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Do We Need Three-Dimensional Fourier Transform Analysis to Evaluate High-Performance TEMs?


Kazuo Ishizuka , 1 , 2 * and Koji Kimoto 2 1 HREM Research Inc. , 14-48 Matsukazedai , Higashimatsuyama , Saitama , Japan 2 National Institute for Materials Science , 1-1 Namiki , Tsukuba , Ibaraki , Japan


* ishizuka@hremresearch.com


Abstract: Linear image transfer down to a few tens of pm can be attained by a modern C s -corrected transmission electron microscope. However, it is diffi cult to accurately evaluate such a high-performance microscope. We examine three-dimensional (3D) Fourier transform (FT) analysis in comparison with diffractogram (2D FT) analysis to evaluate aberration-corrected electron microscopes. The 3D FT can analyze information transfer on the Ewald sphere up to high-angles using a thick sample or a sample containing strong scattering elements. Therefore, the 3D FT analysis is necessary to evaluate C s -corrected microscopes, especially those equipped with a C c -corrector, or a monochromator, or microscopes operated at lower voltages.


Keywords: aberration-corrected transmission electron microscopy (TEM), three-dimensional Fourier transform (FT) analysis, diffractogram analysis, Ewald-sphere envelope, lower accelerating voltages.


Introduction T e image resolution of a high-resolution transmission electron microscope (HRTEM) has been improved to sub-angstrom levels by correcting the spherical aberration (C s ) of the objective lens. In many cases the spatial resolution is claimed using a very faint spot of the highest spatial frequency in the Fourier transform (FT) of the experimental image of a crystalline sample. Alternatively, the fi nest observable spacing of Young’s fringes, which is a FT of a double-exposure image of an amorphous sample, has been used to evaluate the spatial resolution. However, the performance of a TEM should be evaluated by the highest spatial frequency that contributes linearly in image formation, which is controlled by the envelope functions of the contrast transfer function. When the spherical aberration is corrected, the information limit is determined mainly by the temporal envelope that is controlled by chromatic aberration. In order to evaluate an actual information transfer down to a few tens of pm, however, we need a strong scattering object, which will inevitably introduce noticeable non-linear contribu- tions. We may note that the Young’s fringe method cannot discriminate between the linear and non-linear terms. Furthermore, the FT of image intensity will give the spatial frequency that is up to twice that of the image wave frequency. T erefore, new methods to evaluate the focus spread, and thus temporal coherence, have been


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proposed based on the tilted-beam diff ractogram [ 1 , 2 ]. However, the methods based on a diff ractogram (FT of a single image), in principle, cannot exclude the non-linear contribution for the analysis. T is limitation becomes serious, especially when we evaluate a C s -corrected microscope equipped with a C c -corrector or a monochromator as explained in the next section. In addition, an evaluation of lower-voltage TEM using a diff ractogram becomes diffi cult, since the strong interaction of lower-voltage electrons with a specimen introduces substantial non-linear contributions. Contrary to the diff ractogram, the three-dimensional (3D) FT of a stack of the through-focus TEM images can separate the linear terms from the non-linear term. T is is because the non-linear term spreads all over the Fourier space, while each linear term concentrates onto a sphere in the 3D FT. We have applied elsewhere the 3D FT analysis of through-focus TEM images to evaluate the performance of some C s -corrected TEMs at lower-voltages [ 3 , 4 ]. In this article, we compare 3D FT analysis with diff ractogram (2D FT) analysis. We also describe the use of the 3D FT analysis in evaluating our FEI TITAN 3 operated at 80 kV.


Materials and Methods Figure 1 shows an improvement in performance with a monochromator on a FEI TITAN 3 operated at 80 kV. The sample is a thin amorphous Ge film with gold particles.


Figure 1 : Performance improvement with monochromator on FEI TITAN 3 operated at 80 kV. The images are taken from a thin amorphous Ge fi lm with gold particles. The insets show the diffractograms corresponding to the images. The energy spread of incident electrons 0.9 eV (left) is decreased to 0.1 eV (right) when the monochromator is turned on. Without the monochromator we observe a gold diffraction spot associated with an interplanar distance of 104 pm; whereas we can detect a weak spot equivalent to 79 pm when the monochromator is on. Nevertheless, the diffuse scattering from amorphous Ge fi lm appears in both cases up to about 100 pm (10 nm -1 ).


doi: 10.1017/S1551929517001407 www.microscopy-today.com • 2018 March


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