Scanning TEM (STEM) in combination with a small convergence angle (nano-beam electron diffraction, NBED) can be used, e.g., to determine the local strain state of a sample by measuring the distance between two non-overlapping Bragg discs in the diffraction pattern [1]. Automated disc-detection algorithms [2] reveal a high precision which allows for measuring small shifts of diffracted discs relative to the undiffracted disc to determine local strain with a spatial resolution below 1 nm. Simulation of NBED patterns is an important tool to optimize the precision of an experimental measurement as well as to predict the resolution of measured strain profiles at interfaces [3]. In this context, it is important to optimize such simulations to describe experimental measurements as accurately as possible. The present study shows by a comparison of experiment and simulation that for both types of simulations, the absorptive-potential and the frozen-lattice method, deviations to experiment occur if additional effects, such as electron noise or the influence of the modulation-transfer function (MTF) of the CCD camera, are not taken into account.

Fig 1(a) shows the undiffracted 000 disc of an experimental tilt series in pure silicon which was compared with simulations (Fig 1(b) shows the raw absorptive-potential simulations). The selected experimental disc in Fig 2(a) shows smooth edges in contrast to the raw simulation (b) with much sharper edges. Fig 2(c) shows the simulated disc after adding background and applying MTF and noise. It is shown that results for 000-disc detection of the modified simulation agree sufficiently well with experiment for all tilts giving a reliable tool to investigate the effect of sample conditions on NBED-disc detection.

With these optimized simulations, we separately investigated three effects on the 000-disc detection procedure: the effect of (1) scanning into a strained layer (without composition change), (2) scanning into a layer of different material (but without changes in the crystal structure), and (3) the effect of varying specimen thickness.

The latter effect occurs in experiment, e.g., in case of selective layer etching. A GaAs supercell was set up with [001] electron beam direction with two plateaus on the top and on the bottom surface as shown in the schematic illustration in Fig. 3(a). Different NBED disc-detection algorithms [2] were used to detect the deviation of the 000-disc position from the initial center for a scan along the [100] direction across the plateaus. Fig. 3(b) shows the deviations in μrad where each line stands for a certain detection algorithm (Selective Edge Detection [2] and Radial Gradient Maximization [2], both with and without radius fitting) – in all cases the slopes on the surface lead to a measured deviation of the disc position of up to 30-40 μrad. This reveals a consequence for experimental measurements: On the one hand, if non-homogeneous surface topology is an unwanted factor, it can lead to artifacts in disc-position determination. On the other hand, it also might offer the possibility for precise measurements of topology or sample orientation.

[1] F Uesugi et al., Ultramicroscopy 111(2011), p. 995-998

[2] K Müller et al. Microsc. Microanal. 18 (2012), p. 995-1009

[3] C Mahr et al., Ultramicroscopy 158 (2015), p. 38-48

[4] This work was supported by the German Research Foundation (DFG) under contract number RO 2057/11-1 and MU 3660/1-1.

Figures:

000 disc of NBED-tilt series in silicon ([001] zone axis) with tilts in [100] direction (downwards) and in [010] direction (to the right): (a) experiment, (b) simulation using absorptive potentials.

Single disc from Fig.1: (a) experiment, (b) raw simulation, (c) modified simulation by adding background and applying MTF and noise.

Simulation of surface modification on 000-disc detection. (a) Schematic GaAs-[100] super cell with 4.2 nm high plateaus on top and on bottom side (not linearly scaled). (b) Deviation of the 000-disc position from its initial center for scanning along [100] direction across the plateau. Line style visualize disc-detection algorithm.

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EMC Abstracts - https://emc-proceedings.com/abstract/optimization-of-nbed-simulations-to-accurately-predict-disc-detection-measurements/