Abstract: By focusing electrons on probes with a diameter of 50 pm, aberration-corrected scanning transmission electron microscopy (STEM) is currently crossing the border to probing subatomic details. A major challenge is the measurement of atomic electric fields using differential phase contrast (DPC) microscopy, traditionally exploiting the concept of a field- induced shift of diffraction patterns. Here we present a simplified quantum theoretical interpretation of DPC. This enables us to calculate the momentum transferred to the STEM probe from diffracted intensities recorded on a pixel array instead of conventional segmented bright- field detectors. The methodical development yielding atomic electric field, charge and electron density is performed using simulations for binary GaN as an ideal model system. We then present a detailed experimental study of SrTiO3 yielding atomic electric fields, validated by comprehensive simulations. With this interpretation and upgraded instrumentation, STEM is capable of quantifying atomic electric fields and high-contrast imaging of light atoms.

Abstract: This study sheds light on the prerequisites, possibilities, limitations and interpretation of high-resolution differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). We draw particular attention to the well-established DPC technique based on segmented annular detectors and its relation to recent developments based on pixelated detectors. These employ the expectation value of the momentum transfer as a reliable measure of the angular deflection of the STEM beam induced by an electric field in the specimen. The influence of scattering and propagation of electrons within the specimen is initially discussed separately and then treated in terms of a two-state channeling theory. A detailed simulation study of GaN is presented as a function of specimen thickness and bonding. It is found that bonding effects are rather detectable implicitly, e.g., by characteristics of the momentum flux in areas between the atoms than by directly mapping electric fields and charge densities. For strontium titanate, experimental charge densities are compared with simulations and discussed with respect to experimental artifacts such as scan noise. Finally, we consider practical issues such as figures of merit for spatial and momentum resolution, minimum electron dose, and the mapping of larger-scale, built-in electric fields by virtue of data averaged over a crystal unit cell. We find that the latter is possible for crystals with an inversion center. Concerning the optimal detector design, this study indicates that a sampling of 5mrad per pixel is sufficient in typical applications, corresponding to approximately 10x10 available pixels.

Abstract: In materials science, high angle annular dark field scanning transmission electron microscopy is often used for tomography at the nanometer scale. In this work, it is shown that a thickness dependent, non-linear damping of the recorded intensities occurs. This results in an underestimated intensity in the interior of reconstructions of homogeneous particles, which is known as the cupping artifact. In this paper, this non-linear effect is demonstrated in experimental images taken under common conditions and is reproduced with a numerical simulation. Furthermore, an analytical derivation shows that these non-linearities can be inverted if the imaging is done quantitatively, thus preventing cupping in the reconstruction.

Abstract: This work provides values of electron scattering 002 structure factors for InxGa1-xAs as a function of the In concentration x=0 to 1. These results allow accurate compositional analysis of pseudomorphically grown InxGa1-xAs/GaAs layers by transmission electron microscopy methods relying on the chemical sensitivity of the (002) beam. The calculations go beyond the limits of the isolated atom approximation, because they take into account charge redistribution effects between atomic sites in the crystal, strain, and static atomic displacements. The computations were performed by the full potential linearized augmented plane-wave method using a generalized gradient approximation for the exchange and correlation part of the potential. The calculations of strained InxGa1-xAs correspond to the strain state in specimens with large, small, and intermediate thickness in the electron beam direction. Additionally, the effect of static atomic displacements is taken into account. All results are listed in a parameterized form. The calculated 002 structure factor vanishes at an In concentration of 16.4%. This value is in a good agreement with previously reported experimental measurements. Hence, our results are a significant improvement with respect to the isolated atom approximation which is conventionally applied in transmission electron microscopy simulations, and which predicts a value of 22.5%.

Abstract: Inelastic image simulation software is presented, implementing the double channeling approximation which takes into account the combination of multiple elastic and single inelastic scattering in a crystal. The approach is described with a density matrix formalism. Two applications in high resolution energy filtered (EFTEM) transmission electron microscopy (TEM) images are presented: thickness-defocus maps for SrTiO3 and exit plane intensities for an (LaAlO3)3(SrTiO3)3 multilayer system. Both systems show a severe breakdown in direct interpretability which becomes worse for higher acceleration voltages, thicker samples and lower excitation edge energies. Since this effect already occurs in the exit plane intensity, it is a fundamental limit and image simulations in EFTEM are indispensable just as they are indispensable for elastic high resolution TEM images.

Abstract: We report the mapping of polarization-induced internal electric fields in AlN/GaN nanowire heterostructures at unit cell resolution as a key for the correlation of optical and structural phenomena in semiconductor optoelectronics. Momentum-resolved aberration-corrected scanning transmission electron microscopy is employed as a new imaging mode that simultaneously provides four-dimensional data in real and reciprocal space. We demonstrate how internal mesoscale and atomic electric fields can be separated in an experiment, which is verified by comprehensive dynamical simulations of multiple electron scattering. A mean difference of 5.3 +- 1.5 MV/cm is found for the polarization-induced electric fields in AlN and GaN, being in accordance with dedicated simulations and photoluminescence measurements in previous publications.

Abstract: Thermal diffuse scattered electrons significantly contribute to high-resolution transmission electron microscopy images. Their intensity adds to the background and is peaked at positions of atomic columns. In this paper we suggest an approximation to simulate intensity of thermal diffuse scattered electrons in plane-wave illumination transmission electron microscopy using an emission-potential multislice algorithm which is computationally less intensive than the frozen lattice approximation or the mutual intensity approach. Intensity patterns are computed for Au and InSb for different crystal orientations. These results are compared with intensities from the frozen lattice approximation based on uncorrelated vibration of atoms as well as with the frozen phonon approximation for Au. The frozen phonon method uses a detailed phonon model based on force constants we computed by a density functional theory approach. The comparison shows that our suggested emission-potential method is in close agreement with both the frozen lattice and the frozen phonon approximations.

Abstract: We computed Debye-Waller factors in the temperature range from 0.1 to 1000 K for AlN, GaN, InN, ZnO and CdO with the wurtzite-type structure. The Debye-Waller factors were derived from phonon densities of states obtained from Hellmann-Feynman forces computed within the density-functional-theory formalism. The temperature dependences of the Debye-Waller factors were fitted and fit parameters are given.

Abstract: Strain has a strong effect on the properties of materials and the performance of electronic devices. Their ever shrinking size translates into a constant demand for accurate and precise measurement methods with a very high spatial resolution. In this regard, transmission electron microscopes are key instruments thanks to their ability to map strain with a subnanometer resolution. Here, we present a method to measure strain at the nanometer scale based on the diffraction of electron Bessel beams. We demonstrate that our method offers a strain sensitivity better than 2.5 × 10−4 and an accuracy of 1.5 × 10−3, competing with, or outperforming, the best existing methods with a simple and easy to use experimental setup.

Abstract: We have studied the structural and electronic properties of lithium-intercalated graphite (LIG) for various Li content. Atomic relaxation shows that Li above the center of the carbon hexagon in a AAAA stacked graphite is the only stable Li configuration in stage 1 intercalated graphite. Lithium and Carbon 1s energy-loss near-edge structure (ELNES) calculations are performed on the Li-intercalated graphite using the core-excited density-functional theory formulation. Several features of the Li 1s ELNES are correlated with reported experimental features. The ELNES spectra of Li is found to be electron beam orientation sensitive and this property is used to assign the origin of the various Li 1s ELNES features. Information about core-hole screening by the valence electrons and charge transfer in the LIG systems is obtained from the C 1s ELNES and valence charge density difference calculations, respectively.

Abstract: The electronic properties of quaternary AlInGaN devices significantly depend on the homogeneity of the alloy. The identification of compositional fluctuations or verification of random-alloy distribution is hence of grave importance. Here, a comprehensive multiprobe study of composition and compositional homogeneity is presented, investigating AlInGaN layers with indium concentrations ranging from 0 to 17 at% and aluminium concentrations between 0 and 39 at% employing high-angle annular dark field scanning electron microscopy (HAADF STEM), energy dispersive X-ray spectroscopy (EDX) and atom probe tomography (APT). EDX mappings reveal distributions of local concentrations which are in good agreement with random alloy atomic distributions. This was hence investigated with HAADF STEM by comparison with theoretical random alloy expectations using statistical tests. To validate the performance of these tests, HAADF STEM image simulations were carried out for the case of a random-alloy distribution of atoms and for the case of In-rich clusters with nanometer dimensions. The investigated samples, which were grown by metal-organic vapor phase epitaxy (MOVPE), were thereby found to be homogeneous on this nanometer scale. Analysis of reconstructions obtained from APT measurements yielded matching results. Though HAADF STEM only allows for the reduction of possible combinations of indium and aluminium concentrations to the proximity of isolines in the two-dimensional composition space. The observed ranges of composition are in good agreement with the EDX and APT results within the respective precisions.

Abstract: The charge density is among the most fundamental solid state properties determining bonding, electrical characteristics, and adsorption or catalysis at surfaces. While atomic-scale charge densities have as yet been retrieved by solid state theory, we demonstrate both charge density and electric field mapping across a mono-/bilayer boundary in 2D MoS2 by momentum-resolved scanning transmission electron microscopy. Based on consistency of the four-dimensional experimental data, statistical parameter estimation and dynamical electron scattering simulations using strain-relaxed supercells, we are able to identify an AA-type bilayer stacking and charge depletion at the Mo-terminated layer edge.

Abstract: We present a new method to measure structure factors from electron spot diffraction patterns recorded under almost parallel illumination in transmission electron microscopes. Bloch wave refinement routines have been developed to refine the crystal thickness, its orientation and structure factors by comparison of experimentally recorded and calculated intensities. Our method requires a modicum of computational effort, making it suitable for contemporary personal computers. Frozen lattice and Bloch wave simulations of GaAs diffraction patterns are used to derive optimised experimental conditions. Systematic errors are estimated from the application of the method to simulated diffraction patterns and rules for the recognition of physically reasonable initial refinement conditions are derived. The method is applied to the measurement of the 200 structure factor for GaAs. We found that the influence of inelastically scattered electrons is negligible. Additionally, we measured the 200 structure factor from zero loss filtered two-dimensional convergent beam electron diffraction patterns. The precision of both methods is found to be comparable and the results agree well with each other. A deviation of more than 20% from isolated atom scattering data is observed, whereas close agreement is found with structure factors obtained from density functional theory [A. Rosenauer, M. Schowalter, F. Glas, D. Lamoen, Phys. Rev. B 72 (2005), 085326-1], which account for the redistribution of electrons due to chemical bonding via modified atomic scattering amplitudes.

Abstract: <script type='text/javascript'>document.write(unpmarked('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. (C) 2017 Elsevier B.V. All rights reserved.'));