GaN atomic electric fields from a segmented STEM detector: Experiment and simulation.

Atomic electric fields in a thin GaN sample are measured with the centre-of-mass approach in 4D-scanning transmission electron microscopy (4D-STEM) using a 12-segmented STEM detector in a Spectra 300 microscope. The electric fields, charge density and potential are compared to simulations and an experimental measurement using a pixelated 4D-STEM detector. The segmented detector benefits from a high recording speed, which enables measurements at low radiation doses. However, there is measurement uncertainty due to the limited number of segments analysed in this study.

Atom counting based on Voronoi averaged STEM intensities using a crosstalk correction scheme.

If quantitative scanning transmission electron microscopy is used for very precise thickness measurements with atomic resolution, it is commonly referred to as ¼atom counting«. Due to scattering and the finite probe extent the signal recorded in one atomic column is dependent not only on its own height but also on the height of its neighbours. Especially for thicker specimens this crosstalk effect can have significant impact on the measured intensity. If it is not appropriately accounted for in the evaluation, it can result in a deterioration of accuracy that impedes the possibility of actual atom counting. However, as the number of possible neighbour configurations can be excessively large, a comprehensive consideration of all in the evaluation reference is neigh impossible. This work proposes a method that allows for the a-posteriori reduction of crosstalk during the evaluation by algebraic means. Based on a parametric model, which is described in detail in the article, the crosstalk is expressed by an invertible matrix. Applying the inverted matrix to the measurement yields crosstalk corrected intensity values with very little computational effort. These can subsequently be evaluated by direct comparison to simple reference data. The working principle of the method is presented on the example of crystalline gold. The crosstalk parametrisation is found by fitting a model to sets of specifically created multislice simulations. The parameters are given for both aberration corrected and uncorrected STEM. Subsequently the abilities and potential of the technique are assessed in simulative studies on multiple model systems including gold nanoparticles. Overall a significant and robust improvement of the attainable precision can be demonstrated making the proposed method a promising tool for reference-based atom counting.

Dose efficient annular bright field contrast with the ISTEM method: A proof of principle demonstration.

The ISTEM mode for TEM has been demonstrated to have several advantages in regard to resolution and precision. While previous works primarily focussed on the advantages due to the reduced spatial coherence, the actual image contrast, i.e. how bright or dark certain atom columns are imaged, has mostly been of secondary concern. The present work sets out to achieve the contrast of annular bright field STEM in ISTEM, producing the high contrast of light elements, for which this method is popular. It is shown from theoretical considerations that using an annular condenser aperture this aim can be realised. The optimal size of this aperture is found by simulative studies. It is then manufactured from platinum foil and installed in an image-aberration corrected microscope. ABF-like ISTEM images of strontium titanate in [100] projection are acquired. The pure oxygen columns are clearly resolved with significant contrast. The image pattern is indeed identical to what is achieved by ABF STEM. A close look at the image formation also shows that the dose needed for a given signal-to-noise ratio is at least a quarter smaller for ABF-like ISTEM compared to ABF STEM, assuming detectors of similar detective quantum efficiency.

Angle-dependence of ADF-STEM intensities for chemical analysis of InGaN/GaN.

In this paper we perform angular resolved annular-dark field (ADF) scanning-transmission electron microscopy (STEM) to study the scattered intensity in an InGaN layer buried in GaN as a function of the scattering angle. We achieved angular resolution with a motorized iris aperture in front of the ADF detector. Using this setup, we investigated how the intensities measured in various angular ranges agree with multislice simulations in the frozen-lattice approximation. We observed a strong influence of relaxation induced surface-strain fields on the ADF intensity, measured its angular characteristics and compared the result with simulations. To assess the agreement of the measured intensity with simulations, we evaluated the specimen thickness in GaN and the indium concentration in InGaN for each angular interval by comparing the measured intensities with simulations. The thickness was strongly overestimated for scattering angles below 40mrad and also the evaluated indium concentration varies with the considered angular range. Using simulations, we investigated which angular ranges show a high sensitivity to variations of the thickness and which intervals strongly depend on the indium concentration. By combining two angular intervals, the indium concentration and the specimen thickness were determined simultaneously, which has potential advantages over the usual quantification method. It is shown that inelastic scattering, surface contamination and mistilt can have an influence on the measured intensity, especially at lower scattering angles below 30-50mrad, which might explain the observed difference between the frozen lattice simulation and the experiment.

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.

4D-STEM at interfaces to GaN: Centre-of-mass approach & NBED-disc detection.

4D-scanning transmission electron microscopy (4D-STEM) can be used to measure electric fields such as atomic fields or polarization-induced electric fields in crystal heterostructures. The paper focuses on effects occurring in 4D-STEM at interfaces, where two model systems are used: an AlN/GaN nanowire superlattice as well as a GaN/vacuum interface. Two different methods are applied: First, we employ the centre-of mass (COM) technique which uses the average momentum transfer evaluated from the intensity distribution in the diffraction pattern. Second, we measure the shift of the undiffracted disc (disc-detection method) in nano-beam electron diffraction (NBED). Both methods are applied to experimental and simulated 4D-STEM data sets. We find for both techniques distinct variations in the momentum transfer at interfaces between materials: In both model systems, peaks occur at the interfaces and we investigate possible sources and routes of interpretation. In case of the AlN/GaN superlattice, the COM and disc-detection methods are used to measure internal polarization-induced electric fields and we observed a reduction of the measured fields with increasing specimen thickness.

Accuracy and precision of position determination in ISTEM imaging of BaTiO3.

In this paper we study the effect of lens aberrations (spherical aberration and astigmatism), beam tilt, contamination and shot noise on the accuracy and precision of position determination in imaging scanning transmission electron microscopy (ISTEM) on the example of BaTiO3. ISTEM images are simulated as a function of sample thickness and defocus starting from a nearly perfect microscope setting. A defocus range was identified, in which atom column positions were reliably visible and could be decently measured. By averaging over this defocus and thickness range a figure of merit was defined and used to study the influence of above mentioned disturbing effects as a function of their strength. It turned out that column positions might become inaccurate, but distances are measured accurately. These were used to obtain recommendations for the experimental setup to measure the atomic arrangement that induces ferroelectric switching of BaTiO3.

Precise measurement of the electron beam current in a TEM.

Modern quantitative TEM methods such as the ζ-factor technique require precise knowledge of the electron beam current. To this end, a macroscopic Faraday cup was designed and constructed. It can replace the viewing screen in the projection chamber of a TEM and guarantees highly accurate measurement of the electron beam with precision only limited by the used amperemeter. The easy to install, affordable device is shown to be highly apt for precision measurement of currents >5pA. The Faraday cup results are used for an assessment and a comparison of various other beam current measurement methods. It is found that the built-in screen amperemeter of the used TEM is quite inaccurate and that measurements using the screen in general tend to underestimate the current. If present, the drift tube of a spectrometer can also be used as a Faraday cup, but certain described peculiarities have to be taken into account. Direct ultrafast electron detection cameras allow precise measurement at very small currents. For the electron counting technique, which exploits single electron detection capabilities of STEM detectors, a systematic current underestimation was observed and investigated. This results in a reformulated routine for the method and with these improvements it is demonstrated to be capable of accurate high-precision measurements for currents <5pA.

Accurate measurement of strain at interfaces in 4D-STEM: A comparison of various methods.

Strain analysis by nano-beam electron diffraction allows for measurements of strain with nanometre resolution in a large field of view. This is done by evaluating distances between diffraction discs in diffraction patterns acquired while a focussed electron beam is scanned across the sample in a transmission electron microscope. The bottleneck of this method is a precise determination of diffraction disc positions, which suffers from the inner structure of the discs caused by dynamical diffraction. Electron beam precession is a tool that solves this problem but it is not commonly available in every microscope. Without precession significant progress has been reported recently by using patterned condenser apertures. The pattern of the aperture is reproduced in patterns of the diffraction discs allowing for a more precise position determination. In this report the accuracy of measured strain profiles using patterned apertures is investigated by evaluation of realistic simulations. This is done especially at interfaces between regions with different lattice plane spacing. It is found by evaluation of the simulations that measured strain profiles are more blurred and hence the accuracy at the interface is worse the more patterns are imprinted to the condenser aperture. An explanation of this effect is given and as a proof of principle a solution to this problem is provided applying geometric phase analysis ptychography.

Angle-resolved STEM using an iris aperture: Scattering contributions and sources of error for the quantitative analysis in Si.

The angle-resolved electron scattering is investigated in scanning-transmission electron microscopy (STEM) using a motorised iris aperture placed above a conventional annular detector. The electron intensity scattered into various angle ranges is compared with simulations that were carried out in the frozen-lattice approximation. As figure of merit for the agreement of experiment and simulation we evaluate the specimen thickness which is compared with the thickness obtained from position-averaged convergent beam electron diffraction (PACBED). We find deviations whose strengths depend on the angular range of the detected electrons. As possible sources of error we investigate, for example, the influences of amorphous surface layers, inelastic scattering (plasmon excitation), phonon-correlation within the frozen-lattice approach, and distortions in the diffraction plane of the microscope. The evaluation is performed for four experimental thicknesses and two angle-resolved STEM series under different camera lengths. The results clearly show that especially for scattering angles below 50 mrad, it is mandatory that the simulations take scattering effects into account which are usually neglected for simulating high-angle scattering. Most influences predominantly affect the low-angle range, but also high scattering angles can be affected (e.g. by amorphous surface covering).

Influence of plasmon excitations on atomic-resolution quantitative 4D scanning transmission electron microscopy.

Scanning transmission electron microscopy (STEM) allows to gain quantitative information on the atomic-scale structure and composition of materials, satisfying one of todays major needs in the development of novel nanoscale devices. The aim of this study is to quantify the impact of inelastic, i.e. plasmon excitations (PE), on the angular dependence of STEM intensities and answer the question whether these excitations are responsible for a drastic mismatch between experiments and contemporary image simulations observed at scattering angles below [Formula: see text] 40 mrad. For the two materials silicon and platinum, the angular dependencies of elastic and inelastic scattering are investigated. We utilize energy filtering in two complementary microscopes, which are representative for the systems used for quantitative STEM, to form position-averaged diffraction patterns as well as atomically resolved 4D STEM data sets for different energy ranges. The resulting five-dimensional data are used to elucidate the distinct features in real and momentum space for different energy losses. We find different angular distributions for the elastic and inelastic scattering, resulting in an increased low-angle intensity ([Formula: see text] 10-40 mrad). The ratio of inelastic/elastic scattering increases with rising sample thickness, while the general shape of the angular dependency is maintained. Moreover, the ratio increases with the distance to an atomic column in the low-angle regime. Since PE are usually neglected in image simulations, consequently the experimental intensity is underestimated at these angles, which especially affects bright field or low-angle annular dark field imaging. The high-angle regime, however, is unaffected. In addition, we find negligible impact of inelastic scattering on first-moment imaging in momentum-resolved STEM, which is important for STEM techniques to measure internal electric fields in functional nanostructures. To resolve the discrepancies between experiment and simulation, we present an adopted simulation scheme including PE. This study highlights the necessity to take into account PE to achieve quantitative agreement between simulation and experiment. Besides solving the fundamental question of missing physics in established simulations, this finally allows for the quantitative evaluation of low-angle scattering, which contains valuable information about the material investigated.

Comparison of first moment STEM with conventional differential phase contrast and the dependence on electron dose.

This study addresses the comparison of scanning transmission electron microscopy (STEM) measurements of momentum transfers using the first moment approach and the established method that uses segmented annular detectors. Using an ultrafast pixelated detector to acquire four-dimensional, momentum-resolved STEM signals, both the first moment calculation and the calculation of the differential phase contrast (DPC) signals are done for the same experimental data. In particular, we investigate the ability to correct the segment-based signal to yield a suitable approximation of the first moment for cases beyond the weak phase object approximation. It is found that the measurement of momentum transfers using segmented detectors can approach the first moment measurement as close as 0.13 h/nm in terms of a root mean square (rms) difference in 10 nm thick SrTiO3 for a detector with 16 segments. This amounts to 35% of the rms of the momentum transfers. In addition, we present a statistical analysis of the precision of first moment STEM as a function of dose. For typical experimental settings with recent hardware such as a Medipix3 Merlin camera attached to a probe-corrected STEM, we find that the precision of the measurement of momentum transfers stagnates above certain doses. This means that other instabilities such as specimen drift or scan noise have to be taken into account seriously for measurements that target, e.g., the detection of bonding effects in the charge density.

Influence of distortions of recorded diffraction patterns on strain analysis by nano-beam electron diffraction.

Images acquired in transmission electron microscopes can be distorted for various reasons such as e.g. aberrations of the lenses of the imaging system or inaccuracies of the image recording system. This results in inaccuracies of measures obtained from the distorted images. Here we report on measurement and correction of elliptical distortions of diffraction patterns. The effect of this correction on the measurement of crystal lattice strain is investigated. We show that the effect of the distortions is smaller than the precision of the measurement in cases where the strain is obtained from shifts of diffracted discs with respect to their positions in images acquired in an unstrained reference area of the sample. This can be explained by the fact that diffraction patterns acquired in the strain free reference area of the sample are distorted in the same manner as the diffraction patterns acquired in the strained region of interest. In contrast, for samples without a strain free reference region such as nanoparticles or nanoporous structures, where we evaluate ratios of lattice plane distances along different directions, the distortions are usually not negligible. Furthermore, two techniques for the detection of diffraction disc positions are compared showing that for samples in which the crystal orientation changes over the investigated area it is more precise to detect the positions of many diffraction discs simultaneously instead of detecting each disc position independently.

Strain analysis from nano-beam electron diffraction: Influence of specimen tilt and beam convergence.

Strain analyses from experimental series of nano-beam electron diffraction (NBED) patterns in scanning transmission electron microscopy are performed for different specimen tilts. Simulations of NBED series are presented for which strain analysis gives results that are in accordance with experiment. This consequently allows to study the relation between measured strain and actual underlying strain. A two-tilt method which can be seen as lowest-order electron beam precession is suggested and experimentally implemented. Strain determination from NBED series with increasing beam convergence is performed in combination with the experimental realization of a probe-forming aperture with a cross inside. It is shown that using standard evaluation techniques, the influence of beam convergence on spatial resolution is lower than the influence of sharp rings around the diffraction disc which occur at interfaces and which are caused by the tails of the intensity distribution of the electron probe.

Using molecular dynamics for multislice TEM simulation of thermal diffuse scattering in AlGaN.

For simulation of transmission electron microscopic images and diffraction patterns, the accurate inclusion of thermal diffuse scattering by phonons is important. In the frozen phonon multislice algorithm, this is possible, if thermal displacements according to the realistic, quantum mechanical distribution can be generated. For pure crystals, quantum mechanical calculations based on DFT yield those displacements. But for alloys one is usually restricted to the Einstein approximation, where correlations between atoms are neglected. In this article, molecular dynamics simulations are discussed and used as an alternative method for displacement calculation. Employing an empirical Stillinger-Weber type potential, classical motion is used as an approximation for the quantum mechanical dynamics. Thereby, correlations and possible static atomic displacements are inherently included. An appropriate potential is devised for AlGaN by fitting to force constant matrices determined from DFT and elastic constants of AlN and GaN. A comparison shows that the empiric potential reproduces phonon dispersions and displacement expectations from DFT references. The validity for alloys is successfully demonstrated by comparison to DFT calculations in special quasirandom structures. Subsequently, molecular dynamics were used in multislice simulations of both conventional and scanning TEM images. The resulting images are in very good agreement with DFT based calculations, while a slight yet significant deviation from Einstein approximation results can be seen, which can be attributed to the neglect of correlations in the latter. The presented potential hence proves to be a useful tool for accurate TEM simulations of AlGaN alloys.

Ultrathin Au-Alloy Nanowires at the Liquid-Liquid Interface.

Ultrathin bimetallic nanowires are of importance and interest for applications in electronic devices such as sensors and heterogeneous catalysts. In this work, we have designed a new, highly reproducible and generalized wet chemical method to synthesize uniform and monodispersed Au-based alloy (AuCu, AuPd, and AuPt) nanowires with tunable composition using microwave-assisted reduction at the liquid-liquid interface. These ultrathin alloy nanowires are below 4 nm in diameter and about 2 µm long. Detailed microstructural characterization shows that the wires have an face centred cubic (FCC) crystal structure, and they have low-energy twin-boundary and stacking-fault defects along the growth direction. The wires exhibit remarkable thermal and mechanical stability that is critical for important applications. The alloy wires exhibit excellent electrocatalytic activity for methanol oxidation in an alkaline medium.

Quantitative HAADF STEM of SiGe in presence of amorphous surface layers from FIB preparation.

The chemical composition of four Si1-xGex layers grown on silicon was determined from quantitative scanning transmission electron microscopy (STEM). The chemical analysis was performed by a comparison of the high-angle annular dark field (HAADF) intensity with multislice simulations. It could be shown that amorphous surface layers originating from the preparation process by focused-ion beam (FIB) at 30 kV have a strong influence on the quantification: the local specimen thickness is overestimated by approximately a factor of two, and the germanium concentration is substantially underestimated. By means of simulations, the effect of amorphous surface layers on the HAADF intensity of crystalline silicon and germanium is investigated. Based on these simulations, a method is developed to analyze the experimental HAADF-STEM images by taking the influence of the amorphous layers into account which is done by a reduction of the intensities by multiplication with a constant factor. This suggested modified HAADF analysis gives germanium concentrations which are in agreement with the nominal values. The same TEM lamella was treated with low-voltage ion milling which removed the amorphous surface layers completely. The results from subsequent quantitative HAADF analyses are in agreement with the nominal concentrations which validates the applicability of the used frozen-lattice based multislice simulations to describe the HAADF scattering of Si1-xGex in STEM.

Optimization of NBED simulations for disc-detection measurements.

Nano-beam electron diffraction (NBED) is a method which can be applied to measure lattice strain and polarisation fields in strained layer heterostructures and transistors. To investigate precision, accuracy and spatial resolution of such measurements in dependence of properties of the specimen as well as electron optical parameters, simulations of NBED patterns are required which allow to predict the result of common disc-detection algorithms. In this paper we demonstrate by focusing on the detection of the central disc in crystalline silicon that such simulations require to take several experimental characteristics into account in order to obtain results which are comparable to those from experimental NBED patterns. These experimental characteristics are the background intensity, the presence of Poisson noise caused by electron statistics and blurring caused by inelastic scattering and by the transfer quality of the microscope camera. By means of these optimized simulations, different effects of specimen properties on disc detection - such as strain, surface morphology and compositional changes on the nanometer scale - are investigated and discussed in the context of misinterpretation in experimental NBED evaluations. It is shown that changes in surface morphology and chemical composition lead to measured shifts of the central disc in the NBED pattern of tens to hundreds of µrad. These shifts are of the same order of magnitude or even larger than shifts that could be caused by an electric polarisation field in the range of MV/cm.

Imaging theory for the ISTEM imaging mode.

A relatively simple yet accurate analytical model for the image formation in the imaging scanning TEM (ISTEM) imaging mode, which implements partial spatial incoherence using a combination of scanning illumination and conventional imaging, is presented. Based on an object function approximation the ISTEM intensity can be divided into a constant, a linear and a nonlinear term. Under certain conditions, which are discussed, the formation of both linear and nonlinear terms can be expressed by convolutions with point spread functions. A closer inspection of these allows an insight into the advantages of ISTEM compared to conventional TEM (CTEM). The findings of the proposed model are confirmed by comparison to multislice simulations. A close investigation of the linear coherent contrast transfer function allows the derivation of optimal imaging conditions to reach a maximum resolution for a given signal-to-noise ratio. The robustness of ISTEM towards temporal incoherence is finally demonstrated and discussed within the model.