Nanoscale Phase and Orientation Mapping in Multiphase Polycrystalline Hafnium Zirconium Oxide Thin Films Using 4D-STEM and Automated Diffraction Indexing.

Ferroelectric hafnium zirconium oxide (HZO) holds promise for nextgeneration memory and transistors due to its superior scalability and seamless integration with complementary metal-oxide-semiconductor processing. A major challenge in developing this emerging ferroelectric material is the metastable nature of the non-centrosymmetric polar phase responsible for ferroelectricity, resulting in a coexistence of both polar and non-polar phases with uneven grain sizes and random orientations. Due to the structural similarity between the multiple phases and the nanoscale dimensions of the thin film devices, accurate measurement of phase-specific information remains challenging. Here, the application of 4D scanning transmission electron microscopy is demonstrated with automated electron diffraction pattern indexing to analyze multiphase polycrystalline HZO thin films, enabling the characterization of crystallographic phase and orientation across large working areas on the order of hundreds of nanometers. This approach offers a powerful characterization framework to produce a quantitative and statistically robust analysis of the intricate structure of HZO films by uncovering phase composition, polarization axis alignment, and unique phase distribution within the HZO film. This study introduces a novel approach for analyzing ferroelectric HZO, facilitating reliable characterization of process-structure-property relationships imperative to accelerating the growth optimization, performance, and successful implementation of ferroelectric HZO in devices.

On-Chip Topological Photonic Crystal Nanobeam Filters.

We present an on-chip filter with a broad tailorable working wavelength and a single-mode operation. This is realized through the application of topological photonic crystal nanobeam filters employing synthesis parameter dimensions. By introducing the translation of air holes as a new synthetic parameter dimension, we obtained nanobeams with tunable Zak phases. Leveraging the bulk-edge correspondence, we identify the existence of topological cavity modes and establish a correlation between the cavity's interface morphology and working wavelength. Through experiments, we demonstrate filters with adjustable filtering wavelengths ranging from 1301 to 1570 nm. Our work illustrates the use of the synthetic translation dimension in the design of on-chip filters, and it holds potential for applications in other devices such as microcavities.

Mapping Polar Distortions using Nanobeam Electron Diffraction and a Cepstral Approach.

Measuring local polar ordering is key to understanding ferroelectricity in thin films, especially for systems with small domains or significant disorder. Scanning nanobeam electron diffraction (NBED) provides an effective local probe of lattice parameters, local fields, polarization directions, and charge densities, which can be analyzed using a relatively low beam dose over large fields of view. However, quantitatively extracting the magnitudes and directions of polarization vectors from NBED remains challenging. Here, we use a cepstral approach, similar to a pair distribution function, to determine local polar displacements that drive ferroelectricity from NBED patterns. Because polar distortions generate asymmetry in the diffraction pattern intensity, we can efficiently recover the underlying displacements from the imaginary part of the cepstrum transform. We investigate the limits of this technique using analytical and simulated data and give experimental examples, achieving the order of 1.1 pm precision and mapping of polar displacements with nanometer resolution.

Reconstruction of three-dimensional strain field in an asymmetrical curved core-shell hetero-nanowire.

Crystal orientation and strain mapping of an individual curved and asymmetrical core-shell hetero-nanowire (NW) is performed based on transmission electron microscopy. It relies on a comprehensive analysis of scanning nanobeam electron diffraction data obtained for 1.3 nm electron probe size. The proposed approach also handles the problem of appearing twinning defects on diffraction patterns and allows for the investigation of materials with high defect densities. Based on the experimental maps and their comparison with finite element simulations, the entire core-shell geometry including full three-dimensional strain distribution within the curved core-shell NW are obtained. Our approach represents, therefore, a low-dose quasi-tomography of the strain field within a nanoobject using only a single zone axis diffraction experiment. Our approach is applicable also for electron beam-sensitive materials for which performing conventional tomography is a difficult task.

Uncovering polar vortex structures by inversion of multiple scattering with a stacked Bloch wave model.

Nanobeam electron diffraction can probe local structural properties of complex crystalline materials including phase, orientation, tilt, strain, and polarization. Ideally, each diffraction pattern from a projected area of a few unit cells would produce a clear Bragg diffraction pattern, where the reciprocal lattice vectors can be measured from the spacing of the diffracted spots, and the spot intensities are equal to the square of the structure factor amplitudes. However, many samples are too thick for this simple interpretation of their diffraction patterns, as multiple scattering of the electron beam can produce a highly nonlinear relationship between the spot intensities and the underlying structure. Here, we develop a stacked Bloch wave method to model the diffracted intensities from thick samples with structure that varies along the electron beam. Our method reduces the large parameter space of electron scattering to just a few structural variables per probe position, making it fast enough to apply to very large fields of view. We apply our method to SrTiO3/PbTiO3/SrTiO3 multilayer samples, and successfully disentangle specimen tilt from the mean polarization of the PbTiO3 layers. We elucidate the structure of complex vortex topologies in the PbTiO3 layers, demonstrating the promise of our method to extract material properties from thick samples.

Dynamic Stability of Nanobeams Based on the Reddy's Beam Theory.

The dynamic stability of nanobeams has been investigated by the Euler-Bernoulli and Timoshenko beam theories in the literature, but the higher-order Reddy beam theory has not been applied in the dynamic stability evaluation of nanobeams. In this work, the governing equations of the motion and dynamic stability of a nanobeam embedded in elastic medium are derived based on the nonlocal theory and the Reddy's beam theory. The parametric studies indicate that the principal instability region (PIR) moves to a lower frequency zone when length, sectional height, nonlocal parameter, Young's modulus and mass density of the Reddy nanobeam increase. The PIR shifts to a higher frequency zone only under increasing shear modulus. Increase in length makes the width of the PIR shrink obviously, while increase in height and Young's modulus makes the width of the PIR enlarge. The sectional width and foundation modulus have few effects on PIR.

Quantitative Element-Sensitive Analysis of Individual Nanoobjects.

A reliable and quantitative material analysis is crucial for assessing new technological processes, especially to facilitate a quantitative understanding of advanced material properties at the nanoscale. To this end, X-ray fluorescence microscopy techniques can offer an element-sensitive and non-destructive tool for the investigation of a wide range of nanotechnological materials. Since X-ray radiation provides information depths of up to the microscale, even stratified or buried arrangements are easily accessible without invasive sample preparation. However, in terms of the quantification capabilities, these approaches are usually restricted to a qualitative or semi-quantitative analysis at the nanoscale. Relying on comparable reference nanomaterials is often not straightforward or impossible because the development of innovative nanomaterials has proven to be more fast-paced than any development process for appropriate reference materials. The present work corroborates that a traceable quantification of individual nanoobjects can be realized by means of an X-ray fluorescence microscope when utilizing rather conventional but well-calibrated instrumentation instead of reference materials. As a proof of concept, the total number of atoms forming a germanium nanoobject is quantified using soft X-ray radiation. Furthermore, complementary dimensional parameters of such objects are reconstructed.

Wall-free droplet microfluidics for probing biological processes by high-brilliance X-ray scattering techniques.

Here we review probing biological processes initiated by the deposition of droplets on surfaces by micro- and nanobeam X-ray scattering techniques using synchrotron radiation and X-ray free-electron laser sources. We review probing droplet evaporation on superhydrophobic surfaces and reactions with substrates, basics of droplets deposition and flow simulations, droplet deposition techniques and practical experience at a synchrotron beamline. Selected applications with biological relevance will be reviewed and perspectives for the latest generation of high-brilliance X-ray sources discussed.

Local Epitaxial Templating Effects in Ferroelectric and Antiferroelectric ZrO2.

Nanoscale polycrystalline thin-film heterostructures are central to microelectronics, for example, metals used as interconnects and high-K oxides used in dynamic random-access memories (DRAMs). The polycrystalline microstructure and overall functional response therein are often dominated by the underlying substrate or layer, which, however, is poorly understood due to the difficulty of characterizing microstructural correlations at a statistically meaningful scale. Here, an automated, high-throughput method, based on the nanobeam electron diffraction technique, is introduced to investigate orientational relations and correlations between crystallinity of materials in polycrystalline heterostructures over a length scale of microns, containing several hundred individual grains. This technique is employed to perform an atomic-scale investigation of the prevalent near-coincident site epitaxy in nanocrystalline ZrO2 heterostructures, the workhorse system in DRAM technology. The power of this analysis is demonstrated by answering a puzzling question: why does polycrystalline ZrO2 transform dramatically from being antiferroelectric on polycrystalline TiN/Si to ferroelectric on amorphous SiO2/Si?

Towards the interpretation of a shift of the central beam in nano-beam electron diffraction as a change in mean inner potential.

The measurement of electric fields in scanning transmission electron microscopy (STEM) is a highly investigated field of research. The constant improvement of spatial resolution in STEM and the development of new hardware for the fast acquisition of diffraction patterns even paved the way for the measurement of atomic electric fields. Although the basic principle that an electric field leads to a tilt of the focussed electron probe that can be detected as a shift of the diffraction pattern in the back focal plane of the objective lens seems quite simple, many challenges arose in the measurement of fields in a quantitative way. In the present study we investigate whether a shift of the diffraction pattern that occurs at an interface between two materials can be related to the electric field which is caused by the difference of the mean inner potentials of the two materials. To this end, experiments and simulations are compared. It is demonstrated that the difference in mean inner potential has an influence on the observed effect, but a quantitative interpretation is difficult. The influence of image recording effects such as shot noise and the modulation transfer function are investigated as well as further effects such as e.g. sample tilt. In addition, the influence of the observed effect on a strain measurement is shown.

Automated Crystal Orientation Mapping in py4DSTEM using Sparse Correlation Matching.

Crystalline materials used in technological applications are often complex assemblies composed of multiple phases and differently oriented grains. Robust identification of the phases and orientation relationships from these samples is crucial, but the information extracted from the diffraction condition probed by an electron beam is often incomplete. We have developed an automated crystal orientation mapping (ACOM) procedure which uses a converged electron probe to collect diffraction patterns from multiple locations across a complex sample. We provide an algorithm to determine the orientation of each diffraction pattern based on a fast sparse correlation method. We demonstrate the speed and accuracy of our method by indexing diffraction patterns generated using both kinematical and dynamical simulations. We have also measured orientation maps from an experimental dataset consisting of a complex polycrystalline twisted helical AuAgPd nanowire. From these maps we identify twin planes between adjacent grains, which may be responsible for the twisted helical structure. All of our methods are made freely available as open source code, including tutorials which can be easily adapted to perform ACOM measurements on diffraction pattern datasets.

Precise strain mapping of nano-twinned axial ZnTe/CdTe hetero-nanowires by scanning nanobeam electron diffraction.

The occurrence of strain is inevitable for the growth of lattice mismatched heterostructures. It affects greatly the mechanical, electrical and optical properties of nano-objects. It is also the case for nanowires which are characterized by a high surface to volume ratio. Thus, the knowledge of the strain distribution in nano-objects is critically important for their implementation into devices. This paper presents an experimental data for II-VI semiconductor system. Scanning nanobeam electron diffraction strain mapping technique for hetero-nanowires characterized by a large lattice mismatch (>6% in the case of CdTe/ZnTe) and containing segments with nano-twins has been described. The spatial resolution of about 2 nm is 10 times better than obtained in synchrotron nanobeam systems. The proposed approach allows us to overcome the difficulties related to nanowire thickness variations during the acquisition of the nano-beam electron diffraction data. In addition, the choice of optimal parameters used for the acquisition of nano-beam diffraction data for strain mapping has been discussed. The knowledge of the strain distribution enables, in our particular case, the improvement of the growth model of extremely strained axial nanowires synthetized by vapor-liquid solid growth mechanism. However, our method can be applied for the strain mapping in nanowire heterostructures grown by any other method.

Phase Transitions in a Perovskite Thin Film Studied by Environmental In Situ Heating Nano-Beam Electron Diffraction.

The rich phase diagram of bulk Pr1-x Cax MnO3 resulting in a high tunability of physical properties gives rise to various studies related to fundamental research as well as prospective applications of the material. Importantly, as a consequence of strong correlation effects, electronic and lattice degrees of freedom are vigorously coupled. Hence, it is debatable whether such bulk phase diagrams can be transferred to inherently strained epitaxial thin films. In this paper, the structural orthorhombic to pseudo-cubic transition for x = 0.1 is studied in ion-beam sputtered thin films and differences to the respective bulk system are pointed out by employing in situ heating nano-beam electron diffraction to follow the temperature dependence of lattice constants. In addition, it is demonstrated that controlling the environment during heating, that is, preventing oxygen loss, is crucial in order to avoid irreversible structural changes, which is expected to be a general problem of compounds containing volatile elements under non-equilibrium conditions.

High Resolution Powder Electron Diffraction in Scanning Electron Microscopy.

A modern scanning electron microscope equipped with a pixelated detector of transmitted electrons can record a four-dimensional (4D) dataset containing a two-dimensional (2D) array of 2D nanobeam electron diffraction patterns; this is known as a four-dimensional scanning transmission electron microscopy (4D-STEM). In this work, we introduce a new version of our method called 4D-STEM/PNBD (powder nanobeam diffraction), which yields high-resolution powder diffractograms, whose quality is fully comparable to standard TEM/SAED (selected-area electron diffraction) patterns. Our method converts a complex 4D-STEM dataset measured on a nanocrystalline material to a single 2D powder electron diffractogram, which is easy to process with standard software. The original version of 4D-STEM/PNBD method, which suffered from low resolution, was improved in three important areas: (i) an optimized data collection protocol enables the experimental determination of the point spread function (PSF) of the primary electron beam, (ii) an improved data processing combines an entropy-based filtering of the whole dataset with a PSF-deconvolution of the individual 2D diffractograms and (iii) completely re-written software automates all calculations and requires just a minimal user input. The new method was applied to Au, TbF3 and TiO2 nanocrystals and the resolution of the 4D-STEM/PNBD diffractograms was even slightly better than that of TEM/SAED.

Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect.

In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler-Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton's principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton's technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions.

Nanobeams with Internal Discontinuities: A Local/Nonlocal Approach.

The aim of the present work is to extend the two-phase local/nonlocal stress-driven integral model (SDM) to the case of nanobeams with internal discontinuities: as a matter of fact, the original formulation avoids the presence of any discontinuities. Consequently, here, for the first time, the problem of an internal discontinuity is addressed by using a convex combination of both local and nonlocal phases of the model by introducing a mixture parameter. The novel formulation here proposed was validated by considering six case studies involving different uncracked nanobeams by varying the constrains and the loading configurations, and the effect of nonlocality on the displacement field is discussed. Moreover, a centrally-cracked nanobeam, subjected to concentrated forces at the crack half-length, was studied. The size-dependent Mode I fracture behaviour of the cracked nanobeam was analysed in terms of crack opening displacement, energy release rate, and stress intensity factor, showing the strong dependency of the above fracture properties on both dimensionless characteristic length and mixture parameter values.

Fast Grain Mapping with Sub-Nanometer Resolution Using 4D-STEM with Grain Classification by Principal Component Analysis and Non-Negative Matrix Factorization.

High-throughput grain mapping with sub-nanometer spatial resolution is demonstrated using scanning nanobeam electron diffraction (also known as 4D scanning transmission electron microscopy, or 4D-STEM) combined with high-speed direct-electron detection. An electron probe size down to 0.5 nm in diameter is used and the sample investigated is a gold­palladium nanoparticle catalyst. Computational analysis of the 4D-STEM data sets is performed using a disk registration algorithm to identify the diffraction peaks followed by feature learning to map the individual grains. Two unsupervised feature learning techniques are compared: principal component analysis (PCA) and non-negative matrix factorization (NNMF). The characteristics of the PCA versus NNMF output are compared and the potential of the 4D-STEM approach for statistical analysis of grain orientations at high spatial resolution is discussed.

Powder Nano-Beam Diffraction in Scanning Electron Microscope: Fast and Simple Method for Analysis of Nanoparticle Crystal Structure.

We introduce a novel scanning electron microscopy (SEM) method which yields powder electron diffraction patterns. The only requirement is that the SEM microscope must be equipped with a pixelated detector of transmitted electrons. The pixelated detectors for SEM have been commercialized recently. They can be used routinely to collect a high number of electron diffraction patterns from individual nanocrystals and/or locations (this is called four-dimensional scanning transmission electron microscopy (4D-STEM), as we obtain two-dimensional (2D) information for each pixel of the 2D scanning array). Nevertheless, the individual 4D-STEM diffractograms are difficult to analyze due to the random orientation of nanocrystalline material. In our method, all individual diffractograms (showing randomly oriented diffraction spots from a few nanocrystals) are combined into one composite diffraction pattern (showing diffraction rings typical of polycrystalline/powder materials). The final powder diffraction pattern can be analyzed by means of standard programs for TEM/SAED (Selected-Area Electron Diffraction). We called our new method 4D-STEM/PNBD (Powder NanoBeam Diffraction) and applied it to three different systems: Au nano-islands (well diffracting nanocrystals with size ~20 nm), small TbF3 nanocrystals (size < 5 nm), and large NaYF4 nanocrystals (size > 100 nm). In all three cases, the STEM/PNBD results were comparable to those obtained from TEM/SAED. Therefore, the 4D-STEM/PNBD method enables fast and simple analysis of nanocrystalline materials, which opens quite new possibilities in the field of SEM.

Structure Investigations of Islands with Atomic-Scale Boron-Carbon Bilayers in Heavily Boron-Doped Diamond Single Crystal: Origin of Stepwise Tensile Stress.

The detailed studies of the surface structure of synthetic boron-doped diamond single crystals using both conventional X-ray and synchrotron nano- and microbeam diffraction, as well as atomic force microscopy and micro-Raman spectroscopy, were carried out to clarify the recently discovered features in them. The arbitrary shaped islands towering above the (111) diamond surface are formed at the final stage of the crystal growth. Their lateral dimensions are from several to tens of microns and their height is from 0.5 to 3 µm. The highly nonequilibrium conditions of crystal growth enhance the boron solubility and, therefore, lead to an increase of the boron concentrations in the islands on the surface up to 1022 cm-3, eventually generating significant stresses in them. The stress in the islands is found to be the volumetric tensile stress. This conclusion is based on the stepwise shift of the diamond Raman peak toward lower frequencies from 1328 to 1300 cm-1 in various islands and on the observation of the shift of three low-intensity reflections at 2-theta Bragg angles of 41.468°, 41.940° and 42.413° in the X-ray diffractogram to the left relative to the (111) diamond reflection at 2theta = 43.93°. We believe that the origin of the stepwise tensile stress is a discrete change in the distances between boron-carbon layers with the step of 6.18 Å. This supposition explains also the stepwise (step of 5 cm-1) behavior of the diamond Raman peak shift. Two approaches based on the combined application of Raman scattering and X-ray diffraction data allowed determination of the values of stresses both in lateral and normal directions. The maximum tensile stress in the direction normal to the surface reaches 63.6 GPa, close to the fracture limit of diamond, equal to 90 GPa along the [111] crystallographic direction. The presented experimental results unambiguously confirm our previously proposed structural model of the boron-doped diamond containing two-dimensional boron-carbon nanosheets and bilayers.

Electro-mechanical coupling band gaps of a piezoelectric phononic crystal Timoshenko nanobeam with surface effects.

Plane wave expansion (PWE) method is extended to calculate the band structures of a proposed piezoelectric phononic crystal (PC) nanobeam by applying surface elasticity and Timoshenko beam theories. The calculation method is derived and formulized in detail. Further, electrical voltage and external axial force are picked to study the effects of electro-mechanical coupling fields on band gaps, residual surface stress and material intrinsic length are chosen to research the influences of surface effects on band gaps, and ratio between lengths of PZT-4 and epoxy in a unit cell and height-width ratio are picked to investigate the effects of geometric parameters on band gaps. In addition, all the results are compared to those in Euler nanobeam with same parameters. All the results and further analysis demonstrate that the influence rules will play an active role in design process and active control of nano electro-mechanical system based on piezoelectric PC nanobeam.