the specimen surfaces in beam direction. Another important factor to be considered for the quantitative understanding of low-angle scattering is the redistribution of diffracted intensity due to (multiple) plasmon scattering [2], which we demonstrate by energy-filtered MR STEM as depicted in Fig. 1c. Here, the validity of a convolutional Lorentzian model is checked to account for multiple plasmon scattering. By interpreting FM STEM using Ehrenfest&quot;s theorem [3], electric field quantification in 2D materials is now possible at atomic scale as shown in Fig. 2. In addition, spontaneous, piezo- and ferroelectric specimens have thicknesses of several tens of nanometers, requiring a careful assessment of dynamical scattering. Whereas this leads to moderate systematic errors in unit cell averaged FM data in wurtzite GaN [4], field quantification in Pb- and Ba-based ferroelectrics is shown to be prone to substantial errors arising from dynamical scattering, mistilt and bonding, as demonstrated in a combined experimental and simulation study. In Fig. 3a, a PbZrTiO example is used to illustrate the presence of crystallographic tilt gradients across domain boundaries in 90° domains, leading to systematic errors easily misinterpreted as polarisation-induced electric fields. As a remedy, we present the gradient-based retrieval of the ferroelectric structure using mistilt-corrected, parametrised inverse multislice methods applied to the same 4D data set as depicted in Fig. 3b, from which ionic displacements can be measured accurately. Whereas ptychographic phase retrieval is complicated in the presence of dynamical scattering, organic matter such as covalent organic frameworks (COFs) and proteins can be treated as (weak) phase objects. We present a study of the validity of this assumption by dose-dependent multislice simulations of viruses in amorphous ice, justifying the application of single-sideband and Wigner distribution deconvolution ptychography, and the quantitative interpretation of differential phase contrast (DPC) STEM [5], as exemplified for a COF in Fig. 4. These basic results will be used to envisage possible future directions to combine physical and life science microscopy. [1] Ultramicroscopy 233, 113425 (2022) [2] APL 121, 213502 (2022) [3] Nat. Comm. 5, 5653 (2014) [4] PRL 122, 106102 (2019) [5] Nat. Methods 19, 01586 (2022)

Electrical fields in AlN/GaN-nanowires measured with aberration-corrected 4D-STEM

Abstract text (incl. figure legends and references) The functionality and efficiency of electronic or optoelectronic devices can be critically influenced by electric fields in the structures. Such fields may arise from inhomogeneous doping, spontaneous or piezoelectric polarisation or occur during operation due to an externally applied voltage. A prominent example is the quantum-confined Stark effect, which can strongly diminish the output of light emitting structures even if crystalline quality and composition homogeneity are otherwise excellent. This is especially the case for crystals with an inherent polarisation as found in the wurtzite-structured AlN/GaN material system. A position resolved measurement of the electric field strength inside of epitaxially grown structures – ideally with the ability to apply voltages to the specimens in-situ – is hence an important tool for the investigation and optimisation of their growth and subsequent operation. As aberration-corrected STEM allows for imaging with atomic resolution, it is an ideal method for such investigations. But while other specimen properties such as composition or geometry can be characterised from strongly integrated STEM signals acquired with large annular detectors, the signal footprint of electric fields in the sample is more delicate: They mostly manifest in a slight redistribution of intensity in the diffraction patterns. For quantitative field measurements, it is hence necessary to acquire and evaluate 4D-STEM datasets, where the diffraction pattern for each scan point is recorded. From these sets, field strengths can be derived under certain conditions and assumptions. This work focusses on 4D-STEM field measurements in AlN/GaN nanowire heterostructures. These wires are grown by MBE and investigated with a probe-corrected TEM equipped with an ultrafast, pixelated, direct electron detection detector. The measurements are accompanied by multislice simulations to assess their accuracy and precision. Prerequisites for quantitative measurement of polarisation-induced fields are discussed and the management of possible artefacts due to changes in the mean inner potential are addressed. Based on these considerations, experimental results of high-resolution 4D-STEM field-measurements are presented. The conversion into maps of electrostatic potential or charge density is discussed. Due to the high resolution inherent to STEM, the measured signal is at first dominated by the very large atomic fields that obscure the polarisation-induced fields. An appropriate averaging process is therefore warranted and is discussed in detail. One exemplary evaluation is shown in Fig. 1. The resulting mesoscalic fields are compared to the theoretical expectations. In order to investigate the influence of external fields, wires are contacted by electron lithography on ultrathin silicon nitride membranes. Different voltages are applied in-situ employing a dedicated electrical biasing specimen holder. These results can be related to photoluminescence spectra of the same wires. Fig. 1: Measurement of fields in an AlN/GaN layer structure in a nanowire. A 4D-STEM dataset was acquired in the marked area of the overview on the left. It was evaluated yielding a map of electric field strength in growth direction shown in the top right. The different spontaneous and piezoelectric fields in AlN and GaN can be measured.

IM 5: Quantitative image and diffraction data analysis

Abstract talk

Quantitative electric field determination in semiconductor homo- and hetero-interfaces using electron diffraction and 4D-STEM

Abstract text (incl. figure legends and references) Introduction: Nanometer scale characterization of electric fields at semiconductor interfaces is necessary for most electronic devices such as lasers, transistors, solar cells and batteries in order to understand the performance of those devices. Various experimental methods such as electron holography [1], differential phase contrast (DPC) imaging [2], the Fresnel method [3] and the Focault method [4] have been reported in the past for the imaging of built-in electric fields. Recently, we reported the quantitative evaluation on the electric field across a GaAs-based pn-junction using the center of mass (COM) shift of the central beam by 4D-STEM [5]. Objectives: We aim for the quantification of long-range electric fields that build up at the homo- and hetero-interfaces by measuring the COM shift of the central beam disc by combining precession electron diffraction (PED) with 4D-STEM. Materials and methods: In the present study, we use a Nanomegas ASTAR PED system attached to a double aberration corrected JEOL JEM2200FS for quantifying the fields across both homo- and hetero-interfaces. Therefore, we use the parallel beam scanning mode where the convergence angles are in the range of 1-3mrad. Accordingly, dynamical diffraction effects, which destroy the signal at hetero-junctions are reduced as we precess the beam around the optical axis of the microscope. In this way, we manage to get rid of the signal from the atomic fields improving the resolution for the much weaker long-range fields. Results: GaAs-based pn-junctions with different doping concentrations are analyzed to show the potential of this method. We optimize the parameters for observing the COM shift of the central beam disc which is determined by the built-in electric field, the polarity and the doping concentrations of the pn-junction. Fig.1 shows the COM evaluations performed on the GaAs-based pn-junction. Further, we apply this method to hetero-interfaces such as AlAs/GaAs and GaP/Si. Apparently, the observed COM shift at the hetero-interfaces also relates to the change in the mean inner potential (MIP). Fig.2 shows the experimental results across the AlAs/GaAs hetero-interface. Conclusions: Our results clearly indicate that the presence of electric fields caused by doping or interatomic bonding at the interface can be detected. The presentation will explain the PED-4D STEM experiments, the optimum parameters for those as well as will give some experimental examples. Fig 1: Experimental measurements of a GaAs-based pn-junction (a) Virtual Bright Field (BF) image with an inset showing the central beam disc with precession of 0.45° (b) COM shift across the depletion region perpendicular to the growth direction [001] (c) COM shift and electric field profiles at the depletion region and linear fits to the rise and fall of the peak in electric field. Fig 2: Experimental measurements of a AlAs/GaAs heterointerface (a) Virtual BF image with an inset showing the central beam disc with precession 0.45° (b) COM shift at the interface perpendicular to the growth direction [001] (c) COM shift and electric field profiles across the interface. References: Sasaki et al. Microscopy 63, pp.235 (2014). Shibata et al., Sci. Rep. 5, pp.10040 (2015). Merli et al Phys. Status Solidi 1973, 16 (2), K89−K91. Titchmarsh el al status solidi (b), 34(2), K83-K86. Beyer. A. et al Nano Lett. (2021),21,5, 2018-2025.

Can we enhance the depth of focus/depth resolution in STEM with an electrostatic phase plate?

Abstract text (incl. figure legends and references) Introduction In STEM, a trade-off appears between in-plane (xy) and out-of-plane z-resolution due to higher-order aberrations limiting the beam's convergence angle (α). The z-resolution can be demonstrated to scale with 1/α2, whereas the xy resolution scales with 1/α, so we get that the z-resolution is a factor of α lower. In other applications such as tomography, it is necessary to have all features throughout the thickness of a sample in focus to obtain an accurate geometric projection. In this case, the depth of field needs to be increased as much as possible. In this report, we will investigate if the emerging capability of shaping the wavefront of an electron beam with programmable Phase Plates (PP) would offer more freedom. Objectives (1) To enhance the z-resolution by correcting the higher-order aberrations with a PP (2) To enlarge the depth of field attainable in the STEM using an adaptive PP. Methods To achieve objective (1), we correct for higher-order aberrations with a PP, following the lessons learned in our previous study (Fig. 1) [1]. Once we have a design for the PP, we do multislice simulations to observe defects at different depths in a crystal. Fig. 1 Round ap. at 25mrad (a) vs. PP at 40mrad (b), the propagated probe is shown next to each aperture. For objective (2), we propose a novel imaging scheme (see Fig. 2) that takes advantage of the fast and reliable tuneability of the PP that we have demonstrated before [2]; by incoherently adding up different probe configurations, we can create a Bessel-like probe that remains in focus at larger propagation lengths. Fig. 2 Proposed imaging scheme for enhanced depth of field. Results The results show that for objective (1), we can design an aperture capable of correcting higher-order aberrations, thus obtaining an enhanced z-resolution without compromising the xy resolution. For objective (2), we can enlarge the propagation length of the probe by incoherently adding several probes during a dwell time t (up to 5x at α=5mrad). Conclusion We demonstrated how a PP could be used to enhance z-resolution and enlarge the depth of field. However, such implementations need further work to overcome design constraints and the non-ideal effects that arise in real experimental setups. Nonetheless, such PP can potentially adapt to the sample, thus enhancing the imaging capabilities of the instrument. References [1] Vega F, Béché A, and Verbeeck J, "Can a Programmable Phase Plate serve as an Aberration Corrector in the Transmission Electron Microscope (TEM)?" arXiv e-prints (2022): arXiv-2205 [2] Verbeeck J, Vega F, and Béché A, "Demonstration of a 48-pixel programmable phase plate for adaptive electron optics," in Electron Beam Spectroscopy for Nano-Optics, Jun. 2021 [3] Acknowledgments to the financial support of the Research Foundation Flanders (FWO, Belgium) project G042820N. The European Research Council funds ADAPTEM as an ERC POC project under grant nr: DLV-789598. This project has received funding from the European Union"s Horizon 2020 Research Infrastructure - Integrating Activities for Advanced Communities under grant agreement No 823717 – ESTEEM3

IM 1: Progress in instrumentation and ultrafast EM

Structured illumination electron ptychography: probe design and experimental implementation

Abstract text (incl. figure legends and references) Ptychography measures a correlated matrix of diffraction patterns with sufficient real space overlapping between adjoining data, and reconstructs both amplitude and phase of the object as well as of the probe. In a ptychographic measurement, the multiply of real space sampling, i.e. scanning step size, ΔR (Fig. 1a) and reciprocal space sampling, Δθ (Fig. 1b), should be smaller than half of the wavelength [1]. A factor of ½ here is because only amplitude information is recorded in the diffraction patterns and phase information is lost (phase problem). We can then define a sampling figure of merit S = λ / 2 / Δθ / ΔR (λ, wavelength), which must be larger than 1. In practice S is usually larger than 3 and typically takes a value of 10 to 20 (oversampling). With the additional information of the target reconstructed image pixel size (related to spatial resolution) p, detector pixel numbers Nd, one can determine the scanning step size ΔR = Nd * p / 2 / S. Depending on the overlapping ratio, a proper probe size can then be calculated, especially for defocused probe ptychography. Instead of applying defocus aberration, one could realise the desired enlarged probe in focus by adding certain population of vortices in the probe (Fig. 2c) [2, 3]. This can be realised with a patterned Si3N4 thin film phase mask putting in the condenser aperture plane. It would produce a structured enlarged probe with rather uniform intensity level over a wide lateral extent (Fig. 2d). If instead using an amplitude mask or a phase mask with wrong phase shift, the central spot will be much brighter than the surrounding structures and therefore diminish the advantages of the structured illumination. Following the calculation above, we can also determine the population of vortices, if the desired probe size and image pixel size is given, so the fabricated phase mask can match with the designed experimental set up. Structured illumination is also of vital importance in near-field ptychography. In this case, the probe becomes a full-field illumination and the detector measures Fresnel (near-field) instead of Fraunhofer diffraction. Without a structured probe, each diffraction image carries the same information except it is laterally shifted, and thus the ptychography reconstruction reduces to a single phase retrieval loop. We have experimentally demonstrated near-field ptychography with electrons using a thin film phase diffuser [4] and now extended this with an amplitude mask (Fig. 2a, b) which proves to work well and avoids the inelastic scattering from the phase diffuser. References [1] D. J. Batey et al., Physical Review A 89, 043812 (2014). [2] P. M. Pelz et al., Scientific Reports 7, 9883 (2017). [3] W. Van den Broek et al., Microscopy and Microanalysis 25 (S2), 58 (2019). [4] F. Allars et al., Ultramicroscopy 231, 113257 (2021). Fig. 1. Illustration of real space sampling (a) and reciprocal space sampling (b) in ptychographic measurements. Fig. 2. (a-b) Amplitude diffuser for near-field ptychography. (a) SEM image of a FIB-fabricated amplitude diffuser. (b) Experimentally reconstructed amplitude of the probe from a near-field electron ptychography measurement using the diffuser in (a). (c-d) Phase diffuser for far-field ptychography. (c) Design of a phase diffuser. (d) Experimentally measured in-focus probe structured by a FIB-fabricated Si3N4 thin film phase diffuser based on the design in (c).

IM 6
Phase-related techniques & 4D STEM

Appointment

Session chairs

Description

Programme

IM 6Phase-related techniques & 4D STEM

Appointment

Session chairs

Description

Programme

IM 6
Phase-related techniques & 4D STEM