2D strain mapping using scanning transmission electron microscopy Moiré interferometry and geometrical phase analysis

Moiré fringe imaging of heterostructures by scanning transmission electron microscopy

A heterostructured crystalline bilayer specimen is known to produce moiré fringes (MFs) in the conventional transmission electron microscopy (TEM). However, the understanding of how these patterns form in scanning transmission electron microscopy (STEM) remains limited. Here, we extended the double-scattering model to establish the imaging theory of MFs in STEM for a bilayer sample and applied this theory to successfully explain both experimental and simulated STEM images of a perovskite PbZrO3/SrTiO3 system. Our findings demonstrated that the wave vectors of electrons exiting from Layer-1 and their relative positions with the atomic columns of Layer-2 should be taken into account. The atomic column misalignment leads to a faster reduction in the intensity of the secondary scattering beam compared to the single scattering beam as the scattering angle increases. Consequently, the intensity distribution of MFs in the bright field (BF)-STEM can be still described as the product of two single atomic images. However, in high angle annular dark field (HAADF)-STEM, it is approximately described as the superposition of the two images. Our work not only fills a knowledge gap of MFs in incoherent imaging, but also emphasizes the importance of the coherent scattering restricted by the real space when analyzing the HAADF-STEM imaging.

Relation between sampling, sensitivity and precision in strain mapping using the Geometric Phase Analysis method in Scanning Transmission Electron Microscopy

The sensitivity and the precision of the Geometric Phase Analysis (GPA) method for strain characterization is a topic widely discussed in the literature and is usually difficult to quantify. Indeed, the GPA precision is intricately linked to the resolution of the strain maps defined when masking the periodic reflections in Fourier space. In this study an additional parameter, sampling, is proposed to be analyzed regarding the precision of GPA by developing the concept of a phase noise in the GPA equations. Both experimentally and theoretically, the following article demonstrates how the precision, and the sensitivity of the GPA method is improved when using a larger pixel spacing to record an electron micrograph in Scanning Transmission Electron Microscopy (STEM). The counterintuitive concept of increasing the field of view to improve the GPA precision results is an extension of the application of strain characterization methods in STEM towards low deformation levels.

Defect free strain relaxation of microcrystals on mesoporous patterned silicon

A perfectly compliant substrate would allow the monolithic integration of high-quality semiconductor materials such as Ge and III-V on Silicon (Si) substrate, enabling novel functionalities on the well-established low-cost Si technology platform. Here, we demonstrate a compliant Si substrate allowing defect-free epitaxial growth of lattice mismatched materials. The method is based on the deep patterning of the Si substrate to form micrometer-scale pillars and subsequent electrochemical porosification. The investigation of the epitaxial Ge crystalline quality by X-ray diffraction, transmission electron microscopy and etch-pits counting demonstrates the full elastic relaxation of defect-free microcrystals. The achievement of dislocation free heteroepitaxy relies on the interplay between elastic deformation of the porous micropillars, set under stress by the lattice mismatch between Ge and Si, and on the diffusion of Ge into the mesoporous patterned substrate attenuating the mismatch strain at the Ge/Si interface.

Many complex devices rely on epitaxial growth with high crystallinity and accurate composition. Here authors report epitaxial growth of Ge on deep etched porous Si pillars to provide a fully compliant substrate enabling elastic relaxation of defect free Ge microcrystals.

Crystal lattice image reconstruction from Moiré sampling scanning transmission electron microscopy

A wide range of reconstruction methods exist nowadays to retrieve data from their undersampled acquisition schemes. In the context of Scanning Transmission Electron Microscopy (STEM), compressed sensing methods successfully demonstrated the ability to retrieve crystalline lattice images from undersampled electron micrographs. In this manuscript, an alternative method is proposed based on the principles of Moiré sampling by intentionally generating aliasing artifacts and correcting them afterwards. The interference between the scanning grid of the electron beam raster and the crystalline lattice results in the formation of predictable sets of Moiré fringes (STEM Moiré hologram). Since the aliasing artifacts are simple spatial frequency shifts applied on each crystalline reflection, the crystal lattices can be recovered from the STEM Moiré hologram by reverting the aliasing frequency shifts from the Moiré reflections. Two methods are presented to determine the aliasing shifts for all the resolved crystalline reflections. The first approach is a prior knowledge-based method using information on the spatial frequency distribution of the crystal lattices (a common case in practice). The other option is a multiple sampling approach using different sampling parameters and does not require any prior knowledge. As an example, the Moiré sampling recovery method detailed in this manuscript is applied to retrieve the crystalline lattices from a STEM Moiré hologram recorded on a silicon sample. The great interest of STEM Moiré interferometry is to increase the field of view (FOV) of the electron micrograph (up to several microns). The Moiré sampling recovery method extends the application of the STEM imaging of crystalline materials towards low magnifications.

Moiré Fringe Method via Scanning Transmission Electron Microscopy

Moiré fringe, originated from the beating of two sets of lattices, is a commonly observed phenomenon in physics, optics, and materials science. Recently, a new method of creating moiré fringe via scanning transmission electron microscopy (STEM) has been developed to image materials' structures at a large field of view. Moreover, this method shows great advantages in studying atomic structures of beam sensitive materials by significantly reduced electron dose. Here, the development of the STEM moiré fringe (STEM-MF) method is reviewed. The authors first introduce the theory of STEM-MF and then discuss the advances of this technique in combination with geometric phase analysis, annular bright field imaging, energy dispersive X-ray spectroscopy, and electron energy loss spectroscopy. Applications of STEM-MF on strain, defects, 2D materials, and beam-sensitive materials are further summarized. Finally, the authors' perspectives on the future directions of STEM-MF are presented.

Micrometre-scale strain mapping of transistor arrays extracted from undersampled atomic-resolution images

Strain maps extracted from atomic resolution images have the ultimate spatial resolution, but have a field of view limited by the sampling necessary to resolve atomic lattices. This has typically confined strain maps to dimensions less than ∼100 nanometers. To extend the field of view beyond this limit, we apply a modified geometric phase analysis to undersampled images of atomic lattices (i.e. with a pixel size too large to resolve atomic lattices). To reduce the effects of environmental and instrumental instabilities, the images were obtained by aligning series of rapid annular dark field scanning transmission electron microscopy acquisitions. We demonstrate that for undersampled images, a geometric phase analysis can still be performed on aliased frequencies and, as long as the appropriate scaling matrix is applied, provide accurate atomic displacement measurements at large scale. Experimental challenges related to the increased effects of scanning errors as the magnification is lowered are examined. Although such errors are found to significantly reduce geometric phase signals, it was still possible to produce strain maps for arrays of up to sixteen 20nm-technology transistors, corresponding to a field of view exceeding one micrometer.

Wide-view and accurate deformation measurement at microscales by phase extraction of scanning moiré pattern with a spatial phase-shifting technique

A scanning-based second-order moiré method is proposed for high-accuracy deformation measurement in a large field of view (FOV) by analyzing the phase distribution of a single-shot scanning moiré fringe image using a spatial phase-shifting technique. In this method, the grating pitch can be as small as around one pixel in the scanning moiré image to ensure a wide FOV, while high-precision phase measurement is achievable. The strain measurement accuracy has been verified from simulations at different grating pitches, applied strains, and noise levels. The simulation results show that the closer the grating pitch is to the scanning pitch, the smaller the strain measurement error, and the recommended pitch ratio is 0.9∼1.1. Furthermore, the feasibility of this method has been verified from a tensile experiment on an aluminum specimen under a laser scanning microscope with scanning moiré images recorded. The microscale strains of aluminum measured at different tensile loads agree well with the strain gauge results. As an integration of the scanning and sampling moiré methods, this method has the advantages of a large FOV, high accuracy, strong noise immunity, and visualization of magnified deformation. Compared with the traditional phase-shifting scanning moiré method, this method only needs to record a single scanning moiré image and is suitable for dynamic deformation analysis.

Assessment of the strain depth sensitivity of Moiré sampling Scanning Transmission Electron Microscopy Geometrical Phase Analysis through a comparison with Dark-Field Electron Holography

In this study, the Moiré sampling Scanning Transmission Electron Microscopy Geometrical Phase Analysis (or STEM Moiré GPA) strain characterization method is compared to the well-established Dark-Field Electron Holography technique on a thin film stack grown by Molecular Beam Epitaxy. While experimental data obtained with the two techniques are, overall, in good qualitative agreement, small statistically relevant differences are locally observed between the two methods. The results obtained from both techniques are further confronted with Finite Element Method (FEM) mechanical simulations modeling the strain relaxation phenomena from a thin lamella. The FEM simulation highlights a non-uniform deformation field along the beam propagation direction with a higher deformation level near the surface of the lamella compared to the center of the same lamella. The center-surface strain differences obtained from modeling are consistent with the experimentally derived differences accounting for the fact that the SMG method is sensitive to the strain state of the surface of the lamella with a very narrow depth-of-field, and the DFEH technique is measuring the strain state of the center of the same lamella averaging over a large section of the thickness. The depth-of-field difference between both methods can be reasonably related to their respective contrast mechanisms (STEM vs Conventional Transmission Electron Microscopy). As the SMG method is using a convergent probe, the narrow depth-of-field might be used to sense the deformation field over different sections of the lamella using the defocus and potentially retrieve the three-dimensional strain field.

Study of interfacial random strain fields in core-shell ZnO nanowires by scanning transmission electron microscopy

Imaging strain fields at the nanoscale is crucial for understanding the physical properties as well as the performance of oxide heterostructures and electronic devices. Based on scanning transmission electron microscopy (STEM) techniques, we successfully imaged the random strain field at the interface of core-shell ZnO nanowires. Combining experimental observations and image simulations, we find that the strain contrast originates from dechanneling of electrons and increased diffuse scattering induced by static atomic displacements. For a thin sample with a random strain field, a positive strain contrast appears in the low-angle annular dark-field (LAADF) image and a negative contrast in the high-angle annular dark-field (HAADF) image, but for a thick sample (> 120 nm), the positive contrast always occurs in both the LAADF and HAADF images. Through the analysis of the relationship between strain contrast and various parameters, we also discuss the optimum experimental condition for imaging random strain fields.