Stemming Unwanted Interference
Resolution Improvement by Incoherent Imaging with ISTEM
- Fig. 1: Principle of ISTEM: (A) For each scan point of the STEM illumination the objective lens creates an image from the electrons leaving the specimen in a small area (circle). (B) If the camera acquires over the entire scanning process, all the images from the scan positions are added up incoherently and very little interference can occur. The actual path of the electron beam is not of importance for this (arrows).
- Fig. 2: CTEM (left) and ISTEM images (right) of diamond in  projection for increasing chromatic aberration characterized by the defocus spread. The structure is still resolved for large spreads in ISTEM.
- Fig. 3: ISTEM image of GaN in [1-100] projection. The N and Ga atomic columns are distinctly resolved as also can be seen in the line scan.
In Transmission Electron Microscopy (TEM) spatially incoherent image formation can have significant advantages regarding attainable resolution by removing unwanted interference effects. This has been exploited in the scanning TEM mode, which is incoherent but limited by other factors. Combining a scanning beam with the conventional TEM imaging mode can overcome these limitations. This method called ISTEM gives access to the advantages of both modes and facilitates an increase in resolution.
From Traditional TEM to ISTEM
High resolution Transmission Electron Microscopy (TEM) is one of the most important tools for the investigations of nanoscale structures. Historically, it has mostly been divided into two modes:
For Conventional TEM (CTEM) the specimen is illuminated with a plane electron wave and then the image is formed by the objective lens of the microscope. For modern field emission sources the image formation is almost completely coherent here. Because a large area is illuminated, CTEM is influenced neither by the positioning precision of the incoming beam nor by aberrations of the probe forming lenses. Another advantage is the fact that though the size of the electron source has an influence on the images, it is not the factor limiting the resolution. Due to the coherence however, high-resolution CTEM images can show complex interference patterns and hence be difficult to interpret. The high coherence also causes a strong dependence of the image pattern on the energy of the incident electrons. Chromatic aberration is therefore the limiting factor for resolution in CTEM.
In the Scanning TEM (STEM) mode, the electron beam is focused onto the specimen. Then the intensity in a specific area of the diffraction pattern is recorded with an extended, usually circular or annular, detector. The image is formed by scanning over an area of the specimen. It can be shown that STEM is effectively an incoherent imaging mode due to the universal principle of reciprocity . Therefore it is much more robust towards chromatic aberration , while interpretation of its image patterns is much more straightforward compared to CTEM. However, it is intuitive to see that the resolution in STEM is limited by the size of the focused probe, which is proportional to the size of the electron source.
A second limitation to the STEM imaging is the precision with which the electron probe can be positioned during the scan process.
The central idea of ISTEM, which stands for Imaging STEM, is to combine CTEM and STEM to get the best of both modes : For this the focused scanning STEM beam is used to illuminate the specimen, while like in CTEM the objective lens is used to create an image.
Realization of Incoherence
The schematic principle of ISTEM is illustrated in figure 1: Thanks to the focused probe at each time only a very small spot of the specimen is illuminated. The objective lens then creates an image in the camera plane. When at a later time another point is illuminated, again an image is formed. Because of the different times no interference between both scan points can occur. If the camera is set to acquire for the entire time the STEM beam needs to scan over the area of interest, all scan points add up incoherently and there is very little interference. Only specimen points that are simultaneously illuminated by the probe can interfere. From this intuitive description it becomes clear that spatially incoherent image formation can be realized with ISTEM.
Advantages of ISTEM
In detailed wave optical calculations it can even be shown that the images taken with ISTEM do not depend on the aberrations of the probe forming lenses at all . Costly aberration correction of the probe is therefore not necessary for the used microscopes.
Similarly the electron source size is not of importance. Furthermore, looking at figure 1 it can also be understood that the precision of the beam positioning is also not relevant: As long as the scan area is homogeneously filled with STEM beam positions it does not matter whether the path of the electron probe is actually a straight line or a zigzag course, since unlike in STEM the image is directly formed by the objective lens and an unprecise beam position does only shift the illumination but not the image. ISTEM thus has all the advantages of CTEM.
Due to the incoherence of ISTEM, it can also be expected to share the related benefits with STEM and indeed figure 2 clearly demonstrates that the effect of increasingly strong chromatic aberration is much smaller in ISTEM images, which do not change much at all, than for CTEM, where resolution is quickly lost. In similar studies it can also be demonstrated that, like STEM, ISTEM high resolution images are in general relatively simple compared to the more complex CTEM patterns. Therefore ISTEM can legitimately be said to combine all the advantages of CTEM and STEM.
Overcoming Conventional Limits
Because chromatic aberration is the primarily limiting factor in modern microscopes for CTEM, the robustness towards it, which was demonstrated in figure 2, shows ISTEM‘s potential to overcome it. The maximum resolution that can be reached with a TEM is referred to as the information limit. It is usually measured with a Young fringe experiment, which even tends to overestimate the point resolution that is actually possible.
The FEI Titan employed for the ISTEM experiment presented in the following has an information limit of 81 pm at an acceleration voltage of 300 kV and is equipped with an aberration corrector for the objective lens. It was used to take ISTEM micrographs of an 8 nm thin crystalline gallium nitride lamella, where the electron beam fell along [1-100] direction. In this projection, there are two atomic columns, one consisting of gallium and one of nitrogen atoms, that have a distance of only 63 pm. Hence they cannot be resolved separately under conventional operation of the used microscope. With ISTEM however, as figure 3 clearly shows, the images of both columns are distinctly separated. Just changing to the STEM illumination hence indeed allows for a substantial improvement of resolution that overcomes the conventional information limit of the microscope thanks to its realization of incoherence. This is even more remarkable as nitrogen is much lighter than gallium; a fact that makes their simultaneous imaging difficult for many other techniques like e.g. annular dark-field STEM.
It should be emphasized here, that, opposed to other realizations of incoherent illumination, ISTEM can in fact be used on every microscope that allows both CTEM and STEM operation, which is the case for almost all contemporary instruments. It does not require any hardware modifications and is not much more difficult in its application than usual CTEM operation.
With the presented advantages ISTEM is a promising method for many microscopic applications. It can be shown that by an appropriate choice of the apertures ISTEM is able to yield the same images as most established STEM techniques but without the influence of electron source size or unprecise scanning, which again means an improvement of resolution. First experimental studies in this direction have shown encouraging results.
Another recently proposed idea is the use of ISTEM for the acquisition of energy filtered images where simulations prove its capability to suppress unwanted artefacts . In conclusion, the ISTEM method allows pushing the point resolution of electron microscopes well beyond their usual limits by a combination of the two traditional modes realizing incoherent imaging.
The author thanks the EMAT in Antwerp and the ERC in Jülich for fruitful cooperation.
 A. P. Pogany and P. S. Turner: Reciprocity in electron diffraction and microscopy, Acta Cryst. A 24 103-109 (1968) DOI 10.1107/S0567739468000136
 P. D. Nellist et al.: Resolution beyond the 'information limit' in transmission electron microscopy, Nature 374, 630-632 (1995) DOI 10.1038/374630a0
 Andreas Rosenauer, Florian F. Krause et al.: Conventional Transmission Electron Microscopy beyond the Diffraction and Information Limits, Phys. Rev. Lett. 113, 096101 (2014) DOI 10.1103/PhysRevLett.113.096101
 Andreas Rosenauer, Florian F. Krause et al.: Supplementary Information for: Conventional Transmission Electron Microscopy beyond the Diffraction and information Limits, Phys. Rev. Lett. 113, 096101 (2014) DOI 10.1103/PhysRevLett.113.096101
 H.G. Brown et al.: Addressing preservation of elastic contrast in energy-filtered transmission electron microscopy, Ultramicroscopy 160, 90-97 (2016) DOI 10.1016/j.ultramic.2015.10.001
MSc Florian Krause
Institut für Festkörperphysik