Abstract
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.
Highlights
An electron beam is reflected at an equipotential surface, under the condition that the electric potential matches that of the electron beam acceleration voltage
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 applicable to Scanning (Transmission) Electron Microscopes with aberration correctors
Mirror electron microscopy (MEM) [1,2] schemes revolve around this principle, and derived techniques are mainly applied in the field of surface physics [3,4,5]
Summary
An electron beam is reflected at an equipotential surface, under the condition that the electric potential matches that of the electron beam acceleration voltage. Electron mirrors are more typically used for the correction of axial chromatic and spherical aberrations [11] This can be achieved with a concave shaped electric field, which can be created for instance by using an aperture with a radius much larger than the beam envelop as a mirror electrode. The low-voltage foil corrector provides for axial aberration correction and the basic geometry shows close resemblance to a tetrode electron mirror [Fig. 2(a)] that is found in a QEM resonator. For this reason we believe that it is possible to correct for the combined axial aberrations of tetrode mirror systems by means of the mechanical configuration. We are able to etch apertures of typically 0.1 to 1 mm diameter with a roundness better than 1 μm which we can align to within 1 μm
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