Abstract: In the present paper, the principles of detection theory are used to quantify the probability of error for atom-counting from high resolution scanning transmission electron microscopy (HR STEM) images. Binary and multiple hypothesis testing have been investigated in order to determine the limits to the precision with which the number of atoms in a projected atomic column can be estimated. The probability of error has been calculated when using STEM images, scattering cross-sections or peak intensities as a criterion to count atoms. Based on this analysis, we conclude that scattering cross-sections perform almost equally well as images and perform better than peak intensities. Furthermore, the optimal STEM detector design can be derived for atom-counting using the expression for the probability of error. We show that for very thin objects LAADF is optimal and that for thicker objects the optimal inner detector angle increases.

Abstract: Semiconductor heterostructures are used for the fabrication of optoelectronic devices. Performance of such devices is governed by their chemical morphology. The composition distribution of quantum wells and dots is influenced by kinetic growth processes which are not understood completely at present. To obtain more information about these effects, methods for composition determination with a spatial resolution at a near atomic scale are necessary. In this paper we focus on the present state of the composition evaluation by the lattice fringe analysis (CELFA) technique and explain the basic ideas, optimum imaging conditions, precision and accuracy.

Abstract: A model-based method is proposed to relatively quantify the chemical composition of atomic columns using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images. The method is based on a quantification of the total intensity of the scattered electrons for the individual atomic columns using statistical parameter estimation theory. In order to apply this theory, a model is required describing the image contrast of the HAADF STEM images. Therefore, a simple, effective incoherent model has been assumed which takes the probe intensity profile into account. The scattered intensities can then be estimated by fitting this model to an experimental HAADF STEM image. These estimates are used as a performance measure to distinguish between different atomic column types and to identify the nature of unknown columns with good accuracy and precision using statistical hypothesis testing. The reliability of the method is supported by means of simulated HAADF STEM images as well as a combination of experimental images and electron energy-loss spectra. It is experimentally shown that statistically meaningful information on the composition of individual columns can be obtained even if the difference in averaged atomic number Z is only 3. Using this method, quantitative mapping at atomic resolution using HAADF STEM images only has become possible without the need of simultaneously recorded electron energy loss spectra.

Abstract: Annular dark-field (ADF) scanning transmission electron microscopy (STEM) has become widely used in quantitative studies based on the opportunity to directly compare experimental and simulated images. This comparison merely requires the experimental data to be normalised and expressed in units of fractional beam-current. However, inhomogeneities in the response of electron detectors can complicate this normalisation. The quantification procedure becomes both experiment and instrument specific, requiring new simulations for the particular response of each instrument's detector, and for every camera-length used. This not only impedes the comparison between different instruments and research groups, but can also be computationally very time consuming. Furthermore, not all image simulation methods allow for the inclusion of an inhomogeneous detector response. In this work, we propose an alternative method for normalising experimental data in order to compare these with simulations that consider a homogeneous detector response. To achieve this, we determine the electron flux distribution reaching the detector by means of a camera-length series or a so-called atomic column cross-section averaged convergent beam electron diffraction (XSACBED) pattern. The result is then used to determine the relative weighting of the detector response. Here we show that the results obtained by this new electron flux weighted (EFW) method are comparable to the currently used method, while considerably simplifying the needed simulation libraries. The proposed method also allows one to obtain a metric that describes the quality of the detector response in comparison with the ideal detector response.

Abstract: Modern TEM enables the investigation of nanostructures at the atomic scale. However, TEM images are only two-dimensional (2D) projections of a three-dimensional (3D) object. Electron tomography can overcome this limitation. The technique is increasingly focused towards quantitative measurements and reaching atomic resolution in 3D has been the ultimate goal for many years. Therefore, one needs to optimize the acquisition of the data, the 3D reconstruction techniques as well as the quantification methods. Here, we will review a broad range of methodologies and examples. Finally, we will provide an outlook and will describe future challenges in the field of electron tomography.

Abstract: Many microscopic investigations of materials may benefit from the recording of multiple successive images. This can include techniques common to several types of microscopy such as frame averaging to improve signal-to-noise ratios (SNR) or time series to study dynamic processes or more specific applications. In the scanning transmission electron microscope, this might include focal series for optical sectioning or aberration measurement, beam damage studies or camera-length series to study the effects of strain; whilst in the scanning tunnelling microscope, this might include bias-voltage series to probe local electronic structure. Whatever the application, such investigations must begin with the careful alignment of these data stacks, an operation that is not always trivial. In addition, the presence of low-frequency scanning distortions can introduce intra-image shifts to the data. Here, we describe an improved automated method of performing non-rigid registration customised for the challenges unique to scanned microscope data specifically addressing the issues of low-SNR data, images containing a large proportion of crystalline material and/or local features of interest such as dislocations or edges. Careful attention has been paid to artefact testing of the non-rigid registration method used, and the importance of this registration for the quantitative interpretation of feature intensities and positions is evaluated.

Abstract: Colloidal coreshell semiconductor nanocrystals form an important class of optoelectronic materials, in which the exciton wave functions can be tailored by the atomic configuration of the core, the interfacial layers, and the shell. Here, we provide a trustful 3D characterization at the atomic scale of a free-standing PbSe(core)CdSe(shell) nanocrystal by combining electron microscopy and discrete tomography. Our results yield unique insights for understanding the process of cation exchange, which is widely employed in the synthesis of coreshell nanocrystals. The study that we present is generally applicable to the broad range of colloidal heteronanocrystals that currently emerge as a new class of materials with technological importance.

Abstract: A thorough understanding of the three-dimensional (3D) atomic structure and composition of coreshell nanostructures is indispensable to obtain a deeper insight on their physical behavior. Such 3D information can be reconstructed from two-dimensional (2D) projection images using electron tomography. Recently, different electron tomography techniques have enabled the 3D characterization of a variety of nanostructures down to the atomic level. However, these methods have all focused on the investigation of nanomaterials containing only one type of chemical element. Here, we combine statistical parameter estimation theory with compressive sensing based tomography to determine the positions and atom type of each atom in heteronanostructures. The approach is applied here to investigate the interface in coreshell Au@Ag nanorods but it is of great interest in the investigation of a broad range of nanostructures.

Abstract: In thispaperweinvestigatewhichprobesizemaximizesthethroughputwhenmeasuringtheradiusof nanoparticlesinhighangleannulardarkfieldscanningtransmissionelectronmicroscopy(HAADFSTEM). The sizeandthecorrespondingcurrentoftheelectronprobedeterminetheprecisionoftheestimateofa particlesradius.Maximizingthroughputmeansthatamaximumnumberofparticlesshouldbeimaged withinagiventimeframe,sothataprespecifiedprecisionisattained.WeshowthatBayesianstatistical experimentaldesignisaveryusefulapproachtodeterminetheoptimalprobesizeusingacertainamount of priorknowledgeaboutthesample.Thedependenceoftheoptimalprobesizeonthedetectorgeometry and thediameter,variabilityandatomicnumberoftheparticlesisinvestigated.Anexpressionforthe optimalprobesizeintheabsenceofanykindofpriorknowledgeaboutthespecimenisderivedaswell.

Abstract: Tailoring the properties of oxide-based nanocomposites is of great importance for a wide range of materials relevant for energy technology. YBa2Cu3O7−δ (YBCO) superconducting thin films containing nanosized BaHfO3 (BHO) particles yield a significant improvement of the magnetic flux pinning properties and a reduced anisotropy of the critical current density. These films were prepared by chemical solution deposition (CSD) on (100) SrTiO3 (STO) substrates yielding critical current densities up to 3.6 MA cm−2 at 77 K and self-field. Transport in-field J c measurements demonstrated a high pinning force maximum of around 6 GN/m3 for a sample annealed at T = 760 °C that has a doping of 12 mol% of BHO. This sample was investigated by scanning transmission electron microscopy (STEM) in combination with electron energy-loss spectroscopy (EELS) yielding strain and spectral maps. Spherical BHO nanoparticles of 15 nm in size were found in the matrix, whereas the particles at the interface were flat. A 2 nm diffusion layer containing Ti was found at the YBCO (BHO)/STO interface. Local lattice deformation mapping at the atomic scale revealed crystal defects induced by the presence of both sorts of BHO nanoparticles, which can act as pinning centers for magnetic flux lines. Two types of local lattice defects were identified and imaged: (i) misfit edge dislocations and (ii) Ba-Cu-Cu-Ba stacking faults (Y-248 intergrowths). The local electronic structure and charge transfer were probed by high energy resolution monochromated electron energy-loss spectroscopy. This technique made it possible to distinguish superconducting from non-superconducting areas in nanocomposite samples with atomic resolution in real space, allowing the identification of local pinning sites on the order of the coherence length of YBCO (~1.5 nm) and the determination of 0.25 nm dislocation cores.

Abstract: Quantitative atomic resolution annular dark field scanning transmission electron microscopy (ADF STEM) has become a powerful technique for nanoparticle atom-counting. However, a lot of nanoparticles provide a severe characterisation challenge because of their limited size and beam sensitivity. Therefore, quantitative ADF STEM may greatly benefit from statistical detection theory in order to optimise the instrumental microscope settings such that the incoming electron dose can be kept as low as possible whilst still retaining single-atom precision. The principles of detection theory are used to quantify the probability of error for atom-counting. This enables us to decide between different image performance measures and to optimise the experimental detector settings for atom-counting in ADF STEM in an objective manner. To demonstrate this, ADF STEM imaging of an industrial catalyst has been conducted using the near-optimal detector settings. For this experiment, we discussed the limits for atom-counting diagnosed by combining a thorough statistical method and detailed image simulations.