Demonstration of a 2 × 2 programmable phase plate for electrons

TL;DR: In this article, the experimental realisation of a 2'×'2' programmable phase plate for electrons is presented, which consists of an array of electrostatic elements that influence the phase of electron waves passing through 4 separately controllable aperture holes.

About: This article is published in Ultramicroscopy.The article was published on 2018-07-01 and is currently open access. It has received 84 citations till now. The article focuses on the topics: Electrostatic lens & Electron optics.

Summary

1 Introduction

• Adaptive optics, the technology to dynamically change the phase transfer of optical elements has its roots in astrophysics, where dynamically changing telescope mirrors can compensate for time varying atmospheric induced aberrations for optimised observation from earth [1] [2] [3] [4] , as well as in space [5] .
• The technology has greatly improved since and has sparked an avalanche of innovative uses in many different areas where dynamic control over optical elements is wanted.
• The magnetic vector potential in a magnetic multipole corrector is determined by the individual poles that act as boundary conditions to the free space in which the electrons travel.
• The gain in flexibility offered by these electrostatic phase plates comes at the expense of admitting the material lens in the beam path resulting in a partial loss of electrons, decoherence, inelastic losses and charging issues [36, 34, 37] .
• So far, most phase plates have focused on phase contrast improvement and typically consist of a single region in space that is shifted in phase with respect to the rest of the wave that is left mostly unaltered.

2 Experiment

• 1 .a, a set of cylindrical electrodes needs to be created, sandwiched ideally between two ground planes.
• Thanks to the large atomic number difference between the gold and the SiN membrane,it was possible to mill proper electrodes without milling through the SiN membrane, ensuring good insulation between the bottom ground electrode and the four top electrodes.
• When all electrodes are grounded, the pattern displayed in fig.
• The high contrast of the interference patterns in fig.

3 Discussion

• The above experimental results demonstrate the feasibility of a multi-element programmable phase plate for use in electron microscopy.
• Introducing significantly more pixels (c) approaches the ideal case quite closely.
• Note that even though the probe appears similar to the ideal diffraction limited case (d), a significant amount of the probe intensity is scattered to higher angles due to the narrow pixel shape function which would lead to an increased background when using this probe for imaging.
• This puts constraints on the diameter of the individual phase shifting elements and would require elements of the order of 100 nm diameter to obtain high pixel count phase plates as simulated in fig.
• An important advantage of the presented device is the relative insensitivity of the performance to the quality of the voltage sources driving the pixel electrodes.

4 Conclusion

• The experimental implementation and first results demonstrate that such a device holds promise for upscaling towards a more useful higher number of pixels.
• Several design considerations and directions for further research are discussed.
• These make plausible that the presented proof of concept marks just the beginning of an exciting development that could alter the way how one thinks about electron optics, providing vastly increased flexibility, speed, repeatability and offering novel iterative measurement protocols that are difficult if not impossible to implement with current electron optical technology.

Figures

Fig. 4. Simulated diffraction patterns assuming an ideal programmable phase shifting device with dimensions matching the experiment. Note the strong similarity in the intensity patterns for both in focus (top row) and defocused diffraction pattern series.

Fig. 5. a) Fringe contrast integrated from a central region of the experiment with all electrodes grounded (red) as shown in inset compared to a similar region from the simulated profile (black) taking into account the experimental point spread function of the detector. Fringe contrast is estimated as 55% while the simulation shows an expected contrast of 64% assuming a fully coherent incoming electron beam. This shows the excellent preservation of coherence through the device. b) Low loss EELS spectra obtained after passing a focused STEM probe through the center of a phase shift element (black) and integrated over the whole area of the element (red). Less than 2.4% of the electrons passing through the phase shifting element undergo inelastic scattering and could suffer unwanted loss of coherence. Both a) and b) show that at the current dimensions and choice of materials, decoherence and inelastic effects are minor.

Fig. 7. A series of exotic electron beams prepared with a modest programmable phase plate (55 pixels, 41% fill-factor) approximating (from left to right) HG0,1, HG1,0, HG1,1, LG0,1, LG0,2. This shows that even a modest programmable phase plate can be very useful for producing exotic beam types that where hithertho difficult to produce in a TEM requiring time consuming and static (holographic) phase plates.

Fig. 6. Simulated performance of a programmable phase plate as a Cs corrector assuming 300 keV and Cs=1 mm. Two phase plates are simulated, a modest 55 pixel plate and a more demanding 2205 pixel phase plate. The defocus of the lens system was optimised to -75 nm and -250 nm respectively to reach the optimum probe shape. The result is compared to an ideal aberration free system with the same round aperture with opening angle 20 mrad. The resulting probe intensities are shown respectively in (e,f,g,h), the images have dimension 1x1 nm. The azimuthally averaged probe intensity is shown in (i). Note that the low pixel count phase plate in (b) does not significantly improve the probe size but does improve the tails. Introducing significantly more pixels (c) approaches the ideal case quite closely. Note that even though the probe appears similar to the ideal diffraction limited case (d), a significant amount of the probe intensity is scattered to higher angles due to the narrow pixel shape function which would lead to an increased background when using this probe for imaging. The colorwheel shown as inset in (a) shows the colorscale used in (a,b,c,d) to depict both amplitude as intensity and phase as hue.

Fig. 1. (a) sketch of an array of cylindrical electrodes individually controlling the phase of 4 electron beams which recombine in the far field to form a programmable interference pattern. (b) SEM image of a proof of concept implementation of a 2x2 phase plate prepared as described in this paper. (c) TEM image of the aperture showing the geometry of the 4 aperture holes as well as the limited fill factor.

Fig. 3. (top row) Set of diffraction pattern for 5 different applied potential configurations leading to an approximate realisation of the phase symmetry as indicated on each panel. (bottom row) Defocused diffraction patterns for the same potential configuration showing more directly the constructive and destructive interference features between the 4 patches as indicated by arrows.

Fig. 2. Simulated potential of the setup (a) showing the four electrodes at different potential of 0, 103, 206, 309 mV in order to obtain 0, 1/2π, π, 3/2π phase shift. A slice through 2 neighbouring electrodes (b) shows the potential homogeneity inside the cylinders with fringe fields extending above the electrodes due to the missing top ground plane. The projected potential is shown in (c) in units of phase shift assuming 300 kV electrons. The difference with the intended phase plate of 0, 1/2π, π, 3/2π is shown in (d) with a maximum deviation that remains below 0.07π as a result from the cross talk between the neighbouring pixels due to the lack of a top ground plane.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Demonstration of a 2x2 programmable phase plate for electrons" ?

The limitations of the current design and how to overcome these in the future are discussed. Simulations show how further evolved versions of the current proof of concept might open new and exciting application prospects for beam shaping and aberration correction. 

Q2. What future works have the authors mentioned in the paper "Demonstration of a 2x2 programmable phase plate for electrons" ?

Several design considerations and directions for further research are discussed. 

Q3. What is the magnetic vector potential in a multipole corrector?

The magnetic vector potential in a magnetic multipole corrector is determined by the individual poles that act as boundary conditions to the free space in which the electrons travel. 

Q4. How did the authors perform low loss electron energy loss spectroscopy?

The authors performed low loss electron energy loss spectroscopy using a focused STEM probe (convergence angleα = 20 mrad, 300kV, collection angle β = 11 mrad) passing through a single phase shifting element. 

Q5. What is the important shortcoming of the phase plate?

The most important shortcoming lies in the inherent material making up the pixel element electrodes, blocking part of the electron beam. 

Q6. What is the probability of inelastic scattering at the current dimensions?

As this delocalisation distance is very small compared to the diameter of the hole, the probability for inelastic scattering is negligible at the current dimensions. 

Q7. What is the fill-factor of the phase plate?

The fill-factor will of-course depend heavily on the micro machining or lithographic capabilities that will be used in further iterations of the design. 

Q8. What can be done to prove that a functional phase plate has been created?

A quadrupolar pattern and vortex pattern can also be generated, proving that a functional 2x2 programmable phase plate has been created. 

Q9. What is the effect of omission of the top ground plane?

The omission of the top ground plane will lead to a minor leaking of the potential of one cylinder into the space above a neighbouring cylinder electrode. 

Q10. What is the main drawback of the phase plate?

As long as the phase plate is used in setups that shape the electron beam before the sample, this does not have to be a significant drawback, as modern instruments often provide more current or electron dose than the sample can handle, and losing a fraction of this current would not limit the usability of the device. 

Q11. What can be the effect of the presence of the pixel electrodes?

the presence of the pixel electrodes can have unwanted effects, such as charging or decoherence due to thermal current flowing in the electrode material [81–83]. 

Q12. How many pixels are needed to upscale the device to a higher pixel count?

In order to upscale the device to a higher pixel count, lithographic techniques will be required and interconnect density may quickly put a limit to the maximum attainable number of pixels that each need to be individually contacted to a programmable voltage source. 

Q13. What is the effect of the pixel electrodes on the decoherence effect?

In this respect, the short length (1.4 µm) over which the electrons interact with the pixel electrodes, helps to limit the decoherence effect substantially as they are expected to scale with interaction length and inversely with the square of tube radius [82]. 

Q14. What is the simplest way to determine the phase of a multipole corrector?

a sharp change in phase in the center of the field as required for e.g. a Zernike phase plate would require prohibitively large magnetic multipole orders and is impractical for the foreseeable future. 

Q15. What is the ability to open up the field of beam shaping TEM?

This capability would open up the field of beam shaping TEM providing a very desirable flexibility in the quantum state of the electron probe, much like what current spatial light modulators offer in optics. 

Q16. What other studies have used phase plates to enhance the spectral profile of electron beams?

Examples include the study of non-diffracting electron beams[61,54,70–73,48], symmetry mapping of plasmonic excitations[74], mapping of magnetic fields [45,75–79] or edge contrast enhancement [76]. 

Q17. What is the main focus of phase plates?

So far, most phase plates have focused on phase contrast improvement and typically consist of a single region in space that is shifted in phase with respect to the rest of the wave that is left mostly unaltered. 

Q18. How can the authors estimate the sensitivity of the phase to the potential?

It is then possible to estimate the sensitivity of the phase to the potential with a back-of the-envelope calculation making use of the interaction constant of σ = 6.5 V −1µm−1 for 300 kV electrons and a tube length of1.4 µm. 

Q19. What is the difference between a phase plate and an optical Fresnel lens?

As phase is defined modulo 2π and because neighbouring patches of electron waves are divided by opaque walls of the pixel elements, there is no need to apply for more phase shift than this, similar to an optical Fresnel lens.