Sampling optimization of Moiré geometrical phase analysis for strain characterization in scanning transmission electron microscopy

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/InAs_1-xP_x/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.