RESUMO
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.
RESUMO
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.
RESUMO
A strain characterization technique in a Scanning Transmission Electron Microscope (STEM) called "STEM Moiré GPA" (SMG) emerged recently as an efficient method to map the deformation field on large field of views (up to few microns in length scale). The technique is based on the interference between the scanning grid of the STEM electron probe and the periodic lattice of a crystalline material. The interference pattern (STEM Moiré hologram) is the result of an undersampling artifact, commonly named aliasing, occurring when less than two pixels are used to record a lattice spacing. The phase of the STEM Moiré fringes embeds the crystalline structure of the sample, and the variation of the phase can be related to a deformation field. To acquire a STEM Moiré hologram, the current practice is limited to choosing the periodicity of the scanning grid (pixel spacing) close to one lattice spacing. Such empirical recommendations are, however, insufficient since multiple lattice spacings are undersampled at once. The aliased spatial frequencies can overlap with each other in Fourier space making the STEM Moiré hologram not suitable for Geometric Phase Analysis (GPA) processing. In this study, a procedure is proposed to choose the optimal sampling parameters (pixel spacing and scanning rotation) for the STEM Moiré GPA application on any single crystal material. The procedure is then applied on a InP/InAs1-xPx/InP stack grown by Molecular Beam Epitaxy (MBE). Deformation profiles from different sampling conditions are compared to the established High-Resolution STEM GPA method, highlighting the reliability of the SMG method following the optimization process. The optimization protocol and the limits of SMG are finally discussed, and a generalization of the coherent sampling concept is proposed.
RESUMO
A strain characterization technique based on Moiré interferometry in a scanning transmission electron microscope (STEM) and geometrical phase analysis (GPA) method is demonstrated. The deformation field is first captured in a single STEM Moiré hologram composed of multiple sets of periodic fringes (Moiré patterns) generated from the interference between the periodic scanning grating, fixing the positions of the electron probe on the sample, and the crystal structure. Applying basic principles from sampling theory, the Moiré patterns arrangement is then simulated using a STEM electron micrograph reference to convert the experimental STEM Moiré hologram into information related to the crystal lattice periodicities. The GPA method is finally applied to extract the 2D relative strain and rotation fields. The STEM Moiré interferometry enables the local information to be de-magnified to a large length scale, comparable to what can be achieved in dark-field electron holography. The STEM Moiré GPA method thus extends the conventional high-resolution STEM GPA capabilities by providing comparable quantitative 2D strain mapping with a larger field of view (up to a few microns).
RESUMO
The spatial resolution and the indexing quality obtained with an automated orientation and phase mapping tool are analyzed for different Transmission Electron Microscope (TEM) illumination settings. The electron probe size and convergence angle are studied for two TEM configuration modes referred as microprobe and nanoprobe modes. Using a 10µmC2 aperture in a FEI Tecnai F20 (S)TEM, the nanoprobe mode is used to get a small convergent electron beam while the microprobe mode provides a nearly parallel illumination at the cost of a larger probe size. The nanoprobe configuration enables to increase the spatial resolution (â¼1nm vs 3nm) but also affects the fraction of mis-indexed points (15% vs 1%). Indexing errors are attributed to the increase by a factor of three of the convergence angle with respect to the microprobe mode. While intermediate optimum settings may be found and are potentially achievable on electron microscopes providing a 'free lens' control or a larger choice of C2 apertures, it is emphasized that the spatial resolution cannot be considered without reference to the indexing quality and, consequently to the convergence angle.