We have analyzed the possibilities of wave front shaping with miniature patterned electron mirrors through the WKB approximation. Based on this, we propose a microscopy scheme that uses two miniature electron mirrors on an auxiliary optical axis that is in parallel with the microscope axis. A design for this microscopy scheme is presented for which the two axes can be spatially separated by as little as 1 mm. We first provide a mathematical relationship between the electric potential and the accumulated phase modulation of the reflected electron wave front using the WKB approximation. Next, we derive the electric field in front of the mirror, as a function of a topographic or pixel wise excited mirror pattern. With this, we can relate the effect of a mirror pattern onto the near-field phase, or far field intensity distribution and use this to provide a first optical insight into the functioning of the patterned mirror. The equations can only be applied numerically, for which we provide a description of the relevant numerical methods. Finally, these methods are applied to find mirror patterns for controlled beam diffraction efficiency, beam mode conversion, and an arbitrary phase and amplitude distribution. The successful realization of the proposed methods would enable arbitrary shaping of the wave front without electron–matter interaction, and hence we coin the term virtual phase plate for this design. The design may also enable the experimental realization of a Mach–Zehnder interferometer for electrons, as well as interaction-free measurements of radiation sensitive specimen.

@en

We propose a microscopy scheme for the controlled modulation of the electron wave front that utilizes patterned electron mirrors. The ability to control the wave front of the electron finds many applications in electron microscopy, for instance in contrast enhancement techniques, beam mode conversion, low-dose imaging techniques such as quantum electron microscopy (QEM) and multi-pass transmission electron microscopy (MP-TEM), or structural hypothesis testing.@en

Electron beams can be reflected by an electrode that is at a more negative potential than the cathode from which the beam is emitted. We want to design a mirror with a flat mirror electrode where the electrons are reflected at a plane very close to the electrode. The wave front of an electron can then be shaped when the mirror contains a surface topography or modulated potential. However, electron beams reflected by flat electron mirrors are usually characterized by high coefficients of chromatic and spherical aberration. When the mirror is combined with an electrostatic lens to form a tetrode mirror system, the situation deteriorates even further. This places a restrictive limit on the maximum aperture angle of the beam, and consequently also limits the attainable resolution at the image plane. We have numerically studied the dependence of these aberrations as a function of design parameters of the tetrode mirror consisting of a ground, lens, cap, and mirror electrode, and limited ourselves to only using flat electrodes with round apertures, at fixed electrode spacing. It turns out that the third order spherical aberration can be made negative. The negative third order aberration is then used to partially compensate the positive fifth order aberration. This way, a system configuration is obtained that, at 2 keV beam energy, provides a diffraction limited resolution of 7.6 nm at an image plane 25 mm from the mirror at beam semi-angles of 2.3 mrad, enabling an illumination radius of 40 μm at the mirror. The presented tetrode mirror design could spark innovative use of patterned electron mirrors as phase plates for electron microscopy in general, and for use as coherent beam splitters in Quantum Electron Microscopy in particular. An appendix presents a method to calculate the spot size of a focused beam in the presence of both third and fifth order spherical aberration coefficients, which is also applicable to Scanning (Transmission) Electron Microscopes with aberration correctors.

@en

The use of electron mirrors in aberration correction and surface-sensitive microscopy techniques such as low-energy electron microscopy has been established. However, in this work, by implementing an easy to construct, fully electrostatic electron mirror system under a sample in a conventional scanning electron microscope (SEM), we present a new imaging scheme which allows us to form scanned images of the top and bottom surfaces of the sample simultaneously. We believe that this imaging scheme could be of great value to the field of in-situ SEM which has been limited to observation of dynamic changes such as crack propagation and other surface phenomena on one side of samples at a time. We analyze the image properties when using a flat versus a concave electron mirror system and discuss two different regimes of operation. In addition to in-situ SEM, we foresee that our imaging scheme could open up avenues towards spherical aberration correction by the use of electron mirrors in SEMs without the need for complex beam separators.

@en

We designed and built a compact bi-axial electron beam separator. This separator is an indispensable electron optical element in the development of MEMS-mirror-based miniaturized concepts for quantum electron microscopy (QEM) and aberration-corrected low-voltage scanning electron microscopy (AC-SEM). The separator provides the essential cycling of the electron beam between the two parallel optical axes that are part of these systems. This requires crossed electric and magnetic fields perpendicular to the beam path, as can be found in Wien-filter type beam separators. In our miniaturized QEM or AC-SEM concepts, the parallel axes are separated by only 1 mm. Conventional Wien-filter-based beam separator concepts rely on in-plane electric and magnetic multipole electrode configurations that are larger than the restricted available volume in these miniaturized QEM/AC-SEM systems. Our compact beam separator design introduces three stacked dipole electrode layers, which enables simultaneous beam separation at two parallel axes that are in close proximity. The outer layer electrodes maintain an electric field for which the direction on the one axis is opposed to that on the other axis. The middle layer generates a perpendicularly oriented magnetic field that spans both axes. The total field configuration enables the deflection of the beam on one axis and simultaneously provides a straight passage on the other axis. The deflection strength and distortion fields of the beam separator are experimentally obtained with a 2 keV electron beam energy. The results validate the use of the beam separator for electron energies up to 5 keV and deflection angles up to 100 mrad.

@en

The ability to imprint a phase pattern onto a coherent electron wave would find many applications in electron optics, in analogy to what is already possible with photons in light optics. Spatially dependent phase manipulation is achieved in transmission electron microscopy by passing the beam through a phase plate. However, in transmission mode this technique suffers from crystal imperfections and electron-matter interaction. If instead the electron wave is reflected of a spatially modulated potential, these difficulties can be circumvented. To demonstrate this principle, we consider here a periodic topological mirror structure that results in a sinusoidal plane of reflection for the incident electron. The reflection of the electron then takes place just above the physical mirror surface. Such "electron grating mirror" is expected to diffract the incident wave upon reflection by the introduced path length difference. The mirror can then be used as an electron beam splitter and coupler, analogous to semitransparent mirrors used in light optics. This enables for instance a lossless Mach-Zehnder interferometer for electrons. A numerical model that solves the Schrödinger equation for this system is obtained to enable a quantitative description of the grating mirror. The results show that the obtained diffraction order intensities behave like squared Bessel function of their respective order, and thus for instance the results show how an increase in grating pitch reduces the sensitivity to energy spread in the incident electron beam. Additionally, we show how the use of the WKB approximation enables faster calculations in the case of general patterns.

@en