Peter Hartel (Heidelberg / DE), Stephan Uhlemann (Heidelberg / DE), Thomas Riedel (Heidelberg / DE), Svenja Perl (Heidelberg / DE), Martin Linck (Heidelberg / DE), Heiko Müller (Heidelberg / DE), Volker Gerheim (Heidelberg / DE), Maximilian Haider (Heidelberg / DE)
Abstract text (incl. figure legends and references)
The success of hardware aberration correction in transmission electron microscopy started 25 years ago with the first resolution improvements achieved with a two-hexapole design in TEM [1] and a quadrupole-octupole design in STEM [2]. The two-hexapole design was used in STEM later as well [3]. A careful redesign lead to the advanced two-hexapole corrector (DCOR/ASCOR) with full fourth-order correction and effectively vanishing fifth-order aberrations [4]. This design is still state-of-the-art – independent from using additional A5 stigmators or not [5,6].
After these achievements it has been argued, that the usable aperture semi-angle for two-hexapole and even three-hexapole correctors is finally limited by the three-lobe aberration of sixth order D6 [7]. For an objective lens with a medium gap size around 5mm, e.g. for analytical applications, the π/4-phase shift limit due to this intrinsic aberration is just below 40mrad (Fig. 1). As investigated theoretically [4,5] and verified experimentally [6,8,9], these advanced correctors are sufficient for modern CFEG-equipped microscopes to touch the high-resolution limit set by the chromatic aberration. D6 hardly limits the obtainable resolution, if additional D6 phase shifts up to several π/4 are reasonably-well counterbalanced by lower-order three-fold aberrations [6,10]. However, if the intrinsic D6 can be eliminated a-priori in the optics, the counterbalancing techniques wouldn"t be necessary in most situations. This is especially valuable in case of monochromated illumination, which allows for even larger apertures, enabling not only better xy- but also improved z-resolution [11].
Recently, we found first evidence that a novel three-hexapole design can eliminate the three-lobe aberration of sixth order D6 together with higher-order spherical aberrations. Consequently, the theoretical π/4-limit due to intrinsic residual aberrations is shifted further out to 70mrad. Again, compensation techniques can extend the usable aperture even beyond this value. Fig. 2 shows very promising results of experimentally obtained ronchigrams with a radius of ≥80mrad recorded at 200kV. [12, 13]
[1] M. Haider et al., Nature 392, 768 (1998).
[2] P.E. Batson, N. Dellby, O.L. Krivanek, Nature 418, 617-620 (2002).
[3] H. Sawada et al, Microscopy 54 (2), 119-121 (2005).
[4] H. Müller et al., Microscopy and Microanalysis 12 (6), 442–445 (2006).
[5] P. Hartel et. al., Ultramicroscopy 206, 112821 (2019).
[6] R. Sagawa et al., Ultramicroscopy 233, 113440 (2022).
[7] S. Morishita et al., Microscopy 67 (2018) 156-163.
[8] M. Watanabe et al., Microsc. Microanal. 22 (2016) 310-311.
[9] M. Bischoff et al., Microsc. Microanal. 24 (2018) 1134-1135.
[10] S. Morishita et al., Phys.Rev.Let. 117 (2016) 153004.
[11] R. Ishikawa et al., Ultramicroscopy 151 (2015) 122-129.
[12] We acknowledge and highly appreciate the collaboration and support by JEOL company.
[13] CEOS GmbH has received funding from the European Union"s Horizon 2020 research and innovation program under grant agreement No. 823717 – ESTEEM3.
<fig1>
Figure 1: Hexapole corrector generations. The typical size of the intrinsic aberrations and the resulting π/4-limits for 30..300kV are indicated, assuming a medium-size objective lens gap.
<fig2>
Figure 2: A comparison of experimental in-focus ronchigrams at 200kV: a) advanved hexapole corrector with D6 ≈ 2mm b) calibration with gold c) new corrector with D6 ≈ 0.