Position-averaged Convergent Beam Electron Diffraction Research Articles

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).

Angular dependence of fast-electron scattering from materials

Angular resolved scanning transmission electron microscopy is an important tool for investigating the properties of materials. However, several recent studies have observed appreciable discrepancies in the angular scattering distribution between experiment and theory. In this paper we discuss a general approach to low-loss inelastic scattering which, when incorporated in the simulations, resolves this problem and also closely reproduces experimental data taken over an extended angular range. We also explore the role of ionic bonding, temperature factors, amorphous layers on the surfaces of the specimen, and static displacements of atoms on the angular scattering distribution. The incorporation of low-loss inelastic scattering in simulations will improve the quantitative usefulness of techniques such as low-angle annular dark-field imaging and position-averaged convergent beam electron diffraction, especially for thicker specimens.

Surface relaxation of strained Ga(P,As)/GaP heterostructures investigated by HAADF STEM.

The surfaces of thin transmission electron microscopy (TEM) specimens of strained heterostructures can relax. The resulting bending of the lattice planes significantly influences high-angle annular dark field (HAADF) measurements. We investigate the impact by evaluating the intensities measured at the atomic columns as well as their positions in high-resolution HAADF images. In addition, the consequences in the diffraction plane will be addressed by simulated position averaged convergent beam electron diffraction (PACBED) patterns. The experimental column intensities and positions acquired from a strained Ga(P,As) quantum well (QW) embedded in a in a GaP matrix agree very well with frozen phonon contrast simulations, if the surface relaxation is taken into account by finite element relaxation. Neglecting the surface relaxation the As content of the QW can be significantly underestimated. Taking the effects into account correctly, we find that the lower interface of the investigated Ga(P,As) QW is atomically abrupt whereas the upper one is smeared out.

Accuracy and precision of thickness determination from position-averaged convergent beam electron diffraction patterns using a single-parameter metric

Position-averaged convergent beam electron diffraction patterns are formed by averaging the transmission diffraction pattern while scanning an atomically-fine electron probe across a sample. Visual comparison between experimental and simulated patterns is increasingly being used for sample thickness determination. We explore automating the comparison via a simple sum square difference metric. The thickness determination is shown to be accurate (i.e. the best-guess deduced thickness generally concurs with the true thickness), though factors such as noise, mistilt and inelastic scattering reduce the precision (i.e. increase the uncertainty range). Notably, the precision tends to be higher for smaller probe-forming aperture angles.

Extracting Local Crystallographic Structure Using 4D-STEM Datasets

Traditional scanning transmission electron microscopy (STEM) detectors are monolithic and integrate a subset of the transmitted electron beam signal scattered from each electron probe position. These convergent beam electron diffraction patterns (CBED) are extremely rich in information, containing localized information on sample structure, composition, phonon spectra, three-dimensional defect crystallography and more. Many new imaging modes become possible if the full CBED pattern is recorded at many probe positions with millisecond dwell times. In this study, we have used a Gatan K2-IS direct electron detection camera installed on an uncorrected FEI Titan-class transmission electron microscope to record 4D-STEM probe diffraction patterns on a variety of samples at up to 1600 frames per second. As an example, a 4D-STEM dataset for a multilayer stack of epitaxial SrTiO3 and mixed LaMnO3-SrTiO3 is plotted in Figure 1. Figure 1A shows a HAADF micrograph of the multilayer along a (001) zone axis. Only the A sites (Sr and La) are visible in this micrograph and the composition can be roughly determined from the relative brightness. One possible 4D-STEM technique is position-averaged convergent beam electron diffraction (PACBED) described by LeBeau et al. [1]. We can easily construct ideal PACBED patterns by averaging the probe images over each unit cell fitted from Figure 1A, which is shown in Figure 1B. By matching these patterns to PACBED images simulated with the multislice method we can precisely determine parameters such as sample thickness and composition, the latter of which is plotted in Figure 1C. For comparison, the composition has also been determined with electron energy loss spectroscopy (EELS) in a separate experiment, shown in Figure 1D. The composition range of 0-85% LaMnO3 measured by PACBED is in good agreement with the EELS measurements. In this talk we will demonstrate several other possible uses for 4D-STEM datasets.

Nanoscale quantification of octahedral tilts in perovskite films

NiO6-octahedral tilts in ultrathin LaNiO3 films were studied using position averaged convergent beam electron diffraction (PACBED) in scanning transmission electron microscopy. Both the type and magnitude of the octahedral tilts were determined by comparing PACBED experiments to frozen phonon multislice simulations. It is shown that the out-of-plane octahedral tilt of an epitaxial film under biaxial tensile stress (0.78% in-plane tensile strain) increases by ∼20%, while the in-plane rotation decreases by ∼80%, compared to the unstrained bulk material.

Determining ferroelectric polarity at the nanoscale

Position averaged convergent beam electron diffraction (PACBED) in scanning transmission electron microscopy is shown to be capable of determining the direction of ferroelectric polarity at the nanoscale. We show that PACBED patterns of ferroelectric materials such as PbTiO3 and BaTiO3 are sensitive to both unit cell distortion and the absolute direction of polarity within the unit cell. It is shown that the polarity can be determined even in cases where real-space high-resolution transmission electron microscopy would not be capable of resolving the atomic displacements. The method is applied to determine the direction of polarization in an epitaxial BaTiO3 film.