Layered transition metal dichalcogenides (TMDs) have attracted interest due to their promise for future electronic and optoelectronic technologies. As one approaches the two-dimensional (2D) limit, thickness and local topology can greatly influence the macroscopic properties of a material. To understand the unique behavior of TMDs it is therefore important to identify the number of atomic layers and their stacking in a sample. The goal of this work is to extract the thickness and stacking sequence of TMDs directly by matching experimentally recorded high-angle annular dark-field scanning transmission electron microscope images and convergent-beam electron diffraction (CBED) patterns to quantum mechanical, multislice scattering simulations. Advantageously, CBED approaches do not require a resolved lattice in real space and are capable of neglecting the thickness contribution of amorphous surface layers. Here we demonstrate the crystal thickness can be determined from CBED in exfoliated 1T-TaS2 and 2H-MoS2 to within a single layer for ultrathin ≲9 layers and ±1 atomic layer (or better) in thicker specimens while also revealing information about stacking order—even when the crystal structure is unresolved in real space.

The small particle size and the random stacking of layers has previously hindered systematic structure investigations of montmorillonite. By applying the convergent-beam electron diffraction mode (CBED) of a transmission electron microscope (TEM) with a beam spot of ~800 Å we were able to examine undisturbed areas of montmorillonite crystallites.

Because montmorillonite crystallites are mostly thin particles, kinematic theory can be applied and the CBED patterns can be interpreted directly, provided that the particle thickness remains below the critical value of 350 Å. An average thickness of ~90 Å was calculated here for montmorillonite of bulk samples from X-ray diffraction analysis and lattice-fringe images. However, satisfactory diffraction intensity patterns for quantitative evaluation were obtained only from crystallites with a thickness above the average, which yielded a sufficient scattering volume. These patterns could be described in terms of the kinematic theory and therefore these crystallites were <350 Å thick. Yet, crystallites of adequate thickness were extremely rare in the three samples investigated (Clay Spur, Rock River and Upton, all in Wyoming, USA).

The diffraction intensities from the ab plane of single montmorillonite crystallites of the various origins fit the three structural models for a trans-vacancy distribution, a cis-vacancy distribution or a random-cation distribution within the octahedral sheets. The configuration of the diffraction patterns also shows a 1M symmetry of the layer. Due to the limited data set of CBED patterns, a refinement of the structure could not be achieved. However, energy dispersive X-ray spectroscopy data and computation of the cation–anion distances and valences using the ‘distance valence least square’ program permitted a refinement of the models.

This article deals with the measurement of strain in semiconductor heterostructures from convergent beam electron diffraction patterns. In particular, three different algorithms in the field of (circular) pattern recognition are presented that are able to detect diffracted disc positions accurately, from which the strain in growth direction is calculated. Although the three approaches are very different as one is based on edge detection, one on rotational averages, and one on cross correlation with masks, it is found that identical strain profiles result for an InxGa1−xNyAs1−y/GaAs heterostructure consisting of five compressively and tensile strained layers. We achieve a precision of strain measurements of 7–9·10−4 and a spatial resolution of 0.5–0.7 nm over the whole width of the layer stack which was 350 nm. Being already very applicable to strain measurements in contemporary nanostructures, we additionally suggest future hardware and software designs optimized for fast and direct acquisition of strain distributions, motivated by the present studies.

We have developed the focused ion beam (FIB) fold-out technique, for transmission electron microscopy (TEM) sample preparation in which there is no fine polishing or dimpling, thus saving turnaround time. It does not require a nanomanipulator yet is still site specific. The sample wafer is cut to shape, polished down, and then placed in a FIB system. A tab containing the area of interest is created by ion milling and then “folded out” from the bulk sample. This method also allows a plan-view of the sample by removing material below the wafer's surface film or device near the polished edge. In the final step, the sample is thinned to electron transparency, ready to be analyzed in the TEM. With both a cross section and plan-view, our technique gives microscopists a powerful tool in analyzing multiple zone axes in one TEM session. The nature of the polished sample edge also includes the ability to sample many areas, allowing the user to examine a very large device or sample. More importantly, this technique could make multiple site-specific e-beam transparent specimens in one polished sample, which is difficult to do when prepared by other methods.

The first paper on the FFT multislice method was published in 1977, a quarter of a century ago. The formula was extended in 1982 to include a large tilt of an incident beam relative to the specimen surface. Since then, with advances of computing power, the FFT multislice method has been successfully applied to coherent CBED and HAADF-STEM simulations. However, because the multislice formula is built on some physical approximations and approximations in numerical procedure, there seem to be controversial conclusions in the literature on the multislice method. In this report, the physical implication of the multislice method is reviewed based on the formula for the tilted illumination. Then, some results on the coherent CBED and the HAADF-STEM simulations are presented.

Energy filtered convergent beam electron diffraction was used to investigate localized strain in aluminum interconnects. By analyzing the position of higher order Laue zone lines, it is possible to measure the three-dimensional lattice strain with high accuracy (∼10−4) and high spatial resolution (10 to 100 nm). In the present article, important details of the strain analysis procedure are outlined. Subsequently, results of measurements of the local variation of thermal strains in narrow, free-standing interconnects are presented. The strain development in single grains during thermal cycling between −170°C and +100°C was measured in situ and local stress variations along the interconnect were investigated. The interconnects show reversible elastic behavior over the whole temperature range, leading to large stresses at low temperatures. The strain state varies locally within single grains, as well as from grain to grain, by as much as 50% in both types of samples. By comparing the experimental findings with elastic finite element modeling, a detailed understanding of the triaxial strain state could be achieved.

The same Bragg reflection in TiO2 from 12 different (CBED) patterns (from different crystals, orientations, and thicknesses) are analyzed quantitatively to evaluate the consistency of the quantitative CBED method for bond-charge mapping. The standard deviation in the resulting distribution of derived X-ray structure factors is found to be an order of magnitude smaller than that in conventional X-ray work, and the standard error (0.026% for FX(110)) is slightly better than obtained by the X-ray Pendellösung method applied to silicon. This is sufficiently accurate to distinguish between atomic, covalent, and ionic models of bonding. We describe the importance of extracting experimental parameters from CCD camera characterization, and of surface oxidation and crystal shape. The current experiments show that the QCBED method is now a robust and powerful tool for low-order structure factor measurement, which does not suffer from the large extinction (multiple scattering) errors that occur in inorganic X-ray crystallography, and may be applied to nanocrystals. Our results will be used to understand the role of d-electrons in the chemical bonding of TiO2.

Aromatic hydrocarbon (perylene, coronene) and tetracontane films are shown to produce useful convergent-beam electron diffraction (CBED) patterns under low-dose and low-temperature conditions. These were obtained using a Zeiss LEO-921 electron microscope with an omega energy filter at liquid helium and nitrogen temperatures. The usefulness of patterns showing CBED disks of constant intensity (“blank disks,” indicating kinematic scattering) for structure analysis is investigated, with the aim of avoiding film-bending artifacts. Using CBED patterns from thicker areas, sample thickness was experimentally determined using either two-beam or three-beam patterns. Koehler mode illumination (a new form of SAD pattern offering smaller areas) was also used, and the possibility of obtaining structure factor moduli using the kinematic and two-beam approximations was investigated by comparing measured diffraction intensities with experimental ones for these known structures. The commonly used approximation |F| ∼ Ig (intended to account for bending) was found to be a worse approximation than the two-beam approximation with well-defined excitation error for these microdiffraction experiments. A new multiwavelength method of retrieving structure factor moduli and thickness from microdiffraction patterns using two-beam theory is demonstrated for tetracontane.

Lattice strains around a platelet oxygen precipitate in Si wafer is studied by energy filtering convergent-beam electron diffraction (CBED) and calculations based on the finite element method (FEM). Local lattice strains are measured from CBED patterns obtained with a probe size less than 2 nm in a specimen thicker than 450 nm. Strains measured are compressive along a direction normal to a plate of the precipitate and tensile along a direction parallel to the plate. Two-dimensional stress fields near the precipitate are obtained with FEM computer analyses by fitting the measured strains. It appears that shear stresses are concentrated at the end of the precipitate edge and the maximum shear stress at an interface between the precipitate and the Si-matrix is 1.9 GPa. It is demonstrated that a combination of the energy filtering CBED and FEM is very useful for the study of local strains near interfaces in semiconductor devices, in particular for the study of stress fields that are too steep for application of the conventional CBED technique.