Inversion of Dynamical Scattering from Large-Angle Rocking-Beam Electron Diffraction Patterns.

A method for ab initio structure factor retrieval from large-angle rocking-beam electron diffraction data of thin crystals is described and tested with experimental and simulated data. No additional information, such as atomicity or information about chemical composition, has been made use of. Our numerical experiments show that the inversion of dynamical scattering works best, if the beam tilt range is large and the specimen not too thick, because for moderate multiple scattering, the large tilt amplitude effectively removes local minima in this global optimization problem.

Atom-by-atom chemical identification from scanning transmission electron microscopy images in presence of noise and residual aberrations.

The simple dependence of the intensity in annular dark field scanning transmission electron microscopy images on the atomic number provides (to some extent) chemical information about the sample, and even allows an elemental identification in the case of light-element single-layer samples. However, the intensity of individual atoms and atomic columns is affected by residual aberrations and the confidence of an identification is limited by the available signal to noise. Here, we show that matching a simulation to an experimental image by iterative optimization provides a reliable analysis of atomic intensities even in presence of residual non-round aberrations. We compare our new method with other established approaches demonstrating its high reliability for images recorded at limited dose and with different aberrations. This is of particular relevance for analyzing moderately beam-sensitive materials, such as most 2D materials, where the limited sample stability often makes it difficult to obtain spectroscopic information at atomic resolution.

Retrieving depth-direction information from TEM diffraction data under reciprocal-space sampling variation.

For full three-dimensional information retrieval from transmission electron microscope data, retrieving the third-dimension (beam-direction) information is an important challenge. Recently, we have developed an artificial-neural-network-based retrieval algorithm suitable for retrieving three-dimensional nanoscale crystal parameters like strain, including with noisy data (R.S. Pennington, W. Van den Broek, C.T. Koch, Phys. Rev. B 89 (20) (2014) 205409 [12]). In this work, we examine how reciprocal-space sampling conditions influence the retrieved crystal parameters, using crystal tilt as an example parameter, and demonstrate retrieval for 2.5 nm depth resolution. For noise-free data, we find that the total reciprocal-space area is the key parameter; however, when the data are noisy, the number of reciprocal-space points and the amount of noise are also influential. We also apply our algorithm to a simulated bent specimen, and recover the bending as expected. Guidelines for experimental applications are also discussed.

A three-dimensional polarization domain retrieval method from electron diffraction data.

We present an algorithm for retrieving three-dimensional domains of picometer-scale shifts in atomic positions from electron diffraction data, and apply it to simulations of ferroelectric polarization in BaTiO3. Our algorithm successfully and correctly retrieves polarization domains in which the Ti atom positions differ by less than 3 pm (0.4% of the unit cell diagonal distance) with 5 and 10nm depth resolution along the beam direction, and we also retrieve unit cell strain, corresponding to tetragonal-to-cubic unit cell distortions, for 10nm domains. Experimental applicability is also discussed.

Surface effects on mean inner potentials studied using density functional theory.

Quantitative materials characterization using electron holography frequently requires knowledge of the mean inner potential, but reported experimental mean inner potential measurements can vary widely. Using density functional theory, we have simulated the mean inner potential for materials with a range of different surface conditions and geometries. We use both "thin-film" and "nanowire" specimen geometries. We consider clean bulk-terminated surfaces with different facets and surface reconstructions using atom positions from both structural optimization and experimental data and we also consider surfaces both with and without adsorbates. We find that the mean inner potential is surface-dependent, with the strongest dependency on surface adsorbates. We discuss the outlook and perspective for future mean inner potential measurements.

Stacked-Bloch-wave electron diffraction simulations using GPU acceleration.

In this paper, we discuss the advantages for Bloch-wave simulations performed using graphics processing units (GPUs), based on approximating the matrix exponential directly instead of performing a matrix diagonalization. Our direct matrix-exponential algorithm yields a functionally identical electron scattering matrix to that generated with matrix diagonalization. Using the matrix-exponential scaling-and-squaring method with a Padé approximation, direct GPU-based matrix-exponential double-precision calculations are up to 20× faster than CPU-based calculations and up to approximately 70× faster than matrix diagonalization. We compare precision and runtime of scaling and squaring methods with either the Padé approximation or a Taylor expansion. We also discuss the stacked-Bloch-wave method, and show that our stacked-Bloch-wave implementation yields the same electron scattering matrix as traditional Bloch-wave matrix diagonalization.

Geometric reconstruction methods for electron tomography.

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and non-linear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full 180° tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire.