Can we enhance the depth of focus/depth resolution in STEM with an electrostatic phase plate?

Abstract text (incl. figure legends and references)

Introduction

In STEM, a trade-off appears between in-plane (xy) and out-of-plane z-resolution due to higher-order aberrations limiting the beam's convergence angle (α). The z-resolution can be demonstrated to scale with 1/α², whereas the xy resolution scales with 1/α, so we get that the z-resolution is a factor of α lower.

In other applications such as tomography, it is necessary to have all features throughout the thickness of a sample in focus to obtain an accurate geometric projection. In this case, the depth of field needs to be increased as much as possible.

In this report, we will investigate if the emerging capability of shaping the wavefront of an electron beam with programmable Phase Plates (PP) would offer more freedom.

Objectives

(1) To enhance the z-resolution by correcting the higher-order aberrations with a PP (2) To enlarge the depth of field attainable in the STEM using an adaptive PP.

Methods

To achieve objective (1), we correct for higher-order aberrations with a PP, following the lessons learned in our previous study (Fig. 1) [1]. Once we have a design for the PP, we do multislice simulations to observe defects at different depths in a crystal.

Fig. 1 Round ap. at 25mrad (a) vs. PP at 40mrad (b), the propagated probe is shown next to each aperture.

For objective (2), we propose a novel imaging scheme (see Fig. 2) that takes advantage of the fast and reliable tuneability of the PP that we have demonstrated before [2]; by incoherently adding up different probe configurations, we can create a Bessel-like probe that remains in focus at larger propagation lengths.

Fig. 2 Proposed imaging scheme for enhanced depth of field.

Results

The results show that for objective (1), we can design an aperture capable of correcting higher-order aberrations, thus obtaining an enhanced z-resolution without compromising the xy resolution.

For objective (2), we can enlarge the propagation length of the probe by incoherently adding several probes during a dwell time t (up to 5x at α=5mrad).

Conclusion

We demonstrated how a PP could be used to enhance z-resolution and enlarge the depth of field. However, such implementations need further work to overcome design constraints and the non-ideal effects that arise in real experimental setups. Nonetheless, such PP can potentially adapt to the sample, thus enhancing the imaging capabilities of the instrument.

References

[1] Vega F, Béché A, and Verbeeck J, "Can a Programmable Phase Plate serve as an Aberration Corrector in the Transmission Electron Microscope (TEM)?" arXiv e-prints (2022): arXiv-2205

[2] Verbeeck J, Vega F, and Béché A, "Demonstration of a 48-pixel programmable phase plate for adaptive electron optics," in Electron Beam Spectroscopy for Nano-Optics, Jun. 2021

[3] Acknowledgments to the financial support of the Research Foundation Flanders (FWO, Belgium) project G042820N. The European Research Council funds ADAPTEM as an ERC POC project under grant nr: DLV-789598. This project has received funding from the European Union"s Horizon 2020 Research Infrastructure - Integrating Activities for Advanced Communities under grant agreement No 823717 – ESTEEM3